Einstein's Pathway to the Special Theory of Relativity [1 ed.] 9781443878890, 9781443874342

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Einstein’s Pathway to the Special Theory of Relativity

Einstein’s Pathway to the Special Theory of Relativity By

Galina Weinstein

Einstein’s Pathway to the Special Theory of Relativity By Galina Weinstein This book first published 2015 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2015 by Galina Weinstein All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-4438-7434-5 ISBN (13): 978-1-4438-7434-2

This book is dedicated in memory of the late Professor Mara Beller, my PhD supervisor

TABLE OF CONTENTS

Acknowledgments ...................................................................................... ix Introduction ................................................................................................. 1 A. From Einstein's Childhood to Patent Office ......................................... 18 1 Einstein's Parents and Sister Maja 2 The Move to Munich and the Electric Firm 3 Rebellious and Creative 4 Einstein Cannot Take Authority and Demands for Obedience 5 Einstein Teaches Himself Natural Science and Philosophy 6 Secondary School in Aarau 7 Polytechnic in Zurich 8 Einstein Seeks a Position 9 Physics Group 10 Philosophy Group 11 Annus Mirabilis 12 German Scientists Respond to Einstein's Relativity Paper 13 Einstein Teaches His Three Friends at the University of Bern 14 Einstein Leaves the Patent Office For his First Post in Zurich 15 Minkowski's Space-Time Formalism of Special Relativity B. Fizeau's and Michelson and Morley's Experiments .............................. 89 1 Fresnel's Dragging Coefficient and Fizeau's Experiment of 1851 2 The Michelson and Michelson-Morley Experiment 3. Magnet and Conductor and Giving Up the Ether in Fin De Siècle Physics C. Einstein's Pathway to the Special Theory of Relativity ...................... 112 1 Introduction 2 Einstein Believes in the Ether 3 The Chasing a Light Beam Thought Experiment 4 Magnet and Conductor Thought Experiment 5 Ether Drift and Michelson and Morley's Experiment 6 Emission Theory and Ether Drift Experiments 7 Einstein's Route to Special Relativity from 1895 to 1903-1904

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Table of Contents

8 "The Step" 9 Einstein's Steps Toward the "The Step" 10 Biographical Sketch of Poincaré 11 Poincaré's Possible Influence on Einstein's Pathway toward Special Relativity 12 Did Poincaré Explore the Inertial Mass-Energy Equivalence? 13 Poincaré's Groups and Conventions D. The Meaning of Einstein's 1905 Special Relativity ............................ 203 1 Einstein's Methodology and Creativity 2 Kinematics of a "Rigid Body" – No Such Thing 3 Distant Simultaneity 4 Challenges to Einstein's Connection of Synchronisation and Contraction 5 Derivation of the Lorentz Transformation 6 Relativistic Addition Theorem for Velocities and Superluminal Velocities 7 Laue's Derivation of Fresnel's Formula 8 Einstein's Clocks and Langevin's Twins 9 The Magnet and Conductor Thought Experiment 10 Relativity and the Light Quantum 11 Kaufmann's Experiments: "Kugeltheorie" and "Relativtheorie" 12 The Principles of Relativity as Heuristic Principles 13 The Dayton Miller Experiments Appendix: The Sources ........................................................................... 293 1. Introduction 2. Documentary and Non-Documentary Biographies 3 Autobiographies, Memories and Popular Accounts 4 Primary Sources for the Historical Road that Led Einstein to Special Relativity 5 Old Biographies of Poincaré References ............................................................................................... 335 Notes........................................................................................................ 358 Index ........................................................................................................ 371

ACKNOWLEDGEMENTS

This book began in 2010, when I wrote a monograph on Einstein's pathway to the special and general theories of relativity, and in autumn 2011 the Einstein Center at the Hebrew University of Jerusalem sent me to Prof. John Stachel from the Center for Einstein Studies in Boston University. I wish to thank Prof. John Stachel for sitting with me for so many hours discussing Einstein's relativity and its history. Almost every day, John arrived with notes on my draft manuscripts and directed me to books in his Einstein collection, and gave me copies of his papers on Einstein, which I read with great interest. A fellowship arranged by Prof. Hanoch Gutfreund from the Einstein Center and Prof. Yemima Ben-Menahem from the Hebrew University of Jerusalem enabled me to go to Boston. I thank Prof. Gutfreund and Prof. Ben-Menahem for their efficient assistance. I also wish to thank Prof. Alisa Bokulich, Director of the Boston University Center for History and Philosophy of Science, for her kind assistance while I was a guest of the Center, and thank her Assistant, Dr Dimitri Constant, without whose advice and help I would not have been able to get along so well at BU and in Boston in general. I wish to thank the Hebrew University of Jerusalem, the Faculty of Humanities, which has sponsored my book. I warmly thank Prof. Diana Kormos-Buchwald, the general editor of Einstein's papers in Caltech, for her immense efforts in helping me with my book; and Prof. Michel Janssen from the University of Minnesota, Prof. Jürgen Renn and Dr Christoph Lehner from the Max Planck Institute for the History of Science in Berlin, for their great support and help. I would also like to thank my friends of the philosophy of physics discussions club: Dr Avshalom Elitzur from the Weizmann Institute, Dr Boaz Tamir from Bar-Ilan University, Dr Daniel Rohrlich from BenGurion University, Prof. Meir Hemmo from the University of Haifa and Dr Orly Shenker from the Hebrew University of Jerusalem for their great support. Finally, I am especially indebted to Naomi Paz from Tel-Aviv University who spent so much of her spare time editing this book.

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Permission to cite from selected documents in The Albert Einstein Archives and the Collected Papers of Albert Einstein was granted by Princeton University Press and such documents remain property of the Hebrew University of Jerusalem, all rights reserved. Albert Einstein. The Collected Papers of Albert Einstein © 1987-2014 Hebrew University and Princeton University Press. Reprinted by permission of Princeton University Press.

INTRODUCTION

The history of the special theory of relativity abounds in many biographies and historical studies. The topic of Einstein's pathway to the special theory of relativity, however, is still as much a question for debate as it was thirty or forty years ago. It is a question of fundamental significance in the history of modern physics and its discussion raises fundamental issues in the understanding of Einstein's creativity. This book is divided into four chapters. An appendix complements the main text of the book, and presents the history behind the sources mentioned in the text. The appendix allows the main text of the book to place greater emphasis on the historical profound relationships and principles, and on Einstein's path to the relativity theory. The first chapter (A) presents a critical biography of Einstein from childhood until 1908 – the year that Einstein left the Patent Office. The biography is based on primary sources. Einstein was apparently not attracted to biographies. He preferred a representation of events or relations in which the personal remains in the background. I have sought to write a biography according to these guidelines, but I do discuss a few family stories in order to clarify certain historically important topics. I start with Einstein's childhood and schooldays: Albert Einstein and the family members seem to have exaggerated the story of Albert who developed slowly, learned to talk late and whose parents thought he was abnormal. These and other stories were adopted by biographers as if they had really happened in the way that Albert and his sister told them. Hence, biographers were inspired by such stories to create a mythical public image of Albert Einstein. As a child, Albert had had a tendency toward temper tantrums. A young and impudent rebel with an impulsive and upright nature, he rebelled against authority and refused to learn by rote. He could not easily bring himself to study what did not interest him at school, especially humanistic subjects. Consequently his sister told the story that his Greek professor, to

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Introduction

whom he once submitted an especially poor paper, went so far in his anger as to have declared that nothing would ever become of him. Albert would study subjects in advance when it came to the sciences and during the long summer vacation he independently worked his way through the entire Gymnasium syllabus. He also taught himself natural science, geometry and philosophy by reading books obtained from a poor Jewish medical student of Polish nationality, Max Talmud, and from his uncle, Jakob Einstein. I then describe Einstein's student days at the Zurich Polytechnic: he skipped classes, did not attend all the required lectures, and before sitting for an examination he studied instead from the notebooks of his good friend in class, Marcel Grossmann. Einstein the free-thinker had little respect for the two major professors at the Polytechnic – Heinrich Friedrich Weber and Jean Pernet – who eventually turned on him. His beloved science lost some of its appeal to him because Weber's lectures did not include James Clerk Maxwell's electromagnetic theory. He also seldom showed up to Pernet's practical physics course. Through his forthrightness and distrust of authority he alienated his professors, especially Weber, who apparently conceived a particular dislike of him. At the Zurich Polytechnic Einstein could not easily bring himself to study what did not interest him. Most of his time he spent on his own, studying Maxwell's theory and learning at first hand from the works of the great pioneers in science and philosophy: Ludwig Boltzmann, Hermann von Helmholtz, Gustav Kirchhoff, Heinrich Hertz and Ernst Mach. Einstein eventually finished first in his class in the intermediate exams, followed by his note-taker, Grossmann. It might be better, however, not to copy Einstein's recipe for studying in college: after obtaining his diploma, when he sought a university position, he was constantly turned down. Rescue finally came from Grossmann, and thanks to him and Grossmann's father Einstein obtained a post in the Patent Office. There are strong reasons to believe that it was Einstein's rare mastery of Maxwell's electromagnetic theory that ultimately prompted the Director of the Patent Office to offer him a job. And it was there, in the Patent Office that Einstein hatched his most wonderful ideas and there that he spent his Happy Bern Years. Those wonderful ideas led to his miraculous year works of 1905.

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Einstein had no expertise in academic matters and he was outside the academic world; nor did he meet influential professors or attend academic meetings. Rather, he discussed his ideas with his close friends and colleagues from the Patent Office. In 1907, however, he finally got his foot in the academic doorway: Einstein became a privatdozent and gave lectures at the University of Bern.1 His first students consisted of his two close friends and another colleague from the Patent Office. I end my biographical survey with the mathematician, Hermann Minkowski, Einstein's former mathematics professor at the Zurich Polytechnic. During his studies at the Polytechnic Einstein had skipped Minkowski's classes. In 1904 Max Born arrived for the first time in Göttingen. Many years later Born wrote his recollections of the period. In the summer of 1905 Minkowski and David Hilbert gave an advanced seminar on mathematical physics, relating to electrodynamical theory. Minkowski told Born later that it had come to him as a great shock when Einstein published his paper demonstrating the equivalence of the different local times of observers moving relative to each other. Minkowski had reached the same conclusions independently but had not published them because he wished first to work out the mathematical structure in all its splendor. He never made a priority claim and always gave Einstein his full share in the great discovery. Indeed, in his famous talk "Space and Time", Minkowski wrote that the credit for first recognizing clearly that the time of one electron is just as good as that of another, i.e., that t and t' are to be treated the same, should be given to Einstein. The second chapter (B) provides a detailed account of fin de siècle physics. The science of optics underwent drastic changes from the seventeenth to the nineteenth century. Until the beginning of the nineteenth century two rival theories of light were dominant among scientists: the corpuscular or emission theory of light, according to which light is composed of tiny corpuscles; and the wave theory of light, according to which light is just wave-like disturbances in a medium. Isaac Newton's name was linked with the idea underlying the first theory, although Newton himself did not express a strict adherence to any of the alternatives; while Christian Huygens tended to be associated with the idea underlying the second

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Introduction

theory. There were several optical phenomena still requiring explanation, and the adherents of each of the two rival outlooks sought to provide such explanations and, in so doing, to bolster their own position. A major turning point in this ambiguous state of affairs was made at the beginning of the nineteenth century by Thomas Young, Dominique François Arago, Augustin-Jean Fresnel and by the discovery of interference and polarization phenomena. Fresnel and Young proposed independently that one should assume that space was filled with an allpervading subtle substance called The Luminiferous Ether. The consideration of such ether helped scientists to contradict the possibility of action-at-a-distance interaction between electrified bodies. Neither the idea of an ether nor the desire to contradict action-at-a-distance interactions were new. For example, Newton had thought of it in connection with gravitation in his attempt to find a way to avoid action-at-a-distance, and through this to derive a physical explanation for the law of gravitational attraction. Fresnel's ether was supposed to be physically elastic in order to explain the rapid transverse motion of light waves. Many problems arose from these attempts to ascribe mechanical properties to the ether, so that the waves propagating in it would possess all the properties of light. During the nineteenth century analysis of an important astronomical phenomenon led to another type of difficulty that preoccupied scientists in the field of the optics of moving bodies: the phenomenon of stellar aberration. The phenomenon of aberration of starlight was discovered by James Bradley in 1728, as a result of his efforts to detect in certain stars an annual parallax – the change in the observed location of stars as a result of the change in the annual position of the Earth, stars that had passed near the zenith directly above the plane of the Earth’s orbit were the most amenable to accurate measurement of this effect. Explaining stellar aberration was a major problem in nineteenth century physics. As interest in the wave theory of light gradually grew, the phenomenon of aberration demanded an explanation within the framework of wave theory. By 1818, in a letter to Arago, Fresnel explained that in the wave theory of light the velocity at which the waves propagate is independent of the motion of the body from which they emanate, an explanation that ran counter to the Newtonian theorem of the addition of velocities. In addition, it assumed that velocity was constant with reference to the ether. Fresnel postulated that in order to explain aberration within the framework of the new emerging wave theory of light, one was obliged to assume an ether wind or drift, penetrating freely through the pores of

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the Earth, as suggested originally by Thomas Young. Fresnel expanded Young's proposal to what has come to be known as the immobile ether hypothesis. In addition to offering an explanation for the aberration, Fresnel's ether theory could shed light on the absolute motion of the Earth in the ether. If there was immobile ether it further raised the problem of why no optical experiment made on Earth had demonstrated, or could be expected to demonstrate, the motion of the Earth through the ether – whatever the optical phenomenon used to detect this motion. Newtonian classical mechanics was incapable of explaining this in a satisfactory manner. If the ether is immobile with respect to the sun, then the Earth should move with the same velocity of 30 kms/sec with respect to the ether as it moves with respect to the sun. Therefore, the velocity of the Earth relative to the immobile ether must be at least 30 kms/sec. According to Young and Fresnel's supposition, relating to an ether wind passing freely through the Earth, there must thus be a stream of the ether, an ether wind, flowing through our laboratories and attaining velocities of at least as great as 30 kms/sec. Accordingly, one should be able to measure the actual velocity of this supposed stream of ether relative to the laboratory; and from that measurement, infer the velocity of the Earth through the ether. This possibility precipitated the ether drift experiments conducted for the express purpose of measuring the velocity of the Earth relative to the ether. First order terrestrial ether drift experiments investigated effects of the Earth’s motion proportional to v/c (the aberration constant), where v is the speed of the Earth through the ether and c the speed of light. They proved incapable of revealing the Earth’s motion with respect to the immobile ether and thus all the experiments that were aimed at ascertaining this gave negative results. Fresnel tried to supply an explanation through two such experiments: Arago's experiment and that proposed by Roger Joseph Boscovich (carried out much later by Sir George Biddell Airy), whose outcome was that the motion of the planet Earth could not affect the laws of refraction. By viewing the stars with a telescope filled with water, it was hoped to disclose the Earth's motion with respect to the immobile ether. But the experiment provided negative results. Fresnel explained this result by suggesting that most of the ether is immobile, while the ether in transparent bodies, like water and glass, is slightly dragged along. Guided by this partial ether drag hypothesis he derived a formula for the speed of

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Introduction

light in a moving medium known as Fresnel's formula, which included a dragging coefficient. Despite the success of Fresnel's formula, however, his interpretation in terms of partial ether drag remained problematic, and many authors embracing the former explicitly distanced themselves from the latter. There was, of course, a simple, alternative explanation for these experimental results, in which there would seem to be no need for the peculiar partial dragging effect in transparent matter. If all ether inside matter were fully dragged along by it, the ether at the surface of the Earth would be at rest with respect to the Earth, which would explain automatically why no ether drift was ever detected. The concept of dragged along ether was much more natural than that of immobile ether. In 1845 George Gabriel Stokes developed a model in which the Earth drags along the ether. Stellar aberration continued to provide the strongest argument against such a model, and much of Stokes' efforts went into attempts to show that aberration could be accounted for on the basis of a dragged along and on the basis of an immobile ether. In 1851 Armand Hippolyte Fizeau performed measurements of the speed of light in moving water. Fizeau's water tube experiment found that it was possible to measure the actual velocity by the interference method, and in so doing confirmed Fresnel's formula. This formula was found to represent the velocity accurately both for water and for other transparent media. In 1886, Albert Abraham Michelson, together with Edward Williams Morley, repeated the Fizeau experiment with improved accuracy. The experiment confirmed Fresnel's prediction. Michelson and Morley concluded that Fresnel had to be right and Stokes wrong. In 1881 Michelson performed a second order ether drift experiment aimed at measuring the ratio v/c to second order. The means by which this experiment endeavoured to discover the Earth's motion with respect to the ether was mainly through the use of optical instruments (interferometers). It returned a negative result. However, the celebrated Michelson-Morley experiment of 1887 gave the same negative result of Michelson's first attempt in 1881, with reduced experimental error. Now both Fresnel's and Stokes' hypotheses appeared to be untenable. Meanwhile, in 1886 Hendrik Antoon Lorentz argued that all experiments could be accounted for on the basis of a theory somewhere in between Fresnel's and Stokes', a theory that contains Fresnel's coefficient and in which all moving matter partially drags along the ether.

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Two major theories were offered for extending Maxwell’s electromagnetic theory to moving bodies: Heinrich Rudolf Hertz’s 1890 macroscopic electrodynamics of moving bodies, and Lorentz’s 1892 microscopic electron theory. Hertz’s theory was contradicted by Fizeau’s 1851 water tube experiment because it assumed a complete drag of the ether along with the bodies in motion. On the other hand, it was obviously compatible with the negative results of ether drift experiments. Lorentz’s theory explained all that Maxwell’s theory had already explained and left intact the intimate connection between optics and electricity discovered by Maxwell. Lorentz started from the hypothesis that electrical charges are carried by material particles called the electrons and the electrons composing ponderable matter move in immobile ether. The study of the interactions between the immobile ether and the electrons in motion accounted for the observed phenomena: Aberration and Fizeau’s 1851 experimental result both received a satisfactory explanation within Lorentz’s theory. He was able to derive the Fresnel coefficient from his theory, reinterpreting it as due to an interaction between ether and matter that required no ether drag whatsoever. In 1895, Lorentz produced a more general derivation of the Fresnel coefficient with the help of an auxiliary quantity called local time. Formally, this derivation is very close to the derivation of the dragging coefficient in special relativity, based on the relativistic addition theorem for velocities. However, all the experiments seeking to demonstrate the Earth’s motion with respect to the ether contradicted Lorentz’s fundamental hypothesis of immobile ether and moving electrons, in that they failed to reveal the preferred state of rest of the ether. For the purpose of reconciling the hypothesis of immobile ether with the negative results of the MichelsonMorley experiment, Lorentz proposed (in 1892) the contraction hypothesis (which had already been suggested by George Francis FitzGerald in 1889). Lorentz included the contraction and other compensations within later versions of his 1892 theory, his 1895, 1899 and 1904 theories of the electron. In these later versions, Lorentz formulated a theorem of corresponding states. According to this new theorem, there existed mathematical transformations that preserved the elementary electromagnetic equations of Lorentz's electron theory almost in their original form. These transformations required a linear rescaling of time with the distance coordinate x so that the time coordinate t is replaced by the local time; and, for later, more exact, higher order versions of the theorem, lengths were contracted by the factorඥͳ െ ሺ‫ݒ‬Τܿ ሻଶ . By means of

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Introduction

these transformations, Lorentz explained the impossibility of detecting the Earth's motion by electromagnetic and optical means; or, in other terms, the motion of the Earth through the ether had (almost) no observable effect on electromagnetic and optical processes. Before 1905 Einstein had tried to discuss Fizeau's experiment as originally discussed by Lorentz. At that time he was still under the impression that the ordinary Newtonian law of addition of velocities was unproblematic. In 1907 Max Laue showed that the Fresnel dragging coefficient would follow from a straightforward application of the relativistic addition theorem of velocities. Indeed this derivation was mathematically equivalent to Lorentz's derivation of 1895. From 1907 onwards Einstein adopted Laue's derivation. When Robert Shankland asked Einstein how he had learned of the Michelson-Morley 1887 ether drift experiment, Einstein told him that he had become aware of it through the writings of Lorentz, but it had come to his attention only after 1905. Otherwise, he said, he would have mentioned it in his paper. He continued to say that the experimental results that had influenced him most were those of stellar aberration and Fizeau's water tube experiment. They were enough, said Einstein. Indeed, the famous Michelson-Morley experiment is not mentioned in the 1905 relativity paper. Curiously, however, Einstein did not mention Fizeau's experimental result either, and this is puzzling in light of the importance of the experiment in Einstein's pathway to his theory. This topic is discussed in chapter D. The third chapter (C) discusses Einstein’s path to special relativity and Henri Poincaré's contributions to the principle of relativity. There is a major problem still basically unsolved: the vast amount of evidence and sporadic pieces of primary material do not shed too much light on the overall course of Einstein's thinking between 1901 and 1904, because he published nothing on the subject of optics or electrodynamics of moving bodies (relativity) between 1901 and 1904. Apparently, therefore, neither correspondence nor any other source can be said to assist in creating a coherent story of Einstein's path to the special theory of relativity between 1901 and 1904, for there are unfortunately no relevant new letters from this period. In chapter C I confront this problem and present my story of Einstein's path to relativity between 1895 and 1905.

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In 1894-1895 Einstein wrote an essay that he sent to his uncle, Cäser Koch. At the time he believed in the ether theory, but did not show any knowledge of Maxwell's electromagnetic theory. In 1895, at the age of sixteen, Einstein was also familiar with the principle of relativity in mechanics. A year later, in 1895-1896, while in Aarau, Einstein conceived of a thought experiment: the chasing of a light beam thought experiment. In 1899 Einstein studied Maxwell's electromagnetic theory. Around 18981900 he invented the magnet and conductor thought experiment (asymmetries in Lorentz's theory regarding the explanation of Michael Faraday's induction). Between 1899 and 1901 Einstein was occupied with the contradiction between the Galilean principle of relativity and the constancy of the velocity of light in Maxwell's theory. He was also interested in ether drift and appears to have designed at least two experiments: the first in 1899 and the second, two years later. In 1901 Einstein still accepted the Galilean kinematics of space and time, in which the Galilean principle of relativity holds true. Between 1901 and 1903 Einstein was working on two topics: the quantum of light problem and the electrodynamics of moving bodies. The two topics seemingly could, however, be said to depend on one another; they were interwoven. For the telling here, I first unravel them (in chapters C and D), and follow each in turn. Subsequently, I consider the part that Einstein's work on the quantum of light and on relativity played on his path to special relativity. We should remember that between 1901 and 1903, Einstein was still sitting in the Patent Office. One can imagine him trying to hide from his boss, writing notes on small sheets of paper and, according to reports, seeing to it that the small sheets of paper on which he was writing would vanish into his desk-drawer as soon as he heard footsteps approaching behind his door. Einstein nonetheless said that he had enjoyed considerable freedom in the worldly cloister, where during 1901-1903, he was perhaps ruminating (i.e., pondering) his best ideas, brooding upon the Maxwell-Hertz equations for empty space. He tried to solve the conflict between the Galilean principle of relativity and the constancy of the velocity of light. He dropped the ether hypothesis and replaced Lorentz's theory with emission theory. Einstein seems to have engaged with emission theory for

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Introduction

an extra year, from 1903-1904 until almost spring-summer 1904, apparently, remote as possible from Lorentz's theory. Einstein discussed Fizeau's experiment using emission theory but then demonstrated why emission theories could not hold true. Towards springsummer 1904 he dropped emission theory and returned to Lorentz's theory. He tried to discuss Fizeau's experiment in Lorentz's theory, by now firmly believing that Lorentz's theory was correct. The invariance of the velocity of light however contradicted the addition rule of velocities used in mechanics. Einstein realized the difficulty in seeking to resolve this, and spent almost a year in vain trying to modify Lorentz's idea in the hope of solving the problem. In spring 1905 he found the final solution: the step, which solved his dilemma. An additional topic discussed in Chapter C is Henri Poincaré's Dynamics of the Electron and ideas in regard to the principle of relativity. I begin with Poincaré's biography followed by his possible influence on Einstein. I first present a brief biographical sketch of Poincaré, which does not in any way reflect Poincaré's rich personality and immense activity in science. It is interesting to note that, as opposed to the plethora of biographies and secondary papers studying the life and scientific contributions of Albert Einstein, one finds far fewer biographies and secondary sources that discuss Poincaré's life and work. From 1920 on Einstein became a myth and a world famous figure, whereas during his lifetime Poincaré was not a cultural icon. Despite Poincaré's brilliance in mathematics, he was to remain an internationally famous mathematician mainly within the professional circle of scientists. He published more papers than Einstein, performed research in many more branches of physics and mathematics, received more prizes on his studies and was a member of more academies world-wide. Despite this tremendous yield, Poincaré did not win a Nobel Prize. During Poincaré's travels to Europe, Africa and America, his companions noticed his broad knowledge on everything from statistics to the history and curious customs and habits of the local people. He taught almost every subject in science, possessing such an encyclopedic knowledge that he was able to engage with the outstanding questions of the time in the different branches of physics and mathematics. Indeed he altered the thinking in entire fields of science, such as non-Euclidean geometry, Arithmetic, celestial mechanics, thermodynamics and kinetic theory, optics,

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electrodynamics, Maxwell's theory and other topics at the forefront of fin de siècle physical science. Prior to 1905 Poincaré had stressed the importance of the method of clocks and their synchronisation but, unlike Einstein, issues of magnet and conductor or chasing a light beam and overtaking it, were not a matter of great concern for him. In 1905 he elaborated upon Lorentz's 1904 electron theory in two papers entitled "On the Dynamics of the Electron". In May 1905 Poincaré sent three letters to Lorentz at the same time that Einstein wrote his famous May 1905 letter to Conrad Habicht, promising him four works, of which the fourth one was only a rough draft at that point. In the May 1905 letters to Lorentz Poincaré presented the basic equations of his 1905 Dynamics of the Electron. Hence, in May 1905, Poincaré and Einstein both had drafts of papers relating to the principle of relativity. Poincaré's draft led to a space-time mathematical theory of groups at the basis of which stood the postulate of relativity, and Einstein's draft led to a kinematical theory of relativity. Poincaré did not renounce the ether theory. He wrote a new law of addition of velocities but did not abandon the tacit assumptions made about the nature of time, simultaneity and space measurements implicit in Newtonian kinematics. Although before 1905 he questioned absolute time and absolute simultaneity, he did not make tacit new kinematic assumptions about space and time. He also did not require reciprocity of appearances and, therefore, did not discover relativity of simultaneity: those are the main hallmarks of Einstein's special theory of relativity. Nevertheless, as shown by other writers, Poincaré's theory influenced later scientists, especially Hermann Minkowski. Einstein was the first to explore the inertial mass-energy equivalence. In 1905 he showed that a change in energy is associated with a change in inertial mass, equal to the change in energy divided by c2. In 1900 Poincaré considered a device that could create and emit electromagnetic waves. The device would emit energy in all directions, as a result of which it would recoil. No motion of any other material body would compensate for the recoil at that moment. Poincaré found that as a result of the recoil of the oscillator, in the moving system, the oscillator generating the electromagnetic energy would suffer an apparent complementary force.

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Introduction

In addition, in order to demonstrate the non-violation of the theorem of the motion of the centre of gravity, Poincaré needed an arbitrary convention, the fictitious fluid. Einstein had demonstrated that if the inertial mass E/c2 is associated with the energy E, and assuming the inseparability of the theorem of the conservation of mass and that of energy, then – at least as a first approximation – the theorem of the conservation of the motion of the centre of gravity would also be valid for all systems in which electromagnetic processes take place. Prior to 1905 (and also afterwards) Poincaré had not explored the inertial mass-energy equivalence. In 1908 Einstein wrote the German physicist Johannes Stark that he was a little surprised to see that Stark had not acknowledged his priority regarding the relationship between inertial mass and energy. Present-day relativistic kinematics follows the general pattern established by Einstein in 1905. Therefore, much effort has been invested in determining whether Poincaré had in fact preceded the main features of Einstein's 1905 relativistic kinematics. The history of Poincaré's contributions is usually understood in terms of Poincaré was just a step away from Einstein's 1905 special relativity. Poincaré, however, created a space-time mathematical theory of groups, at the basis of which stood the postulate of relativity, to which I also briefly refer from the philosophical point of view. Poincaré's philosophy of conventionalism sprang from his research into geometry during a period (the end of the 1880s) when non-Euclidean geometries were constantly considered a matter of possibility. Poincaré developed two kinds of conventionalism: conventionalism applicable to geometry and conventionalism for the principles of physics. Both sprang from his mathematical group theory. He adopted the notion of Lie groups, developed by the Norwegian mathematician Marius Sophus Lie, and demonstrated that all geometries could be generated from Lie groups, arriving thereby at the conclusion that they are all logically equivalent. Poincaré began to think of conventionalist ideas as a result of the development of non-Euclidean geometry in the nineteenth century. The non-Euclidean geometries arose as a logical alternative to Euclidean geometry. However, they were not considered as geometries that could represent bodies in the real world, unlike Euclidean geometry. Poincaré agreed with this contention and it underlined his philosophy of

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conventionalism, which complied with the basic thesis of his mathematical group theory. The final chapter (D) engages with Einstein's methodology and presents a critical analysis of his relativity theory. The status and meaning of the special theory of relativity is still as much a question for debate as it was a hundred years ago. This chapter discusses the various methodological problems in special relativity that occupied scholars when Einstein's relativity theory was first introduced. Fairly soon after Einstein had formulated his relativity theory, his friend Paul Ehrenfest reasoned that the theory was simply a reformulation of Lorentz's electrodynamic theory. Einstein's response to his friend was that the theory of relativity is a theory of principle; and he explained that, beyond kinematics, the 1905 heuristic relativity principle could offer new connections between non-kinematical concepts. Indeed when Einstein appreciated that the results of the Dayton Clarence Miller ether drift experiments might be confirmed, he declared that relativity theory could not be maintained, since the experiments would then prove that, relative to the coordinate systems of the appropriate state of motion (the Earth), the velocity of light in a vacuum would depend upon the direction of motion. With this, the principle of the constancy of the velocity of light, which forms one of the two foundation pillars on which the theory is based, would be refuted. He was prepared to give his relativity theory up completely in the case of irrefutable contrary empirical evidence since special relativity is a heuristic system of two principles; it is not a constructive theory like the ether-based electron theory, then one cannot modify principles without giving up the whole theory. However, a theory of principle has a solid theoretical basis, and therefore there is little chance that experiments like that of Miller's (and also like that of Walter Kaufmann's discussed in Chapter D) would turn out to be right. Another topic discussed in this chapter is Einstein's methodology. Einstein himself seems to have made different statements regarding the process that results in a new idea, ranging from discovering the principle of relativity to the theory of relativity as an invention. Einstein desired to invent, and he compared the inventive science to music ("Thinking for its own sake, as in music"), and music was also an inspiration for his scientific inventions. Einstein characterized the process

14

Introduction

of his creativity using the words: free creations of the human mind. Those are theoretical scientific ideas and musical sonatas, both enhancing one another. For Einstein, the process of thinking consists of two stages. The first stage is primary non-verbal in nature. Words or the language, as they are written or spoken, do not seem to play any role in his mechanism or thought. The psychical entities which seem to serve as elements in thought are clear images. Many of the crucial thought experiments Einstein later reports confirm the existence of this first stage of the thinking process (for instance, the chasing a light beam and the magnet and conductor thought experiments). At a secondary stage, it was necessary for him to transform the results of the primary process into forms communicable to others. The need to put ideas into communicable form led Einstein to search throughout his early life for people to act as sounding boards for his ideas. At the age of four or five, young Albert experienced a wonder. His father Hermann showed him a compass. This experience, so recounts Einstein himself in his Autobiographical Notes, changed his life. His thinking went on for the most part without use of signs (words), and he wondered quite spontaneously about this experience. The significance of a wonder for Einstein was that Einstein had the ability to keep the child alive in the man. Towards the end of his life Einstein mused that he was brought to the formulation of relativity theory in good part because he kept asking himself questions concerning space and time that only children wonder about. For Einstein a wonder was an apparent conflict between a phenomenon and our established conceptual framework. Einstein's 1905 relativity paper became famous as the one in which he inferred odd and curious effects. One immediate consequence of this was that of discussions of the misunderstandings and paradoxes in the theory. Einstein wrote in his 1905 relativity paper that the theory developed here was based on the kinematics of the rigid body. It was shown that a rigid body cannot exist in the special theory of relativity. In addition, it was claimed that special relativity assumes a connection between synchronisation and contraction; a connection that was challenged. It should be keep in mind that a discussion of these topics requires additional philosophical reinforcement (which is beyond the scope of this

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book); and, therefore, the discussion of these topics in this book is restricted. Reformulations of the elements of the relativity theory that appear to render the theory applicable to similar phenomena were also suggested: distant simultaneity can be defined with respect to a given frame of reference without any reference to synchronised clocks; and a theory of relativity without light was posited. In 1905 Einstein presented the Clock Paradox and in 1911 Paul Langevin expanded Einstein's findings to human observers, as the Twin Paradox. I explain the difference between Einstein and Langevin. Einstein did not present the so-called Twin Paradox, but later continued to speak about the clock paradox. Einstein might not have been interested in the question of what happens to the observers themselves, possibly because he dealt with measurement procedures, clocks and measuring rods. Einstein's observers were measuring time with these clocks and measuring rods and he might not have been interested in studying the so-called biology of the observers themselves, as to whether they were getting older, younger or had undergone any other changes. Such changes appeared to be beyond the scope of his principle of relativity, or kinematics. The processes and changes occurring among the observers seemed to be more appropriate for philosophical rather than scientific discussions. To the later writers, who criticized Einstein's clock paradox, such as the anti-Semites who blamed the theory of relativity as an anti-German science, he quickly replied with witty retorts. In 1907 Einstein discussed with Wilhelm Wien the occurrence of superluminal velocities in dispersive and absorptive media. He tried to present to Wien an expression for the group velocity in dispersive media based on his 1905 addition theorem for relative velocities, which he claimed to be valid for absorptive media, and to demonstrate the impossibility of superluminal velocities. However, he recognized that his expression required an amendment and correction. Having failed to convince Wien, he was finally confused, lacking a correct expression for the group velocity in dispersive media. However, he wrote to Wien that it was beyond doubt that the electromagnetic theory of dispersion could never yield superluminal velocity for the propagation of an optical signal.

16

Introduction

We should recall that Einstein was occupied among others, with the microstructure of radiation (light quantum paper). In 1905 the well-known physicist Max Planck was coeditor of the Annalen der Physik, and he accepted Einstein's paper on light quanta for publication, even though he disliked the idea of light quanta. Einstein's relativity paper was received by the Annalen der Physik at the end of June 1905 and Planck was the first scientist to take note of Einstein's relativity theory and to report favorably on it. In his 1905 relativity paper Einstein used a seemingly conventional notion, light complex, and did not refer to his novel quanta of light heuristic with respect to the principle of relativity. He chose the language light complex for which no clear definition could be given. With hindsight, however, in 1905 Einstein had made exactly the right choice not to mix concepts from his quantum paper with those from his relativity paper. He focused on finding the solution to his relativity problem, whose farreaching ramifications Planck had already sensed. Before ending with Dayton Clarence Miller's experiments I discuss Einstein’s 1905 relativity theory of the motion of an electron. He obtained expressions for the longitudinal and transverse masses of the electron using the principle of relativity and that of the constancy of the velocity of light. It was quite natural and presumably expected that Einstein's expression for the mass of the electron would seem to resemble that of Lorentz. And indeed, I have already remarked that Einstein's above solution appeared to Ehrenfest to be very similar to Lorentz's one: both clearly suggested a deformed electron. Einstein commented on Ehrenfest's paper and characterized his work as a theory of principle and reasoned that, beyond kinematics, the 1905 heuristic relativity principle could offer new connections between non-kinematical concepts. Walter Kaufmann concluded that his own measuring procedures were not compatible with the hypothesis posited by Lorentz (Lorentz's electron) and Einstein. However, unlike Ehrenfest, he gave the first clear account of the basic theoretical difference between Lorentz's and Einstein's views. Finally, Alfred Bucherer conducted experiments that confirmed Lorentz's and Einstein's models, while Max Born analyzed the problem of a rigid body and demonstrated the existence of a limited class of rigid motions, concluding that the main result was a confirmation of Lorentz's formula. The final topic is that of Miller's ether drift experiments. The negative result of the Michelson-Morley experiment stimulated many repetitions of this experiment during the next fifty years, especially in light of the

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implications of Einstein's special theory of relativity. Every trial of this experiment yielded a null result within the accuracy of the observations. Then in the 1920s, the history of relativity took some interesting turns. A repetition of the experiment, performed by Miller, appeared to be perplexing, as he had observed very small fringe displacements. There was great excitement amongst experimentalists and the scientific community; and even Einstein declared that, if these results would be substantiated, he would give up his special theory of relativity, and with it also his general theory of relativity! Einstein nonetheless announced that there was practically no likelihood of Miller being right, and upon hearing the rumor about Miller's experiments for the first time, Einstein produced one of his classical aperçus: "The Lord God is Subtle, but malicious he is not".

A. FROM EINSTEIN'S CHILDHOOD TO PATENT OFFICE

1 Einstein's Parents and Sister Maja Albert was born on the morning of March 14, 1879, at 11:30 a.m, in the city of Ulm, at the former Bahnhofstraße 135B, which vanished in 1945 (Birth Certificate, CPAE 1, Doc. 1). It is quite symbolic that Einstein was born in a street named "Station Street", as if he was born into his thought experiments of stations and trains. The house in Ulm where he was born no longer stands. World War II reduced it to rubble. A street in Ulm has since been named Einsteinstraße.2 Ulm is a Swabian town on the Danube, in the state of Württemberg, in southern Germany. In the correction to Seelig's biography it was noted that the word Swabian should not be taken literally, because in Switzerland the Germans were all called Swabians. Einstein's childhood was spent in Munich, the capital of Bavaria, but Einstein was especially Swabian because he had a Swabian sense of humour. There is a particularly Swabian good-natured humour, curiously like English humour, and a Swabian taste for practical jokes (EA 39-084; Vallentin 1954, 6).3 On his birth certificate Einstein is recorded as born to the merchant Hermann Einstein and his wife Pauline née Koch, both of the Israelite religion. Helen Dukas told Abraham Pais that Einstein's name was supposed to be Abraham, for his paternal grandfather, Abraham Rupert Einstein, but his parents found the name too Jewish and adopted only the initial A, naming him Albert instead (Pais 1982, 35; Calaprice 2005, 352). Hermann Einstein was a native of the small town of Buchau on the Federsee and Pauline Koch of Kannstatt on the Neckar. He was a merchant who possessed a particular inclination for technical matters. He ran an electrical business and enjoyed solving technical problems and the mathematics taught in the lower forms of the German secondary schools. Music meant little to him as a distant and not very necessary pleasure. He

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did not concern himself with politics but he loved literature and, in the lamp-lit evenings, he read Schiller and Heine (Talmey 1932a, 160, 1932b, 68; Reiser 1930, 26). Albert Einstein was thus quite the opposite of his father, except for his love of mathematics. Empires and rising mighty powers disgusted him and his concern with politics was as a pacifist and humanist. Furthermore, he showed no inclination for commercial and business matters. Hermann Einstein had several brothers and sisters. Jakob Einstein, a younger brother, was the only brother to acquire an higher education, attending the Polytechnische Schule (polytechnic school) in Stuttgart from 1867 to 1869. He served as an engineer in the army during the FrancoPrussian War and in 1876 he moved to Munich and started a gas-fitting and plumbing firm (CPAE 1, l-li, notes 7-9). In contrast to Albert's father, his mother Pauline Koch, was in many respects more serious and did not always see the world through his optimistic eyes. She enjoyed her life, loved people and her household and possessed a genuine and hearty humour (of the Swabian kind). Of little Albert, she often prophesied that "some day he will be a great professor" (Reiser 1930, 27). Einstein's mother had a brother, Cäser Koch, Einstein's uncle. He lived in Stuttgart and often visited Einstein's family. In January 1885 Uncle Koch returned to Germany from Russia, where some of his family were living. With him he brought a model steam engine as a present for Albert purchased during a visit to Munich that year. Shortly afterwards Uncle Koch married and moved to Antwerp – where the young Albert was subsequently taken on a conducted tour. The uncle was a grain merchant, hardly close to science and physics, but nevertheless it was to Cäser that Einstein was to send, as a boy of sixteen, his first essay on physics. Regarding religion, the family never attended the local synagogue, nor did they keep a kosher home. Hermann saw in Jewish customs and traditions "an ancient superstition". There is one story that sounds more like a family legend or, better, an Einstein anecdote, than a reality. The family had one particularly hard-bitten agnostic uncle, whom Einstein used as a peg for an old Jewish joke. He would always describe with relish how he had surprised him one day in full formal dress preparing to go to the synagogue. The uncle had responded to the nephew's astonishment at seeming him there with the warning: "Ah, but you never know". Thus,

20

A. From Einstein's Childhood to Patent Office

writes Ronald Clark in his biography, Einstein was nourished on a family tradition that had broken with authority; one that dissented, sought independence and deliberately did not tow the line (Clark 1971, 8-9).4 The story perfectly suits both Einstein's Swabian sense of humour and the legend of Einstein the atheist. Einstein later, in Zurich of 1909, displayed an atheistic approach to religious issues (Seelig, 1954, 133, 1956a, 113). Though he would identify with great passion and care with his tribe, the Jewish people, and endeavoured to assist the Jews and the Jewish people on every occasion, he himself was not religious. On November 18, 1881, a daughter was born to Hermann and Pauline. She was named Maria (Miriam), but throughout her life she was called Maja. In 1924, in her Biographical Sketch (after Einstein had become world famous), Maja recounts a family story: when the two-and-a-half-year-old Albert was told of the arrival of his little sister, with whom he could play, he must have imagined a kind of toy, for at the sight of his new sister he asked, with great disappointment, "Yes, but where are its wheels?" ["Ja, aber wo hat es den seine Rädchen?"] (Winteler-Einstein 1924b, 1vii, 1924c, xviii). The famed psychoanalyst Erik Erikson explained his interpretation of the story (Erikson 1979, 152): "Now, as to the little wheels, the German word for it is Rädchen, or in Swabian, Rädele, which rhymes with that for little girl (Mädchen, or Mädele). Is it not possible that a play with rhymes began early in this thoughtful child, even as it continued throughout his life as an humorous need at the oddest moments 'ein Gedichte zu mache' – to make a little poem or 'ditty'? More, one might consider a special preoccupation with 'the way things rhyme' to be an important trend throughout Albert's development".

Maja recounted that Albert as a child would play by himself for hours. As a boy he "developed slowly in childhood, and he had difficulty with language that those around him feared he would never learn to speak. But this fear also proved unfounded" (Winteler-Einstein 1924b xlviii-lxvi; 1924c, xviii). In 1930 Einstein's son-in-law, Anton Reiser (Rudolf Kayser), recounted the same story, "Slowly, and only after much difficulty, he learned to talk. His parents thought he was abnormal. The hired governess called the still, backward, slow-speaking Albert, 'Pater Langweil' (Father Bore)" (Reiser 1930, 27).5

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The elderly Einstein also recalled in a letter from 1954 to Sybille Blinoff: "My parents were worried because I started to talk comparatively late, and they consulted the doctor because of it". Einstein could not say how old he was at the time, but admitted that he was certainly not younger than three. He also added that his later development was completely normal except for the peculiarity that he used to repeat his own words softly (Hoffmann and Dukas 1973, 14; CPAE 1, note 37, 1vii). Maja too reports on this strange linguistic habit. Every sentence Albert uttered, no matter how routine, he would repeat to himself softly, moving his lips. This odd habit persisted until he was seven (Winteler-Einstein 1924b, 1vii, 1924c, xviii). In the above 1954 letter Einstein did go on to say, "Also, I never exactly became an orator later" (Hoffmann and Dukas 1973, 14). It appears that it did indeed take Einstein quite a long time to become a good lecturer. Maja, Albert Einstein, and the family members seemed to have exaggerated the story of Albert who developed slowly, learned to talk late and whose parents thought he was abnormal. There is no doubt that there is grain of truth to these stories and Maja and Einstein recount their recollections in all sincerity. These stories, however, sound like family tales, and as such may be exaggerated. These and other stories were then adopted by biographers as if they had really happened in the way that Maja and Albert had told them. Biographers were thus inspired by them to create a widespread mythical public image of Albert Einstein that embodies stories about Einstein the retarded genius.6

2 The Move to Munich and the Electric Firm At the time of Albert's birth, Hermann Einstein, age thirty-two, was in a business partnership with a cousin. At the beginning of 1882, when Albert was about eighteen months old, the family moved to Munich (Talmey 1932a, 160, 1932b, 68). The decision was of two-fold significance. First, Hermann's younger brother, Jakob, had finished his studies in engineering and started the plumbing and electrical business in Munich. Since he now wished to borrow money from Hermann's wife's family, he prevailed upon Hermann to join in the venture, both personally as business manager and with a large investment (Winteler-Einstein 1924b, 1i, 1924c, xvi). In 1885 they inaugurated the J. Einstein & Co. Electrotechnical Factory. Second, the world was beginning to install electric lighting and, although the Einstein enterprise had good prospects in Munich Jakob Einstein was

22

A. From Einstein's Childhood to Patent Office

apparently more ambitious. He wanted to produce on a large scale, to construct a large plant, a dynamo of his own invention, and none of these two achievements was possible without financial assistance, i.e., they required substantial funds. The entire family, and especially Hermann's father-in-law Julius Koch, who lived with the Einsteins for some years after his wife's death in 1886, participated financially, making the new enterprise possible (CPAE 1, li, note 12). The business failed in Munich. Maja did not really understand why this gigantic enterprise failed to prosper. She assumed that Jakob Einstein, constantly seeking novelty and change was unable to learn from failure. Hermann Einstein was also not of help and it was the wealthy Koch who paid (Winteler-Einstein 1924b, 1i-1ii, 1924c, xvi). In other words, the children of Hermann Einstein very likely grew up with the understanding that they had a rich grandfather, Julius Koch, who was willing to invest, without which the firm could not have survived; and even when it was finally relocated from Munich, the rich Koch continued to pay. The ambitious uncle, Jakob Einstein, who invented a large dynamo but had a small firm and few funds, invested a lot of money in his inventions but could not learn from his failure. Their father was easily drawn into the business but could not contribute to its flourishing. In a word, the children were disappointed with commercial and business matters. In Munich of the 1880s there were few social and religious contrasts to be seen. The Jews, although united in common interests with the Christians, lived, as everywhere and at all times, in certain seclusion. Einstein's childhood was thus passed in a characteristically Jewish environment (Reiser 1930, 24). In Munich the family shared an house together with Jakob Einstein's family. The electro-technical factory adjoined the house. A large garden shaded by big trees separated the two buildings from the main road and kept the noise of the city away from the peaceful residence of the two families. There they associated little with other people. Albert passed his boyhood in this environment, until he was fifteen years old (Talmey 1932a, 160-161, 1932b, 68). The children of the family and other relatives often got together in Albert's parents' garden in Munich. However, Albert seldom joined their boisterous games, occupying himself with quieter things. As a child he preferred

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working on puzzles, doing fretsaw work and erecting complicated structures with the set of stone building blocks for children by Anker, Ankersteinbaukasten. His favourite pastime was to build multi-storied houses of cards, as high as fourteen stories (Winteler-Einstein 1924b, 1vii1ix, 1924c, xviii-xix).

3 Rebellious and Creative In 1940, Einstein recounted in a draft of a letter to Philipp Frank that he had taken violin lessons from age six to fourteen but had had no luck with his teachers, for whom music did not transcend mechanical practice (CPAE 1, 1viii, note. 39). Until Albert was twelve the violin lessons gave him no pleasure, remaining only a duty as burdensome as school. His musical experience grew out of listening and pleasure in his playing came but slowly (Reiser 1930, 31). Indeed, Albert the boy showed little sign of behaving in an expected way. At the age of six, for example, he referred to his music teacher "Du, Herr Schmied..." instead of "Sie, Herr Schmied...". In Germany one used the polite form "Sie" for adults and for people who were not members of one's family, while "Du" was used only within the family, among children, and between close friends (Winteler-Einstein 1924b, 1vii-1viii, 1924c, xviii-xix). At the age of five-six Albert also received his first preschool instruction at home from a woman teacher. Albert's sister Maja, who was probably quite annoyed with her brother from time to time, as he sometimes threw things at her, wrote in 1924 that Albert had inherited from his grandfather Julius Koch a tendency toward violent temper tantrums. Indeed people later spoke of Einstein's impulsive albeit upright nature (Winteler-Einstein 1924b, 1vii, 1924c, xviii; Seelig 1954, 44, 1956a, 38). Albert opposed authority as well illustrated by the following tale. Maja, as she remembered, saw that Albert's "face would turn completely yellow, the tip of his nose snow-white, and he was no longer in control of himself. On one such occasion he grabbed a chair and struck at his teacher, who was so frightened that she ran away terrified and was never seen again" (Winteler-Einstein 1924b, 1vii, 1924c, xviii); for the excellent reason that she had probably criticized the young Albert.

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A. From Einstein's Childhood to Patent Office

4 Einstein Cannot Take Authority and Demands for Obedience 4.1 Primary School In October 1885, when Albert was seven, he entered the public primary school, öffentliche Volksschule. There were no Jewish schools and no secular schools in Munich at that time. Thus Hermann and Pauline registered young Albert for the Volksschule Peterschule, a Catholic elementary school near their home. As the one Jew alongside seventy Catholic children he learned Catholic lessons and made good progress in them. He was even able to assist his classmates (Winteler-Einstein 1924b, 1viii, 1924c, xix). In 1886, Albert's mother, Pauline, wrote to her mother Jette Koch saying that Albert was once again top of his class and had received a brilliant report (Hoffmann and Dukas 1973, 19). Albert had a rather strict teacher whose methods included teaching children arithmetic, especially the multiplication tables, with the help of a whack on the hands. This style of teaching was not unusual at the time and "prepared the children early for their future role as citizens" (Winteler-Einstein 1924b, 1viii, 1924c, xix). On the whole, Einstein felt that school was not so very different from any other place where individuals were subjected to the power of an organization that pressurized them, leaving no area open within which they might carry on some activity more suited to their nature. The students were required to learn mechanically the material presented to them, with the main emphasis placed on inculcating obedience and discipline (Frank 1949, 23, 1947, 10). Einstein told Alexander Moszkowski with bitter sarcasm that his teachers in the elementary school had the character of army sergeants, while those in the gymnasium (the secondary school) were of the nature of lieutenants. Moszkowski explained that both terms were used in the pre-armistice sense and Einstein's words had been directed against the self-opinionated tone and customs of the military schools of earlier times (Moszkowski 1921a, 221, 1921b, 223). Frank reported exactly the same story, based on Moszkowski, foregrounding the historical aspect of the problem. He explained that the sergeants in the German army of Wilhelm II were notorious for their coarse and often brutal behaviour toward the common soldiers; while the

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lieutenants were members of the upper classes and did not come into direct contact with the men, extracting their desire for power in an indirect manner. Thus, when Einstein compared his teachers to sergeants and lieutenants, he perceived their task as that of enforcing mechanical order upon the pupils (Frank 1949, 24-25, 1947, 11).7 Einstein said later that the worst of all, in his view, was when a school was mainly run by means of fear, power and artificial authority. He thought that such treatment destroyed the healthy feelings, integrity and selfconfidence of the pupils, producing only servile helots (Seelig 1954, 17, 1956a, 14). A few words about Einstein's religious feelings. The older more tolerant and humanist Einstein spoke with Frank while the latter was writing Einstein's biography in the 1940s. In this connection Frank reported that it was very characteristic of the young Einstein that he saw no noticeable difference between what he had learned of the Catholic religion at school and the rather vaguely remembered remnants of the Jewish tradition with which he was familiar at home (Frank 1949, 23, 1947, 10). It is important to emphasize that the young Albert, only six or seven years old, when he entered public school, his religious instruction, then compulsory in Bavaria, also had to begin. A liberal spirit and nondogmatic in matters of religion, which both parents had brought from their respective homes, prevailed within the Einstein family. There was no discussion of religious matters or rules, since Albert was obliged to receive Jewish religious instruction, he was taught at home by a distant relative (Winteler-Einstein 1924b, 1ix, 1924c, xx). Reiser tells the story of the teacher bringing a nail to the class one day. The Catholic teacher of religious knowledge liked Einstein. "But one day this teacher brought a large nail to class and told the pupils that it was the nail with which the Jews had nailed Jesus to the Cross". The incident stimulated anti-Semitic feelings in the pupils which was turned against their Jewish fellow-student Einstein. For the first time Albert experienced the frightful venom of anti-Semitism (Reiser 1930, 30). Frank, in contrast, wrote that the teacher told the pupils, "The nails with which Christ was nailed to the Cross looked like this". He did not add, however, as sometimes happens, that the Crucifixion was the work of the Jews. Nor did the idea enter the minds of the students that because of this they must alter their relations with their classmate Albert. Nevertheless,

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A. From Einstein's Childhood to Patent Office

according to Frank, Einstein found this kind of teaching rather uncongenial, because it recalled the brutal act connected with it and because he sensed that it could awaken latent sadistic tendencies (Frank 1949, 22-23, 1947, 9). Max Jammer explains in his book, Einstein and Religion, that Frank's biography is known to be based largely on epistolary correspondence with Einstein, whereas Reiser's account is based on personal conversations. In his brief preface to Reiser's biography, Einstein declared, "I found the facts of the book duly accurate". Jammer notes that it is of course difficult today to determine which of the two versions is the true one. It is also difficult to assess how such an anti-Semitic incident, had it really happened, might have affected Albert's attitude toward Judaism (Jammer 1999, 21).8 Einstein was about to leave elementary school. Moszkowski described him at the age of eight or nine: "He presented the picture of a shy, hesitating, unsociable boy, who passed on his way alone, dreaming to himself, and going to and from school without feeling the need of a comrade. He was nicknamed 'Biedermeier' (Honest John), because he was looked on as having a pathological love for truth and justice" (Moszkowski 1921a, 220, 1921b, 222). The pathological love for truth (the Biedermeier trait) was also described later, in 1952, by Einstein's former classmate, Hans Byland, at the secondary school Aargau Cantonal School (Seelig 1954, 17, 1956a, 14). Frank adopted Moszkowski's description. According to Frank, when Albert was nine years old and in the final year of elementary school he still lacked fluency of speech, and everything he said was expressed only after thorough consideration and reflection. In the English translation of Frank's biography of Einstein "(Honest John)" is added in parentheses for the English reader. No evidence of any special talent was revealed at the time and his mother occasionally remarked: "Maybe he will become a great professor someday" but Frank noted: "perhaps she meant only that he might develop into some sort of eccentric" (Frank 1949, 23, 1947, 10). In this context, Reiser wrote of the young Albert, however, that his mother often prophesied: "Someday he will be a great professor" (Reiser 1930, 27). I have already remarked that in 1886, when Albert was eight, Pauline had written to her mother, Jette Koch, saying that Albert was top of his class and had received a brilliant report (Hoffmann and Dukas 1973, 19). Albert's mother clearly recognized that her son was talented and it does not seem that she thought he would develop into some sort of eccentric.

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Frank probably based his above report on one of Maja's stories pertaining to Einstein's early childhood.

4.2 Secondary School On October 1, 1888, at the age of nine and a half, Albert entered the Luitpold Gymnasium. The building was almost completely destroyed during World War Two and today the school is called after Albert Einstein, Gymnasium Albert Einstein, even though, as we shall soon see, Einstein would not have settled down well in this school. In accord with the Gymnasium's humanist orientation, primary emphasis was placed on Classical languages, Latin and later Greek, while mathematics and the natural sciences received less emphasis (Winteler-Einstein 1924b, 1x, 1924c, xx). At the time, it was more common for well-to-do Jewish families to send their children to Realschulen, which offered a more practical education centered on modern culture and the sciences – specializing in sciences (Mosse 1964, 3). Albert's parents choice of a Gymnasium, with its emphasis on Classical languages and literature – specializing in linguistic and humanistic studies, was somewhat unusual. In retrospect, Einstein apparently felt a Realschulen would have been the better choice (Einstein to Hans Albert Einstein, January 25, 1918, CPAE 8, Doc. 442). In 1955 – the year Einstein died – he attested that, as a pupil in the Gymnasium he had been neither particularly good nor bad. His principal weakness was a poor memory and especially a poor memory for words and texts. In language studies Albert was only mediocre, lacking both phonetic, and the mnemonic, gift. He hated the burden of so much memorizing and showed not the slightest talent for learning by rote, which for the study of Classical languages was particularly necessary. Albert the rebel refused to study the humanities and refused to learn by rote. Indeed, he found it hard to study what did not interest him (Hoffmann and Dukas 1973, 19-20, 28; Reiser 1930, 37). Einstein told Frank about the spiritless and mechanistic method of teaching at school, which seemed pointless when he confronted difficulties because of his poor memory for words. He said that he preferred to accept any kind of punishment rather than having to learn things by heart (Frank 1949, 24-25, 1947, 11).

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A. From Einstein's Childhood to Patent Office

Einstein was not as good in Latin as he was in the natural sciences and he rebelled against authority, and Maja told the story of this that has since been repeated in many biographies: "His Greek professor, to whom he once submitted an especially poor paper, went so far in his anger to declare that nothing would ever become of him. And in fact Albert Einstein never did attain a professorship of Greek grammar" (WintelerEinstein 1924b, 1x-1ix, 1924c, xx). The older Einstein told Seelig the same story, but that it was his Latin master who had prophesied: "You will never amount to anything, Einstein" (Seelig 1954, 15, 1956a, 12). In light of the growing fame of Einstein the genius, this anecdote indeed seemed incredible and so his biographers grabbed at the story. For instance, Clark told the story in his biography in the following way, a family legend tells that "when Hermann Einstein asked his son's headmaster what profession his son should adopt, the answer was simply: 'It doesn't matter; he'll never make a success of anything' " (Clark 1971, 27). Einstein was indeed very talented in the sciences. At fourteen he had already mastered higher mathematics, which the secondary school, based on humanist principles, did not teach (Reiser 1930, 37). In the Gymnasium Albert was supposed to begin the study of algebra and geometry at the age of thirteen. By that time however he already had a predilection for solving complicated problems in applied arithmetic, although the computational errors he made kept him from appearing particularly talented in the eyes of his teachers. He then wanted to see whether he could learn about these subjects in advance of their being taught, and so during his vacation he asked his parents to obtain the textbooks for him. He forgot all about playing and playmates, but set out instead to work on the theorems, not by accepting the proofs from books but rather by attempting to prove them for himself. He sat all alone for days, immersed in the search for solutions and proofs, and he often arrived at proofs that differed from those found in the books. During this vacation period Albert independently worked his way through the entire prospective Gymnasium mathematics syllabus (Winteler-Einstein 1924b, 1xi, 1924c, xx).

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5 Einstein Teaches Himself Natural Science and Philosophy 5.1 Max Talmud Recommends Bernstein and Kant The Jewish community had obtained free meals with the Einstein family for a poor Jewish medical student of Polish nationality, Max Talmud (who later changed his name to Max Talmey when he immigrated to the United States and became an ear-nose-and-throat doctor). Each Thursday Albert's parents invited Talmud to dinner, a practice that was a form of customary beneficence silently exercised in Jewish circles. It was Talmud who initiated Albert into the world of natural science and philosophical thought (Winteler-Einstein 1924b, 1xii, 1924c, xx-xxi; Reiser 1930, 36). In 1932, Talmud recalled those visits to the Einstein's family home. Early in the winter of 1889-1890, shortly after he had graduated as a medical student at the University of Munich, he was introduced into the comfortable, cheerful Einstein home. Talmud met Albert, an handsome, dark-haired, brown-eyed boy, then in the third grade of the Luitpold Gymnasium. Although Talmud was his senior by eleven years, a close friendship soon developed between them, for Albert was able to converse with a college graduate on subjects beyond the comprehension of children of his own age. He showed a particular inclination towards physics and took pleasure in talking about physical phenomena (Talmey 1932b, 6869). Talmud gave him Aaron David Bernstein's Naturwissenschaftlichen Volksbücher (Popular Books on Physical Science), Ludwig Büchner's Kraft und Stoff (Force and Matter) to read; two works that were then quite popular in Germany. Einstein later said that indeed at the age of thirteen he had read with enthusiasm Büchner's Force and Matter, but when he grew up he perceived its philosophical weakness and found it to be rather childish in its ingenuous realism (Reiser 1930, 38; Seelig 1954, 14, 1956a, 12). Talmud recalled that Albert was at the time profoundly impressed by these books, especially Bernstein's books, which describe physical phenomena lucidly and engagingly, and had a great influence on Albert, enhancing considerably his interest in physical science. "He never forgot Bernstein's books" (Talmey 1932a, 162). The elderly Einstein recollected memories from reading Bernstein's books in his Autobiographisches (Autobiographical Notes) (Einstein 1949, 1415):

30

A. From Einstein's Childhood to Patent Office "At the age of twelve-sixteen I familiarized myself with elements of mathematics together with the principles of differential and integral calculus. […] I also had the good fortune of getting to know the essential results and methods of the entire field of the natural sciences in an excellent popular exposition, which limited itself almost throughout to qualitative aspects (Bernstein's People's Books on Natural Science, a work of five or six volumes), a work which I read with breathless attention".

Bernstein's books were very popular little works. Twenty-one of them were published and they had at that time an extraordinary large circulation. They offered a gaily-coloured, beautiful atlas of nature presented within the limits of a child's comprehension. These volumes were less involved with theoretical physics. They were indeed an atlas that presented the wonders of science; and as such the emphasis was on technical innovations, applied science, new horizons in planetary and comet discoveries, Earth science, Darwin's theory and so forth. The books supplied scientific answers to children's and lay people's questions and Bernstein often presented the explanations using imaginary fantastic stories (Reiser 1930, 36; Bernstein 1867-1870). Starting in the third volume, Bernstein began to explain electricity and magnetism (Bernstein 1880 3). Volume 8 contains an essay "On the Rotation of the Earth", the first chapter of which is Die Uhr (The clock). Bernstein starts with an explanation of our tacit notion of a clock from daily life and then relates it to the daily rotation of the Earth (Bernstein 1880 8, 88-92). He then describes the pendulum (Bernstein 1880 8, 93100) and the machinery of pocket watches that causes the "Tick-Tock"; finally he discusses in a few pages the rotation of the Earth (Bernstein 1880 8,106-109). This followed by an essay, "On The Speed of Light", the first chapter of which is "On Light". Bernstein begins the essay by declaring: "Light travels forty thousand miles per second!" A modern day equivalent of this is almost 306,000 kilometers per second (Bernstein 1880 8, 124). He then discusses attempts to measure the velocity of light by two ways: one by Jupiter satellites, and the other that of Bradley's attempts (Bernstein 1880 8,133-147). After science and mathematics Talmud went on to philosophy. He recommended Immanuel Kant's Critiques of Pure Reason to Einstein and philosophy then became a frequent subject of their conversations. Talmud had recommended that Albert read Kant although he was only thirteen years old at the time. Even at that age, however, the works of Kant, "difficult as they are to most readers, seemed to be clear to him" (Talmey

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1932b, 69). "Kant became Albert's favourite philosopher after he had read through his 'Critique of Pure Reason' and the works of other philosophers" (Talmey 1932a, 164). Einstein had read all three main works of Kant before he was sixteen: Kritik der reinen Vernunft (Critique of Pure Reason), Kritik der praktischen Vernunft (Critique of Practical Reason), and Kritik der Urteilskraft (Critique of Judgment). During the same period Einstein was also becoming immersed in music. In 1940 he told Frank that he had really begun to learn the violin only when he was about thirteen years old, mainly after he had fallen in love with Wolfgang Amadeus Mozart's sonatas. Einstein felt that his attempt to reproduce the artistic content and singular grace of Mozart's sonatas compelled him to improve his technique, which he achieved without practicing systematically. "I believe, on the whole, that love is a better teacher than sense of duty – with me, at least, it certainly was" (CPAE 1, 1viii, note. 39).

5.2 Einstein Reads a Small Geometry Book In addition to Bernstein's books, Einstein also read a geometry book and taught himself geometry. Talmud says that, contrary to popular belief, Albert had an unusual predilection for mathematics and because of this Talmud gave him, after he entered the fourth grade, Theodor Spieker's Lehrbuch der ebenen geometrie mit übungsaufgaben für höhere lehranstalten (Textbook of Plane Geometry with Exercises for HighSchool), a popular textbook from 1890 (Talmey 1932b, 69). Talmud used to visit Albert's home every week and whenever he came Albert delighted in showing him new problems from the book that he had solved during the previous week. After a period of only a few months he had worked his way through the entire book of geometry (Talmey 1932a, 163-164). Geometry was not yet an assigned study in Albert's secondary school. That would only begin a little later. The twelve-year-old Albert, however, already possessed a geometry textbook that caused him tremendous excitement. Reiser refers to this textbook as "The first small geometry book held in his tender hands" (Reiser 1930, 35). Could this have been Spieker's geometry book? Maja reports that at that time Albert's Uncle Jakob, an engineer with a comprehensive mathematical education, set difficult mathematical problems for Albert. Albert invariably found a correct solution and even found an entirely original proof for the Pythagorean Theorem. When he

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obtained such results Albert "was overcome with great happiness" says Maja, "and was already then aware of the direction in which his talents were leading him" (Winteler-Einstein 1924b, 1xi-1xii, 1924c, xx). Moszkowski reported that Einstein had plunged himself for three weeks into the task of solving the Pythagorean Theorem, using all his power of thought. "He came to consider similarity of triangles (by dropping a perpendicular from one vertex of the right-angled triangle on to the hypotenuse), and was thus led to a proof for which he had so ardently longed!" (Moszkowski 1921a, 222-223, 1921b, 224-225). This style of work, "considering the similarity" of two objects or things, was going to be an heuristic guide in Einstein's later work. Reiser recapitulated Moszkowski and Maja's above descriptions, noting that Uncle Jakob had also told Albert of the Pythagorean Theorem. "Soon the small textbook was his favourite reading […] When he secured Spieker's geometry, he at once succeeded in solving all the exercises, including the most difficult, with the exception of two or three". Reiser explained that Einstein had worked through Spieker's geometry book, but only after he had read "the first small geometry book" (Reiser 1930, 3536). Einstein wrote in his Autobiographical Notes that at the age of twelve he had experienced a wonder "in a little book dealing with Euclidean plane geometry, which came into my hands at the beginning of a school year" (Einstein 1949, 10). This first small geometry book, which he had considered a wonder, was probably the textbook that he had received from his Uncle Jakob, Adolf Sickenberger's Leitfaden der Elementaren Mathematik, Zweiter Teil, Planimetrie (Textbook of Elementary Mathematics, Part Two, Plane Surfaces), 1888. The book was published in three separate parts and Part Two fits the description Einstein later gave of "Holy Geometry Book" that he had received at the age of twelve at the beginning of the school year (CPAE 1, lxi, note. 49). Einstein recounted in his Autobiographical Notes (Einstein 1949, 13): "At the age of twelve through sixteen I familiarized myself with the elements of mathematics, including the principles of differential and integral calculus. In doing so I had the good fortune of encountering books that were not too particular regarding logical rigor, but that permitted the principal ideas to stand out clearly. This occupation was, on the whole, truly fascinating."

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5.3 Einstein Is Free in Italy The Einstein's firm in Munich was liquidated and transferred to Italy. Einstein's father had suffered one mishap after another in his business undertakings. The electrical engineering plant failed to prosper and he found it impossible to make a living. When Italy showed a great promise for the future the Italian representative of the firm proposed moving the plant there. Albert's ambitious uncle, Jakob Einstein, was at once taken with the idea and he persuaded Albert's father to make the change, sweeping him along in his enthusiasm. In the summer of 1894, the plant was therefore transferred to Pavia. Albert's parents, his sister and Uncle Jakob all moved, first to Milan in 1894 and a year later to Pavia (WintelerEinstein 1924b, 1ii-1iii, 1924c, xvi-xvii; Reiser 1930, 38). Maja recalls with much agony how the firm in Munich was liquidated. The lovely estate with the villa in which she and her brother had spent an happy childhood was sold to a building constructor, who immediately turned the handsome grounds into a construction site, cutting down the magnificent old trees and erecting an entire row of ugly apartment houses (Winteler-Einstein 1924b, 1iii, 1924c, xvii). Albert remained alone in Munich to complete his schooling. When the family moved to Italy in 1894 they had decided to leave young Albert in Munich to ensure that he would graduate from school and finish the last three years of the Gymnasium. He boarded with a family in Munich and relatives took care of him (Winteler-Einstein 1924b, 1xiii, 1924c, xxi; Reiser 1930, 40). When Einstein had been very small, young cousins had come to visit the family from Genoa and told him of Italy and its people, of harbours, ships and sailors. Using old factory chests, they had played at going to sea. Albert was now fifteen and alone, and Italy seemed a paradise to him. Now his parents lived there and their letters painted a picture for him of this land of sunshine, colour, and free, ordinary people (Reiser 1930, 28, 40). Einstein clearly felt miserable at having to occupy himself at school with things in which he was not interested, and which he was supposed to learn solely because he had to take an examination in them. This feeling of dissatisfaction increased when his parents departed and left him alone in a boarding-house. He described the situation in a letter written in 1940. When he was in the seventh grade at the Luitpold Gymnasium, and thus

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about fifteen, he was summoned by his home-room teacher who expressed a wish that he leave the school. That home-room teacher was the same Joseph Degenhart who had prophesied that Einstein would never amount to anything (Frank 1949, 30, 1947, 16; CPAE 1, lxiii, notes 56, 58). To Einstein's remark that he had done nothing amiss Degenhart replied only that "your mere presence spoils the respect of the class for me". Einstein indeed wanted to leave the school and follow his parents to Italy, although the main reason for this was the dull, mechanized method of teaching. Because of his poor memory for words this presented him with great difficulties that it seemed pointless for him to try to overcome. He preferred, therefore, to endure all sorts of punishments from Degenhart rather than learn to gobble by rote. The rebellious and miserable Einstein, whose behaviour was intolerable in school and who was willing to study only those topics he liked, wanted to leave. His teacher, who demanded total obedience, could not stand his presence in class. His situation at school was thus absolutely miserable and he naturally longed for home and his parents. He felt that the style of teaching at the school was repugnant and militaristic, worshipping authority, and he could not stand the systematic training that was supposed to accustom pupils at an early age to a military discipline. He could not even think about the moment he would have to wear a soldier's uniform and fulfill his military duty. According to the then German citizenship laws, a male citizen must have emigrated by the age of sixteen; otherwise, if he failed to report for military service, he would be declared a deserter. Albert thus decided to leave Germany as quickly as possible (Hoffmann and Dukas 1973, 25; Winteler-Einstein 1924b, 1xiii, 1xiv, 1924c, xxi-xxii). He was depressed and nervous, seeking a way out of school. Hence, when Degenhart annoyed him yet again, he decided he would leave. He obtained a certificate from the family doctor, presented it to the school principal, left the school on December 29 1895 and set off by train, crossing the Alps straight into Italy, Milan, to his parents (Winteler-Einstein 1924b, 1xiii, note 58, 1924c, xxi). Upon arriving at his parents' home in Milan, Albert announced that he would not return to Munich. The young rebel told his (here I should add, perhaps, shocked) father that he wanted to renounce his German citizenship. Albert's father, however, had kept his own citizenship so the situation was rather unusual. In January 1896 Albert nonetheless gave up his German citizenship and was no longer subject to military service in the German army. As he could not immediately acquire any other citizenship

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he therefore remained stateless until much later becoming a Swiss citizen. Simultaneously, he renounced his legal affiliation to the Jewish religious community and thus become Konfessionslos (a person devoid of any religious affiliation) (Frank 1949, 34, 1947, 17). Albert nonetheless promised his stunned parents that he was going to prepare himself independently for the entrance examination to the Eidgenössische Polytechnische Schule (Swiss Federal Polytechnic School) in autumn (Winteler-Einstein 1924b, 1xiv, 1924c, xxi). He used to call this school the Zürcher Polytechnikum (Zurich Polytechnic [School]), the "Poly" in Zurich. It was one of the best teaching and research institutes in all Europe. In Milan Einstein gained some practical experience while working in the family factory, and at the same time he resumed his scientific and mathematical studies to prepare for the exams. He purchased the three volumes of the advanced large textbook by Jules Violle, Lehrbuch der Physik (Physics Textbook), and worked through nearly all of them (Winteler-Einstein 1924b, 1xiv, 1924c, xxii; Violle 1892-1893).9 Maja considered her brother's work habits rather odd: "Even in a large, quite noisy group, he could withdraw to the sofa, take pen and paper, in hand, set the inkstand precariously on the armrest, and lose himself so completely in a problem that the conversation of many voices stimulated rather than disturbed him; an indication of remarkable power of concentration" (Winteler-Einstein 1924b, 1xiv, 1924c, xxii). At the age of sixteen Albert had already taught himself calculus and acquired an extraordinary scientific and technical insight. As evidence of the latter, Banesh Hoffmann and Helen Dukas offer this excerpt from a letter (March 12, 1929) greeting Einstein on his birthday. It came from Otto Neustätter, his hiking companion during the year that Einstein had spent with his parents in Milan before leaving for Aarau. The excerpt tells of an incident when Albert was fifteen. His Uncle Jakob had told Neustätter that he had encountered great difficulty with the calculations for the construction of a particular machine. Some days later Jakob told one of his apprentices: "You know, it is really fabulous with my nephew. After I and my assistant-engineer had been racking our brains for days, that young sprig had got the whole thing in scarcely fifteen minutes. You will hear of him yet" (Hoffmann and Dukas 1973, 27-28).

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At around the same time Einstein sent to his uncle Cäser Koch his first essay on physics, "Über die Untersuchung des Aetherzustandes im magnetischen Feld" (On the Investigation of the State of the Ether in a Magnetic Field). (CPAE 1, Doc 5).

6 Secondary School in Aarau At the beginning of October 1895, at the age of sixteen and a half, Einstein went to the Polytechnic Institute in Zurich to sit the entrance examination (Winteler-Einstein 1924b, lxv; Reiser 1930, 44). He lacked Maturitätszeugnis (a certificate from the Munich Gymnasium) and was two years below the regular admission age of eighteen. With the aid of Gustav Maier, a family friend, he received permission from the Polytechnic director, Albin Herzog, to take the entrance examination required of applicants without a certificate. He was seeking to enroll in the engineering section of the Polytechnic. The examination began on October 8, 1895 and extended over several days. The results were announced on October 14, 1895. Einstein had failed to gain admission. He had done so well with his autodidactic preparations that he passed the entrance examination with the best results in maths and the sciences but, unsurprisingly, failed in languages and history (Albin Herzog to Gustav Maier, September 25, 1895, CPAE 1, Doc. 7, "ETH Entrance Examination and Aargau Kantonsschule", 10-11). Einstein's parents were advised to have their son attend the final year of a Swiss secondary school with the prospect of certain admission to the Polytechnic the following year, despite the fact that Albert would still be six months below the official age of admission (Winteler-Einstein 1924b, 1xv, 1924c, xxii). Einstein begins his Autobiographische Skizze (Autobiographical Sketch) of 1955 by recounting the examinations he had taken in October 1895. He then says that the physicist Heinrich Friedrich Weber invited him to attend his college physics lectures, provided that he remains in Zurich. However, continues Einstein, he enrolled according to the advice of the Rector, Prof. Albin Herzog, in the Kantonsschule (Cantonal School) in Aarau, a small Swiss town near Zurich whose schools had an high reputation and as a result were often attended by overseas students. From the end of October 1895 to the early autumn of 1896 Einstein was thus a pupil in the third and fourth classes in the technical stream of the Aargau Cantonal School. It was originally founded as a private school in 1802 and later taken over in

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1813 by the "state" – the Kanton (Canton) Aargau (Einstein 1955, 9; Winteler-Einstein 1924b, 1xv, 1924c, xxii; correction to Seelig's biography, EA 39-084). During his year in Aarau Einstein boarded with a teacher from the Aargau Cantonal School, Prof. Jost Winteler. Winteler taught German and history in the liberal arts division of the school. He was a liberal-minded man to whom Einstein would later be related; for some years later the professor's son, Paul Winteler, married Albert's only sister, Maja (Reiser 1930, 47). Einstein's former Cantonal School classmate, Hans Byland, one year older than Einstein, had painted a verbal portrait of Einstein as a teenage: Einstein as a young man could not be fitted into any pattern; an impudent Swabian, sure of himself, his grey felt hat pushed back on his thick, black hair; a restless spirit that carried a whole world in itself. Nothing escaped the sharp gaze of his large bright brown eyes. "A sarcastic curl of his rather full mouth with the protruding lower lip did not encourage Philistines to fraternize with him". His friend added that his attitude towards the world was that of a laughing philosopher and his witty mockery pitilessly lashed out at any conceit or pose. Einstein made no bones about voicing his personal opinions, whether they were offensive or not, and his courageous adherence to the truth gave his personality a certain cachet which, in the long run, was bound to impress even his opponents (Seelig 1954, 15-17, 1956a, 13-14). By 1952 the aging Byland had probably forgotten that when he had studied with the young impudent rebel Einstein (who was not yet famous), and the latter had voiced his personal opinions (whether offensive or not), his opponents had probably not been impressed at all… As noted earlier, when Einstein was nine years old, because of his conscientiousness in not making false statements or telling lies, he was called Biedermeier (Honest John) by his classmates. He told only the truth and, later, the rebel Einstein still thought the most important and useful thing was to tell the truth; and thus he always voiced his personal opinions, whether welcome or not. The Aargau Cantonal School was a Realschule, not a Gymnasium. Einstein thus could study the topics he really loved. It was also a democratic school. The combination of these two traits suited Einstein's spirit. The system of teaching was liberal, unburdened by too much authority, and resembled university lectures in approach more than that of

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an high-school institution. The classes were not confined each to their own room but there was a room for each subject, so that the students moved about for the different subjects as at a university, divided according to subject at definite hours as in college. Furthermore, the teachers were enlightened, modern individuals. In this school Albert immediately felt at home and made friends with his schoolmates (Seelig 1954, 14, 1956a, 12; Reiser 1930, 46). In the 1955 Sketch Einstein recalled that the "liberal spirit" of the Aargau Cantonal School had created an "unforgettable impression" on him. "By comparison with the six years training at the Deutsche, authoritative Gymnasium, I have become aware", noted Einstein, that "real democracy is not an empty delusion". In the democratic and free-thinking environment of the Aargau Cantonal School, Einstein imagined a "childish thought experiment that has to do with the special theory of relativity" (Einstein 1955, 9-10).10 This was the chasing after light beam thought experiment (discussed in chapter C, section 3). Einstein graduated from the Aarau secondary school and on November 7, 1896 he sent his curriculum vitae to the Aargau authorities (Dukas and Hoffmann 1979, 8-9, 121): "[…] I have attended the Cantonal school in Aarau, and I now take the liberty of presenting myself for the graduation examination. I then plan to study mathematics and physics in division 6 of the Federal Polytechnic Institute". In his matriculation examination essay in French, entitled "My Future Plans", written at the age of seventeen (September 18, 1896), Einstein also expressed his inclination and desire to study mathematics and abstract subjects (CPAE 1, Doc. 22). It was very clear to Einstein at that time that he would not be able to pursue his original aims, which had corresponded to the aims of his parents: to join his father's engineering enterprises. He felt unable to apply himself to technical work or join the complicated organism of a practical economic life. He felt he needed to study only those special subjects that corresponded to his intellectual gifts mathematics and physics (Reiser 1930, 48; Dukas and Hoffmann 1979, 17, 124). Einstein later wrote to his friend Heinrich Zangger that he was originally supposed to have become an engineer, but he "found the idea intolerable of having to apply his inventive faculty to matters that make everyday life even more elaborate – and all, just for dreary moneymaking" (Einstein to Zangger, April 22, 1918, CPAE 8, Doc. 514).

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7 Polytechnic in Zurich 7.1 Professors Weber and Pernet Turn On Einstein In October 1896 Einstein enrolled in division VI of the Schule für Fachlehrer mathematischer und naturwissenschaftlicher Richtung (School for Specialized Teachers in the Natural Science) of the Polytechnic in Zurich. He was almost eighteen and one of the youngest students to have entered the Polytechnic. The Institute had two chairs, one for Mathematical and Theoretical Physics, held by Prof. Heinrich Friedrich Weber, and the other for Experimental Physics, held by Prof. Jean Pernet – eventually both Professors Weber and Pernet turned on Einstein. As a regular student at the school, from the winter term 1896-1897 to the summer term 1900, Einstein registered for all of Weber's lectures and laboratory courses, taking the following courses and laboratories: Physics, Principles and Methods of Measurements in Electrotechnology, Oscillations, Electrotechnical Laboratory, Scientific Work in the Physics Laboratories, Introduction to Electromechanics, Alternating Currents, Ac Systems and Dc Motors, System of Absolute Electrical Measurements, and Introduction to the Theory of Alternating Current (CPAE 1, Doc. 28). In 1898 Einstein had remarked that Weber lectured masterfully on heat (temperature, heat qualities, thermal motion, dynamic theory of gases), and he was eagerly anticipating every class. Later, however, he understood that Weber's lectures were a little old-fashioned (Einstein to Mariü, February 16, 1898, CPAE 1, Doc. 39; Reiser 1930, 48). Weber's main enthusiasm was to construct, equip and direct a new physics institute for the Polytechnic. From the narrow professional point of view being the director of the physics institute there was the highlight of Weber's career. Between 1871 and 1874 Weber had worked as an assistant to Hermann von Helmholtz at the University of Berlin. He helped Helmholtz to set up and equip the Berlin laboratory and also helped him direct the student laboratories. Helmholtz's laboratory was the first substantial and major laboratory in which Weber had worked, giving him the means to conduct both laboratory instruction and research. He explicitly acknowledged Helmholtz as his teacher and scientific pathfinder. Indeed, Helmholtz had been one of the leading German scientists, and had also worked with Albert Michelson.

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Weber's work was essentially empirical. He would develop empirical laws and empirical theory to explain empirical findings. Even when he developed a theory, he always sought to turn his results to practical and technical use for sources of illumination, telephony and the establishment of electrical standards. Between 1883 and 1902 he worked on highly practical, technological subjects, including studies of the transmission of electrical energy between various cities, reports on the use of alternating current systems in electrical railroads and a report on Swiss federal law concerning low-and high voltage equipment. All this is only the gist of Weber's achievements. Later, however, during Einstein's years at the Polytechnic, Weber was to publish only one scientific paper, and that on a topic closely related to electro-technological concerns: alternating currents. Fairly soon after this paper he retired from scientific research. Weber's lectures on electromagnetic phenomena and the laws of electromagnetism remained those of a previous generation. It would seem that although wishing to occupy himself with empirical research he did not have enough time to keep up with modern research, with state-of-the-art science. From the late 1890s, his preoccupation with building his new institute and his practical and technical studies apparently left him with little time and energy to become adequately acquainted with the latest innovations in science; especially with Maxwell's results and their implications for the foundations of physics and practical physical problems. This was the state of affairs during Einstein's years at the Polytechnic (Cahan 2000, 45-52, 54). Heinrich Hertz had demonstrated the phenomenon of electric waves and Maxwell's theory had certainly begun to gain recognition, even though in the German-speaking countries his ideas were accepted more slowly. Change was not immediate and abrupt, but Europe's leading physicists gradually began to discuss Maxwell's ideas, and Helmholtz (Weber's mentor) in particular was the first to embrace them. This was the state of affairs in the late 1880s. Prof. Adolf Fisch, who had been in a parallel class at the Aargau Cantonal School with Einstein, told Seelig about the position of physics in those days at the Zurich Polytechnic. He commented that theoretical physics was taught by Weber, whose lectures were outstanding and a magnificent introduction to theoretical physics, but that anything that came after Helmholtz was simply ignored. "At the close of our studies we knew all the past of physics but nothing of their present and future. We were recommended to study the newer literature in private" (Seelig 1954, 34,

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1956a, 29). Dr Joseph Sauter, Weber's assistant and later Einstein's colleague at the Bern Patent Office, recalled that Maxwell's theory was not yet on the official program of the Zurich Polytechnic School (Sauter 1960, 154). Weber was in his forties when Einstein entered the Polytechnic, and when Weber later turned on Einstein the latter probably regarded Weber as a man distanced from pure science; a man who had apparently lost interest in and contact with the forefront of research in physics, especially in the field of electromagnetics. Einstein the free-thinker did not respect Weber, who seemed to have been quite the opposite. Einstein's beloved science had somewhat lost its appeal to him. Through his directness and his distrust of authority he had alienated Weber, who apparently conceived a particular dislike of him. This was the same Weber who, five years before, had generously gone out of his way to encourage the youth who had failed the entrance examinations. The relationship had since deteriorated and Einstein learned from many quarters that Weber had a particular dislike for him. Einstein persisted in calling him "Herr Weber" instead of "Herr Professor", and Weber on one occasion said to Einstein, with probably justified exasperation, "You're a clever fellow! But you have one fault. You won't let anyone tell you a thing" (Hoffmann and Dukas 1973, 32; Seelig 1954, 35, 1956a, 30). I mentioned earlier Maja telling the story that when Einstein was five or six years old he had referred to his music teacher as "Du Herr Schmied" instead of "Sie Herr Schmied". The eighteen-year-old Einstein did not show any sign of change. Einstein apparently also did not get along with another professor at the Poly, the French-Swiss experimental physics professor Jean Pernet, whose practical laboratory courses he took. Joseph Sauter told the following story about Einstein: One day Einstein was working in Pernet's laboratory. In common with every other experimenter, Einstein had been given a slip of paper noting his task and the method to be employed. With his usual independence Einstein flung the paper into the waste-paper basket and started to solve the problem in some other than the official way. Furious at seeing this, Pernet asked his assistant, Schaufelberger, "What do you make of Einstein? He always does something different from what I have ordered". The assistant replied: "He does indeed, Herr Professor, but his solutions are right and the methods he uses are always of great interest". On another occasion, in June 1899, Einstein was working in Pernet's laboratory when he seriously injured his right hand in an explosion (Seelig 1954, 35-36, 1956a, 30).

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Einstein seldom showed up to Pernet's practical physics course. As a result, for his course "Introduction to the practice of physics – elementary practice of physics", Pernet gave him the lowest possible grade, 1, and entered the only sanction in his Polytechnic record: "March 1899: reprimand from the Director on account of lack of diligence in the Physics Practicum" (CPAE 1, 47). Margarette von Uexküll was a fellow student of Einstein, studying biology, and she and Einstein's Serbian classmate and future wife, Mileva Mariü, shared the same lodgings at the house of Johanna Bächtold. Thirty years after Einstein's studies at the Poly, von Uexküll reported that Einstein had told her that Prof. Pernet had once kindly given him food for thought by saying: "There is no lack of eagerness and goodwill in your work, but a lack of capability". Pernet told Einstein that he (the latter) had no idea of how difficult was the path of physics; hence: "Why don't you study medicine, law or philology instead?" "Because I feel that I have a talent, Herr Professor" replied Einstein. "Why shouldn't I least try with physics?" "You can do what you like, young man", said Pernet, abruptly closing the conversation. "I only wanted to warn you in your own interests" (Seelig 1954, 47, 1956a, 40-41).11 Von Uexküll told the following story in 1956. One day in Pernet's experimental course, she had spent the whole of a warm June afternoon wrestling with an experiment in the Polytechnic's laboratory. Frustration overwhelming her, she was drawn into an argument with the small, chubby physics professor, Pernet, who refused to let her seal a test-tube with a cork for fear it would break. Suddenly she noticed Einstein's pair of large shining eyes that were clearly warning her. He suggested that she give him her laboratory notes so that he could cook up some better results. At the next review, the professor exclaimed: "There, you see, with a little goodwill, and despite my impossible methods, you can apparently work out something useful". It is possible, however, that Von Uexküll may have somewhat embellished this anecdote (Highfield and Carter 1994, 39-40). 12

7.2 Einstein Never Shows Up or Skips the Classes of Mathematicians The teaching of mathematics was on a much higher level than Weber's classes, but Einstein nonetheless skipped most of these classes too. During the first three semesters in the Polytechnic he attended the courses for engineers and mathematicians given by the German theoretician of

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numbers and functions, Prof. Adolf Hurwitz. Hurwitz was a teacher and later Einstein's colleague at the ETH – Eidgenössische Technische Hochschule (Swiss Federal Institute of Technology).13 Einstein took Hurwitz's two courses: Differential and Integral Calculus and Integral Calculus. Hurwitz lectured on differential equations, except for partials, as well as Fourier series, as well as some discussion of the calculus of variations and double integrals ("ETH Record and Grade Transcript", CPAE 1, Doc. 28; Einstein to Mariü, February 16, 1898, CPAE 1, Doc. 39). Hurwitz was a talented mathematician and was invited in 1892 to the Polytechnic from Königsberg, where, at the age of twenty-four, he had worked as an associate professor. Although suffering for many years from a painful kidney disease, he continued to teach even to the extent of finally holding his seminar in his own home. He had a great sense of humour and a love of music, which he considered to be a complement to mathematics. He played the piano, and chamber music was often to be heard in his home. Later, in 1908, when Einstein was to return to Zurich after his post in Bern in the Patent Office, he would join these musical sessions "with the whole chicken run!" (his wife and two sons) (Seelig 1954, 132-133, 1956a, 112). Einstein had never shown up at Hurwitz's mathematical seminars, despite the possibility that he could have received a good mathematical training from Hurwitz. At that time, however, Einstein was less interested in (what he perhaps considered as) "mathematical speculation" than in theoretical physics. He felt that the most fascinating subject at the time that he was a student was Maxwell's theory. For a long time he found it difficult to accept the importance of abstract mathematics and found higher mathematics necessary only when developing his gravitation theory – he only "discovered" the qualities of higher mathematics around 1912 (Einstein 1949, 31; Reiser 1930, 48-49).14 Einstein was probably not even very enthusiastic about Carl Friedrich Geiser's lectures, which he skipped as much as he skipped Hurwitz's classes. Geiser clearly took great pains to make his lectures almost artistic. Indeed, Seelig spoke about the outstanding Geiser from Bern who had already earned his rank of professor at the age of twenty-six (Seelig 1954, 34, 1956a, 29). Einstein took the following courses given by Geiser: Analytical Geometry, Determinants, Infinitesimal Geometry, Geometry theory of Invariants, Exterior Ballistics. (CPAE 1, Doc. 28). Later, after advancing the general theory of relativity, Einstein seemed to have been

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able to appreciate the value of Geiser's lectures; to remember his lectures of infinitesimal geometry in the second year; and even to say that they were true masterpieces of pedagogic art that had helped him in the struggle after general relativity (Einstein 1955, 11, 1922a, 47). During his studies at the Polytechnic Einstein also skipped another teacher's classes those of the mathematician Hermann Minkowski, who ten years later developed the mathematical formalism for Einstein's relativity theory. Minkowski, a Russian by birth, although still a young man was already regarded as one of the most original mathematicians of his time. He was not a very good lecturer, however, but Einstein was also not a very good student, i.e., not much interested in his class (Frank 1949, 38, 1947, 20; Seelig 1954, 32, 1956a, 27). Einstein "attended" the following lectures given by Minkowski: Geometry of Numbers, Function Theory, Potential Theory, Elliptic Functions, Analytical Mechanics, Calculus of Variations, Algebra, Partial differential Equations, and Applications of Analytical Mechanics (CPAE 1, Doc. 28). Minkowski, the first to recognise the formal mathematical importance of Einstein's relativity theory, once admitted to his student, physicist Max Born, "For me it came as a tremendous surprise, for in his student days Einstein had been a real lazybones; he never bothered about mathematics at all" (Seelig 1954, 33, 1956a, 28). Einstein told his best friend Besso as late as 1916, "The study of Minkowski will not help you, his work is just extra complication" (Einstein to Besso, January 3, 1916, in Einstein and Besso 1971, Letter 13). Einstein explained in his Autobiographical Notes: "I had excellent teachers (for example, Hurwitz, Minkowski), so I should have been able to obtain in depth mathematical training". However, he worked most of the time in a laboratory, fascinated by the direct contact with experience and used the remaining time mostly to study the works of Kirchhoff, Helmholtz and Hertz, etc at home. Mathematics possessed some interest of its own, but Einstein saw that it was split into numerous specialties – so he did not know what to do. His interest in the study of nature was no doubt stronger. It was not clear to him as a young student that access to a more profound knowledge of the basic principles of physics depends on the most intricate mathematical methods. This dawned upon him only gradually after years of independent scientific work (Einstein 1949, 14-15). Arnold Sommerfeld's recollections further clarify Einstein's attitude towards mathematics prior to 1912. According to Sommerfeld, strangely

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enough no personal relationship developed between Einstein and his mathematics teacher, Hermann Minkowski. Later on, when Minkowski built up the special theory of relativity into his "world-geometry", Einstein commented: "Since the mathematicians have invaded the theory of relativity, I do not understand it myself any more". Soon thereafter, at the time of the conception of the general theory of relativity, Einstein readily acknowledged the indispensability of Minkowski's four-dimensional scheme (Sommerfeld 1949, 102). Likewise, Abraham Pais reported that Einstein told Valentine Bargmann (his assistant in Princeton) that before 1912 he regarded the transcription of his theory into tensor form as "überflüssige Gelehrsamkeit" (superfluous learnedness) (Pais 1982, 152). In 1912 Einstein wrote a manuscript on the special theory of relativity. He wrote a lengthy exposition on Minkowski's four-dimensional space-time continuum: Section 3, "Some Concepts and Theorems of the FourDimensional Vector and Tensor Theories that are Necessary for the Comprehension of Minkowski's Presentation of the Theory of Relativity" (Einstein 1912, 43-54). By 1912, Einstein had come to understand the great importance of Minkowski's concepts, and incorporated his mathematical structure into his own way of thinking. The 1912 manuscript on the special theory of relativity is the first evidence for Einstein's use of Minkowski's formalism (Einstein 1912, introduction, 34). Indeed, in 1912 Einstein retracted his attitude towards mathematics in the oft-quoted letter to Sommerfeld, dated October 29, 1912 (Einstein and Sommerfeld 1968, 26). "But one thing is certain […] I have gained great respect for mathematics, whose more subtle parts I considered until now, in my ignorance, as pure luxury" (Einstein to Sommerfeld, October 29, 1912, CPAE 5, Doc. 421). Louis Kollros, professor of geometry and mathematics at the ETH, and a former classmate of Einstein, wrote in "Erinnerungen-Souvenirs" (souvenirs-memories) that in 1912 Einstein felt that elegance of special relativity "should remain a matter for tailors and shoemakers" (Kollros 1955, 27).15 Finally, as stated previously, Einstein had already read and appreciated Kant as a boy thanks to study sessions with Max Talmud. Later, Einstein revisited Kant at the Zurich Polytechnic, through Prof. Dr August Stadler's course, "The Theory of Scientific Thought – Kantian Philosophy", delivered during the summer semester of 1897 (Seelig 1954, 30, 1956a, 25).

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7.3 Einstein's Friends: Grossmann, Besso and Mariü During his studies at the Zurich Polytechnic, Einstein found it difficult to study subjects that did not interest him. He spent most of his time alone in exploration of science, performing experiments and studying, first-hand, the works of great pioneers in science and philosophy (Hoffmann and Dukas 1973, 28). During his student days, Einstein concentrated on classic theoretical physics. Between 1899 and 1900 he read the works of Ludwig Boltzmann ("Boltzmann is absolutely magnificent") (Einstein to Mariü, September 13, 1900, CPAE 1, Doc. 75), Gustav Kirchhoff's "Famous Investigations of the Motion of the Rigid Body" (Einstein to Mariü, August 1, 1900, CPAE 1, Doc. 69), Ernst Mach, Helmholtz, and Hertz. "I returned the Helmholtz volume (Helmholtz 1895) and am now rereading Hertz's 'Propagation of Electric Force' (Hertz, 1892) with great care because I don't understand Helmholtz's treatise on the principle of least action in electrodynamics" (Einstein to Mariü, August 10, 1899, CPAE 1, Doc. 52); "but within a week I can have the municipal library send books by Helmholtz, Boltzmann, and Mach to me in Milan" (presumably Helmholtz 1897) (Einstein to Mariü, September 10, 1899, CPAE 1, Doc. 54). While a student at the Polytechnic, Einstein read two of Ernst Mach's historical-critical studies, the 1897 Die Mechanik in ihrer Entwicklung/ Historisch-Kritisch dargestellt (The Science of Mechanics), and the 1896 Die Prinzipien der Wärmelehre/Historisch-Kritisch Entwickelt (Principles of the Theory of Heat), Michele Besso recommended these to Einstein in 1897 (Einstein to Mariü, September 10, 1899, CPAE 1, Doc. 54). Einstein, therefore, did not attend all his lectures, did not put enormous effort into taking notes in class, and carelessly skipped many lessons. Luckily, before sitting the two major examinations he was required to pass during his four-year course, he studied from the notebooks of his loyal friend Marcel Grossmann. Marcel Grossmann In 1955, Einstein relayed the following story in Sketch (Einstein 1955, 11): During his student days, Einstein developed a strong friendship with his fellow student Marcel Grossmann. He solemnly went with him once a week to Café Metropol on the Limmat embankment where they spoke about their studies among other topics. "He was not a vagabond and

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Eigenbrödler" – a loner like Einstein. On the contrary, Grossmann possessed just those gifts that Einstein lacked: He was a quick learner and well organised. He not only attended all obligatory courses, but he also took exceptional notes. In preparation for the exams he lent Einstein these notebooks, which were a lifesaver; "what would have happened to me without it? I would rather not write and speculate". In his Autobiographical Notes Einstein acknowledged his debt to Grossmann without mentioning his name (Einstein 1949, 16-17): "There were altogether only two examinations; aside from these, one could just about do as one pleased. This was especially the case if one had a friend, as did I, who attended the lectures regularly and who worked over their content conscientiously. This gave one freedom in the choice of pursuits until a few months before the examination, a freedom I enjoyed to a great extent, and I have gladly taken into the bargain the resulting guilty conscience as by far the lesser evil".

Michele Angelo Besso Besso was six years older than Einstein. He was born near Zurich to a Jewish family, and raised in Italy. Besso subsequently returned to Zurich in October 1891 and enrolled in the mechanics department of the Zurich Polytechnic. There he took courses from the same professors who later taught Einstein. After four years of brilliant study he obtained his diploma in mechanical engineering and quickly found a position in an electrical machinery factory in Winterthur, near Zurich. Like Einstein, Besso played the violin, and he often travelled to Zurich to attend musical soirées. Einstein and Besso first met toward the end of 1896 or early 1897 – during Einstein's first semester at the Polytechnic – at the Zurich home of a woman named Selina Caprotti; here groups often gathered on Saturday afternoons to play music (Speziali 1979, 263-264). Besso later worked with Einstein at the Patent Office in Bern. Besso continued to work there after Einstein had left to take up his first academic position Friedrich Adler During this period the Polytechnic enjoyed a great international reputation and had a large body of international students. Among them were many eastern and southern Europeans who could not or would not study in their native countries. One such student was Friedrich Adler from Austria.

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Friedrich was a thin, pale and blond young man with a fanatical faith in the revolutionary development of society. His father, Viktor Adler, founder of the Social Democrat party of Vienna, tried to keep his son out of politics by sending him to study physics in Zurich (Frank, 1949, 39; 1947, 20). Einstein met Adler in 1908 – after the graduating. Mileva Mariü Mileva Mariü a Serbian from Novi Sad, then in Hungary, was more than three years older than Einstein. She was the only woman in the mathematical department of the school for Mathematics and Physics Teachers in the Polytechnic. Mileva Mariü was Einstein's girlfriend and lover from early 1899; she became his first wife in January 1903. Mileva Mariü moved to Zurich to study since the University of Zurich and the Polytechnic were among the few tertiary institutes in Europe to accept female students, and the best option for German women. Mariü was almost twenty-one years old when she began her first semester of medical studies at the University of Zurich. However, in 1896, she transferred to the Zurich Polytechnic, to the Mathematics and Physics Department for teacher training. In Zurich, Mileva met Helene Saviü, a history student from Vienna. Mileva and Helene lived in the same pension, of Fräulin Engelbrecht at Plattenstrasse 50, along with four other women. Their friendship developed quickly. Besides living and studying together, the women frequently attended concerts and the theater, travelled into the countryside around Zurich, and played their instruments. Sometimes, the pension's lively atmosphere irritated some of the other residents. Milana Bota, a psychology student from Serbia, who was friendly with the women, complained to her parents that the noise often bothered her (Popoviü 2003, 3). One of the pension's most frequent visitors was Albert Einstein, who often joined in the women's musical performances. Einstein often brought treats from his mother to the pension. In October 1899, Einstein asked Mileva to pick up a copy of Helmholtz's Electromagnetic Theory of Light (Einstein to Mariü, October 10, 1899, CPAE 1, Doc. 63). Einstein, who favoured Helmholtz at that time, felt the author included in his books much that was found to be needed in Maxwell's theory. During the summer of 1899 Einstein wrote to Mileva, "When I read Helmholtz for the first time I could not – and still cannot – believe that I was doing so without you

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sitting next to me. I enjoy working together very much, and find it soothing and less boring" (Einstein to Mariü, August 1899, CPAE 1, Doc. 50). However, when Moszkowski later met Einstein in Berlin in 1916, he wrote, "Whenever Einstein talks of Helmholtz he begins in warm terms of appreciation, which tends to become cooler in the course of the conversation" (Moszkowski 1921a, 64, 1921b, 53). Einstein came to the pension with his violin and physics books. Mileva played the tamburitza (a mandolin-like instrument), and later the piano; Helene, the piano; and Einstein, the violin. Milana Bota informed her parents: "Miss Mariü has introduced me to her good friend, a German; his name is Einstein. He plays violin beautifully, he is a real artist, and so I'll have someone to play with again" (May 21, 1898). Two weeks later she wrote to them that she had meant to reply to their letter the day before, but had visitors, "it was Miss Mariü with the German I told you about and we played music the whole afternoon" (June 3, 1898) (Popoviü 2003, 3-4). Mileva wore orthopaedic boots to correct a physical deformity. She was born with a dislocated left hip, leaving one leg shorter than the other. In a letter to her parents, Milana Bota described Mileva as a very good girl – clever and serious, small, frail, dark, and ugly, and who talks like a real Novi Sad girl, limps a little bit, but has very nice manners (March 18, 1898). (Popoviü 2003, 4-5). Referring one day to Mileva's limb, one of Einstein's colleagues said: "I should never have the courage to marry a woman unless she was absolutely sound". Whereupon Einstein replied quite calmly that she has such a lovely voice (Seelig 1954, 44-45, 1956a, 38). Mileva Mariü never graduated from the Polytechnic. She failed the final examinations in Funktionen (Functions) and Astronomie (Astronomy) due to poor grades in mathematics. Einstein finished first in his class in the intermediate exams of October 1898; second after him was his note taker Marcel Grossmann. Einstein wrote about the exams in his Autobiographical Notes: "One had to cram all this stuff into one's memory for the examinations, whether one liked it or not". This coercion had such a deterring effect upon Einstein that he admitted, "After I had passed the examinations, I found the consideration of any scientific problems distasteful to me for an entire year" (Einstein 1949, 15-17). Even though he received his diploma, Einstein may have been too reliant on Grossmann's notes, because he did not repeat his success in the final examination. Weber even forced Einstein to rewrite his final essay, which

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dealt with heat conduction. Weber took issue that the essay on heat and transference, a subject that did not interest Einstein, had been submitted on non-regulation paper (Seelig 1954, 35, 1956a, 30). Small wonder that Einstein – the rebel – wrote an essay that did not interest him on nonstandard paper.

7.4 Einstein's Residence in Zurich When Einstein arrived at Zurich on October 29, 1896, he lived at the student quarter of Zurich 7; first with Frau Kägi at Unionstraße 4. There he remained for two years until he moved to the boarding house of Frau Stephanie Markwalder at Klosbachstraße 87, and then finally with the Hägi family at Dolderstraße 17 (Seelig 1954, 40-41, 1956a, 35). The primary school teacher, Susanne Markwalder, in whose mother's house Einstein lived as a student, told Seelig that in the evening the guests and students from different nationalities played music and Einstein was their violinist. He preferred playing Mozart, and Susanne Markwalder accompanied him on the piano (Seelig 1954, 41-42, 1956a, 35-36). Susanne Markwalder recalled Einstein's impulsive and upright nature, he never annoyed her mother except when he forgot the house door key – which he did constantly. The doorbell would ring at the most impossible hours of the night and she would be awoken by the cry: "It's Einstein; I've forgotten my key again" (Seelig 1954, 44, 1956a, 38). Of course, Markwalder's report of these incidents, which occurred fifty years earlier when Einstein was still anonymous, should be critically read, as should the other reports in Seelig's book.16 One could guess that, Susanne Markwalder's mother may have found Einstein's impulsive and upright nature more annoying than she later admitted.

8 Einstein Seeks a Position 8.1 The Rebel Graduate Einstein Is Rejected Einstein wanted to be a theoretical physicist and hoped to become an assistant to a professor at the Polytechnic. Assistants were selected by professors to help guide students, and assist during experiments in the laboratories. After obtaining the diploma, Albert Einstein was equally qualified to assist in both these aspects. However, stated Einstein's sister Maja, "None of his professors remembered their promises" (Winteler-

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Einstein 1924, 18-19). At any rate, Einstein skipped classes during his student days in the Polytechnic, and it became evident that the same professors who had praised his scientific interest and talent so highly, had no intention whatsoever of employing him as an assistant (Frank 1949, 41, 1947, 21).17 Maja appears to have reported Einstein's disappointment, which he perhaps expressed to her after graduation. He very likely felt that professors had promised him assistantship following graduation, and then none of them kept their promises. Einstein's forthrightness and distrust of authority had alienated his professors, among them Heinrich Friedrich Weber. When Einstein sought university positions, he was rebuffed (Hoffmann and Dukas 1973, 31-32). Reiser provides a similar description: "It was clear that Albert Einstein would first turn to his professors. They had promised him an assistantship at the Polytechnic Academy, had even declared that they might establish a new position for him. When he reminded them of the matter, and explained the importance of this question for his whole life, his professors drew back timidly". Einstein saw at once that they had forsaken him, and understood that something must have happened to turn things against him. He suspected that someone must have slandered him (Reiser 1930, 59-60). Actually, the professors in the engineering department needed several assistants to cope with its large student body. With relatively few students enrolled in the less lucrative fields of mathematics and physics, virtually any graduate after his final exams could, if he wanted, become an assistant for a few years. This, however, did not apply to the rebel Einstein. With Professors Pernet and Weber he had no prospects – both were of course not fond of him at this stage (Weber was fond of Einstein in 1898, but later became alienated). Weber preferred to engage anybody but Einstein, and employed two mechanical engineers instead. Einstein was reluctant to believe that he was not going to get an assistantship at the Polytechnic, and he turned his hopes to the mathematicians. Einstein approached his mathematics teacher, Prof. Adolf Hurwitz, for an assistantship. Hurwitz was probably very surprised since Einstein had rarely shown up to his seminars. Einstein confessed his omissions in a letter to Hurwitz, dated September 26, 1900. Einstein wrote that a lack of time forced him to skip Hurwitz’s mathematical seminar, where there was

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no chance of practice in practical and theoretical physics. He did, however, attend most of the seminars, and mentioned that in his student years he was primarily occupied with analytical mechanics and theoretical physics. That was an excellent reason "Honest John" gave for skipping Hurwitz's lessons (Einstein to Adolf Hurwitz, September 23 and September 26, 1900, CPAE 1, Doc. 77 and 78).

8.2 Professor Weber Is Behind Einstein's Difficulties In March 1901, Einstein was convinced that Weber was to blame. He ceased writing to more professors who, he was certain, would approach Weber for a reference (Einstein to Mariü, March 27, 1901, CPAE 1, Doc. 94). In April 1901, Einstein told Grossmann that for the past three weeks he had been with his parents, where he was trying to find a job as an assistant in a university. He was still certain that, if not for Weber, he would have been successful. Nevertheless, he left no stone unturned and maintained his sense of humour. "God created the donkey and gave him a thick skin". Einstein also remarked: "As regards to science, I have got a few wonderful ideas in my head that have to be worked out in due course" (Einstein to Grossmann, April 14, 1901, CPAE 1, Doc. 100). As to Grossmann, he was given an assistant post under Prof. Wilhelm Fiedler, who taught Descriptive Geometry and Projective Geometry. Grossmann later succeeded Fiedler as a professor in the Polytechnic in the autumn of 1907 (Seelig 1954, 35, 129, 1956a, 24, 109). Einstein graduated from an excellent European institute. However, he slowly realised that he would have to look further afield to advance his career. He thus wrote pleading letters to physicists throughout Europe: "I will have soon graced all the physicists from the North Sea to the southern tip of Italy with my offer!" (Einstein to Mariü, April 4, 1901, CPAE 1, Doc. 96). In mid-March 1901, a desperate Einstein wrote to the great physical chemist at the University of Leipzig, Prof. Wilhelm Ostwald (who later won the Nobel Prize), that he was inspired by his book on general chemistry to write his article on capillarity (Einstein 1901, 513-523): "I am taking the liberty of sending you a copy. On this occasion I venture also to ask you whether perhaps you might have use for a mathematical physicist who is familiar with absolute measurements". He told Ostwald that he was

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making such a request only because he was without means, and such a position would give him the possibility of further education. Einstein did not receive a reply. As the days passed with no responses, Einstein became even more desperate. In early April 1901, he followed up his letter with a postcard saying how important the decision of his paper would be for him and – perhaps as a pretext for writing the postcard – wandered whether he had included his address in Milan in the earlier letter, which Ostwald had received (Einstein to Wilhelm Ostwald, March 19, April 3, 1901, CPAE 1, Doc. 92 and 95). Still there was no response. A week later, Einstein tried elsewhere, writing a brief note to Prof. Heike Kamerlingh-Onnes in Leiden, Netherlands, again enclosing a reprint of his paper on capillarity. Nothing came of this application (Einstein to Heike Kamerlingh-Onnes, April 12, 1901, CPAE 1, Doc. 98). A day afterwards, Einstein's father Hermann – the unsuccessful merchant, in ill health and a stranger to the academic community, wrote to Prof. Ostwald (Hermann Einstein to Wilhelm Ostwald, April 13, 1901, CPAE 1, Doc. 99). "I beg you to excuse a father who dares to approach you, dear professor, in the interests of his son". Hermann mentioned that his son Albert Einstein was 22 years old, has studied for four years at the Zurich Polytechnic and had brilliantly passed his diploma examinations in mathematics and physics the previous summer. He also mentioned the young Einstein’s unsuccessful attempts to find an assistant position, which would enable him to further his education. Hermann went on to say that his son honoured and revered the professor the most among all the great physicists of the time, after which Hermann pleaded with Ostwald to at least read Albert's capillarity paper. Please "write a few lines of encouragement to him so that he may regain his joy in his life and his work". Hermann also asked whether Ostwald may find an assistant position for his son. It is unknown whether Prof. Ostwald wrote to Einstein as result of this letter. What is known is that Einstein did not receive an assistantship.

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8.3 Einstein Finds Temporary Positions and Grossmann Rescues Him In the meantime, Einstein had become a citizen of the canton of Zurich. His citizenship dates from February 21, 1901 (Seelig 1954, 60, 1956a, 51). His chances of finding a job in Switzerland were now greater than they were as a rebellious German Jew. Finally, rescue came from Einstein's Polytechnic classmate, Marcel Grossmann. Grossmann could not offer Einstein the assistantship he would have liked, as he was still only an assistant himself. However, in April 1901 (when Einstein wrote to Grossmann complaining bitterly about his jobless predicament) Grossmann spoke with his father, Jules Grossmann, about Einstein's troubles. His father strongly recommended Einstein to his friend Friedrich Haller, a railroad engineer and director of the Eidgenössischen Amtes für geistiges Eigentum (Swiss Federal Office for Intellectual Property) – or the Patentamt (Patent Office) in Bern. The Patent Office opened on November 15, 1888, at Lorrainestraße 3, following the first federal decree on patents. In 1901 it was moved to the corner of the Bollwerk-Speichergasse. Haller was in charge of the Swiss Patent Office and was its director until 1921 (Hoffmann and Dukas 1973, 34). In April 1901, Grossmann wrote to Einstein informing him about a likely opening for an examiner at the Swiss Patent Office in Bern. In his letter to Grossmann, dated April 14, 1901, Einstein thanked Grossmann who again came to his rescue. He thanked Marcel’s father for having taken the trouble and for the confidence that he had shown in him by his recommendation to Friedrich Haller (Einstein to Grossmann, April 14, 1901, CPAE 1, Doc. 100). On April 15, 1901, Einstein told Mileva Mariü that he had received a letter from Grossmann informing him of the possibility of a permanent position at the Swiss Patent Office in Bern. "Isn't this too much to ask for all at once? Just think what a wonderful job this would be for me! I'd be overjoyed if something came of it. Just think how nice it is of the Grossmanns, once again, to have taken the trouble of helping me" (Einstein to Mariü, April 15, 1901, CPAE 1, Doc. 101). On May 3, 1901, Einstein wrote a letter from Milan to Prof. Alfred Stern, telling him "I received an offer. There is also a chance that later I shall obtain a permanent position in the Swiss Patent Office". On that very day

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Einstein had received a temporary position at Winterthur (Einstein to Stern, May 3, 1901, CPAE 1, Doc. 104). Starting May 15, 1901, Einstein became a substitute teacher for two months until July 15, at Winterthur's Technical High School, while the resident professor was away on military service. He taught five to six hours in the mornings and spent the afternoons working in the library or at home (Pais 1982, 46; Seelig 1954, 58-59, 1956a, 48). After Winterthur, another temporary position arose: Dr Jakob Nüesch placed an advertisement in the Swiss Teachers Journal for a Privatlehrer (private tutor) to prepare a young man, Louis Cahen, from his boys' Realschule at Schaffhausen for the engineering section of the ETH. Einstein was finally engaged on the recommendation of his friend from Schaffhausen, Conrad Habicht. He was appointed for one year, to begin in September 1901, at a private school in Schaffhausen (CPAE 1, notes 3-4, 316). Einstein wrote on December 18, 1901: "Since September 15, 1901, I have been an house tutor at Schaffhausen. During the first two months of my work here, I wrote my doctoral dissertation on the kinetic theory of gases, which I submitted a month ago to the second section of the Faculty of Philosophy at the University of Zurich" (Einstein to the Swiss Patent Office, December 18, 1901, CPAE 1, Doc. 129). This work was not accepted as a thesis, however. This setback, writes Pais, was the last one in Einstein's career. It came about the time he left Schaffhausen for Bern (Pais 1982, 46). Einstein is reported to have later (after 1919) spoken of the rejection of his dissertation as "a comic example of academic obscurantism" (Plesch 1949, 219).18 Einstein left Schaffhausen for Bern. Actually, Einstein already understood that he would probably accept the position in the Patent Office in Bern and he quarrelled with Nüesch. Einstein wrote to Habicht from Bern stating he had left Nüesch in Schaffhausen "with a bang" (Einstein to Habicht, February 4, 1902, CPAE 1, Doc. 133). In 1936, upon receiving news from Zurich of Grossmann's death, Einstein wrote to his friend’s widow that he remembered their student days, "he, the irreproachable student, I myself, unorderly and a dreamer; he, on good terms with the teachers and understanding everything, I a pariah, discontent and little loved. We were good friends and our conversations over iced coffee in the Metropole every few weeks are among my happiest

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memories. At the end of our studies – I was suddenly abandoned by everyone, standing at a loss on the threshold of life. However, he stood by me and thanks to him and his father I obtained a post later with Haller in the Patent Office. It was a kind of salvation and without it, although I probably should not have died, I should have been intellectually damaged" (Seelig 1954, 245-246, 1956a, 208). At some point Haller called Einstein for an interview in Bern. The interview lasted two hours. Haller quickly revealed Einstein's lack of relevant technical qualifications in patent law. When Haller asked Einstein if he possessed any knowledge of patents, Einstein replied, "No, nothing" (Hoffmann and Dukas 1973, 34). The vacancy, officially advertised in the Schweizerisches Bundesblatt (December 11, 1901), listed the qualifications for the Patent Office post as follows: "Academic education in technical mechanics, or special leaning towards physics, a mastery of German and knowledge of French, or mastery of French and knowledge of German, and possibly knowledge of Italian". The stated salary was 3500-4500 francs, and the final application date of December 28 was given (CPAE 1, 327, note 1). Einstein was raised in a technical environment in Munich and Milan thanks to his father Hermann and Uncle Jakob Einstein's electrical firm. Hence, he very likely did not entirely lack technical knowledge, such as understanding the operation of dynamos, electrical generators, and electrical equipment. This may be one of the reasons Haller employed him. Einstein's mastery of Maxwell's electromagnetic theory may have also added to this decision. Although Einstein lacked the technical qualification for a technical patent examiner, and understood nothing about intellectual property, Haller realised that there was something about the young man that transcended technicalities. There are strong reasons to believe that it was Einstein's rare mastery of Maxwell's electromagnetic theory that ultimately prompted Haller to offer him a provisional job in the Patent Office. Since there was no immediate opening, and since the law required that all openings be advertised, Einstein’s starting date at the Patent Office was delayed. Perhaps Einstein received some assurances of a position at that time. In any event, he resigned his job at Schaffhausen and settled in Bern in February 1902, before receiving any formal appointment. At first, his means of support were a small allowance from his family and some private

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tutoring (Einstein to Mariü, 22? July 1901, CPAE 1, Doc. 119; Pais 1982, 46). However, pupils were hard to find and not very lucrative. Einstein even proposed that an easier way of earning a living would have been to play the violin in public places (Einstein and Solovine 1956, VII; Solovine 1979, 10).

9 Physics Group 9.1 The Patent Office On March 14 Einstein turned twenty-three years old. Later, on June 23, 1902, he started his new job as a technical expert (provisional) third-class in the Swiss Patent Office, with a salary of 3500 francs per year. The Patent Office was on the upper third floor of the new Postal and Telegraph Administration Building, near the railroad station and the medieval clock tower in Bern (Frank 1949, 45, 1947, 23). After Einstein's rise to fame, Max Flückiger wrote that the new employee at the Patent Office was known for his indifference to appearances and for his casual dress; indeed, he writes that Einstein often appeared at work in green slippers trimmed with flowers. Officials in the Patent Office called him "The man with the green slippers". A colleague also recalled that Einstein showed up at the Patent Office one day with a saw and proceeded to shorten the legs of his chair, because it was not adjustable and was too high for him (Flückiger 1974, 62). These examples proliferate the image of Einstein as a weirdly shabby dressed genius saint.19 Einstein's first home in Bern was a small room in Gerechtigkeitsgasse 32 (February 11, 1902, to May 31, 1902). His second home was located at Thunstraße 43a (June 1, 1902, to August 14, 1902), his third home was on Archivstraße 8 (August 15, 1902, to October 15, 1903), and prior to his marriage he moved again to Tillierstraße 18 (October 16 to October 28, 1903) (Flückiger 1974, 134). From his one-bedroom flat he walked every morning to the Postal and Telegraph building. In April 1902 Max Talmud visited him in Bern, spent a day with him, and saw his Gerechtigkeitsgasse 32 flat. Talmud recalled that his flat betrayed a good deal of poverty. He lived in a small, poorly furnished room. Talmud learned that Einstein struggled with the scant salary of an official at the Patent Office. "His hardships were aggravated through obstacles laid in his way by people who were jealous of him"

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(Talmey 1932b, 67). Talmud says that he visited Einstein in April 1902; however, Einstein only started his job at the Patent Office in June 1902. Einstein's job at the Patent Office was, on the whole, interesting because it provided insights into inventions and registering patents. Einstein's work there involved examining the submitted patent applications, and ensure that they were correctly followed. Once the Patent Office received the application, it was legally required to protect the inventor and the invention against infringement. Therefore, a patent examiner was required to have knowledge of patent law. Further, the assignments were limited with the intention of formulating a patent application in technical, legal, logical and linguistic language. The range of inventions was unpredictable, often including impossible ideas or else possible working contraptions and other special arrangements. At times the descriptions provided by the inventors were awkward or even funny. Einstein's role was to formulate the application in a clear, concise language (Winteler-Einstein 1924a, 21). According to Moszkowski, Einstein's position in the Patent Office from 1902 to 1905 gave him the chance to roam the realms of technical science. Einstein himself strongly emphasised that this position made great demands on clearly defined and accurate thought. Einstein, according to Moszkowski, recognised a definite relationship between the knowledge that he gained at the Patent Office and the theoretical results that appeared at the same time as products of intensive thought (Moszkowski 1921a, 226-227, 1921b, 229). When Einstein was asked how things functioned in the Patent Office, he replied that above all one must be able to express clearly and correctly the wording of the original patent from the description of the discovery and the patentee's claims. The work was not particularly exciting and apart from one or two exceptions it was rather soul-destroying. In any case one had to sit every day for eight hours on a stool and in return for that one was given a decent wage (Seelig 1954, 67, 1956a, 55). According to patent protection rules, all patent applications were destroyed after eighteen years. As such, we cannot know the exact details of specific patents Einstein examined. Even in the 1920s, upon recognition that no other employee of the Bern Patent Office or any Patent Office, would achieve Einstein's success, neither Friedrich Haller nor his successor agreed to bypass the patent rules for the benefit of future biographers.

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Consequently, with the exception of one comment, Einstein's works on inventions were disposed of until 1927 (Fölsing 1997, 104). The single comment that survived did so as a court record. It was compiled on December 11, 1907, and rejected a patent claim by the AEG Company of Berlin for an alternating-current machine as "incorrectly, imprecisely, and not clearly prepared" (Swiss Patent Office Letter on the AEG Alternating Current Machine, CPAE 5, Doc. 67). By 1905 Einstein may not have been an expert in academic matters, but it appears that he was an expert in the work of the Patent Office. Since he was no longer involved in academics, and worked eight hours a day, Einstein had little knowledge of the latest scientific publications. Even though he may have read papers in the Annalen der Physik, Physikalische Zeitschrift, and other German physics journals, his knowledge probably still lagged as did his contact with his professional peers. Organised meetings among physicists presented the best opportunity for meeting influential professors and even finding a position in the academic job market. Physicists would often meet in specialised groups within the framework of the annual general meeting of the Deutsche Gesellschaft der Naturforscher und Ärzte (German Society of Scientists and Physicians). In 1906, the society met in Stuttgart; there, Einstein could have become acquainted with leaders in his field. A prior notice of the meeting had been placed in the Physikalische Zeitschrift (Physikalische Zeitschrift 7, 1906, 432). Einstein’s absence was probably the result of his responsibilities to the Patent Office. The following year, when the meeting was held in Dresden, Einstein was again absent. Nevertheless, Einstein later revealed to his friend Besso that some of his best ideas originated in the Patent Office: "In this worldly cloister I hatched my most beautiful thoughts, and there we spent such happy days together" (Einstein to Besso, December 12, 1919, in Einstein and Besso 1971, letter 51). Einstein often described the Patent Office to his friends as a weltliche Kloster (worldly cloister) (Seelig 1954, 68, 1956a, 56); likewise, he referred to his life in Bern as Die glücklichen Berner Jahre (the happy Bern years) (Herneck 1963, 77). Einstein was, in any case, not the professional type, and he valued his independence more than any formal position (Plesch 1949, 202). This impression, by Dr János Plesch from around 1919, accurately portrays Einstein's patent years in Bern. Einstein felt free; free of academic authority and rules. The Patent Office provided a comfortable place for this free-thinker to hatch and brood upon

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his most beautiful theories. Einstein soon discovered that he could find time to devote to his own scientific studies if he completed his work in less time. Discretion was necessary, for although Haller could find slow work acceptable, saving time for personal pursuits was officially forbidden. As Reiser reports: "Worried, Einstein saw to it that the small sheets of paper on which he wrote and figured vanished into his desk drawer as soon as he heard footsteps approaching behind his door". Evidently, if Einstein had been discovered, he would have been ridiculed as well as harmed. Director Friedrich Haller would have laughed at him in addition to being angry (Reiser 1930, 66). It appears that Einstein wrote his notes on "small sheets of paper", because later one of the students at the University of Zurich described him entering class with notes "the size of a visiting card on which he had scribbled what he wanted to tell us" (Seelig 1954, 119-120, 1956a, 100). It is likely that on these papers Einstein wrote his ground-breaking 1905 theses; these small sheets of paper, the size of visiting cards, could enter his deskdrawer perfectly without being discovered by Haller. German physicist, Rudolf Ladenburg, told his student that during his visit to Bern he saw Einstein pulling out a drawer in his desk and announcing that this was his department of Theoretische Physik (theoretical physics) (Fölsing 1993, 254, 1997, 222). However, whether Ladenburg really visited Einstein at the Patent Office before 1905 it is doubtful (Seelig 1954, 100, 1956a, 85).20 For Biographers, Einstein's friends at the Patent Office, his table and drawer, and especially the thoughts he hatched there, were eventually turned into the best department of theoretical physics in the world.

9.2 Michele Besso, Joseph Sauter and Lucian Chavan Although Einstein did not meet influential professors, he did discuss his ideas with office colleagues. As mentioned, Einstein originally met his good friend Michele Besso at the Zurich home of a woman named Selina Caprotti (Einstein to Besso, March 6, 1952, in Einstein and Besso 1971, 464-465). Toward the end of 1903 a vacancy for a "technical expert, second-class examiner" in the Patent Office was advertised. Einstein immediately presented it to Besso, who successfully joined the Patent Office on March 4, 1904. The two friends often walked to and from work together (CPAE 1, 379).

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One colleague whom Einstein was not particularly intimate with at work was Dr Joseph Sauter, who was eight years his senior. While Einstein respected him, a close friendship never developed. Sauter, a French Swiss, had studied at the Polytechnic, was chief assistant to Prof. Weber, and served as technical expert in the Patent Office from 1898 to 1936 (Seelig 1954, 87, 1956a, 73). Einstein's third associate in Bern, Lucian Chavan, came from Nyon in Lake Geneva, and was eleven years older than him. Chavan had worked as technical secretary in the Federal Postal and Telegraph Administration in Bern since 1900 (CPAE 5, 637). In August 16, 1952, Seelig wrote to Einstein that by an happy coincidence the librarian of the Federal Postal and Telegraph Administration in Bern kindly let him look at the manuscript collection of notebooks dispensed by Lucian Chavan. The notebooks, deposited in the library after Chavan's death (at the age of seventy-four) in August 1942, are the intellectual fruits of his private studies and scientific lectures with Einstein during the winter term (1908-1909) at the University of Bern. In these neatly written notebooks Seelig also found photographs and newspaper cuttings of Einstein (very likely in a magnificent condition) (EA 39-029). Under one of these photos was a profile of Einstein from the Patent Office. Chavan had described Einstein as "1.76 meters tall, broad shoulders and slight stoop; unusually broad, short skull. Complexion – a matt light brown. A garish black moustache sprouts above his large, sensual mouth. Nose – rather aquiline and soft deep, dark brown eyes. The voice is compelling, vibrant like the tone of a cello" (Seelig 1954, 70-71, 1956a, 58).

10 Philosophy Group 10.1 Maurice Solovine and Conrad Habicht Immediately on arriving in Bern, and in order to earn some money, Einstein advertised his services as a private mathematics and physics tutor in a local paper, the Berner Stadtanzeiger. He even offered "free trial lessons". Maurice Solovine recalled his introduction to Einstein many years later (Einstein and Solovine 1956, VI; Solovine 1979, 9): Solovine was walking one day in the streets of Bern during the Easter vacation of 1902. He

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bought a newspaper and happened to see an announcement saying that Albert Einstein, former student at the Zurich Polytechnic, offered physics lessons for three francs an hour. Solovine thought: "Perhaps this man can introduce me to the mysteries of physics". He went to the address given in the announcement, ascended the stairs and rang the bell. He heard a loud "herein" followed by Einstein's appearance. Solovine entered, sat down, and explained to Einstein that he was studying philosophy, but also wished to deepen his knowledge of physics. Einstein replied that he, when younger, had a keen interest in philosophy, but at present he confined himself to physics. Solovine recounted that their first conversation lasted almost two hours and involved all sorts of questions. Solovine felt that they had "a community of ideas and a personal affinity". After the meeting Einstein escorted Solovine to the street. When Solovine prepared to leave, Einstein came with him, and they conversed in the street for about half an hour before agreeing to meet again the next day (Einstein and Solovine 1956, VI; Solovine 1979, 9). During their third meeting, Einstein declared that meeting for free discussions of philosophy would be much more fun than paid lessons. They decided to read together the works of the greatest philosophers and afterwards discuss their ideas. Einstein apparently liked Solovine and referred to him as, "very kind" in a letter he wrote to Seelig on May 5, 1952 (EA 39-020). Einstein and Solovine were soon joined by another friend. With much enthusiasm, Conrad Habicht joined the meetings, and the three formed a discussion club. As stated earlier, Einstein met Habicht during his stay in Schaffhausen (Habicht's hometown). The latter came to Bern to complete his (PhD) studies, as he wanted to teach mathematics in secondary school. In 1904, he was elected to the post of mathematics and physics teacher at the Protestant Educational Institute in Schies (Graubünden), where he stayed until his return to Schaffhausen in 1914 (Flückiger 1974, 73). Einstein enjoyed close relations with Habicht and Solovine. On January 3, 1903, Einstein and Mileva Mariü married. Mileva was aged twenty-seven and Albert, twenty-four. The wedding took place at the registry office in the old city; no guests from either family arrived for the occasion. The witnesses were Conrad Habicht and Maurice Solovine. There was no

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honeymoon, and one account states the couple made their way home to Einstein's small apartment at Tillierstraße 18, only to discover that he had locked them out! (Highfield and Carter 1994, 100). In November 1903, the Einsteins moved to a third-floor apartment in the city, at Kramgasse 49. The modest dwelling was reached by a steep narrow staircase and consisted of two rooms, one with large windows and a view to the street. Hans Albert Einstein was born here on May 14, 1904; a year later they moved to Besenscheuerweg 28, in the Mattenhof district, to be closer to Michele Besso and his wife (Flückiger 1974, 73). Around this time, Einstein wrote his now famous letter to Habicht announcing his four miraculous year papers (Einstein to Habicht, May 18 or 25, 1905, CPAE 5, Doc. 27). It was soon after, in September 1905, that Einstein tried to persuade Habicht to come work with him in the Patent Office: "If an opportunity arises I shall give you a boost with Haller, perhaps we may manage to smuggle you in among the patent boys". Einstein asked Habicht: "Would you, in fact, be prepared to come? Think that each day there are eight working hours, leaving eight hours for leisure, and then there is Sunday. I should be very pleased if you were here" (Einstein to Habicht, June 22– September 30, 1905, CPAE 5, Doc. 28). On April 27 or on May 3, 1906, Einstein also attempted to persuade Solovine to join the Patent Office. "There is still some possibility that you might find work and, in due course, even a permanent appointment here. Do write your thoughts to me soon" (Einstein to Solovine, April 27, 1906, CPAE 5, Doc. 36, May 3, 1906, Einstein and Solovine 1993, 18-19).21

10.2 The Olympia Academy Solovine, Habicht and Einstein used their discussion club to poke fun at pompous, scholarly societies. Maurice Solovine, the philosopher among them, gave their clique the grandiose title Akademie Olympia (Olympia Academy), which they later referred to as Die unsterbliche Akademie Olympia ("Immortal Olympia Academy") (Herneck 1963, 72). Einstein, the youngest of the three, was the designated Akademiepräsident, (president), and received the ironic title of Albert Ritter von Steißbein ("Albert the knight from Backbone") (Herneck 1963, 70). Solovine prepared a certificate with a drawing of Einstein's head in profile: Der Mann von Hechingen (The Man of Hechingen, a town in central Württemberg): This Man possesses some interesting and noble features

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and qualifications. He was (Solovine, "Dedication: Einstein as Member of the Olympia Academy", A.D. 1903, CPAE 5, Doc. 3): "Expert in the noble arts, versed in all literary forms – leading the age toward learning, a man perfectly and clearly erudite, imbued with exquisite, subtle and elegant knowledge, steeped in the revolutionary science of the cosmos, bursting with knowledge of natural things, a man of the greatest peace of mind and marvellous family virtue […]".

Einstein was obviously the leading spirit in the group. The friends read and discussed major works of philosophy and science that eventually and powerfully influenced the development of Einstein's ideas. The Olympia Academy was, in earnest and above all, fun (Hoffmann and Dukas 1973, 38). Solovine, Habicht and Einstein used to dine together. These frugal dinners were usually made up of sausage, a piece of Gruyère cheese, fruit, a small jar of honey and one or two cups of tea. They pursued their discussions at Café Bollwerk, located a few steps from the Patent Office, and also in their homes (Einstein and Solovine 1956, VII; Solovine 1979, 9). Solovine and Habicht decided to serve Einstein caviar as a special surprise for his birthday on March 14. They joined Einstein for dinner at his flat and, just as he would have served the sausage, Solovine placed the caviar on three plates. Einstein, however, was so absorbed in his soliloquy about Galileo's principle of inertia that he consumed the caviar without even noticing. Habicht and Solovine exchanged astonished glances; once Einstein had finished all the caviar Solovine asked: "Do you realise what you have been eating"? Einstein Looked at Solovine with his big brown eyes and queried: "What was it"? Solovine cried: "For heaven’s sake, that was the celebrated caviar". Einstein expressed his astonishment at learning "that was caviar". After a short silence he added: "Well, if you offer gourmet foods to peasants like me, you know they won't appreciate it" (Einstein and Solovine 1956, IX-X; Solovine 1979, 10-11). During his later years in Princeton, Einstein, already aged, would often reminisce about his days at the Olympia Academy. He once wrote to Solovine about this (Einstein to Solovine, April 3, 1953; Einstein and Solovine 1993, 142-143): "To the Immortal Olympia Academy, During your, short active life of existence you took a childish delight in all that was clear and reasonable. We three members, all of us at least

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remained steadfast. Though somewhat decrepit, we still follow the solitary paths of our lives by your pure and inspiring light; for you did not grow old and shapeless along with your members, like a plant that goes to seed".

With this in mind he swore fidelity and devotion until his last learned breath. Earlier Einstein's letters to Solovine also included memories from the wonderful times in Bern at their cheerful "Academy", which was revealed to be less childish than the respectable ones he later got to know at close quarters. He told Solovine that one of Habicht's sons, a mathematician like his father, had come to Princeton (Einstein to Solovine, November 25, 1948; Einstein and Solovine 1993, 104-107). Through him, Einstein received news of the "old man", regaling him to recall the academy and the "wonderful time in Bern" (Seelig 1954, 69, 1956a, 59).

10.3 The Reading List of the Academy The academy's reading list included the following books and papers (CPAE 2, xxiv-xxv). Solovine and Einstein started to read Karl Pearson's Grammar of Science, before Habicht joined them. After Habicht had joined, the three of them read and discussed Ernst Mach's Analyse der Empfindungen (Analysis of Sensation) (1900 or 1902 or 1903), and Die Mechanik in ihrer Entwicklung (Science of Mechanics), the first edition was published in 1893; they probably read the fourth or fifth edition of 1901 or 1904. They also read John Stuart Mill's System of Logic, David Hume's, A Treatise of Human Knowledge, partly translated in 1895 as Traktat über die menschliche Natur, and Baruch Spinoza's Ethik (Ethics). A few papers by Helmholtz, and Bernhard Riemann's 1854 famous Göttingen lecture, "Über die Hypothesen welche der Geometrie zu Grunde liegen" (On the Hypotheses which lie at the Bases of Geometry) were also read and discussed. Several chapters of Aufsatz über die Philosophie der Wissenschaften (Essay on the Philosophy of Science) or the French edition L'essai sur la philosophie des sciences (1834) by André-Marie Ampère were also covered.

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The three also included William Kingdon Clifford's 1903 essay "On the Nature of Things-in-Themselves", and writings by Richard Avenarius and Richard Dedekind's 1888 paper, "Was Sind und was Sollen die Zahlen?" (What Are Numbers and What Should They Be?). Finally, the group also read Poincaré's 1902 La science et l'hypothese (Science and Hypothesis). Einstein may have used the 1904 German edition Wissenschaft und Hypothese (published in January 1904). Solovine recalled that Poincaré's book "profoundly impressed us and kept us breathless for many weeks"; he remembered that the academy members also "devoted weeks to the discussion of David Hume's eminently penetrating criticism of conceptions of substance and causality" (Einstein and Solovine 1956, VIII; Sonnert 2005, 305). Einstein often acknowledged his intellectual debt to Hume. For Einstein, Hume's philosophy complemented Mach's and Avenarius' works. Kant's works, however, were absent from the academy's extensive reading list (Sonnert 2005, 303; Einstein and Solovine 1956, VII-VII). Before August 1904 Habicht returned to Schaffhausen to take up a teaching position. Solovine left a year later for Paris, where he found a job as an editor and writer; later becoming the authorised translator of Einstein's books into French. While the academy existed only briefly, the three friends kept in touch, and continued to recall the Bern days in their memories and letters (Hoffmann and Dukas 1973, 38-39).

11 Annus Mirabilis 11.1 Letters to Habicht Einstein longed for the happy days of the Olympia Academy meetings, and to discuss his ideas with Habicht. On August 1, 1904, Einstein wrote to Habicht: "Your postcard just arrived. Please do come at once. I am still on vacation this week, and nothing would please me more than to see you here". Five days later on Saturday August 6, Einstein again wrote to Habicht, "Dear Habicht, […] All the rest hopefully soon in person in Bern". Einstein felt so lonely on that Saturday, August 6, without Habicht, that he wrote him another letter that very day, "Dear Habicht, […] have you perhaps not received the card I sent you on Monday?" (Einstein to Habicht, August 1, August 6, 1904, CPAE 5, Doc. 21, 22, 23).

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Why was Einstein so in need of his friend in early August 1904? What did he want to tell him? Possibly, he wanted to speak with him about his imminent discoveries? The next surviving letter is dated a few months later. On March 6, 1905 Einstein again wrote Habicht two letters on the same day: "Don't forget Bern and the academy, and be sure to come and see us", and: "You are herewith warned and challenged to attend a number of academic meetings of our praiseworthy 'academy' and to increase forthwith by 50 per cent your present membership fee" (Einstein to Habicht, March 6, 1905, CPAE 5, Doc. 25, 26). Einstein very likely did not write to Habicht between March and mid-May 1905. He was busy working on his Annus Mirabilis papers during these months. However, two months after the last letter, Einstein sent Habicht another letter from Bern. The letter was undated, but appears to have been written between May 18 and 25, 1905: (Einstein to Habicht, May 18 or 25, 1905, CPAE 5, Doc. 27): "Dear Habicht! A strange silence seems to reign between us, so that it appears to me to be almost a blasphemy if I now break it with a little insignificant prattle. […] But why have you not yet sent me your thesis? Don't you know, you miserable, that I should be one of the few fellows who would read it with interest and pleasure? I can promise you in return four works, the first of which I shall soon be able to send you as I am getting some free copies. It deals with the radiation and energy characteristics of light and is very revolutionary, as you will see if you send me your work in advance. The second work is a determination of the true atomic dimensions from the diffusion and inner friction of diluted liquid solutions of neutral matter. The third proves that on the premise of the molecular theory of heat, particles of the size 1/1000mm, when suspended in liquid, must execute a perceptible irregular movement that is generated by the movement of heat. Movements of small, lifeless, suspended particles have in fact been examined by physiologists, and these have been called by them 'Brownian Molecular Movement'. The fourth work is only a draft, at this point, about the electrodynamics of moving bodies; it employs a modification of the theory of space and time. The purely kinematical part of this work will surely interest you".

Einstein ended the letter by saying that Solovine spends much time (in Bern) giving lessons.

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Einstein would soon tell his friend Habicht about yet another, fifth, ground-breaking paper; an addendum to his work on the electrodynamics of moving bodies containing Einstein's first derivation of the mass-energy equivalence (and in this letter persuade him to come and work with him in the Patent Office). Einstein told Habicht that, one more consequence of the electrodynamics paper (1905a) has crossed his mind (Einstein to Habicht, June 30 – September 22, 1905, CPAE 5, Doc. 28): "Namely, the relativity principle, together with Maxwell’s fundamental equations, requires that mass be a direct measure of the energy contained in a body. Light carries mass with it. A noticeable reduction of mass would have to take place in the case of radium. The consideration is amusing and seductive; but for all I know, God Almighty might be laughing at the whole matter and might have been leading me around by the nose".

11.2 Einstein's Annus Mirabilis Papers Before June 1905, Einstein was twenty-six-years-old. He sat in the Patent Office in the Postal and Telegraph Administration Building. He probably sent his papers to the Annalen der Physik from there. Einstein signed, "Bern, June, 1905"; in accordance with the Annalen regulations, he wrote the name of the city from which the paper was sent. Consequently, many scholars looked for him at the University of Bern, not thinking to go to the Patent Office (Winteler-Einstein 1924, 24). Einstein's burst of ideas in the Annus Mirabilis of 1905 was amazing. He published five papers in the Annelen der Physik that solved some of the most persistent problems confronting the fin de siècle physics at the turn of the nineteenth and twentieth centuries. Of course, prior to publication of these papers Einstein was immersed in years of tedious work, leading to this burst of creativity (Seelig 1954, 81-82, 1956a, 68): 1) "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" (On a Heuristic Viewpoint Concerning the Generation and Transformation of Light) was sent to the Annalen on March 17, 1905, and received by the Annalen a day afterwards (three days after Einstein's twenty-sixth Birthday). It argues in a heuristic manner for the existence of light quanta and derives photoelectric law. Einstein won the 1922 Nobel Prize for physics ostensibly for this work. 2) Eine neue Bestimmung der Moleküldimensionen (A New Determination of Molecular Dimensions), his doctoral thesis submitted to the

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mathematical and natural science branch of Zurich University. The thesis was dedicated "to my friend Dr Marcel Grossmann", and was approved by Einstein's mentor, Prof. Alfred Kleiner, and by Prof. Heinrich Burkhardt. The elder Joseph Sauter told Seelig in the 1950s that he recommended that Einstein send his doctoral thesis to Zurich because it would be absolute child's play for him to get a doctorate there (Seelig 1954, 87, 1956a, 73). At first, Einstein attempted to submit his recently completed paper, "Zur Elektrodynamik bewegter Körper" (On the Electrodynamics of Moving Bodies) (the theory of relativity) as a doctoral thesis to the University of Zurich, but the relativity paper did not seem quite right to the leading professors, "as the wholly unknown author paid no heed to authority figures, even attacked them! So the work was simply rejected (an irony of fate!), and the candidate saw himself compelled to write and submit another, more harmless work, on the basis of which he then obtained the title of Doctor Philosophiae" (Winteler-Einstein 1924, 23). Einstein had already created the myth of the genius whose achievements it was most difficult to understand. He would do it again in 1907 when he applied for a teaching position at the University of Bern. Here, he again failed to follow the rules and send along with the application an unpublished scientific paper; he enclosed the 1905 relativity paper (see section 13). 3) "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen" (On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat). This is the Brownian Motion paper; it was received by the Annalen on May 11, 1905. 4) "On the Electrodynamics of Moving Bodies", received by the Annalen on June 30, 1905. The original thirty-page manuscript relativity paper was destroyed after publication. In the 1960s Gerald Holton worked with documents from Einstein's Estate. At that time, Einstein’s secretary, Helen Dukas, had been organising the documents into systematic order. For three years, under Holton's general supervision, the material was catalogued. One of the first things Holton looked for was, of course, any manuscript or draft of Einstein’s 1905 paper on relativity theory, particularly the early papers. However, Einstein destroyed or discarded the manuscripts that were returned from the printer (Holton 1966, 227-228).

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Einstein's secretary explained that Einstein probably made his calculations on odd slips of paper; although, for the submission of his now-famous works to Annalen der Physik in 1905 he presumably wrote them out reasonably neatly, once they were in print he discarded the manuscripts, perhaps after using them as scraps of paper on the backs of which to perform additional calculations. This explains why the originals no longer exist (Hoffmann and Dukas 1973, 69). During World War II, the American War Loan in the United States asked Einstein to donate his manuscripts to raise money for the war-bond drive. He was thus persuaded to rewrite the paper by hand. Helen Dukas recalls that in 1943 she dictated it aloud to him from his published 1905 paper, and that he kept interrupting by claiming there were simpler, more elegant ways of expressing matters. In early 1944 it was auctioned in Kansas City for $6,000,000, and donated to the Library of Congress in Washington (Holton 1966, 228; Seelig 1954, 82, 1956a, 68). 5) "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" (Does the Inertia of a Body Depend on its Energy Content?) The first derivation of the mass energy equivalence; received by the Annalen on September 27, 1905. Einstein had completed the watershed papers while working full-time at the Patent Office (Hoffmann and Dukas 1973, 60). Einstein was now Herr Doktor. Friedrich Haller approached the Swiss Federal Council, proposing a long, overdue promotion for Einstein. Haller told the council that Einstein had increasingly familiarised himself with patent technology; he very successfully processed quite different technical patent applications, and was one of the most highly respected experts of the Patent Office (CPAE 5, 39, note 1). On April 1, 1906, Einstein became an expert, second class examiner. Until then Einstein earned 3500 francs, annually. His new salary increased by 600 francs to 4500 francs, annually (Flückiger 1974, 68). When Haller informed him of his promotion, says Seelig, Einstein responded with a question seldom heard in a civil servant’s office: "But what shall I do with all that money?" (Seelig 1954, 67, 1956a, 55).

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12 German Scientists Respond to Einstein's Relativity Paper 12.1 Professor Max Planck Writes to Einstein When Einstein submitted his work on relativity in 1905 to the Annalen der Physik, he was afraid for some time that it might be rejected. Upon publication, he expected sharp and severe criticism. The Annalen was widely read by young scholars, and Einstein anticipated an immediate reaction. The complete silence that followed left him incredibly disappointed. Subsequent issues of Annalen der Physik did not mention his publication and the physics world did not respond (Winteler-Einstein 1924a, 23). Toward the end of November 1905, Walter Kaufmann, in an account of his experiments with electron beams, first mentioned Einstein's paper in the Sitzungsberichte (Proceedings) of the Prussian Academy of Sciences in Berlin: "Finally, another recent publication mentions the theory of electrodynamics by Hrn. A. Einstein, which leads to conclusions that are formally identical to Lorentz's theory" (Kaufmann 1905, 954). Einstein finally received a letter from Berlin. It came from Prof. Max Planck, the well-known physicist who asked him to explain some obscure points in the paper. After Einstein’s long wait, this was the first sign that his work had actually been read. The joy of the young scholar was so great, because he received recognition from one of the greatest living physicists (Winteler-Einstein 1924a, 23). In the following years Einstein and Planck corresponded and, despite the age difference, a solid friendship developed between them. Maja recollects Planck spreading Einstein's theory, and by that raised Einstein's morale. After the publication of the relativity paper Planck brought to light the patent clerk's ideas by organising a seminar on the new theory with his students. Further, Planck dedicated the first lecture of a physics colloquium to a report on the new relativity paper. Planck's students also became interested in what seemed to be unsolved problems of the theory, and started to correspond with the young physicist in Bern. Naturally, says Maja, they sent their letters to "Professor Einstein" and directed them to the University of Bern, "because no one suspected that the author of the publications that by then had aroused a great stir had an humble official position in the Patent Office" (Winteler-Einstein 1924, 23-24; Hoffmann and Dukas 1973, 83-84).

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Einstein wrote twice to Planck before receiving an answer from him on July 6, 1907. Plank told Einstein he would probably be going to the Bernese Oberland next year, and that he would be happy to think that perhaps he would meet Einstein there (Planck to Einstein, July 6, 1907, CPAE 5, Doc. 47). However, Einstein and Planck only met two years later in Salzburg in 1909, the first nationwide congress attended by Einstein.

12.2 Max Laue Meets Einstein Max Laue, who was the same age as Einstein, was Planck's assistant in Berlin. He was appointed in the autumn of 1905. Laue wrote to Einstein to request a meeting with him in Bern during the summer of 1906. It seems – though the evidence is unclear – that Laue automatically assumed that Einstein was at Bern University (like the other scholars according to Maja's above report) and went there to look for Einstein (Seelig 1954, 91, 1956a, 77; Hoffmann and Dukas 1973, 84). Seelig tells the story as the elderly Laue recounted it (Seelig 1954, 92-93, 1956a, 78). Laue used his summer holiday, after a mountain tour, to become personally acquainted with Einstein in Bern. After a written appointment he looked him up and found him in the Patent Office. In the general waiting room an official instructed him to follow the corridor and Einstein would come out and meet him. Laue followed his instructions but the young man who came to meet him made such an unexpected impression on him that Laue did not believe he could possibly be the father of the relativity theory. So Laue let him pass and only when he returned from the waiting room did they finally become acquainted. Laue could not remember the actual details of what they discussed, but from that visit he came away with some understanding of the relativity theory. Planck wrote to Einstein, "Herr Laue told me about his very pleasant meeting with you" (Planck to Einstein, November 9, 1907, CPAE 5, Doc. 64).

13 Einstein Teaches His Three Friends at the University of Bern 13.1 Patent Clerk Rebels against Academic Rules Shortly after Einstein started to work at the Patent Office in 1902, he joined Joseph Sauter at meetings of the Naturforschende Gesellschaft

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(Natural Science Society) in Bern, an association of professors, high school teachers and prominent figures in medicine and pharmacology, of which Sauter was a regular member. During a meeting on May 2, 1903, Einstein met a friend of Sauter's, Dr Paul Gruner, who was at that time a high school teacher and a privatdozent in physics at Bern University (Flückiger 1974, 71, 111). In 1906, a professorship of theoretical physics was created at the University of Bern and the post was given to the fiftyfour-year-old Gruner (Seelig 1954, 103, 1956a, 88). In 1907, Einstein decided to apply for a post of as privatdozent while retaining his position at the Patent Office. Pais writes that it was often said in those times that a university career could be contemplated only if one was independent or wealthy; of course, neither applied to Einstein (Pais 1982, 184).22 After consulting with Gruner, who had learned of his extraordinary capabilities, Einstein applied for admission to the Faculty of Theoretical Physics in 1907 (Seelig 1954, 103, 1956a, 88). On June 17, 1907, Einstein sent a letter to the cantonal authorities in Bern enclosing copies of his doctorate thesis, 17 published papers (including the ground-breaking ones of 1905), and a curriculum vitae. Several faculty members spoke in favour of the application when the matter arose for discussion. In his application, the rebellious Einstein did not follow the rules when he failed to send the Habilitationsschrift – (habilitation, a not hitherto published scientific paper) along with his application. Instead, he enclosed as the habilitation the 1905 relativity paper. Prof. Gruner received his essay, but felt that the whole theory at that time seemed highly problematical (Pais 1982, 184; Seelig 1954, 103, 1956a, 88). Prof. Aimé Forster, who had been teaching experimental physics at Bern University since 1896, felt it unnecessary and unsuitable to engage, in addition to Gruner, a privatdozent in the field of theoretical physics in which there were no more than half a dozen students. He returned Einstein's work, "The Electrodynamics of Moving Bodies" with the following remark: "I can't understand a word of what you've written here!" (Seelig 1954, 103-104, 1956a, 88). He could not easily accept a work which attacked the tacit assumptions of physics, and he expected a work that followed the accepted rules. In his application, Einstein should have submitted a work that met the rules and appeased the faculty members in the department. Moreover, the regulations insisted upon a hand-written thesis; however, as mentioned earlier, Einstein had discarded the original 1905 hand-written relativity manuscript (Hoffmann and Dukas 1973, 69).

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Einstein was so irritated that he momentarily abandoned the idea of pursuing an academic career. Einstein's request was denied until such time as Herr Einstein saw fit to produce the habilitation. Meanwhile, Einstein's close friend from the Polytechnic, Marcel Grossmann, had become professor at the Zurich Polytechnic in 1907, succeeding Prof. Otto Wilhelm Fiedler. It should be remembered that Grossmann was not like his close friend Herr Einstein, a rebel, vagabond and Eigenbrödler (loner) (Einstein 1955, 11). On January 3, 1908, a despairing Einstein wrote to Grossmann, asking him the best way to apply for a vacant high school position: "At the risk of you thinking me ridiculous, I must ask your advice on a practical matter. I want very much to launch an attack on a teaching position at the Technical School in Winterthur (Mathematics and Physics). A friend who is a teacher there has told me in strictest confidence that the position will probably become vacant pretty soon". Einstein said that "I come to this hankering only because of an ardent desire to be able to continue my private scientific work under less unfavorable conditions". He told Grossmann that he once taught there for a few months as a substitute teacher. "I now ask you: How does one go about it? Should I perhaps pay someone a visit? […] Furthermore, would it make sense if, at this interview, I were to extol my scientific papers?" (Einstein to Grossmann, January 3, 1908, CPAE 5, Doc. 71). The job never eventuated. The principal of the school at Winterthur wrote to Einstein that the chances a position would become vacant very soon looked dim (Adolf Gasser to Einstein, mid-January, 1908, CPAE 5, Doc. 74). Soon after, Einstein changed his mind about the habilitation thesis. He wrote to Gruner on February 11, 1908, that the conversation he had with him in the library, as well as the advice of several friends, has caused him to change his mind again and to apply once more for admission to Bern University. To this end Einstein decided to forward a habilitation to the dean (Einstein to Gruner, February 11, 1908, CPAE 5, Doc. 81). Einstein changed his mind because Prof. Alfred Kleiner – who was involved in both the rejection and acceptance of doctoral theses submitted by Einstein to Zurich University – sent Einstein a postcard expressing a desire to get in touch with him about a matter of mutual importance. Seeking to bring Einstein to Zurich University, Kleiner urged him not only to try once more to become privatdozent at Bern University, but also to report any developments, so that if things went badly, Kleiner could try to

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think of less orthodox ways in which Einstein might meet the prerequisites for a professorship (Kleiner to Einstein, January 28, CPAE 5, Doc. 78). On February 8, 1908, Kleiner told Einstein that if Forster was to evaluate his habilitation, he could easily procrastinate with the delivery of his vote if, for some reason or other, this habilitation was not to his liking. Kleiner, therefore, encouraged Einstein to garner support from acquaintances, like Gruner, from within the faculty who could help promote a favourable agenda that semester. He encouraged Einstein to contact Gruner regarding his habilitation and explained that it was imperative Einstein began lecturing. If he did not lecture next semester via habilitation, then Kleiner would need to arrange an opportunity of another kind to prove himself, such as lecturing at the Natural Science Society or something similar. "Please keep me up to date" (Kleiner to Einstein, February 8, 1908, CPAE 5, Doc. 80). Einstein prepared a new habilitation thesis under the title, Folgerungen aus dem Energieverteilungsgesetz der Strahlung schwarzer Körper, die Konstitution der Strahlung betreffend (Consequences for the Constitution of Radiation of the Energy Distribution Law of Black Body Radiation), and submitted it to the Philosophical Department II. The thesis was circulated among the faculty members, and on February 24, Prof. Forster proposed that it be accepted and that Herr Einstein be invited to an inaugural lecture. Three days later, on February 27, 1908, Einstein presented "Über die Gültigkeitsgrenze der klassischen Thermodynamik" ("On the Limit of Validity of Classical Thermodynamics"). The faculty members recommended that the candidate be made a privatdozent of theoretical physics (CPAE 5, 622; Pais 1982, 185).

13.2 Jakob Johann Laub Meets Einstein in Bern Jakob Johann Laub, who was born in Austria and graduated under Prof. Wilhelm Wien, received his doctorate three years after Einstein (at the beginning of 1907). During his oral examination on his doctoral thesis, Laub referred to Einstein's new relativity theory. Laub wrote to Seelig that in Würzburg, immediately after the publication of Einstein's paper "On the Electrodynamics of Moving Bodies", Prof. Wien entered the room of the students working on their doctoral theses one morning and instructed him to give a colloquium on the theory. Wien organised the colloquium on the relativity paper immediately after its publication. Laub's oral examination fuelled a heated discussion on several points that could not be clarified; so,

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upon Wien’s advice, Laub intended to visit the author of the theory in person. (Seelig 1954, 85-86, 1956a, 72). Laub wrote to Einstein on January 27, 1908, asking him to send reprints of papers connected to the relativity principle. He told Einstein that he had the relativity paper (1905a) and the energy-mass paper (1905b). Laub wrote to Einstein again on February 2, 1908. He told Einstein that he was interested in his relativity physics, and asked whether Einstein would agree to a three-month visit in Bern (Laub to Einstein, January 27, February 2, 1908, CPAE 5, Doc. 77, 79). Laub came to Bern. Together he and Einstein found so much to discuss that for several weeks at midday and evening Laub fetched Einstein from the Patent Office. Einstein informed Mileva: "I've just come home from a long walk with Laub. I work with him a great deal […] Nowadays I always take my meals with him" (Einstein to Mariü, April 17, 1908, CPAE 5, Doc. 96). Between 1908 and 1909 Einstein and Laub collaborated in three joint works (Einstein and Laub 1908). As the well-trained mathematician, Laub naturally took over the complicated mathematical tasks. Einstein, as usual, refrained from mathematics at this early stage of his work. He explained to Mileva that Laub was doing the calculations, which he would not find time to do, and this was good (Einstein to Mariü, April 17, 1908, CPAE 5, Doc. 96; Seelig 1954, 86, 1956a, 72). On March 1, 1908 Laub wrote Einstein, "I must confess to you that I was surprised to read that you have to sit in an office for eight hours a day. But, history is full of bad jokes" (Laub to Einstein, March 1, 1908, CPAE 5, Doc. 91).

13.3 Einstein's Students: Besso and Chavan Einstein was now a step away from an academic position. In the 1908 summer term, he lectured on "Zur Molekulartheorie der Wärme" (the Kinetic Theory of Heat). He lectured at Bern in the 1908-1909 winter term from six to seven in the evening on the theory of radiation (the subject of his habilitation thesis). Einstein's first audience consisted of his two friends from the Patent Office, Michele Besso and Lucian Chavan, and another colleague from the Patent Office, Heinrich Schenk. Chavan reported on these lectures in his notebook (written in French), which was deposited in the Federal Postal and Telegraph Administration Library after his death in August 1942.

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Flückiger's book reproduces two pages of these notebooks, and a description: Meticulous, clean, and ordered pages of the notebooks, with figures and equations (Flückiger 1974, 122). The Tuesday and Saturday lectures were scheduled for seven in the morning, forcing Einstein, Besso and Chavan to get up early and climb the hill, and still be in time for work at the Patent Office at eight. In 1909, Besso and Chavan gave up and Einstein was left with only one student, Max Stern. For this reason, he cancelled his class and sent Stern a postcard advising that he would not deliver the lectures, but that he was always prepared to give him advice outside the university (Seelig 1954, 104, 1956a, 89).

14 Einstein Leaves the Patent Office for his First Post in Zurich 14.1 A University Professor at Zurich In the winter semester of 1908-1909 a position opened at the University of Zurich for a professor of physics. I mentioned earlier Kleiner urging Einstein to become privatdozent at Bern University, because he wanted to bring him to Zurich University (Kleiner to Einstein, January 28, CPAE 5, Doc. 78). Kleiner already had a candidate for the post – Friedrich Adler, Einstein's acquaintance from his student days at the Polytechnic of Zurich. Adler in the meantime had found an interesting job at the German Museum in Munich. Kleiner persuaded Adler to return to Zurich. While Adler was the natural choice, Kleiner wanted to consider another scientist. Adler suggested Einstein. On June 19, 1908, Adler described his competitor, Einstein, to his father (quoted in Galison 2008, 185-186): "Our development is seemingly parallel […] But no one supported him, and for a time he half starved. As a student he was treated contemptuously by the professors, the library was often closed to him, etc. He had no understanding of how to get on with important people. Finally he found a position in the Patent Office in Bern and throughout the period he has been continuing his theoretical work in spite of all distractions. Today he is […] one of the most distinguished and recognised".

In early 1909, while Einstein was a privatdozent at the University of Bern, Alfred Kleiner attended one of his lectures. However, his impression of

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Einstein’s lecturing skills was not favourable. For this reason, Einstein believed that negative rumours of his lecturing skills had reached his friend Laub via Matthias Cantor. Einstein thought he knew the route by which this rumour travelled: Kleiner – Burkhardt – Cantor – Laub – Einstein. Einstein told Laub that he wrote a letter to Kleiner, in which he reproached him for spreading unfavourable rumours about him and thus turning his position, which was already so difficult, into a final and definitive one. Einstein felt that such a rumour destroyed any hope of getting into the teaching profession. Kleiner repented and promised to get Einstein an extraordinary professorship in Zurich if he could satisfy himself that the latter had some teaching ability. Einstein suggested a lecture at the Physikalischen Gesellschaft Zürich (Zurich Physical Society). On February 11, 1909, Einstein gave a lecture to the Physical Society in the auditorium of the Physics Institute of the University of Zurich. This time Einstein was lucky. He lectured well on "Elektrodynamik und Relativitätsprinzip" (Electrodynamics and the Relativity Principle), and was able to correct the impression (Einstein to Laub, May 19, 1909, CPAE 5, Doc. 161). Einstein did not expect much, and said: "I certainly don't demand to be made a university professor at Zurich"; but on April 28, 1909, Einstein reported to his close friend Conrad Habicht, that he was fairly sure now of getting the post at Zurich University (Hoffman and Dukas 1973, 88; Seelig 1954, 107, 1956a, 90-91). The faculty was not eager to accept Einstein. They wrote, "Herr Dr Einstein is an Israelite and since precisely to the Israelites among scholars are ascribed (in numerous cases not entirely without cause) all kinds of unpleasant peculiarities of character, such as intrusiveness, impudence, and a shopkeeper's mentality in the perception of their academic position". By apparent contrast, the faculty was aware that, among the "Israelites there exist men who do not exhibit a trace of these disagreeable qualities". Consequently, "it is not proper, therefore to disqualify a man only because he happens to be a Jew". The committee and faculty did not consider it compatible with their dignity in democratic Zurich to adopt anti-Semitism as a matter of policy; so that the information which Kleiner provided about Einstein reassured them (Pais 1982, 186). On May 7, 1909, Einstein was appointed by the Governmental Council of the Canton of Zurich, for the period of six years, with a salary of 4500 francs. He assumed his position at the beginning of the winter semester on

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October 15, 1909. In his letter to Laub he wrote: "So now I am an official of the guild of whores [der Gilde der Huren], etc" (Einstein to Laub, May 19, 1909, CPAE 5, Doc. 161). Einstein called Kleiner-Burkhard-Cantor and their Colleagues, "guild of whores", because of the unfavourable rumours they spread about him while they knew of his difficulties obtaining the position in Zurich. Einstein felt uncomfortable to be an official of such a Gilde of people. On July 6, 1909, Einstein handed his resignation notice, effective October 15, 1909, to Haller at the Patent Office (Einstein to the Swiss Department of Justice, July 6, 1909, CPAE 5, Doc. 169). Haller recorded that the expert second-class had performed highly valued services. His departure is a loss to the office. However, Herr Einstein feels that teaching and scientific research are his real profession, and for that reason the director of the office made no attempt to bind him to the office by better financial arrangements (Flückiger 1974, 70). After Einstein had been appointed professor of theoretical physics at Zurich University, he was also appointed teacher of theoretical physics. His doctorate student, Hans Tanner later recalled Einstein’s informal teaching approach. In a surviving letter Einstein ended by telling Tanner, "If there is anything you feel especially upset about or if you have anything else to report, then write to A. Einstein". In another letter to Tanner a year later (April 26, 1912) Einstein wrote, "Do not be angry with me because of this frank criticism; it does not stem from a lack of good feeling toward you". In further correspondence, dated October 13, 1912, Einstein informed Tanner that in his opinion his study is certainly suitable as a doctoral dissertation. He ended the letter with the personal "ich Ihr A. Einstein" (Einstein to Tanner, April, 24, 26, October, 13, 1912, CPAE 5, Doc. 265, 388, 393). Tanner recollects that Einstein entered classes (during 1909-1911) "in his rather shabby clothes with trousers too short and an iron watch chain". The students were rather skeptical. According to Tanner, "the only script he carried was a strip of paper the size of a visiting card on which he had scribbled what he wanted to tell us. Thus, he had to develop everything himself and we obtained some insight into his working technique" (Seelig 1954, 119-120, 1956a, 100). As stated before, Einstein's secretary Helen Dukas mentioned that Einstein did his calculations on odd slips of paper (Hoffmann and Dukas 1973, 69). Likewise, Reiser reported that in the Patent Office, Einstein wrote his

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ground-breaking papers on small sheets of paper (probably the size of a visiting card), which vanished into his desk-drawer as soon as he heard footsteps approaching behind his door (Reiser 1930, 66). Einstein's lectures were based on improvisation. According to reports, he developed everything himself in class and in front of the audience. He "always liked to improvise", said his son, Hans Albert, much later; "for instance, when he had to give a talk he never knew ahead of time exactly what he was going to say. It would depend on the impression he got from the audience in which way he would express himself and into how much detail he would go" (Whitrow 1967, 19).23 In class at the University of Zurich, the students were allowed to interrupt Einstein's lecture if anything was unclear; but they were all afraid that they would ask something stupid so they refrained. This did not prevent Einstein from being at their disposal during the breaks. In his impulsive naturalness he would take one or more of the students by the arm and, in a most comradely manner, to discuss the subject of the class with them. After class, Einstein would encourage his students to join him at Café Terrasse on the bank of the Limmat River, where the discussions would continue from physics and mathematics to other subjects. Tanner recalls that they felt at home with Einstein during these discussions, which took place weekly from eight to ten in the evening (Seelig 1954, 119-121, 1956a, 100-102). Tanner recollects additional memories. He paid Einstein a visit and was sitting in his study in front of a heap of papers covered with mathematical formulae. Einstein was writing with his right hand and holding his young son in between his elder son Albert, who was playing with his bricks. With the words, "wait a minute, I've nearly finished!" Einstein gave Tanner the children to look after for a few moments and went on working. This "gave me a glimpse into his immense powers of concentration" (Seelig 1954, 123-124, 1956a, 104). As stated before, his sister Maja already noticed Einstein's remarkable power of concentration when he was aged sixteen: Even in a large, noisy group, he could withdraw to the sofa, pen and paper in hand, and lose himself so completely in a problem that the conversation of many voices stimulated rather than disturbed him (Winteler-Einstein 1924b, 1xiv, 1924c, xxii).

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14.2 Einstein Invents with the Habicht Brothers On April 4, 1908, while still at the Patent Office, Einstein wrote to Paul Habicht: "Today I came somewhat closer to the solution of an old problem". In 1902 in Bern, Einstein and Conrad Habicht discussed a device aimed at amplifying the tones emitted by a telephone by attaching an external source of energy to it. Einstein told Habicht, "Not too much value has come out of it", but "now" he had the following idea: A telephone membrane has a small pin in the middle that closes an opening in a chamber. Einstein went on to describe his idea (Einstein to Paul Habicht, April 4, 1908, CPAE 5, Doc. 95). Joseph Sauter, Einstein's colleague from the Patent Office, recalled fifty years after working with Einstein that the latter had the advantage of being an inventor (Sauter 1960, 156). Sauter was referring to Einstein's inclination to patents, like the Maschinchen (Little Machine), which he built with the Habicht brothers. It appears that Einstein was indeed fascinated by technical inventions. Between 1908 and 1910 Einstein and the Habicht brothers (Conrad and Paul) experimented on an induction machine (the little machine) for measuring small voltages by multiplication (a detector). "Einstein's 'little machine' for the Measurement of Small Quantities of Electricity" (CPAE 5, 51-55). Einstein's part in experimenting with the little machine probably had its roots in Einstein's childhood environment followed by his work in the Patent Office in Bern. The Habicht brothers and Einstein's attempts to perfect the induction machine lasted several years. Nothing worldshattering ever came from it, but as "team-work" it helped to tighten the bond of friendship (Seelig 1954, 73, 1956a, 60). Einstein's own detailed description of the means by which his induction machine could be used to measure the minutest electric voltages (exceeding about 10-6 volts) were detailed in his paper, "Eine neue elektrostatische Methode zur Messung kleiner Elektrizitätsmengen" (A New Electrostatic Method for the Measurement of Small Quantities of Electricity), which appeared in the 1908 issue of the Physikalische Zeitschrift (Einstein 1908). While still somewhat speculative, the little machine was apparently still promising at the time that Einstein was working at the Patent Office.

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Two years later, the Habicht brothers described the Einstein-Habicht Potential-Multiplikator, which they succeeding building after numerous attempts, and had even carried out experiments together with Einstein in the Zurich University laboratory. Finally, they applied for a patent to produce this new measurement apparatus in their own factory (Seelig 1954, 73, 1956a, 60-61).

14.3 Einstein's First Lecture at the Salzburg Meeting Einstein was going to meet Max Planck for the first time at a congress in Salzburg. In 1909, Einstein was invited to give his first lecture at the Salzburg meeting of the German Society of Scientists and Physicians, which took place between September 21 and 25, 1909. For Einstein, this was the first time he presented his thoughts in front of a large circle of scholars. He was going to meet the top physicists face-to-face, with whom he had only corresponded until then, including Max Planck, Arnold Sommerfeld and others. He was also given the opportunity to interact with colleagues through personal exchanges of ideas (Einstein 1909b; Benz and Hermann 1972, 130-131). Einstein came to the conference and was lionised as the founder of the relativity theory. Reports from the conference said that Einstein's lecture attracted more than hundred listeners, largely made up of leading German physicists (Einstein 1909b; Benz and Hermann 1972, 130-131). He could have shown his thanks by a comprehensive lecture on the subject. Planck had probably invited him with just that intention. Planck presided over the afternoon meeting on September 21 when Einstein lectured, and he was therefore responsible for the programme; so it seems very likely that the suggestion that Einstein should give one of the keynote addresses did come from Planck. Einstein spoke instead on "Über die neueren Umwandlungen, welche unsere Anschauungen über die Natur des Lichtes erfahren haben" (On Recent Transitions That Our Views Have Undergone Concerning the Nature of Light). Einstein published his talk, however, under the title "Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung" (On the Development of Our Views Concerning the Nature and Constitution of Radiation) (Einstein 1909b). Why did Einstein choose to speak about this subject and not about the principle of relativity? According to Max Born Einstein had proceeded beyond special relativity, "which he left to lesser prophets", while he himself already pondered about two subjects – the quantum structure of

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light and gravitation theory, the latter at that time, so tells us Born, was still not ripe for discussion (Born 1959, 193, 1969, 107). In his 1909 lecture, Einstein linked his work on relativity and the quantum hypothesis; he connected black body radiation, statistical mechanics, the principle of relativity and the quantum hypothesis of light problem. He represented a thesis which made a fusion of wave and emission theory, and introduced into optics the duality principle. Einstein's reputation, obtained primarily through his principle of relativity, led a few physicists to seriously consider the quantum problem. It appears that Einstein chose to speak about the above subject and not about the principle of relativity, because of the Swiss theoretical physicist Walter Ritz's emission theory. Ritz first published his emission theory in 1908 with the aim of replacing Einstein's special theory of relativity.24 In 1909 Ritz and Einstein exchanged views on the question of radiation in the Physikalische Zeitschrift. In April 1909, Ritz and Einstein issued a joint statement concerning their debate (CPAE 2, Doc. 57). Shortly afterwards – on July 7, 1909 – Ritz died before completing his emission theory, and two months later, on September 21, Einstein was invited to give his first lecture at the meeting of the German Society of Scientists and Physicians (Einstein 1909b, 482; Tolman 1912, 141). Einstein asserted right at the beginning (Einstein 1909b, 482; CPAE 2, Doc. 60): "It is even undeniable that there is an extensive group of facts concerning radiation that shows that light possesses certain fundamental properties that can be understood far more readily from the standpoint of Newton's emission theory of light than from the standpoint of the wave theory. It is, therefore, my opinion that the next stage in the development of theoretical physics will bring us a theory of light that can be understood as a kind of fusion of the wave and emission theories of light".

He closed his paper by saying: "It is not out of the question that in such a theory the entire energy of the electromagnetic field might be viewed as localized in these singularities [singularity points = light quanta], exactly like in the old theory of action at a distance" (Einstein 1909b, 499). Many years later Einstein provided a strong argument against singularities, within the context of Maxwell's electromagnetic theory, in his 1922 book The Meaning of Relativity: "It has been attempted to […] consider […] the charged particles as proper singularities. But in my opinion this means

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giving up a real understanding of the structure of matter. It seems to me much better to give in to our present inability rather than to be satisfied by a solution that is only apparent" (Einstein 1922b, 53).25

15 Minkowski's Space-Time Formalism of Special Relativity Hermann Minkowski, Einstein's former mathematics professor at the Polytechnic, had been a professor at Göttingen since 1902. Starting 1905 or earlier, he had been occupied with the problem of electrodynamics theory. In 1904, Max Born arrived, for the first time, in Göttingen. In his recollections, written years later, Born wrote that his stepmother gave him a letter of introduction to Minkowski, whom she had met years before at dancing lessons and balls in Königsberg. After delivering the letter, Born received an invitation to dinner (German style, at 1:30 p. m.) from Frau Minkowski for Sunday. He was received most cordially and enjoyed an excellent meal. After the dinner, Minkowski asked Born whether he would like to join a little excursion to a ruined castle in the neighbourhood. They walked through the fields and woods to the castle. By August 1904, Born was David Hilbert's private assistant – Hilbert offered Born this unpaid position at the end of his first year in Göttingen. Born recounted that Minkowski and Hilbert, who were intimate friends during their school days at Königsberg, were inseparable at university. The dominant figure in mathematics in Germany and Göttingen at that time was Felix Klein. He had an immense influence on all things concerned with mathematics. In 1895, he persuaded his faculty to nominate Hilbert to a second professorship, to which the Prussian Ministry agreed. From that time on Hilbert was the mathematical star of Göttingen. However, he missed his friend Minkowski and worked incessantly to get him to Göttingen. In 1902, he succeeded, and a third professorship was offered to Minkowski (Born 1978, 80, 82-83, 89). In the summer of 1905, Minkowski and Hilbert led an advanced mathematical physics seminar on electrodynamic theory. The seminar was led not by physicists, but by mathematicians. Seminar participants included the three Maxes (Max Laue, Max Born and Max Abraham), Arnold Sommerfeld and more. Participants at the seminar studied the papers of Hendrik Lorentz, Henri Poincaré and others on the difficulties

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which the theories of the electrodynamics had run into as a result of Michelson's celebrated experiment. Born says at that time the ether was considered well established; some opinions were that its properties were better known than those of matter. Ether was the word most used by the theoretical physicist from Göttingen, Prof. Woldemar Voigt in his lectures on optics. However, by the summer of 1905 all crucial experiments to detect the ether provided negative results (Born 1978, 98). Born also recounted in 1955 in his talk "Physik und Relativität" (Physics and Relativity) his vague impressions of the seminar on the electron theory (Born 1957, 186, 1969, 101). Born was quite sure that in this seminar they all discussed and studied the works by Heinrich Hertz, George Francis FitzGerald, Joseph Larmor, Lorentz, Poincaré, and others. They also got an insight into Minkowski's own ideas, which were first published two years later. This seminar was the starting-point for Minkowski's celebrated work on the electrodynamics of moving bodies. Minkowski gave a lecture about space and time, titled "Das Relativitätsprinzip" (The Relativity Principle), on November 5, 1907, to the Göttingen Mathematical society.26 One month before this talk, on October 9, 1907, Minkowski had written to Einstein asking for a reprint of his 1905 paper, in order to discuss it in his seminar with Hilbert on the electrodynamics of moving bodies (Minkowski to Einstein, October 9, 1907, CPAE 5, Doc. 62). On December 21, 1907, Minkowski talked to the Göttingen Scientific Society. On April 5, 1908, his talk was published in Göttinger Nachrichten as a technical paper, "Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern" (The Basic Equations for Electromagnetic Processes in Moving Bodies) (Minkowski 1908a). This was Minkowski’s only publication on the topic of electrodynamics and relativity to appear before his death on January 12, 1909. In this paper, Minkowski – for the first time – presented the Maxwell-Lorentz equations in their modern tensor form; the inadequacy of the Newtonian gravitational theory from the relativistic point of view is also discussed (Pais 1982, 151-152). Born tells the story about his first encounter with Einstein's relativity paper. One day Fritz Reiche asked him whether he knew a paper by a man named Einstein on the principle of relativity. Born said Planck considered

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it most important, but he had not heard of it. When Born learned that it had something to do with the fundamental principles of electrodynamics and optics, which years ago had fascinated him in Hilbert and Minkowski's seminar, he agreed at once to join Reiche in studying it. From that moment, relativity became their principal interest, and Rudolf Ladenburg was also infected with their enthusiasm. Born was going to meet Einstein for the first time at the congress in Salzburg. Born began to work on some relativistic problems; when he got stuck over some difficulties he wrote a letter to Minkowski asking his advice. Minkowski told Born that he was himself working on the same subject and would like to have a young collaborator who knew something of physics and of optics, in particular. He asked Born whether he would like to return to Göttingen. He suggested that Born attend the annual meeting of the German Society of Scientists and Physicians, which was to be held in Köln (Cologne) in September 1908. There he could answer Born's questions and substantiate his proposition (Born 1978, 130-131). On September 21, 1908, in the eightieth annual general meeting of the German Society of Scientists and Physicians in Cologne, Minkowski presented his famous talk, "Raum und Zeit" (Space and Time); a culmination of his 1907-1908 burst of creativity. The Cologne talk, Minkowski's last talk before he died, aroused great interest at the Cologne Congress and became the basis of the modern mathematical apparatus of the relativity theory.27 Minkowski opened his Cologne talk with the famous paragraph (Minkowski 1908b, 104): "M. H.! [Ladies and Gentleman!] The views of space and time, which I would like to develop, have sprung from the experimental-physical soil. Therein lays their strength. They tend to be radical. Henceforth space by itself and time by itself, fade away completely into shadow, and only a kind of union of the two will preserve independent permanency".

Minkowski presented new notions, "Weltpunkt x, y, z, t" (world-point), "Welt" (world) and "Weltlinie/Weltlinien" (world-line) (Minkowski 1908b, 104): "I will call a point in space at a given time, that is, a system of values x, y, z, t, a world-point. The multiplicity of all thinkable x, y, z, t systems of values will be called the world. […] We fix our attention on the substantial point which is at the world-point x, y, x, t, and imagine that we can recognise this substantial point at any other time. Let the changes […] of the space coordinates of this substantial point correspond to a time

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element […]. We then get an image, so to speak, of the eternal course of life of the substantial point, a curve in the world, a world-line, whose points can be clearly related to the parameter t from […minus infinity to plus infinity]. The whole world is seen to resolve itself into such worldlines, and I would like to say in advance, that in my opinion the laws of physics can find their most complete expression as interrelations between these world-lines".

In 1921 Born described Minkowski's world in the xt-plane (Born 1922, 218-219, 1962, 305): We are not dealing with ordinary Euclidean geometry in which all straight lines that originate from the zero-point are equivalent, and the unit of length on them is the same as the calibration curve, a circle. In Minkowski's xt-plane, straight lines that are inside the light cones are called time-like and lines that are outside the light cones are called spacelike. Hence, the space-like and time-like straight lines are not equivalent, there is a different unit of length on each, and the calibration curve consists of the upper and lower branch of the hyperbole, the light cone: ܿ ଶ ‫ ݐ‬ଶ െ ‫ ݔ‬ଶ ൌ േͳǤ An important property of Minkowski's world is the following: Consider the x-t axes. Suppose we have a world-line, straight and parallel to the t axis. This line corresponds to a point at rest. If the world-line is straight at an angle to the t axis, this corresponds to a point in uniform motion. If the point is in non-uniform motion, the world-line is curved. We can draw new axes t' – x' in such a way that a substance that is in uniform motion in x – t is at rest in x'– t'. Born went to Cologne, met Minkowski and heard his celebrated lecture "Space and Time", delivered on September 21, 1908. After having heard Minkowski speak about the above ideas, Born's mind was made up at once, he would go to Göttingen to be his assistant. Minkowski later told Born that it came to him as a great shock when Einstein published his paper in which the equivalence of the different local times of observers moving relative to each other was pronounced; for he had reached the same conclusions independently but did not publish them because he wished first to work out the mathematical structure in all its splendor. Minkowski told Born that he never made a priority claim and always gave Einstein his full share in the great discovery (Born 1978, 130-131).

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Einstein was supposed to meet Planck at the Cologne meeting, but Einstein did not attend the meeting due to work obligations at the Patent Office (Planck to Einstein, September 9, 1908, CPAE 5, Doc. 118). Born arrived for the second time in Göttingen, just a few weeks before Minkowski died. He came to Göttingen rather late, in December 1908, long after the semester had started. Upon arriving, he called on Minkowski and was received very kindly. Minkowski explained his ideas on electrodynamics and relativity to Born, who listened patiently to his suggestions. Born felt fortunate to meet a leading man in his branch of science and in being allowed to watch him work on a subject that fascinated him. Alas, it lasted only a few weeks. When he returned from a short Christmas holiday at home, he learned that Minkowski had been taken to hospital dangerously ill, and that an appendectomy had been performed. Born did not see him again. Minkowski died on January 12, 1909. Minkowski's numerous papers and unfinished manuscripts were given to Born and to Andreas Speiser, a young Swiss mathematician, for sifting through and possibly finishing (Minkowski 1911). They first of all separated the pure mathematics from mathematical physics; the latter was entrusted to Born. It was a formidable bundle, but most of it turned out to be either manuscripts of papers already published, or indecipherable sketches. Only one investigation which Born knew in outline from his last interview with Minkowski was advanced enough for him to complete for publication, which he succeeded in doing. The article appeared in May 1910, together with a reprint of Minkowski's celebrated paper "The Basic Equations for Electromagnetic Processes in Moving Bodies" (Minkowski 1908a), as the first in a series of monographs edited by Blumenthal (Minkowski 1910; Born 1978, 132-133).

B. FIZEAU'S AND MICHELSON AND MORLEY'S EXPERIMENTS

1 Fresnel's Dragging Coefficient and Fizeau's Experiment of 1851 1.1 Emission and Wave Theories of Light Isaac Newton was unwilling to accept that light was composed of ether vibrations, and apparently he advocated the corpuscular or emission theory of light. During Newton's time, the undulatory theory was incapable of explaining several phenomena that obtained satisfactory explanation within the confines of the corpuscular theory, one of which was polarisation. The polarisation of light was recognised by both Christian Huygens and Newton before the end of the Seventeenth century (Arago 1830b, 221). Huygens developed a wave theory based on the analogy between light waves and sound waves. He claimed that two light rays interfere in much the same way as do water waves. On the other hand, on the basis of the corpuscular theory, two particles collide with each other. Huygens had suggested a theory of refraction on the basis of the wave theory of light. Newton rejected Huygens's theory, and substituted one founded on measures of his own. However, the measurements showed that Huygens's theory was far more accurate than Newton's. Huygens's theory was recast many times since then, but in the eighteenth century several scholars rejected it. Indeed, various modifications had been made to both corpuscular and wave theory. For a long time afterwards, both undulatory and emission theories were actually capable of explaining all the phenomena then known. It seemed impossible to decide between them. However, "from this moment the progress of optics was arrested for more than a century" (Arago 1830b, 193; Michelson 1903, 46).

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Bernard Cohen, after interviewing Einstein in 1955, wrote that in 1905 Einstein knew that Newton had espoused a corpuscular theory of light, but he had evidently not known until many decades later about Newton's attempts to blend a corpuscular and wave theory. Newton had attempted to infer from what we call interference or diffraction phenomena the size of the corpuscles of matter. Einstein agreed that these intuitions were very profound, but not necessarily fruitful, because Newton could not derive precise information about the structure of matter (Cohen 1955, 218). Back to the 1800s, at a time when the theory of light showed little sign of settling down into any agreed form, refraction could lead one to choose one theory over another. Refraction takes place when light passes from a rarer to a denser medium, and consists of bending the incident ray toward the normal to the surface of the denser medium. Suppose we have a plate of glass, for example, and a ray of light falls upon the surface in any direction. According to the corpuscular theory, the substance below the surface exerts an attraction, a force in a direction perpendicular to the surface, upon the light corpuscles. We separate this force into two components – one in the surface and one normal to it. Due to the presence of the denser medium, the normal component of the velocity of the particle is increased, with no change of the component of the velocity in a direction parallel to the surface; the resultant velocity of light is also greater in the denser medium. According to wave theory, a wave front approaches the surface of a denser medium from the direction of the air. This direction is changed by refraction in the water, creating a new direction and a new wave front. During the time that the wave moves through a certain distance in the rarer medium, it moves through a smaller distance in the denser medium. Hence, light travels slower in a denser medium. Thus, the results, according to the two theories, are exactly reversed. It was pointed out that the corpuscular theory made it necessary to suppose that light travelled faster in a denser medium, such as water or glass, than it does in a rarer medium, such as air. According to the undulatory theory the case is reversed. Hence, if we could measure the speed of light, it would be possible to put the two theories to the test. In order to accomplish this we must compare the velocities of light in air and in some denser, transparent medium, such as water (Michelson 1903, 46-47).

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1.2 Arago and Fresnel In 1810, Dominique-François Arago still accepted emission theory, and he devised a simple method to test the following hypotheses (Arago 1810): If, according to the corpuscular theory, light travels faster in a denser medium, then the angle of refraction would be different for light particles moving at different speeds. Hence, different stars would emit light rays that would reach the Earth at different speeds. The aberration would thus be different when viewed through air or dense media. Arago glued an achromatic prism to the lens of a telescope, and examined the deviation of light rays after passing through the prism. He measured the angle of refraction and deduced the speed of light from it. The result of the experiment showed that the rays from all stars were refracted at the same time by the same angle. At the time, Arago found it quite difficult to accept this result. He explained that although stars radiate light over an infinite range of speeds, we can only observe light whose speeds lie within a limited range of values. After this experiment, Arago became a vocal critic of the Newtonian emission theory and, by 1816, an ardent supporter of the undulatory theory (Hahn 1970). Arago later explained, "It is easy to conceive in what way this result is a mathematical consequence of the system of waves". According to emission theory, if two stars are at very different distances from the Earth, their rays will arrive at our eyes with dissimilar velocities. "Is it not then a formidable objection against the theory of emission, that there should be this perfect equality of velocity in all cases, which all observations testify?" (Arago 1830b, 242-243). Hence, Arago admitted that the hypothesis, "incandescent bodies emit rays with all sorts of velocities, but that a special and determined velocity is necessary to make them rays of light […] deprives the system of emission of the simplicity which constitutes its main recommendation". He explained that "the rays proceeding from all stars, in whatever region they are situated, undergo precisely the same refraction. The disagreement between this [emission] theory and experience, could not be more manifest, and from that moment the system of emission seemed to be overturned from its very foundations" (Arago 1830b, 244-245).

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Arago performed another experiment. He covered half a telescope with an achromatic prism. He reasoned that if the velocity of light in glass varied from its velocity in a vacuum, then the aberration of a light ray from a star, as a result of the Earth's motion, would also be different in glass. Thus, the optical deviation caused by a glass prism would vary accordingly, as light traverses it in the direction of Earth's motion or in the opposite direction. He found that the aberration angle was independent of whether light passed through the prism or not (Fresnel 1818, 633). In 1838, Arago communicated to the French Academy the following suggestion for another experimental arrangement. A mirror was mounted so that it could be revolved about an axis parallel to its surface at a very high rate. A light-spark was allowed to fall on the mirror. The images of two sparks were observed in the revolving mirror, which spun in one direction. Suppose one beam of light was passed through water and the other through air. If the first suffers a displacement in the direction of the mirror's rotation, the undulatory theory is correct, owing to the longer time taken by the light to pass through water. If the first beam of light suffers a very small displacement in the direction of the mirror's rotation, the velocity of light is greater in water than in air, as it should be according to the corpuscular theory. In 1850, Léon Foucault performed Arago's experiment and found the displacement greater. Experimenters in fin de siècle during the nineteenth and early-twentieth centuries provided a strong interpretation of this result: "The corpuscular theory received its death-blow" (Michelson 1903, 50). Foucault announced his results to the French Academy in Arago's presence (Hahn 1970). Arago's suggestion and Foucault's experiment probably influenced Fizeau when he designed his 1851 water-tube experiment (see section 1.3 below). Michelson's daughter wrote that Fizeau's result was widely regarded as a coup de grâce for corpuscles and a triumph for waves (Michelson Livingston 1973, 99). She did not say from whom she had heard it, but in light of Michelson's above quotation she had probably heard it from her father. Between 1812 and 1845 Arago gave popular lectures in astronomy, which were published posthumously in a few volumes under the title, Astronomie populaire: oeuvre posthume (Popular Astronomy: Published posthumously) (Arago 1854, 1855). The French Academy was assembled on Monday July 26, 1830, with the outbreak of the Second French Revolution. At the Institute of France,

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Arago delivered a eulogy of Augustin-Jean Fresnel, into which he introduced some spiritual allusions to the glaring usurpation which had been attempted on the liberties of France ("The Three Days of July", September 1848, 563). The eulogy also included a few valuable scientific insights. Arago explained that he offered a humble description of Fresnel, but apologised if, "it should happen that the eulogy should be accused of some exaggeration" (Arago 1830a, 1830b, 185-186). Arago told the academy that Fresnel accomplished so much during his short life. Fresnel’s efforts almost exclusively relate to optics. Arago recounts that Fresnel’s first experimental investigations do not date earlier than 1815. On December 28, 1814, Fresnel wrote from Nyons, "I do not know what is meant by the polarisation of light; beg my uncle, M. A. Mérimée, to send me the best works from which I may obtain information on this subject". Arago says that, eight months had scarcely elapsed, when highly skillful researchers placed Fresnel among the most celebrated physicists of their era; and fairly soon after this, in 1819, Fresnel carried off the prize proposed by the French Academy on "the difficult question" of diffraction (Arago 1830b, 185). In 1827, when Fresnel was approaching his end, the Royal Society of London charged Arago with the office of presenting to him the Rumford Medal. "I thank you", Fresnel said to Arago, in a feeble voice, "for having undertaken this mission. I guess how much it must have cost you, for you have perceived that the most beautiful crown is worth little when it is only to be deposited on the tomb of a friend!" Fresnel died eight days after receiving the medal (Arago 1830b, 279). Interesting developments took place in the field of optics during the 1810s. Arago asked his friend Fresnel if the wave theory could provide an explanation to his first prism and second aberration experiments from 1810. In an 1818 letter to Arago, Fresnel attempted to explain both aberration and Arago’s prism experiment. Fresnel’s work on the wave theory was based on the hypothesis of stationary or immobile ether. On this basis, the explanation of Arago’s first prism experiment was obvious: The speed of propagation of a wave in a medium is independent of the velocity of the source of the wave. In the letter to Arago, Fresnel explained Arago's second experiment by saying that, terrestrial movement exercised no change on the appearances of the phenomenon. That is, one expected no effect of change to occur in the aberration angle when a telescope tube filled with water was used. Fresnel

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could not explain the null result of Arago’s second experiment without an additional hypothesis attributing some mobility to the ether within a moving medium. Fresnel explained that Earth's motion does not have any influence on the laws of refraction because the ether is partially carried along by the Earth, and light waves inside the optical medium are partially dragged along with the ether. He supposed that in the interior of a body light is propagated with less velocity than in a vacuum; this change in velocity occurs because the density of the ether within a body is greater than that in a vacuum. Fresnel derived a formula known as Fresnel's formula, which included a dragging coefficient, for the argument of this partial drag (Fresnel 1818, 634-636). Fresnel's formula in modern notation is: ܿᇱ ൌ

ܿ ͳ ൅ ‫ ݒ‬൬ͳ െ ଶ ൰ǡ ݊ ݊

where c' is the velocity of light in the medium and v the velocity of the medium with respect to the Earth; c is the velocity of light in vacuum and ଵ n is the refractive index. The extra factor ቀͳ െ మቁ is called Fresnel's ௡ dragging coefficient. Fresnel terminated his 1818 letter to Arago with an application of the same theory to an experiment proposed by Ruggero Giuseppe Boscovich. The experiment consisted of observing the phenomena of aberration through a telescope filled with water or with another fluid very much more refracting than air, to ascertain whether the changing of the liquid affected the movement of light and the direction in which one notices a star (Fresnel 1818, 633-634). Boscovich actually proposed the experiment in the eighteenth century as a test that would lend proof to the Copernican theory. He thought that if one filled the tube of the telescope with water and inclined it towards a star so that the light from the star would enter the tube of the telescope, it would supply a demonstration for the motion of the Earth around the sun. He did not think of the ether, and motion with respect to the ether. This experiment was performed in the nineteenth century by Sir George Biddell Airy, a British astronomer, after Fresnel's theory was proposed. He adapted Boscovich's test for the purpose of searching for a demonstration for the motion of the Earth with respect to the ether.

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1.3 Fizeau's Water Tube Experiment of 1851 Fresnel's predictions were confirmed in 1851 by the measurements of Fizeau on the velocity of light in moving water, an experiment usually referred to as the water tube experiment. On September 29, 1851, Fizeau presented the paper to the Academy of Sciences in Paris (Fizeau 1851): "Sur les Hypothèses relatives à l'éther lumineux, et sur une experience qui paraît démontrer que le mouvement des corps change la vitesse avec laquelle la lumière se propage dans leur intérieur" – (On the Effect of the Motion of a Body Upon the Velocity With Which it is Traversed by Light). This paper confirmed Fresnel's formula, not the mechanical explanation given by Fresnel to this hypothesis (i.e. partial ether drag). Fizeau began his notable paper acknowledging that many theories have been proposed in an attempt to account for the aberration of light phenomenon according to wave theory. After Fresnel's theory, Christian Doppler, George Gabriel Stokes, James Challis, and several others published important research on the subject. These hypotheses could be reduced to three states in which the ether was considered to exist in the interior of a transparent body (Fizeau 1851, 349, 1860, 245): 1) The ether is fixed to the molecules of the body, and consequently shares all the motions of the body. Between 1845 and 1846 Stokes proposed a theory in which he assumed that a medium completely carries along the ether within it (Stokes 1845, 1946). Therefore, light will propagate with respect to that medium in the same way as if the medium were at rest; its velocity of propagation in a transparent refracting medium at rest will also be the velocity of propagation of light with respect to the moving medium. This contradicts Fresnel's hypothesis, according to which light is only partially, but not fully, carried along by moving water. Nevertheless Stokes endeavoured to obtain Fresnel's dragging coefficient and failed to do so from his theory. Stokes suggested a curious explanation for aberration; he believed that he could reconcile Fresnel’s two kinds of ether – the stationary ether and the portion of the ether that is carried along by transparent bodies. According to Stokes, the ether in the Earth’s vicinity is carried along by all matter (partially by transparent bodies according to Fresnel’s theory and fully by non-transparent bodies), whereas the ether is at rest at a great distance

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from Earth (Stokes 1846, 147). This was most peculiar, since Fresnel's formula suggested that light waves were partially carried along by the moving refracting body, and this could by no means correspond to the hypothesis of the ether being completely carried along. Thus, Stokes' theory was soon plagued by severe problems. Two other hypotheses mentioned by Fizeau include (Fizeau 1851, 349, 1860, 245): 2) The ether is free and independent, and consequently is not carried with the body in its movements, and, 3) Only a portion of the ether is free, the rest being fixed to the molecules of the body and, alone, sharing its movements. The last hypothesis was proposed by Fresnel, but was far from being considered an established truth. Although Fresnel's mechanical explanation given to his hypothesis has been regarded by some as too extraordinary to be admitted without direct proofs, others simply considered the hypothesis to be at variance with experiment (Fizeau 1851, 350, 1860, 246). Fizeau proposed an experiment the result of which promised to throw light onto the question. His method of observation was "capable of rendering evident any change of velocity due to motion. It consists of obtaining interference bands by means of two rays of light after their passage through two parallel tubes, through which air or water can be made to flow with great velocity in opposite directions" (Fizeau 1851, 350, 1860, 246247). One of the two rays of light, say the upper one, travels with the current in both tubes; the other, starting at the same point, travels against the current in both tubes. Upon reversing the direction of the current of water the circumstances are exactly the reverse: the ray of light that previously travelled with the current now travels against it. With this arrangement, if there is any shifting of the fringes, it must be due to the reversal of the change in velocity due to the current of water (Michelson 1903, 154).28 Fizeau concluded from the observed displacement in the interference bands: "For water there is an evident displacement. The bands are displaced towards the right when the water recedes from the observer in the tube at his right, and approaches him in the tube on his left" (Fizeau 1851, 353, 1860, 249).

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After observing the displacement of interference bands, Fizeau estimated the observed magnitude of this displacement (Fizeau 1851, 353, 1860, 249-250). He varied the parameters of the experiment ("magnification of the bands", "the velocity of the water", and so on), to measure the magnitude of the displacement. Fizeau calculated the magnitude of the displacement of the interference bands for water velocity at 7.059 metres per second (the observations were made with this velocity), and arrived at the mean value of 0.23 millimetres for the displacement of the interference bands. Next, Fizeau compared the observed displacement of the interference bands, 0.23 millimetres, with that which would result from theoretical considerations: firstly, with that which results from the first hypothesis (which is equivalent to Stokes' hypothesis, a mobile ether), and then with that which results from the third hypothesis (Fresnel's hypothesis of partial ether drag). Fizeau does not consider the second hypothesis (of immobile ether). He reasons that, we can readily admit that the second hypothesis may be at once rejected, because the very existence of the displacements produced by the motion of water is incompatible with the supposition of ether perfectly free and independent of the motion of bodies. Fizeau starts with the first hypothesis of the mobile ether, which results in a value of 0.4597 millimetres for the displacement of the interference bands. He remarks that this is the difference of path which ought to exist between the two rays with reference to the vacuum. As mentioned above, he previously calculated an observed displacement of the interference bands of 0.23 millimetres. Consequently, there is no agreement between the theory and Fizeau's experiment. Fizeau thus concludes that the first hypothesis conflicts with his experiment, directing him to the third hypothesis – Fresnel's hypothesis for ordinary phenomena of refraction, which claims that in the interior of a body, light is propagated with less velocity than in a vacuum (Fizeau 1851, 353, 1860, 251-252). Fizeau then applies Fresnel's theory to his experimental set-up. He queries the velocity of the propagation of waves in a medium comprised of an immovable and movable part, when one supposes the body to be moving in the direction of the propagation of the waves, and calculates a numerical value of 0.2022 millimetres for the displacement of the interference bands. His observed value in his experiment was 0.23 millimetres, and concluded that these values were almost identical (Fizeau 1851 353-354, 1860, 252-

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254). Thus, Fizeau found an excellent correlation between Fresnel's dragging coefficient and his experiment. It is important to note that Fizeau discovered an observable displacement in the interference bands. This observable displacement agreed with the theoretical displacement predicted by Fresnel's formula. As to partial ether drag, Fizeau did not observe any moving ether, and he did not prove the partial ether drag hypothesis.

1.4 Lorentz Derives Fresnel's Dragging Coefficient in his Electron Theory In his 1892 paper, "La théorie électromagnétique de Maxwell et son application aux corps mouvants" (Maxwell's Electromagnetic Theory and its Application to Moving Bodies), Lorentz advanced a version of the theory of the electron, based on Maxwell's electromagnetic theory, in order to explain electromagnetic and optical phenomena in bodies at rest and in motion. Lorentz demarcated ponderable matter from the imponderable luminiferous stationary immobile ether. In Section §160 of his paper, "Die Mitführung der Lichtwellen durch die ponderable Materie" (Entrainment of Light Waves in Ponderable Matter), Lorentz derived Fresnel's dragging coefficient from his interpretation of Maxwell's equations. He interpreted Fresnel's formula in such a way that it was the waves that were partially dragged by the dielectric medium and not the ether. This was in fact Fizeau's original interpretation of Fresnel's result in his 1851 paper, as discussed above (Lorentz 1892, 162-164). As in 1892, Lorentz derived Fresnel's formula in Sections §68 and §69 of his 1895 book Versuch einer theorie der electrischen und optischen erscheinungen bewegten körpern (Attempt at a Theory of Electrical and Optical Phenomena in Moving Bodies). This derivation does not explicitly involve electromagnetic theory (Lorentz 1895, 87). The crux of the matter and of the whole derivation was that Lorentz implemented his theorem of corresponding states – local time – from Section §59, in the 1895 publication: ‫ݐ‬ᇱ ൌ ‫ ݐ‬െ

‫ݒݔ‬ ǡ ܿଶ

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where t' is the time coordinate for an observer moving in the ether and t is the time coordinate for an observer resting in the ether. The factor ‫ݒݔ‬ൗܿ ଶ implies that the time for a moving observer varies with location. Lorentz obtained an equation equivalent to Fresnel's formula and concluded that it agreed with the known Fresnel hypothesis (Lorentz 1895, 96-97).

2 The Michelson and Michelson-Morley Experiment 2.1 Maxwell's Letter to Todd Albert Abraham Michelson graduated from the U.S. Naval Academy in 1873. After graduation, his research in optics was exclusively concerned with measurements of the speed of light. He served as an instructor in physics in Annapolis between 1875 and 1879. In November 1877, he made his first determination of the speed of light with a demonstration for the students, in which he repeated, with essential improvements, Foucault’s rotating-mirror experiment (a modification of Fizeau's 1849 rotating wheel experiment). These simple trials provided such good results that Michelson decided to repeat and extend them with improved apparatus (Shankland 1964, 17; Michelson Livingston 1973, 46, 51-53).29 This led to his transfer in 1879 to the Nautical Almanac Office in Washington D.C., where the astronomer, Prof. Simon Newcomb was a director. Newcomb investigated physical phenomena for the aid of navigation, and was also interested in measuring the speed of light. There Michelson made measurements of the speed of light between stations at Fort Myer, Virginia, the Old Naval Observatory, and the Washington Monument (Millikan 1949, 343; Shankland 1964, 17; Michelson Livingston 1973, 54). On March 19, 1879, shortly before his untimely death at age of forty-eight, James Clerk Maxwell wrote to David Peck Todd, Director of the Nautical Almanac Office, with a question about the possibility of a measurement of the ether drift. While Michelson was at the Nautical Almanac Office, he studied Maxwell's letter. Maxwell proposed a test utilising the velocity of the Earth in its orbit. Since this velocity is so much greater than anything we can produce at the Earth's surface, it was supposed that such measurements could be made with considerable ease; these measurements were actually tried by different experimenters in quite a considerable

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number of ways (Michelson 1903, 156; Michelson Livingston 1973, 73). However (Michelson 1903, 156-157): "We cannot utilise the velocity of the Earth in its orbit for such experiments, for the reason that we have to determine our directions by points outside of the Earth, and the only thing we have is the stars, and the stars are displaced by this very element which we want to measure; so the results would be entirely negative. It was pointed out by Lorentz that it is impossible by any measurements made on the surface of the Earth to detect any effect of the Earth's motion. Maxwell considered it possible, theoretically at least, to deal with the square of the ratio of the two velocities; that is, the square of 1/10,000 or 1/100,000,000. He further indicated that if we made two measurements of the velocity of light, one in the direction in which the Earth is travelling in its orbit, and one in a direction at right angles to this, then the time it takes light to pass over the same length of path is greater in the first case than in the second […] The difference in the times is, however, so exceedingly small, being of the order of 1 in 100,000,000, that Maxwell considered it practically hopeless to attempt to detect it".

Michelson regarded Maxwell's statement as a challenge, which led him to his studies of optical interference methods and to his determination to pursue this problem as the principal objective of his study and research in Europe, while on a leave of absence from regular navy duty, which had been arranged for him by Newcomb (Shankland 1964, 17; Michelson Livingston 1973, 74-75).

2.2 Michelson in Helmholtz's Lab In September 1880 Michelson sailed with his family to Europe. He brought with him from Washington the preliminary plan for the interferometer.30 After a short stay in London and Paris, Newcomb arranged meetings with some leading physicists; Michelson went straight to the distinguished laboratory of Hermann von Helmholtz in the Physikalisches Institut at the University of Berlin. He began his research there in the winter semester and perfected his interferometer in Helmholtz's laboratory. Shankland raised the possibility that Michelson might have been influenced by the interference devices developed by Jean Jamin in Paris (Shankland 1964, 18). On November 22, 1880, Michelson wrote to Newcomb from Berlin that Helmholtz recommended he would better wait until his return to the U.S. before performing the experiments. In addition, the necessary funds did

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not seem to eventuate, and Michelson could not perform the experiments. However, he stayed in Berlin. With the necessary funds – £100 – furnished by Alexander Graham Bell at the suggestion of Newcomb – Michelson spent two years until 1880 setting up the first Michelson interferometer. Before patenting his telephone, Bell had also been pressed to find financial backing. He took an immediate interest in Michelson's interferometer and arranged to make him eligible for a grant from the Volta Foundation, which Bell had recently established for such a purpose. The next year, Michelson used it to undertake the earliest attempt at an ether drift determination. Michelson selected the firm of Schmidt and Haensch in Berlin to build the instrument. Additional optical equipment was ordered from Maison Breguet from Paris, who was a well-known supplier of plates for Jamin's interferometers. When the interferometer was ready, Michelson set it up in Helmholtz's laboratory. Michelson referred to his new instrument as an Interferential Refractometer (Shankland 1964, 19-20; Michelson 1903, 51; Michelson Livingston 1973, 75-77). The apparatus was erected on a stone pier in Helmholtz's laboratory to minimise disturbances. However, vibrations from street traffic made observation of the interference fringes wholly impossible, except during brief intervals after midnight. Prof. Helmholtz was acquainted with Hermann Carl Vogel, the director of the Astrophysikalische Observatorium (Astrophysical observatory) of Potsdam, almost fifty kilometres away from Berlin. Through this friendship Helmholtz arranged for the experiment to be performed in the observatory of Potsdam. There, it was conducted in the cellar, whose circular walls formed the foundation for the stone pier of the instrument. Here, observations were possible, and Michelson finally completed these in April 1881. In Potsdam Michelson made his first experiment on ether drift, only two years after he had risen to fame (Millikan 1949, 343; Shankland 1964, 21; Michelson Livingston 1973, 78). Michelson knew that according to Fresnel, "The opacity of the Earth is not then a sufficient reason to negate the existence of an ether current between its molecules, and one can suppose it is porous enough for it not to communicate to that fluid but a very small part of its movement" (Fresnel 1818, 629). Under this supposition, one should expect that in the sense of motion, the velocity of light should be subtracted from that of the Earth, and when moving in the opposite direction, it should be added to that velocity. A calculation based on Fresnel’s supposition shows that the time taken for light to pass from one point to another on the Earth's surface is

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dependent on the direction in which it travels (with or against the Earth's motion). Michelson calculated the time required for light to travel to and fro when the interferometer's arm L1 was oriented parallel to the direction of the motion of the Earth's velocity in space, and the time that it took light to make the same journey to and fro along the other arm L2, which was perpendicular to the direction of the Earth's motion. He thought that the time that it would require light to travel along the arm at right angles to the Earth's motion would not be affected by the Earth's motion. This turned out to be untrue, but at this stage he was not aware of this error. Michelson's end result for equal interferometer arms was a quantity of second order in v/c (as predicted by Maxwell). Michelson's observations gave the positions of the fringes, and not the times. Hence, the quantity of importance for the experiment was the change in optical path in the two arms of the interferometer. His end result for equal interferometer arms was: ‫ ݒ‬ଶ ܿο‫ ݐ‬ൌ ʹ‫ ܮ‬ቀ ቁ Ǥ ܿ In Michelson's apparatus L = 120cm, and in terms of some average wavelength of white light this distance equals 2 x 106 wavelengths. The orbital speed v of the Earth around the sun is approximately 30 km/sec. Hence, (v/c)2 = 10–8 and cǻt = 4 x 106 x 10–8. Hence, the expected fringe shift was approximately 0.04 wavelengths (Shankland 1964, 20-21). As already stated, Michelson neglected the effect of the Earth's motion on light travelling in the interferometer arm set at right angles to the motion. When this effect is included, the expected fringe displacement is reduced by half, and the result is 0.08 wavelengths. In addition, strains and vibrations also played an important role as interfering factors in the experiment (Shankland 1964, 23, 30). Michelson concluded his exposition of the experimental results (Michelson 1881): "The interpretation of these results is that there is no displacement of the interference bands. The result of the hypothesis of a stationary ether is thus shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous.

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This conclusion directly contradicts the explanation of the phenomenon of aberration which has been hitherto generally accepted, and which presupposes that the Earth moves through the ether, the latter remaining at rest".

On April 17, 1881, Michelson informed Bell of the successful termination of the experiments concerning the relative motion of the Earth with respect to the ether, and told him: "The result was however negative". Later, in 1903, Michelson stressed that, "The experiment is to me historically interesting, because it was for the solution of this problem that the interferometer was devised. I think it will be admitted that the problem, by leading to the invention of the interferometer, more than compensated for the fact that this particular experiment gave a negative result" (Michelson 1903, 159; Michelson to Alexander Graham Bell, April 1881, in Michelson Livingston 1973, 83-84).

2.3 Michelson in Paris In March 1881, Michelson was appointed as a physics instructor at the Case School of Applied Science. In the autumn of 1881, he moved to Paris to continue his studies and research at the Collège de France and the Ơcole Polytechnique. He remained in Paris until his return to America in June 1882. In Paris he met the leading French optical physicists, Marie-Alfred Cornu, Éleuthère Mascart, Jean Jamin, Alfred Potier and other leading French physicists. Michelson took his interferometer to Paris and demonstrated it to the physicists there. At first, Cornu was not convinced that the fringes were produced as Michelson claimed. He asked for a demonstration, and Michelson set up the interferometer so that it would perform, though only imperfectly. Using white light, he worked for three days without success. Cornu came to the laboratory and saw the effort it was taking, and Michelson begged for a little more time. Suddenly the fringes appeared. Handing a glass to Cornu, Michelson asked the professor to see for himself. When the glass was inserted in the path of one of the divided rays, the fringes vanished. Hence, when Michelson showed Cornu that the fringes disappeared when a piece of glass was placed in one of the arms, the latter was at once satisfied (Shankland 1964, 21-23; Michelson Livingston 1973, 87-88). As to Potier and Mascart: Alfred Lienard wrote that Potier had sought to spread some theories that were little known in France. He knew about a theorem of Wilhelm Veltmann and he indicated how it explained the impossibility found by the first order experiments of Mascart to render

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evident the motion of the Earth relative to the ether, while the sources and observation apparatuses were on the Earth (Lienard, 1909). Therefore, Potier, Veltmann, and Mascart were all convinced of the impossibility of rendering the Earth’s motion evident with respect to the ether to the first order in v/c.31 Potier was the one who identified the error in Michelson's calculations. At a meeting on February 20, 1882, at the Paris Académie des Sciences (Academy of Sciences) Michelson presented a paper in which he corrected this 1881 error. The paper was sponsored by Cornu, and Jamin was the chair of the meeting. Michelson credited Potier with calling his attention to this error, although Potier had in fact concluded that the effect would reduce the expected fringe shift to zero and not raise it (from 0.04 to 0.08 wavelengths) (Michelson Livingston 1973, 88, 124). Neither Michelson nor the scientific world ever considered the Potsdam experiments conclusive (Michelson to Lord Rayleigh, March 6, 1887, in Michelson Livingston 1973, 124). These trails therefore did not yet lead to a revision of Lorentz's theory. Michelson returned to the U.S. to the Case School of Applied Science in Cleveland, received a big grant, and from 1882 to 1884 he worked constantly to improve his methods. In July of 1883, he went to visit Bell in Washington. The disappointment of the negative result in Potsdam made him all the more anxious to explain the experiment fully to Bell and to stress the many other important uses he foresaw for his interferometer (Shankland 1964, 22-24; Michelson Livingston 1973, 96). At John Strutt's (Lord Rayleigh) invitation, Michelson met him in Washington in October 1884 and accompanied him to hear Lord Kelvin’s (then Sir William Thomson) lectures delivered at Johns Hopkins University in nearby Baltimore (Michelson Livingston 1973, 103-104).

2.4 Michelson Returns to Cleveland and Works with Morley At about the same time an older professor, Prof. Edward Williams Morley of the Adelbert College of Western Reserve University in Cleveland, was drawn into the problem. He was a well-known leader in experimental work. At the Baltimore Lectures of Lord Kelvin in 1884, both he and Lord Rayleigh urged Michelson and Morley to repeat the Fizeau experiment as an essential preliminary to their more famous ether-drift MichelsonMorley experiment (Michelson Livingston 1973, 103-104; Shankland 1973, 896).

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In December 1885, Michelson received permission from Newcomb to use funds for the repetition of Fizeau's experiment. Between December 1885 and March 1886 Michelson and Morley first performed a repetition of Fizeau's 1851 water tube experiment with Michelson's 1881 interferometer. It was hoped that Fizeau's results would be proved correct, that the velocity of light would be affected by the motion of the medium through which it moved. If, however, the new test proved Fizeau wrong, this would presage another negative result, and Michelson and Morley might have to give up the ether-drift idea (Michelson and Morley 1886; Shankland 1964, 25; Michelson Livingston 1973, 110-111, 116). Michelson explained that he and Morley started with Fizeau's experiment because they thought the latter was not as conclusive as would be desired, for his observed dragging coefficient differed considerably from Fresnel's theoretical value for water. The experiment produced a displacement of less than what should have been produced by the motion of the liquid. To this extent, the experiment was imperfect. Michelson said that he wanted to repeat the experiment to determine, not only the fact that the displacement was less than could be accounted for by the motion of the water, but also, if possible, how much less. For this purpose the interferometer was modified. Morley had improved Michelson's interferometer by installing in the attic a large tank from which distilled water was to flow through two brass tubes in opposite directions. Michelson explained that this arrangement made it possible to make accurate measurements of the displacement of the fringes. In the months that followed, Michelson and Morley made sixty-five recorded trials (Michelson 1903, 155-156; Michelson Livingston 1973, 116). On March 27, 1886, Michelson and Morley reported their findings to Lord Kelvin: "The result fully confirms the work of Fizeau. The factor by which the velocity of the medium must be multiplied to give the acceleration of the light was found to be 0.434 in the case of water, with a possible error of 0.02 or 0.03. This agrees almost exactly with Fresnel's formula" (Michelson to Lord Kelvin, March 27, 1886, in Michelson Livingston 1973, 117). Between August and September 1886, Michelson and Morley built an improved instrument. The new interferometer was set up in the southeast corner basement laboratory of the Case Main Building, a room with heavy stone walls and a constant temperature. There they carried on the preliminary work of their experiment, but were prevented from making

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final observations for, on October 27, 1886, the Case Main Building suffered a disastrous fire. A large part of Michelson's equipment, which he had purchased in Europe in 1881-1882, was destroyed in this fire, but the apparatus for the Michelson-Morley experiment was rescued by students living in the dormitories of nearby Adelbert Hall. The Michelson-Morley equipment was moved to the southeast corner of the basement of the Adelbert Hall. Michelson began reconstructing his instruments in Morley's laboratory. He worked patiently throughout the winter. The gloom was lightened by the arrival of a letter from Lord Rayleigh, suggesting that the time had come to repeat the 1881 Potsdam ether-drift experiment. Michelson knew that if Rayleigh took a positive stand on the importance of the experiment, money would be forthcoming (Shankland, 1964, 31; Michelson Livingston 1973, 121-123). Lorentz reacted immediately to Michelson's 1881 and 1886 results. He attempted to combine the 1881 Potsdam results with a combination of the theories by Fresnel and Stokes, and Michelson and Morley's new determination of the Fresnel dragging coefficient. Lorentz also recomputed the expected fringe shift for the Potsdam experiment, showing it to be only half that originally calculated by Michelson. Lord Rayleigh wrote to Michelson calling his attention to Lorentz's 1887 paper, "De l'influence du mouvement de la terre sur les phénomènes lumineux" (The Influence of the Motion of the Earth on the Optical Phenomena), and urged him to repeat his 1881 experiment on the relative motion of the Earth and the ether. Michelson replied to him that Potier first pointed out this error, and that he was never satisfied with the Potsdam experiments (Michelson 1881, 129; Shankland, 1964, 31; Michelson to Lord Rayleigh, March 6, 1887, in Michelson Livingston 1973, 123). Michelson wrote in 1881 that the "result of the hypothesis of a stationary ether is thus shown to be incorrect". He thus demanded a repetition of his experiment with an improved interferometer that would provide measurements of considerable precision of the fringe shift. The point that concerned Michelson was that, "it would have been satisfactory, if it had been possible, to have put the two theories [Stokes and Fresnel's] to the test of some decisive experiment" (Michelson 1881, 128-129). Many weeks were required to set up the Michelson-Morley equipment for trial observations on the interferometer, and mechanical refinements were made that permitted the stone on which the interferometer stood to rotate freely without introducing strains or vibrations. Michelson adopted Rayleigh's suggestions concerning the use of tubes for the arms of the

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interferometer and Rayleigh's further improvements: the whole arrangement floated in mercury and the number of reflections was doubled. Michelson and Morley placed the mirrors so that the light was reflected over a path about ten times longer than that of the earlier experiment (Michelson Livingston 1973, 125, 130). Later, Michelson described his setup (Michelson 1903, 158). The problem which Maxwell stated in his letter to Todd: "[…] was practically solved by reflecting part of the light back and forth a number of times and then returning it to its starting-point. The other path was at right angles to the first, and over it the light made a similar series of excursions, and was also reflected back to the starting-point. This startingpoint was a separating plane in an interferometer, and the two paths at right angles were the two arms of an interferometer. […] the apparatus was mounted on a stone support, about four feet square and one foot thick, and this stone was mounted on a circular disc of wood which floated in a tank of mercury. The resistance to motion was thus exceedingly small, so that by a very slight pressure on the circumference the whole could be kept in slow and continuous rotation. It would take, perhaps, five minutes to make one single turn. With this slight motion there was practically no oscillation. The observer needed to follow [the apparatus] around [the cellar], and at intervals, observe whether there was any displacement of the fringes".

In April 1887, Michelson had begun a new experiment. Finally, in July 1887, Michelson and Morley were able to make their definitive observations. According to the results, instead of the shift 0.08 wavelengths of the distance between the fringes, "It seems fair to conclude from the figure that if there is any displacement due to the relative motion of the Earth and the luminiferous ether, this cannot be much greater than 0.01 [wavelengths] of the distance between the fringes" (Michelson and Morley 1887, 340; Michelson Livingston 1973, 126, 130). Michelson and Morley seem to have shown little sign of settling down into any agreed theory or hypothesis. Michelson and Morley rejected both Stokes' theory and Fresnel's stationary ether (Michelson and Morley 1887, 341): "It appears, from all that precedes, reasonably certain that if there be any relative motion between the Earth and the luminiferous ether it must be small; quite small enough entirely to refute Fresnel's explanation of aberration. Stokes has given a theory of aberration which assumes the ether at the Earth's surface to be at rest with regard to the latter, and only

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B. Fizeau's and Michelson and Morley's Experiments requires in addition that the relative velocity have a potential; but Lorentz shows that these conditions are incompatible. Lorentz then proposes a modification [in his 1887 paper] which combines some ideas of Stokes and Fresnel, and assumes the existence of a potential, together with Fresnel's coefficient. If now it were legitimate to conclude from the present work that the ether is at rest with regard to the Earth's surface, according to Lorentz there could not be a velocity potential, and his own theory also fails".

Michelson could neither pick out the right hypothesis nor could he reject the ether. As late as 1903 he wrote, "From all that precedes it appears practically certain that there must be a medium whose proper function it is to transmit light waves" (Michelson 1903, 159). Robert Millikan summarised by saying: "It was not until 1887 that this experiment, repeated at Case School of Applied Science with great care and refinement by Michelson and Morley, began to take its place as the most famous and in many ways the most fundamentally significant experiment since the discovery of electromagnetic induction by Faraday in 1831" (Millikan 1949, 343).

3 Magnet and Conductor and Giving Up the Ether in Fin De Siècle Physics Einstein started his paper with the problematic asymmetries that were inherent in the electrodynamical explanation of the phenomenon of induction by Michael Faraday (the magnet and conductor experiment). According to Faraday, when a magnet and a closed electric circuit are in relative motion, an electric current is induced in the electric circuit. This current is actually a result of the relative motion between the magnet and the conductor. If the conductor is at rest in the ether and the magnet is moved with a given velocity, a certain electric current is induced in the conductor. If the magnet is at rest, and the conductor moves with the same relative velocity, a current of the same magnitude and direction is in the conductor. However, the ether theory gives a different explanation for the origin of this current in the two cases. In the first case an electric field is supposed to be created in the ether by the motion of the magnet relative to it (Faraday’s induction law). In the second case, no such electric field is supposed to be present since the magnet is at rest in the ether, but the current results from the motion of the conductor through the static magnetic field [Lorentz’s force law, F =q(v x B) in modern terms].

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Einstein claimed that this asymmetry of the explanation is foreign to the phenomenon. Subsequently, Einstein said that examples of the sort of the magnet and conductor experiment, together with the unsuccessful attempts to detect the Earth's motion relative to the ether "lead to the conjecture that the phenomena of electrodynamics as well as those of mechanics possess no properties corresponding to the idea of absolute rest". Hence, "The introduction of a 'light ether' will prove to be superfluous" (Einstein 1905a, 891). Maxwell explained, using an asymmetric approach, the magnet and conductor experiment using two types of electromotive forces – one for the case when the magnet is moved in the presence of a conductor, and the other for the case when the conductor is moved in a field of a magnetic force (Maxwell 1861, 838): "(7) When an electric current or a magnet is moved in the presence of a conductor, the velocity of rotation of the vortices in any part of the field is altered by that motion. The force by which the proper amount of rotation is transmitted to each vortex, constitutes in this case also an electromotive force, and, if permitted, will produce currents. (8) When a conductor is moved in a field of magnetic force, the vortices in it and its neigbourhood are moved out of their places, and are changed in form. The force arising from these charges constitutes the electromotive force on a moving conductor, and is found by calculation to correspond with that determined by experiment".

On April 15, 1846, Faraday gave a lecture at the Royal Institution in which he abandoned the ether. The talk was delivered under the title "Experimental Researches in Electricity". Faraday began by saying (Faraday 1846, 396): "I incline to believe that when there are intervening particles of matter (being themselves only centers of force), they take part in carrying on the force through the line, but when there are none, the line proceeds through space […] we can at all events affect these lines of force in a manner which may be conceived as partaking of the nature of a shake or lateral vibration […] It may be asked, what lines of force are there in nature which are fitted to convey such an action and supply for the vibrating theory the place of the aether?"

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The lines of force could be electrical, magnetic or gravitational. All Faraday could say was (Faraday 1846, 396): "I do not perceive in any part of space, whether (to use the common phrase) vacant of filled with matter, anything but forces and the lines in which they are exerted […] The view which I am so bold to put forth considers, therefore, radiation as a high species of vibration in the lines of force which are known to connect particles and also masses of matter together. It endeavours to dismiss the aether, but not the vibrations".

Faraday says that the vibrations that occur on the surface of disturbed water, or the waves of sound in gases or liquids, are direct or to and fro from the centre of action, whereas the (radiant) vibrations are "lateral" (transverse vibrations). Faraday then explains the problem that is inherent in an ether model: "the resultant of two or more lines of force is an apt condition for that action which may be considered as equivalent to a lateral vibration; whereas a uniform medium, like the ether does not appear apt, or more apt than air or water" (Faraday 1846, 396). Thirty years earlier, Thomas Young, Arago and Fresnel arrived at the idea of transverse vibrations. When Fresnel said that the only possible vibrations are transverse, Arago did not have the courage to publish such a conception. It appears that the reason was that Arago (like Faraday after him) knew that it entailed giving up the ether. Arago wrote in 1830 that an important question formed the object of a difficult investigation, which Fresnel undertook in conjunction "with one of his friends (Arago)" (Arago 1830b, 211-212). On January 16, 1800, Young said: "That a medium resembling, in many properties, that which has been denominated ether, does really exist, is undeniably proved by the phenomena of electricity" (Young 1800, 126). In 1817, Young began to entertain the idea that the molecules of the ether might oscillate in parallel directions transverse to the direction of the ray of light, though he thought that longitudinal vibrations might also exist. Fresnel independently reached the idea of transverse vibrations, but both Young and Fresnel could not account for it dynamically. In his History of Inductive Sciences, Vol. 2, William Whewell quotes the remarks of Fresnel: "Mr Young, more bold in his conjectures and less confiding in the views of geometers, published it before me, though perhaps he thought of it after me" (Whewell 1837, 417-418). Whewell wrote in a remark that "I take the liberty of stating this from personal

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knowledge". Hence, from personal information of the progress of the theory of transverse waves (Whewell 1837, 418): "Mr Arago was afterwards wont to relate that when he and Fresnel had obtained their joint experimental results, of the non-interference of oppositely-polarised pencils, and when Fresnel pointed out that transverse vibrations were the only possible translation of this fact into the undulatory theory, he himself protested that he had not the courage to publish such a conception; accordingly, the second part of the memoir was published in Fresnel's name alone. What renders this more remarkable is that it occurred when Arago had in his possession Young's very letter, in which he proposed the same suggestion".

In Fresnel's memoir on the colours of crystalline plates he says: "A remark in a letter of Dr Young, dated on the 29th April, 1818, which M. Arago communicated to me, helped to raise in my mind a doubt of the existence of longitudinal vibrations" (Peacock 1855, 392). Faraday’s electric and magnetic lines of force inspired Maxwell in developing electric and magnetic field theory, but Maxwell did not follow Faraday in rejecting the ether. Maxwell originally based himself on a mechanical ether-theoretical model of the electromagnetic field (vortices in the electromagnetic field), and on the basis of this view, in 1861 he explained the magnet and conductor experiment. By the time of his 1873 Treatise on Electricity and Magnetism, this model had receded into the background, giving way to a description of electricity, magnetism and matter in terms of certain fields in space, presumably having the ether as their support, but not associated with any explicit mechanical model. Einstein explained the magnet and conductor experiment in terms of the problematic asymmetries that were inherent in the electrodynamic explanation of the phenomenon of induction by Faraday. It is interesting to ask whether before 1905 Einstein knew about Faraday's 1846 rejection of the ether. No evidence of Einstein reading Faraday's paper can be found. Moreover, it seems unreasonable that Einstein would read this paper, because Einstein learned English many years after 1905.

C. EINSTEIN'S PATHWAY TO THE SPECIAL THEORY OF RELATIVITY

1 Introduction Helen Dukas said that wherever Einstein went, his ideas went with him (Hoffmann and Dukas 1973, 11-12). Einstein went to the Patent Office and his ideas went with him. Between 1900 and 1905 Einstein probably discarded many pieces of papers and calculations and flung them in the waste paper basket in the Patent Office. He may have made calculations on old pieces of paper that were once patent drafts. "Ideas went with him" also when he walked back home with his close friend Michele Besso, the latter functioned as Einstein's sounding board (Seelig 1954, 85, 1956a, 71). The end result was that Einstein published nothing in optics and electrodynamics of moving bodies prior to 1905. Scholars know that for many years before 1905 he had been concerned with the topic; in fact, he was busily working on the problem for seven or eight years prior to 1905. Unfortunately, there are no surviving notebooks and manuscripts, no notes and papers or other primary sources from this critical period where we can learn about the crucial steps that led Einstein to his great discovery. Historians of science have been working on this problem and endeavoured to present the intricate complicated network that might have led Einstein to the special theory of relativity.32 The most difficult work, with which historians are confronted, is to piece together a coherent jigsaw puzzle from all the scattering and fragmentary pieces of evidence. The great difficulty lies in contradictory evidence. From time to time Einstein answered a few important questions, but his answers are themselves sometimes puzzling or even contradictory. For instance, he could say in 1916 that the Michelson-Morley experiment was not a major factor in his development prior to writing his ground-breaking papers of 1905 (Einstein 1905a, 1905b, 1905c). Then some years later, in other circumstances, he would give replies almost just the opposite to this

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answer. It appears that it is not necessarily because he changed his mind; it is rather the circumstances in which he found himself that dictated an answer; his memory was also a factor. I will try to piece together a coherent jigsaw puzzle of Einstein's pathway to the special theory of relativity. All documentary biographies "skip" the patent years in Einstein's scientific life. They start with Einstein's childhood, they proceed to the story of Einstein at the Patent Office (and examining patents), Einstein and the Olympia Academy, and then continue to Einstein's later life. However, they do not cover Einstein's scientific work while at the Patent Office, because they have no information about it. Einstein wrote to his best friend Michele Besso on March 6, 1952, from Princeton about Seelig's 1952 biography (Seelig 1952a, 1952b); he already knew Seelig was dealing with his childhood. This was justified to some extent, since the rest of his existence was known in detail, which was not the case concerning the years he spent in Switzerland. "This gives a misleading impression, as if, so to speak, my life had begun in Berlin!" (Einstein to Besso, March 6 1952, in Einstein and Besso 1971, letter 182). Einstein very likely did not want people to know "in detail" about his "existence" in the Patent Office.33 As we already know (see Chapter A, section 9.1), many of Einstein’s best ideas were developed in "this worldly cloister", there he "hatched his most beautiful thoughts" (Einstein to Besso, December 12, 1919, in Einstein and Besso 1971, Letter 51). It appeared Einstein wanted to keep his worldly cloister a private, personal cloister.

2 Einstein Believes in the Ether I shall begin discussing Einstein's pathway to special relativity starting from 1895. In the spring of 1895 Einstein took his entrance examinations for the Polytechnic. He failed the humanistic-linguistic part and went to Aarau to finish his secondary education. In this same year Lorentz published his seminal work, Attempt at a Theory of Electrical and Optical Phenomena in Moving Bodies, which Einstein would later read (Lorentz 1895). Before Einstein went to Zurich to take the examinations – probably a few weeks or months earlier – he sent an essay from Milan to his uncle Cäser Koch, "Über die Untersuchung des Ätherzustandes im magnetischen Felde" ("On the Investigation of the State of the Ether in a Magnetic

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field"). The essay was written in sloping and spidery Gothic script on five pages of lined paper (Summer? 1895, CPAE 1, Doc. 5). Einstein sent a letter to Uncle Koch in which he wrote: "My dear uncle, […] I always hesitated to send you this [attached] note because it deals with a very special topic; and besides it is still rather naïve and imperfect, as is to be expected from a young fellow like myself. I shall not mind it at all if you don't read the stuff […]" (Einstein to Cäser Koch, Summer 1895, CPAE 1, Doc. 6). While neither the letter nor paper were dated; the letter was dated summer 1895 by reference to Einstein's first attempt to enter the ETH, and the paper was dated by the fact of its enclosure in the letter, on the assumption that it was written shortly before the letter (CPAE 1, 6, note 1, 10). The covering letter Einstein sent with the essay to his uncle later received the following added note in Einstein's own hand: "1894 or 95. A. Einstein (date supplied 1950)". That is, in 1950, Einstein dated the essay to be from 1894 or 1895 (Holton 1988, 396-397). Gerald Holton and Abraham Pais analysed Einstein's essay in which he wrote: "The marvelous experiments of Hertz, most ingeniously elucidated the dynamic nature of these phenomena, the propagation in space, as well as the qualitative identity of these motions with light and heat" (CPAE 1, Doc. 5). Holton explains that the essay shows Einstein had already encountered Hertz's work on the electrodynamic field. Pais adds that he did not know how Einstein became aware of Hertz's work. At any rate, it is evident that at that time he already knew that light was an electromagnetic phenomenon, but was still unfamiliar with Maxwell's papers (Holton 1988, 377; Pais 1982, 131). Einstein wrote in the essay (CPAE 1, Doc. 5): "The most interesting, and also most subtle, case would be the direct experimental investigation of the magnetic field formed around an electric current, because the exploitation of the elastic state of the ether in this case would permit us a look into the enigmatic nature of electric current. The analogy would also permit us to draw sure conclusions about the state of the ether in the magnetic field surrounding the electric current, provided the previously mentioned investigations attain their ends".

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According to Pais, the main questions raised in the essay are: How does a magnetic field, generated when a current is turned on, affect the surrounding ether? And, how, in turn, does this magnetic field affect the current itself? Holton also says that Einstein was thinking up experiments to probe the state of the ether which, he says, forms a magnetic field around the electric current (Pais 1982, 131; Holton 1988, 377). Einstein wrote in the essay (CPAE 1, Doc. 5): "First of all, however, it has to be possible to prove that there does exist a passive resistance against the production of the magnetic field by the electric current, and that this [resistance] is proportional to the length of the current circuit and independent of the cross section and material of the conductor".

Pais writes that the young Einstein independently discovered the qualitative properties of self-induction (a term he did not use here). It seems clear that he was not yet familiar with Joseph Henry's work on this phenomenon (Pais 1982, 131; Henry 1832). Holton reminds the reader that it would be an error to think of that essay as a draft of ideas on which the later relativity theory is directly based, or even to regard it necessarily as his first scientific work. Holton stresses that what is most significant about Einstein's first essay at age sixteen is the idea of the light beam as "a probe of a field". From the contemplation of how to measure the wavelengths of such a beam, it would only be a small step to the recognition of the chasing a light beam paradox that Einstein discovered soon afterwards at school in Aarau (Holton 1988, 377). In addition, the essay "On the Investigation of the State of the Ether in a Magnetic Field" could be a very early predecessor to the magnet and conductor thought experiment; but at this stage Einstein believed in the ether. One can ask, with good reason, whether Einstein already started to think about the problem in Pavia in 1894–1895, which later led him to the special theory of relativity. Was the starting point in Milan, or was it only the next year in Aarau? In 1920, Moszkowski seemed to have proposed his answer to this question. Apparently, problems had taken root in the sixteen-year-old pupil in Aarau. "If a biographer should state that the first beginnings of the doctrine of relativity occurred at that time, he would not

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be making an objectively false statement" (Moszkowski 1921a, 225, 1921b, 227-228).

3 The Chasing a Light Beam Thought Experiment Between 1895 and 1896 in Aarau, Einstein was aged sixteen. Now the story becomes complicated and odd. If we thought the starting point could be Milan, we better return three or four years back to Munich, when Einstein was twelve or thirteen-years-old. Here, he met once a week with Max Talmud who exposed him to Aaron Bernstein's The People's Natural Science Books (Bernstein 1870, 1880). Einstein was thrilled, and read Bernstein's books enthusiastically. In volume 16, Bernstein describes the wonders of the skies, and dedicates a chapter to each planet. Finally he invites his readers to join him on a fantasy journey into space. Under the title, "Eine Phantasie-Reise im Weltall, 1. Die Abreife" (Fantasy Journey into Space, 1. The Departure), Bernstein describes his imaginary journey: Suppose you want to perform a voyage to space. You need a passing-card, and some provisions, food, a suitcase. Although our voyage is going to be very fast, we are going deep into space. In our suitcase we will take our thoughts. "Do we travel by water? On the back of the horse? By train? None of that! We travel with the help of an electrical telegraphic apparatus!" (Bernstein 1870, 16, 11). A few years later, Einstein, at school in Aarau, also imagined a journey on a light beam (not exactly on a telegraphic signal), a thought experiment of him chasing a light beam. Friedrich Herneck thought that Bernstein might have inspired Einstein when he propounded his Aarau thought experiment. According to Herneck, Einstein's later thoughts about the speed of light could have been influenced by his earlier reading of Bernstein's popular science books. Herneck suggested that Einstein might have thought of the speed of light already in Munich when he was twelve years old (Herneck 1963, 50).34 Einstein did not pronounce anything on this matter. Einstein's own comments on the Aarau thought experiment appear in a few sources: 1) 1955, Autobiographical Sketch: The thought experiment was recounted by Einstein in his Autobiographical Sketch, written a month before he died in March 1955 (Einstein 1955, 10):

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"During this year in Aarau the following question came to me: If one chases a light wave with the speed of light, one would have in front of him a time independent wave field. Such a thing seems, however, not to exist! This was the first childish thought experiment that was related to the special theory of relativity".

2) 1946, Autobiographical Notes: These were written by Einstein in 1946 and published in 1949; forty to fifty years after the events in question (Norton 2004, 77). In his Autobiographical Notes Einstein explains that reflections that a radiation must possess – a kind of molecular structure – made it clear to him in the early 1900s, that neither mechanics nor electrodynamics could (except for limiting cases) claim exact validity. While working simultaneously on the quantum problem and the nature of radiation, and on the electrodynamics of moving bodies, he gradually despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. Einstein came to the conviction that only the discovery of a general formal principle could lead him to assured results. He was looking for a general principle for the electrodynamics of moving bodies, a principle of the kind one finds in thermodynamics (Einstein 1949, 48-51): "After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with a velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. However, there seems to be no such thing; neither on the basis of experience nor according to Maxwell's equations".

From the essay that Einstein sent his uncle Koch, probably in 1895, we presume that he was not yet acquainted with Maxwell's equations. A year later he conceived his thought experiment; he was to write years later about the paradox and mention these equations. Thus the sixteen-year-old Einstein was not yet acquainted with Maxwell's theory. He mentioned Maxwell's equations above in the thought experiment because of later knowledge acquired after he had learned of these equations. Einstein explained that from the very beginning it appeared intuitively clear to him that, judged from the standpoint of such an observer who pursues a light beam with velocity c, "everything would have to happen according to the same laws as for an observer who, relative to the Earth, was at rest. For how should the first observer know, or be able to determine, that he is in a state of fast uniform motion?" (Einstein 1949, 5051).

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After speaking about the paradox in the thought experiment, Einstein goes on to explain the fundamental importance of it: "One sees that in this paradox the germ of the special theory of relativity is already contained. Today everyone knows, of course, that all attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of time, or simultaneity, was rooted unrecognised in the unconscious." However, "To recognise clearly this axiom", says Einstein, "and its arbitrary character already implies the essentials of the solution of the problem" (Einstein 1949, 50-51). 3) 1947, Phillip Frank's report: Before 1947 Einstein seemed to have told the same story about the thought experiment of age sixteen to his friend Philipp Frank. Einstein very likely told Frank about this thought experiment at the same time as he wrote his Autobiographical Notes in 1946. Einstein told Frank the following version, which appeared in the German edition of Frank's 1949 book. Frank reports that at this time (when he was in Zurich) Einstein was satisfied with passive strange thoughts. In him the seeds of ideas about the mysteries of nature had already been sown, these would grow and deepen. Soon after his entry to the Polytechnic in Zurich the question, which he had already asked in the Cantonal School in Aarau, began to trouble him more and more (Frank 1949, 39-40): "Light is something that moves, and moves very quickly. The speed of light is very high, but finite and known. Now, if someone with the same speed as that of light were to run after the light, he must have remained in line with the light. For him the light would not move. But, can there be a 'ray of light at rest'? That seems impossible. How can something be both moving and resting? If one desires to avoid this, the movement of light should not be defined as the movement of a body or as the propagation of waves in a medium. Otherwise one would be able to pursue after light and overtake it. But if it is not there and yet it is something real, what should we actually think of a beam of light? This question troubled the student Einstein throughout his time in the Polytechnic. He studied all the works of the great physicists to see whether they could contribute to a solution to the problem of the nature of this light thing".

In the forward to Frank's biography, Einstein promised the reader that he would find clever, interesting and plausible explanations in Frank's book that would be – at least in part – new and surprising (Frank 1949, Einstein's forward). The above explanation could be one of these new and surprising explanations.35

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Frank explained how Einstein's thought experiment creates difficulties for the ether. Frank wrote that if one wants to avoid seeing a frozen light wave then the motion of light should not be defined as the propagation of waves in a medium. Otherwise, one would be able to pursue after light and overtake it. If Frank reported what Einstein had told him, then it might signify that in his year at Aarau, between 1895 and 1896, at age of sixteen, Einstein was familiar with the principle of relativity in classical mechanics, and as a student at the Polytechnic he understood that ether was problematic. Einstein aged sixteen, was presumably also familiar with the principle of relativity. While preparing for the Polytechnic entrance examination in 1895, he had studied the German edition of Violle's textbook. Violle based his treatment of dynamics on the principle of relativity in classical mechanics together with the principle of inertia (Violle 1892-1893, 90-91; CPAE 2, 259). 4) 1954, Biographies relying on the Notes: Vallentin writes: "The question that worried the youth of sixteen was: What would happen if a man tried to imprison a ray of light? The question was naturally more complex, but as scientific formulae were beyond me, it was with these simple words that Einstein explained what he himself considered to be the starting point of his work. Once he had asked himself the question, the problem haunted him. It was always present as he continued his studies at the Polytechnic and struggled with the material difficulties in his path" (Vallentin 1954, 18). On December 20, 1954, Einstein wrote on Vallentin that she, "knows me superficially and what she tells about me is essentially pure invention (Rosenkranz and Wolff 2007, 245). The above description of Einstein's thought experiment was very likely taken from Einstein's Autobiographical Notes; in addition, Vallentin might have picked up from Frank's biography and added some "pure invention" to what Einstein had written. Seelig reported that the origins of the special theory of relativity went back to Einstein's early youth during which he pondered for a long time on the image of a man who runs after a ray of light. This "image of the ray of light had led to the special relativity theory" (Seelig 1954, 84, 1956a, 70). Like Vallentin, Seelig probably also took the story of the beam rider from Einstein's Autobiographical Notes. On February 25, 1952, Einstein referred Seelig to his Autobiographical Notes (EA 39-011).36

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5) 1916/1945, Max Wertheimer's report: In 1916 Wertheimer met with Einstein in order to probe the psychology of his work. He interviewed Einstein at that time, ten years after he had devised his thought experiment. Later, the interviews were published posthumously in 1945 after Wertheimer's death in 1943.37 Wertheimer reported that the problem started when Einstein was sixteen years old, a pupil in the Aarau, Cantonal School. He said that, the process started in a way that was not very clear, and is therefore difficult to describe. "First came such questions as: What if one were to run after a ray of light? What if one were riding on the beam? If one were to run after a ray of light as it travels, would its velocity thereby be decreased? If one were to run fast enough, would it no longer move at all?" Wertheimer wrote that to young Einstein this seemed strange. "The same light ray, for another man, would have another velocity". Then he asked Einstein, whether, during this period, he already had some idea of the constancy of light velocity, independent of the movement of the reference system. Einstein answered, decidedly: "No, it was just curiosity. That the velocity of light could differ depending upon the movement of the observer was somehow characterised by doubt. Later developments increased that doubt" (Wertheimer 1916, 170). As opposed to Einstein in his Autobiographical Notes, written some thirty years after Wertheimer's interview with him, the latter does not mention Maxwell's equations, nor does he mention the absolute character of time, or simultaneity in relation to the thought experiment. John Norton writes that, Wertheimer's and Einstein's 1955 reports "portray the thought experiment in its original form as much less of the well-reasoned and polished display pieces that characterise Einstein's scientific writing" (Norton 2004, 78).38 It appears that, Phillip Frank's report concerns Einstein's pondering the problem of the optics and electrodynamics of moving bodies and thought experiment while he was a student at the Polytechnic. Einstein's own account in his Autobiographical Notes mixes the sixteen-year-old's thought experiment with his later understanding. However, Einstein did not give temporal locations in his Notes; thus his Notes are not an historical account of his route to his theories, but rather a scientific explanation of his route.39 This explains the apparent muddle between earlier events and later understanding.

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Wertheimer's report was created by someone who was not a physicist (Wertheimer was a pioneer Gestalt psychologist). Einstein explained to Wertheimer the thought experiment in a popular manner, and Wertheimer reported Einstein's intuitive explanation. Finally, Einstein's 1955 explanation in the Sketch, unlike the Notes, contains locations, names and events. The thought experiment is described within the framework of the years Einstein spent in the Cantonal School in Aarau. He opens the Sketch with an account of his happy years there; it was during his time in Aarau that he imagined the childish thought experiment of chasing a light beam. It seems that – from the historical point of view – Frank supplies the most important information. At first, in 1895, Einstein arrived in a non-verbal manner at the thought experiment of chasing after a beam of light. This thought experiment later troubled Einstein during his student days at the Zurich Polytechnic, and might have led him to decide that the ether was problematic.

4 Magnet and Conductor Thought Experiment In later recollections, Einstein stressed the importance of several thought experiments that led up to the final special theory of relativity: 1. the chasing a light beam thought experiment; and 2. his magnet and conductor thought experiment. They do not include any thought experiments on clocks and their synchronisation (Norton 2008, 1-2).

4.1 Maxwell's Equations and Induction Einstein started his 1905 relativity paper with the problematic asymmetries that were inherent in the electrodynamic explanation of the phenomenon of induction by Faraday. Thus the magnet and conductor thought experiment opens Einstein’s 1905 relativity paper and not the famous Michelson-Morley second order in v/c ether drift experiment. In fact, this latter experiment is not even mentioned in the relativity paper. Max Born recalled in 1955 that in the spring of 1915, he was called to Berlin by Planck, to assist him in teaching. Einstein was living at that time in Berlin. Born, therefore, was near Planck and Einstein. It was the only period when Born saw Einstein frequently, at times almost daily, and when he could watch the working of his mind and learn his ideas on

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physics and many other subjects. When speaking of the physical facts, which Einstein used in 1905 for his special relativity, Born said that it was the law of electromagnetic induction that seemed to have guided Einstein even more than Michelson's experiment. The induction law was at that time about seventy years old – Faraday discovered it in 1834 – and everybody had known all along that the effect depended only on relative motion (Born 1957, 193-194, 1969, 107-108). In his 1920 manuscript, "Grundgedanken und Methoden der Relativitätstheorie in ihrer Entwicklung dargestellt" (Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development), Einstein explains that the magnet and conductor experiment (magneto-electric induction) played a leading role during his establishment of the special theory of relativity. Induction seemed to have occupied Einstein from the technical and theoretical points of view. He was fascinated with inventions and was attracted to the technical aspects of induction. He spoke about the crucial role of the magnet and conductor experiment in his thought. Einstein laid emphasis upon the magnet and conductor experiment and explained that, according to Faraday, during the relative motion of a magnet and an electric circuit, an electric current is induced in the latter. Whether the magnet or the conductor is moved doesn't matter; it only depends on the relative motion. However, according to the MaxwellLorentz theory, the theoretical interpretations of the phenomenon vary significantly between the two cases. Einstein emphasised that, "the phenomena of magneto-electric induction forced me to postulate the principle of (special) relativity" (Einstein 1920a, 20).40 Analysing the magnet and conductor experiment within the framework of Maxwell’s theory – as then interpreted – seemed to preclude that the mechanical (physical) principle of relativity should hold for electromagnetic phenomena. According to this principle, the laws of mechanics take the same form in all inertial reference frames. In what way, then, does Maxwell’s theory differ from the Galilei-invariant theory (a theory which is in accord with the principle of relativity)? The answer is through the presence of the Faraday induction term, which destroys their exact Galilei invariance – thereby creating their Lorentz invariance. Hence, the law of induction – or the magnet and conductor thought experiment – sets up the conflict between electrodynamics and the Galilean principle of relativity (Jammer and Stachel 1980, 5-6).

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4.2 What Prompted Einstein to Invent the Magnet and Conductor Thought Experiment? It appears that Einstein's thoughts about the magnet and conductor thought experiment can be traced to a number of sources. 1) Einstein's Childhood and Technical Background: The electrotechnological environment in which Einstein grew up in Munich (the electro-technical company of his father Hermann and his uncle Jakob) can explain his affinity to technical inventions. Einstein studied Faraday's induction at secondary school, the Luitpold Gymnasium. Einstein studied from a physics book by Joseph Krist. In his book Krist explains magneto-induction, and associates it with Faraday's induction (Krist 1891, 94). During Einstein's patent years, from June 1902 until October 1909, machines surrounded him. Indeed a letter from the Swiss Patent Office on the AEG Alternating Current Machine shows that Einstein examined the specifications of induction machines (Swiss Patent Office Letter on the AEG Alternating Current machine, December 11, 1907, CPAE 5, Doc. 67). Peter Galison writes in his 2003 book Einstein Clocks, Poincaré's Maps that during Einstein's patent years he examined and worked through numerous patents, all day, including dynamos (Galison 2003, 249). Among these patents Einstein very likely found patents based on induction. 2) The Polytechnic and August Föppl's book on Maxwell's Theory: Weber's courses at the Polytechnic may have also influenced Einstein. The combination of Einstein's work in Weber's laboratories and his technical background from home could have led him to invent the magnet and conductor thought experiment. Holton refers to another source for the magnet and conductor thought experiment: During his student days at the Polytechnic, the young Einstein read August Föppl's 1894 Einführung in die Maxwellsche Theorie der Elektrizität (Introduction to Maxwell's Theory of Electricity) (Föppl 1894). Reiser writes, "Just then his one great love among the sciences was physics. But the scientific courses offered to him in Zurich soon seemed insufficient and inadequate, so that he habitually cut classes. His

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development as a scientist did not suffer thereby. With a veritable mania for reading, day and night, he went through the works of the great physicists – Kirchhoff, Hertz, Helmholtz, Föppl" (Reiser 1930, 49). Frank reported exactly the same story, probably relying on Reiser. Frank noted that day and night Einstein buried himself in Kirchhoff, Helmholtz, and Föppl's books, from which he learned the electromagnetic theory of Maxwell and Hertz (Frank 1949, 38).41 The fifth main section of Föppl's book was entitled, "Die Elektrodynamik bewegter Leiter" (The Electrodynamics of Moving Conductors) (Föppl 1894, 307-355). In this section there is a chapter called, "Die durch Bewegungen inducirte elektromotorische Kraft" (Electromotive-Force Induction by Movement) (Föppl 1894, 307-330). The first paragraph §114, in this chapter deals with "Relative und absolute Bewegung im Raume" (Relative and Absolute Motion in Space). It starts: "The discussion of kinematics, namely of the general theory of motion, usually rests on the axiom that, in the relationship of bodies to one another only relative motion is of importance. There can be no recourse to an absolute motion in space since any means to find such a motion is absent if there is no reference object at hand from which the motion can be observed and measured". Föppl continues in the second paragraph §115, in this way: "When, in the following, we make use of the laws of kinematics for relative motion, we must proceed with caution. We must not consider it as a priori settled that it is, for example, all the same whether a magnet [moves] in the vicinity of a resting electric circuit or whether it is the latter that moves while the magnet is at rest" (Föppl 1894, 307, 309). Holton says that this describes precisely the experimental situation with which Einstein's paper starts (Holton 1988, 221).42 We do not know when Einstein read Föppl's book, since it's not mentioned in his writings; thus, it is difficult to say whether this book inspired him to invent the magnet and conductor thought experiment.

5 Ether Drift and Michelson and Morley's Experiment 5.1 Einstein Designs Ether Drift Experiments between 1899 and 1901 A year after inventing the chasing a light beam thought experiment, Einstein was a student at the Zurich Polytechnic. By 1899, he was interested in ether drift experiments, and appears to have designed one.

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According to his 1922 Kyoto lecture, Einstein said he wanted to verify the flow of the ether with respect to the motion of the Earth. When he first thought about this problem, he did not doubt the existence of the ether or the motion of the Earth through it. He thought of the following experiment using two thermocouples: "Set up mirrors so that the light from a single source is to be reflected in two different directions, one parallel to the motion of the Earth, and the other antiparallel. If we assume that there is an energy difference between the two reflected beams, we can measure the difference in the generated heat using two thermocouples" (Einstein 1922a, 46).43 The above paragraph may well have described the idea that Einstein had in 1899 during a visit to Aarau. In September 1899, Einstein came up with an idea in Aarau for investigating the way in which a body's relative motion – with respect to the luminiferous ether – affects the velocity of the propagation of light in transparent bodies. He invented a theory about it, which seemed quite plausible to him, and he had also written to Prof. Wien in Aachen about his paper on the relative motion of the luminiferous ether relative to ponderable matter (Weber handled this paper in an offhanded fashion) (Einstein to Mariü, September 10, September 28? 1899, CPAE 1, Doc. 54, 57; Renn and Schulmann 1992, 85, note 3). In his second year of college, Einstein encountered the problem of light, ether and the Earth's movement. He wanted to construct an apparatus that would accurately measure the Earth's movement with respect to the ether. Einstein did not yet know that he shared the same intentions of other important theorists. He was at that time unacquainted with Lorentz’s earlier contributions and with the subsequently famous attempt by Michelson. He wanted to proceed empirically, to suit his scientific feeling at the time, and believed that an apparatus such as he sought would lead him to the solution of a problem, whose far-reaching perspectives he already sensed. However, there was no chance to build this apparatus, because his teachers' skepticism was too great, forcing Einstein to temporarily turn aside from his plan (Reiser 1930, 52). Wertheimer describes Einstein's efforts at finding experimental methods for detecting the motion of the Earth with respect to the ether. Einstein was puzzled to think that under certain conditions light should travel more quickly in one direction than another. Einstein believed that if this was correct, there would be a way of finding out through experiments with light whether one is in a moving system (on Earth). Einstein's interest was captured by this, and he tried to find methods by which it would be

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possible to establish or to measure the movement of the Earth. He learned only later that physicists had already created such experiments (Wertheimer 1916, 169). In September 1899, Einstein told Mariü that he read a very interesting paper by Wien from 1898 on the relative motion of the luminiferous ether relative to ponderable matter. Wien's 1898 paper was his report to the Society of German Scientists and Physicians, "Über die Fragen, welche die translatorische Bewegung des Lichtäthers betreffen" (On Questions Concerning the Motion of Translation of the Luminiferous Ether) (Einstein to Mariü, September 28? 1899, CPAE 1, Doc. 57, Wien 1898). Wien discussed both Hertz's concept of moving ether and Lorentz's concept of immobile ether. He also briefly considered thirteen experiments bearing on the question, the last of which was the Michelson-Morley experiment. It is reasonable to conjecture that Einstein read this account in 1899, and knew something about the Michelson-Morley experiment from this paper. Two years later, Einstein wrote to Mariü, "I want to get down to business now and read what Lorentz and Drude have written about the electrodynamics of moving bodies" (Einstein to Mariü, December 28, 1901, CPAE 1, Doc. 130). Therefore, by 1902 Einstein had already read Lorentz's 1895 book from which he probably learnt about the MichelsonMorley experiment (if he had not done so earlier from Wien). Michelson and Morley's experiment became increasingly famous at that time. After graduating from the Polytechnic, Einstein appeared to have designed a second ether drift experiment. In December 1901, Einstein spent all afternoon with Prof. Alfred Kleiner in Zurich telling him his ideas about the electrodynamics of moving bodies. Kleiner advised Einstein to publish his ideas on the electromagnetic theory of light of moving bodies along with the experimental method. He found the method Einstein proposed to him to be "the simplest and most appropriate one imaginable". Einstein was quite happy about the success, and told Mariü: "I will write the paper in the next few weeks for sure" (Einstein to Mariü, December 19, 1901, CPAE 1, Doc. 130). Einstein, however, was still not ready to publish his ideas on electrodynamics. The experimental method was presumably the method for investigating the motion of matter with respect to the ether mentioned in Einstein's letter to Marcel Grossmann of September 1901 (Renn and Schulmann 1992, 100, note 4). Einstein wrote in a letter to Grossmann that

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he was working on Bolzmann's kinetic gas theory. He also wrote that during his investigation of the relative motion of matter with respect to the luminiferous ether, "a considerably simpler method had occurred to me, which is based on customary interference experiments". Einstein promised Grossmann that when they next saw each other, he would tell him about it (Einstein to Grossmann, September 6? 1901, CPAE 1, Doc. 122).

5.2 Einstein's Different Statements as to the Role that Michelson's Experiment Played in his Development Michelson's experimental result is usually cited as preliminary problem that demanded abandoning the ether, and which finally have led to Einstein's solution. According to this scenario, which usually appears in textbooks, it appears obvious that, on his pathway to special relativity, Einstein must have based himself on Michelson's experimental result; if he did not explicitly use this experimental result, he at least knew about the famous experiment prior to publication of the relativity paper. Over the years Einstein was asked many times whether the Michelson's experiments influenced his thought. Einstein himself made different statements about the influence of the Michelson experiments, ranging from "there is no doubt that Michelson's experiment was of considerable influence on my work" to "the Michelson-Morley experiment had a negligible effect on the discovery of relativity". Holton differentiates between the statements Einstein made in direct response to repeated requests to deal with the possible genetic role of the Michelson experiment, and the rather different statement he made whether he volunteered any comments concerning the genesis of relativity (in which case Einstein almost always spoke only about the experiment of Fizeau and the aberration measurements, insofar as he spoke of measurements at all) (Holton 1988, 280-281, 1969, 969). It appears that when Einstein worked on problems of the electrodynamics of moving bodies he took for granted that one did not have to go over every ether-drift experiment in order to convince oneself about the nonexistence of absolute motion. Einstein did not remember whether he knew of Michelson's experiment, because for him it was not a problem of etherdrift experiments. He was rather concerned with heuristic principles. Wertheimer explained the situation after talking to Einstein: "He felt that the trouble went deeper than the contradiction between Michelson's actual and the expected result. […] for him this was not a problem with regard to

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the Michelson experiment only, but a problem in which more basic principles were at stake" (Wertheimer 1916, 174). In 1892 Michelson began teaching at the University of Chicago. Robert Andrews Millikan met Michelson for the first time in the summer of 1894. Millikan had left his studies in Berlin in order to work under Michelson. He had been Michelson's pupil in 1895, his assistant and associate for twenty years. In 1921, Millikan had assumed the role of director of the Norman Bridges Laboratory of Physics as well as chairman of the executive council of the former Throop Polytechnic Institute, which had been renamed California Institute of Technology (Caltech) in 1920. Soon after his arrival, Millikan announced his desire to put physics on the map in southern California, and initiated a visiting-scholars programme. Distinguished physicist Michelson, the first American Jew to win the Nobel Prize in 1907, was immediately recruited. Einstein first met Michelson on his trip to America in 1930. Einstein came to California on December 31, 1930 and spent the next three months at Caltech's Norman Bridges Laboratory in association with some of the leading figures in American science. Einstein's visit to Caltech capped Millikan's campaign to make the institute one of the physics capitals of the world (Michelson Livingston 1973, 182-183, 264; Kramer 2004, 10). On January 15, 1931, distinguished scholars, researchers and other guests assembled to honour Einstein at the Athenaeum, the elegant dining hall of the Caltech's faculty. Among them was Michelson, seventy-nine-yearsold, who had been weakened by a serious stroke. The picture taken on the occasion of the meeting shows the frail old Michelson standing next to Einstein. This was Michelson's last public appearance; he died three months later. Millikan set the stage with some remarks on what he saw to be the characteristic features of modern scientific thought. It is, in fact, largely, the very same material Millikan was to republish eighteen years later in 1949 as part of his introduction for the Einstein issue of the Review of Modern Physics (Kramer 2004, 2, 4, 11; Holton 1969, 973). In the 1949 Einstein issue of Reviews of Modern Physics, celebrating Einstein's seventieth birthday, Millikan's paper, titled "Albert Einstein on his Seventieth Birthday", claims that "In the case of relativity the prime experimental builder had been my own chief at the University of Chicago, Albert A. Michelson, who made his first experiment on aether-drift at Berlin in 1881" (Millikan 1949, 343). Millikan then went on to tell the following story (Millikan 1949, 343-344):

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"But this experiment, after it had been performed with such extraordinary skill and refinement by Michelson and Morley, yielded with great definiteness the answer that there is no such time-difference and therefore no observable velocity of the Earth with respect to the aether. That unreasonable, apparently inexplicable experimental fact was very bothersome to 19th century physics and so for almost twenty years after this fact came to light physicists wandered in the wilderness in the disheartening effort to make it seem reasonable. Then Einstein called out to us all, 'Let us merely accept this as an established experimental fact and from there proceed to work out its inevitable consequences', and he went at that task himself with an energy and capacity which very few people on Earth possess. Thus was born the special theory of relativity".

After the sentence, "Thus was born the special theory of relativity", Millikan went on to say in 1931, "I now wish to introduce the man who laid its experimental foundations, Professor Albert A. Michelson" (Holton 1969, 973). Millikan had paid tribute to Michelson as the man who laid the experimental foundations to special relativity, and Michelson thanked him for this great honour. Einstein cooperated in this tribute without questioning the narrative. He turned to Michelson and said:44 "You, my honored Dr Michelson, began with this work when I was only a little youngster, hardly three feet high. It was you who led the physicists into new paths, and through your marvelous experimental work paved the way for the development of the theory of relativity. You uncovered an insidious defect in the ether theory of light, as it then existed, and stimulated the ideas of H. A. Lorentz and FitzGerald, out of which the special theory of relativity developed. These in turn pointed the way to the general theory of relativity and to the theory of gravitation".

At any rate, Michelson was known to be no friend of relativity, the destroyer of the ether. Einstein had heard that Michelson was ill and he wished to come over to cheer him up. "Please don't get him started on the subject of the ether", Michelson's wife whispered to Einstein when he arrived. Like so many others, Michelson was convinced that his own illfated experiments were the basis for the theory of relativity. Einstein reminisced later that Michelson told him more than once that he did not like the theories that had followed from his work, and that he had told Einstein he was a little sorry that his own work "had started this monster" (Shankland 1963, 57; Michelson Livingston 1973, 334-335). Similarly, Einstein told the astronomer Charles Nordmann during his visit to Paris in 1922 that Michelson once said: "If I had guessed that the results of my experiment would lead to this thing, I really believe that I never would have done it" (Nordmann 1922, 142).

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In a letter in honour of Michelson's hundredth birthday, dated December 19, 1952, Einstein describes the influence of the Michelson-Morley experiment on him (quoted in Norton 2004, 82): "I am not sure when I first heard of the Michelson experiment or its more precise repetition by Michelson and Morley. I was not conscious that it influenced me directly during the seven and more years that the development of the special theory of relativity had been my entire life; for I had taken it for granted as being true".

The typescript note is in English, with German corrections in Einstein’s hand. A handwritten notation corrects the stricken typescript: "My thought was more indirectly influenced by the famous Michelson-Morley experiment. I learned of it through Lorentz's path breaking investigation on the electrodynamics of moving bodies (1895), of which I knew before the establishment of the special theory of relativity". Einstein then explained that his direct path to the special theory of relativity was mainly determined by the magnet and conductor experiment (transformations for the electric and magnetic field). But, the result of Fizeau's experiment and the phenomenon of aberration also guided him (quoted in Norton 2004, 49-50). Holton started his 1969 paper, "Einstein and the 'Crucial' Experiment' ", with a letter dated February 2, 1954, about a year before Einstein's death, from Francis Garvin Davenport of the Department of History at Monmouth College, Illinois. Davenport wrote to Einstein that he was looking into evidence according to which Michelson had influenced his thinking and perhaps helped him to work out his theory of relativity. Davenport, not being a scientist, asked Einstein for a brief statement, in non-technical terms, indicating how Michelson helped to pave the way, if he did, for his theory. Einstein answered a long reply very soon after receipt, on February 9, 1954. Einstein explained to Davenport that Michelson's experiment had a great effect in extending the range of validity of the principle of relativity, but Michelson's experiment did not have an effect on his own development and pathway toward the special theory of relativity (Holton 1969, 999): "In my own development Michelson's result has not had a considerable influence. I even do not remember if I knew of it at all when I wrote my first paper on the subject (1905). The explanation is that I was, for general reasons, firmly convinced that there does not exist absolute motion and

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my problem was only how this could be reconciled with our knowledge of electrodynamics".

Einstein ended his letter by giving Davenport the permission to publish the letter. He also told Davenport that he was also willing to give him further explanations if required (Holton 1969, 999). Holton said that this is a thoughtfully composed reply, and the last letter of Einstein he had been able to find on this subject. There are good reasons to ask why the Michelson-Morley experiment is so intimately connected with the special theory of relativity? For years after Einstein's first publication no new experimental results came forth that could be used to verify his theory in the way most physicists were and still are used to looking for verification. As Max Planck noted in 1907, Michelson's experimental result was then still regarded as the only experimental support (Planck 1907, 546): "[...] the principle of relativity as expressed by H.A. Lorentz and in the most general form by A. Einstein. Although only a single direct confirmation of the validity of this principle, yet very important, is to be mentioned: the result of the experiments of Michelson and Morley, yet on the other hand no fact is known so far, directly preventing us to ascribe general and absolute accuracy to that principle".

Holton says that in retrospect it seems therefore inevitable that during the decade following Einstein's 1905 paper there occurred – especially in the didactic literature – a symbiotic joining of the puzzling Michelson experiment and the all-but-incredible relativity theory. The undoubted result of Michelson's experiments could be thought to provide an experimental basis for the understanding of relativity theory, which otherwise seemed contrary to common sense itself. The relativity theory, in turn, could provide an explanation of Michelson's experimental result in a manner not "artificial", as reliance on the supposed Lorentz-FitzGerald contraction was widely felt to be. Holton says that it proved to be a longlasting marriage (Holton 1988, 287).

5.3 Robert Shankland's Interviews with Einstein on Michelson's Experiments Between 1950 and 1954 Einstein pronounced his views regarding the Michelson experiments to Robert Shankland. Shankland recalled that the first visit to Princeton to meet Einstein was made primarily to learn from him what he really felt about the Michelson-Morley experiment, and to

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what degree it had influenced him in his development of the special theory of relativity (Shankland 1963, 41, 47).45 Shankland reported, that on February 4, 1950, he met Einstein at his office in Princeton (Shankland 1963, 48): "When I asked him how he had learned of the Michelson-Morley experiment, he told me that he had become aware of it through the writings of H. A. Lorentz, but only after 1905 had it come to his attention! 'Otherwise', he said, 'I would have mentioned it in my paper'. He continued to say the experimental results which had influenced him most were the observations on stellar aberration and Fizeau's measurements on the speed of light in moving water. 'They were enough', he said".

In light of the importance of Fizeau's experiment and aberration in Einstein's thought he was convinced that absolute motion did not exist when one examined first order ether-drift experiments. For him this was enough. On October 24, 1952, Shankland walked down Mercer Street to Prof. Einstein's home. He went up to his study, and there he asked Einstein where he had first heard of Michelson and his experiment. Einstein replied, "This is not so easy, I am not sure when I first heard of the Michelson experiment. I was not conscious that it had influenced me directly during the seven years that relativity had been my life. I guess I just took it for granted that it was true" (Shankland 1963, 55). After 1905 Einstein wrote expositions of special relativity. In most of them he mentioned the Michelson-Morley experiment. Shankland wrote that Einstein told him that in the years 1905-1909, he thought a great deal about Michelson's result, in his discussions with Lorentz and others in his thinking about general relativity. Einstein told Shankland that then he realised that he had also been conscious of Michelson's result "before 1905 partly through his reading of the papers of Lorentz and more because he had simply assumed this result of Michelson to be true" (Shankland 1963, 55). According to Shankland, Einstein said on Michelson that he was "a great genius – he will always be thought so in this field". Einstein added that it was very remarkable that Michelson with little mathematics or theoretical training and without the advice of theoretical colleagues could devise the Michelson-Morley experiment. Einstein thought it was scarcely possible to perform an experiment without completely understanding the related

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theories, but Michelson had instinctive feeling for the essentials of a crucial experiment, and this Einstein considered the surest sign of Michelson's genius. Einstein felt that this was in large measure due to Michelson's artistic sense and approach to science, especially his feeling for symmetry and form (Shankland 1963, 49).

6 Emission Theory and Ether Drift Experiments 6.1 Ritz's Emission Theory I mentioned earlier in Chapter A, section 14.3 that Walter Ritz first published his emission theory in 1908 with the aim of replacing Einstein's special theory of relativity. Einstein's special theory of relativity assumes as its second postulate the famous light postulate: the velocity of light is independent of the state of motion of its source. After 1905 some scientists felt they could explain the phenomena of electrodynamics without this postulate, but with an alternative postulate – namely that the speed of light depends on the motion of its source. In other words, light from a source moving relative to an observer has a velocity equal to the vector sum of the velocity of light from a stationary source and the velocity relative to the observer of the source itself at the instant of emission. Theories based on the principle of relativity and such a postulate were called emission theories. Ritz outlined an emission theory of light that was consistent with classical mechanics in an attempt to develop a new electrodynamics of moving bodies. While Einstein's final solution posited that all light rays travel with the same speed in empty space, Ritz argued that their speeds vary depending on the motion of the sources at the instant of emission – as with any other mechanical projectile. He considered light to consist of particles, and to be shot like projectiles, and not like rays or waves. According to Ritz, electrodynamics was thus based on forces and not on fields. If this was the sort of mechanistic picture that Ritz was intending to offer, then it was obvious that Maxwell's field equations were inadequate to precisely describe the laws of propagation of physical actions – first these equations dealt with fields, and second, Ritz could not accept propagation of waves in a medium, such as was the ether. Towards 1908 Ritz became increasingly antagonistic to Maxwell's theory in general and to Lorentz's electron theory in particular. He then sought to devise a synthesis of optics with a new electrodynamics that would better account for experimental facts (Martínez 2004a, 4, 6-8).

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In 1908, Ritz thus rejected the ether of electrodynamics theory, and thought it should be eliminated. According to Ritz, "it is clear that one would then have to abandon not only the idea of the existence of an ether but also Maxwell's equations for the vacuum", explained Wolfgang Pauli in his 1921 encyclopedia article on relativity, "Relativitätstheorie" (Theory of Relativity), "so that the whole of electrodynamics would have to be constructed anew" (Pauli 1958, 6, 1921, 539, 20 [550]). Ritz thus thought that, in renouncing classical mechanics, Einstein had paid too high a price to resolve the difficulties at issue. Einstein had changed kinematics, but left the fundamentally problematic equations of electromagnetism untouched; Einstein assumed that the Maxwell-Lorentz equations were fundamental, and changed Newtonian kinematics. Ritz attempted to solve the problems by taking the inverse route: Let us drop the fundamental field equations of Maxwell-Lorentz theory but leave intact Newtonian kinematics and dynamics, with its force concept and ballistic theory of light, and of course the Galilean principle of relativity (Martínez 2004a, 8). In November 1911 Ehrenfest sent a paper, "Zur Frage der Entbehrlichkeit des Lichtäthers" (The question of the dispensability of light ether) to the Physikalische Zeitschrift, comparing Einstein's views on light propagation with those of Ritz. Shortly afterwards, in 1912, the paper was published (Ehrenfest 1912). Ehrenfest reacted to Einstein's 1905 relativity and 1909 papers, the latter titled, "Zum gegenwartigen Stand des Strahlungsproblems (On the Present Status of the Radiation Problem) (Einstein 1905a, 1909a). In January 1909 Einstein wrote: "The experimental investigation of the consequences of the theory of light quanta is, in my opinion, one of the most important tasks that the experimental physics of today must solve" (Einstein 1909a, 191). Ehrenfest noted that although both approaches (Einstein's and Ritz's) involved a particulate description of light – Einstein invoked the quanta of light and Ritz proposed particles of light – nevertheless, Ritz's theory constituted a "real" emission theory (in the Newtonian sense), while Einstein's relativity theory was more akin to the ether conception; since it postulated that the velocity of light is independent of the velocity of its source. Ehrenfest suggested possible experiments to distinguish between the two theories and noted the necessity of carrying out such empirical test. Richard Tolman suggested the Michelson-Morley experiment would serve as experimentum crucis. Tolman explained that according to Ritz's theory, light retains the component of velocity v which it obtained from its

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original moving source. Thus, all the phenomena of optics would occur as though light were propagated in the ether that is stationary with respect to the original source. Light coming from a terrestrial source would behave as though propagated by stationary ether with respect to the Earth, while light coming from the sun would behave as though propagated by an ether stationary with respect to the sun (Tolman 1912, 141; Martínez 2004a, 9). Of course, on the basis of either Einstein's or Ritz's theory, there was no ether! Hence, said Tolman, "If the Ritz theory should be true, using the sun as a source of light we should find on rotating the apparatus a shift in the fringes of the same magnitude as originally predicted for the MichelsonMorley apparatus where a terrestrial source was used. If the Einstein theory should be true, we should find no shift in the fringes using any source of light" (Tolman 1912, 143). The Michelson experiment with extra-terrestrial light (sun and stars) was actually carried out with a negative result by Rudolf Tomaschek (from Heidelberg) (Pauli 1958, 8; 1921, 22-23 [552-553]; Tomaschek 1924).

6.2 Einstein's First Reaction to Ehrenfest's Paper: Einstein Rejected Ritz's Emission Theory On April 25, 1912, Einstein reacted to Ehrenfest's 1912 paper by writing that before 1905 he himself explored emission theory, before returning to Lorentz's theory; but had abandoned it due to mounting difficulties: "I was not annoyed in the least by your article! On the contrary, such considerations are quite familiar to me from the pre-relativistic time. I certainly knew that the principle of the constancy of the velocity of light is completely independent of the relativity postulate; and I considered what would be more probable, the principle of the constancy of c, as was demanded by Maxwell's equations, or the constancy of c, exclusively for an observer sitting at the light source. I decided in favor of the first […]". However, Einstein realised that an emission theory based on NewtonGalilean kinematics was inadmissible because it led to paradoxical conclusions when attempting to explain such simple things as the reflection of light from a moving mirror. "Such complications seemed to me much more unwarranted than those brought by the new concept of time" (Einstein to Ehernfest, before June 20, 1912, CPAE 5, Doc. 409).

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From what Einstein wrote in his letter to Ehrenfest, we can infer that prior to 1905 he seriously considered an emission theory similar to that of Ritz and Ehrenfest's treatment of Ritz's theory. In 1950, Shankland came to talk with Einstein on Ritz's theory because of his personal interest in the Michelson-Morley experiment. During their meeting, Shankland mentioned to Einstein the experiments disproving the Ritz emission theory of light. Einstein responded that he considered the most decisive experiment along these lines to be the repetition of the Michelson-Morley experiment performed with starlight at Heidelberg by a student of Philipp Lenard's (Tomaschek) in 1924. In Berlin, Lenard, along with Stark, was a violently pro-Nazi German scientist and anti-relativity theorist; nonetheless, Einstein referred to him with complete fairness and without "the slightest trace of malice or bitterness" (Shankland 1963, 49). This led Einstein to a discussion of emission theories of light. He told Shankland that he had thought of, and abandoned a Ritz-like form of emission theory before 1905. He gave up this approach because he could think of no form of differential equations that could have solutions representing waves whose velocity depended on the motion of the source. In Ritz's case, Einstein explained to Shankland, the emission theory would lead to phase relations such that the propagated light would be all badly "mixed up" and might even "back up on itself". Einstein asked Shankland: "'Do you understand that?' I said no and he carefully repeated it all. When he came again to the 'mixed up' part he waved his hands before his face and laughed, an open heartily laugh at the idea!" Then he continued to explain that, "The theoretical possibilities in a given case are relatively few and relatively simple, and among them the choice can often be made by quite general arguments. Considering these tells us what is possible but does not tell us what reality is". When Shankland suggested that Ritz's theory was the best of the several emission theories of light, "he shook his head and replied that Ritz's theory is very bad in spots. But he quickly added, 'Ritz made a great contribution when he showed that frequency differences are the crucial thing in spectral series'" (Shankland 1963, 49). In February 1952, Einstein elaborated on this point. He said that, before setting up the special theory of relativity, he had himself thought of investigating the possibility of an emission theory. At that time he had only a weighing of the plausibility of theoretical arguments at his disposal. According to Einstein, if a suitably accelerated light source emits light in the direction of the acceleration, then the planes of equal phase move with different speed, so all the surfaces of equal phase coincide at a particular

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place, and the wavelength there is infinitely small. "Moreover, the light will be so turned around that the rear part overtakes the front" (Norton 2004, 72).

6.3 Einstein Falls into the Jungle: Emission Theory and Fizeau's Experiment As previously mentioned, in 1912 Ehrenfest published a paper comparing Einstein's views on light propagation with those of Ritz's emission theory (Ehrenfest 1912). On April 25, 1912, Einstein responded to Ehrenfest's paper (Einstein to Ehernfest, before June 20, 1912, CPAE 5, Doc. 409). Several months later, Einstein wrote a manuscript on the special theory of relativity, the first forty-six leaves were probably written between late summer and early autumn in 1912 (Einstein 1912, 35). In these pages, Einstein discusses Fizeau's experiment and emission theory, presumably a response to Ehrenfest's 1912 paper on Ritz's theory. It is reasonable and compelling to attempt to see in this discussion Einstein's struggles from 1904 with emission theory.46 In Section seven of his 1912 manuscript on the special theory of relativity, Einstein explains Fizeau's experiment and assumes that the velocity of light depends on the state of motion of the light source. The velocity of the source of light will simply have to be added to the velocity of the propagation of light of the stationary light source. However, Einstein was dissatisfied with the explanation of Fizeau's experiment by emission theory, which led him to increasingly unlikely conclusions and complicated hypotheses. Subsequently, Einstein discusses the difficulties facing any attempt to explain Fizeau's experiment from the standpoint of emission theory. A crossed-out paragraph contains additional objections to explaining Fizeau's experiment from the standpoint of emission theory. The velocity of light in the medium traversed by the light M (Einstein 1912, 84): "[…] depends on the velocity of motion of the light source with respect to M (Ritz and Ehrenfest). This being so, light rays of all possible propagation velocities, arbitrarily small or arbitrarily large, could occur in M. Intensity, colour, and polarisation state would not suffice to define a plane light wave; one would also have to add the determinative element of velocity […] one is forced to make the most peculiar assumptions if one pursues this point of view, as for example the following: if light of velocity c + v strikes a mirror perpendicularly, then the reflected light has

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Fizeau's experiment thus appears to have assisted Einstein in scrutinising emission theories and disposing of them. Einstein despaired of using emission theory to find answers to his problems in electrodynamics of moving bodies and the structure of matter and radiation. He decided to return to the Maxwell-Lorentz theory, and to reconsider it. He searched for a solution that would make the Maxwell-Lorentz equations compatible with the principle of relativity once the ether concept was abandoned. In the spring and summer of 1904 Einstein returned to Lorentz's theory and the light postulate. He attempted to discuss Fizeau's experiment according to Lorentz's theory. As mentioned in Section 2.4, in 1895 Lorentz derived the Fresnel Formula from the first principles of his theory (stationary ether and moving electrons) without the need of any partial ether drag. Lorentz thus adhered to Fizeau's original 1851 experimental result, but not to Fresnel's theoretical interpretation of partial ether drag hypothesis, used to derive his dragging coefficient. Before 1905, Einstein discussed Fizeau's experiment "as originally discussed by Lorentz" in 1895. During his 1922 Kyoto lecture Einstein stated: "Then I tried to discuss the Fizeau experiment on the assumption that the Lorentz equations for electrons should hold in the frame of reference of the moving body as well as in the frame of reference of the vacuum as originally discussed by Lorentz" (Einstein 1922a, 46). However, Einstein was still under the impression that the ordinary Newtonian law of addition of velocities was unproblematic.

7 Einstein's Route to Special Relativity from 1895 to 1903-1904 The following is a summary of Einstein's route to special relativity from 1895 to 1903-1904: 1) In 1894-1895 Einstein wrote an essay and sent it to his uncle Cäser Koch. He believed in the ether and had heard of Hertz's experiments on the propagation of electromagnetic waves; but he did not show any knowledge of Maxwell's theory. The covering letter that Einstein sent with the essay was later dated by Einstein as "1894 or 1895". In 1895 by the age of sixteen, Einstein was also familiar with the principle of relativity in mechanics.

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2) A year later, in 1895-1896, while in Aarau, Einstein developed a thought experiment: what would happen if an observer tried to chase a light wave? Could he catch up with it? If so, he ought to see a standing light wave form – this, however, seemed strange to him. 3) In 1899 Einstein studied Maxwell's electromagnetic theory, including Hertz's papers on Maxwell's theory. Einstein wrote to Mariü – probably on August 10, 1899 – that he was now rereading Hertz's propagation of electric force with great care: "I'm convinced more and more that the electrodynamics of moving bodies as it is presented today doesn't correspond to reality, and that it will be possible to present it in a simpler way". Einstein thought that "electrical forces can be directly defined only for empty space, something also emphasised by Hertz". He reasoned that "Electrodynamics would then be the theory of the movements of moving electricities and magnetisms in empty space (Einstein to Mariü, August 1899, CPAE 1, Doc. 52). Reiser and Frank reported that, with a veritable mania for reading, day and night, Einstein went through the works of the great physicists – Kirchhoff, Hertz, Helmholtz and Föppl (Reiser 1930, 49; Frank 1949, 38). 4) Around 1898-1900, the combination of Weber's courses (which Einstein took at the Polytechnic) in addition to his technical background from childhood and his self-directed readings of electromagnetism and electrodynamics may have led him to invent the magnet and conductor thought experiment. 5) Between 1899 and 1900, Einstein was occupied with the contradiction between the Galilean principle of relativity and the constancy of the velocity of light in Maxwell's theory. Maja writes in her biography that, Einstein was troubled by the apparent conflict or discrepancy between classical mechanics and electrodynamics (Maxwell's theory), but was still not acquainted with Lorentz's theory of electrons. Maja writes that the following year (1900) Einstein graduated and received his diploma from the Polytechnic (Winteler-Einstein 1924, 18).47 6) Between 1899 and 1901 Einstein was interested in ether drift experiments, and appears to have designed at least two such experiments, the first in 1899. Later he was reported to have said: "Then I myself wanted to verify the flow of the ether with respect to the Earth [...]. When I first thought about this problem, I did not doubt the existence of the ether or the motion of the Earth through it" (Einstein 1922a, 46). Two years later, after graduating from the Polytechnic, Einstein designed a second

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ether drift experiment. On December 19, 1901, he wrote to Mariü that he spent all afternoon with Prof. Alfred Kleiner in Zurich telling him his ideas about the electrodynamics of moving bodies. Kleiner advised Einstein to publish his ideas on the electromagnetic theory of light of moving bodies along with the experimental method (Einstein to Mariü, Dec 19 1901, CPAE 1, Doc. 130). 7) On December 17, 1901, Einstein wrote to Mariü: "I am busy working on an electrodynamics of moving bodies, which promises to be quite a capital piece of work. I wrote to you that I doubted the correctness of the ideas about relative motion, but my reservations were based on a simple calculation error. Now, I believe in them more than ever" (Einstein to Mariü, Dec 17, 1901, CPAE 1, Doc. 128). In 1901 Einstein still accepted the Galilean kinematics of space and time, including the Galilean principle of relativity. Einstein realised that once the induction term in the magnet and conductor thought experiment was considered, Galilei transformations led to an asymmetry in the explanation. He felt that there should only be an electric field acting on the electrons in the conductor. In 1901, Einstein still had no solution to the problem of electrodynamics. 8) In 1902 Einstein read Lorentz's 1895 memoir, Attempt at a Theory of Electrical and Optical Phenomena in Moving Bodies. On December 28, 1901, Einstein wrote to Mariü, "I want to get down to business now and read what Lorentz and Drude have written about the electrodynamics of moving bodies" (Einstein to Mariü, Dec 28, 1901, CPAE 1, Doc. 130). 9) It appears that between 1901 and 1903, Einstein was working with the Maxwell-Hertz equations for empty space. He tried to find solutions to two problems: I) The magnet and conductor experiment and Faraday's induction law concluded that there is an asymmetry in the explanation depending on whether the magnet moves or the conductor moves. Einstein analysed the magnet and conductor thought experiment according to Maxwell's theory and the Galilean transformations.48 However, covariance of Maxwell's equations failed. He wrote in the 1920 manuscript, "Fundamental Ideas and Methods of the Theory of Relativity" that, according to Faraday, during the relative motion of a magnet and an electric circuit, an electric current is induced in the latter. Whether the magnet is moved or the conductor doesn't matter; the electric current only depends on the relative motion. However, around

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1902 when he read Lorentz's 1895 book he realised that, according to the Maxwell-Lorentz theory, the theoretical interpretation of the phenomenon is very different for the two cases (Einstein 1920a, 20). Einstein thus chose the relativity principle and dropped Lorentz's theory. II) Conflict between the principle of Galilean relativity and the constancy of the velocity of light. Max Wertheimer reports that in the Maxwell equations of the electromagnetic field, the velocity of light plays an important role and is constant. We may reason that Einstein explained to Wertheimer that, "if the Maxwell equations are valid with regard to one system, they are not valid in another. They would have to be changed. When one tries to do so in such a way that the velocity of light is not assumed to be constant, the matter becomes very complicated". Apparently, Einstein could not explain to Wertheimer the problem more simply than that. According to Wertheimer, "for years Einstein tried to clarify the problem by studying and trying to change the Maxwell equations. He did not succeed in formulating these equations in such a way as to meet these difficulties satisfactorily". He tried hard to clarify the relationship between the velocity of light and the facts of movement in mechanics. However, whichever way he tried to unify the question of mechanical movement with the electromagnetic phenomena led him to difficulties (Wertheimer 1916, 171). 10) Between 1901 and 1903, when Einstein dropped the ether hypothesis and chose the principle of relativity instead of the postulate of the constancy of the velocity of light, he found a (temporary) solution for his conflict in the form of an emission theory. According to Wertheimer, one of Einstein's questions was: What would happen to the Maxwell equations and to their agreement with the facts if one were to assume that the velocity of light depends on the motion of the source of the light? (Wertheimer 1916, 171). Einstein replaced Lorentz's theory with emission theory. What led Einstein to the realisation that the ether was superfluous and space was empty (of ether)? I) Emission theories probably encouraged Einstein to arrive at these realisations.

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II) In April 1901 Einstein told Mariü, "I've begun to have reservations of a fundamental nature about Planck's [1900] studies on radiation" (Einstein to Mariü, April 4 and 10, 1901, CPAE 1, Doc. 96, 97). Einstein's search for an emission theory could be one source for his study of light quanta. In his 1909 lecture, "On the Development of Our Views Concerning the Nature and Constitution of Radiation", Einstein explains "that one can obtain a satisfactory theory only if one drops the ether hypothesis. In that case the electromagnetic fields that constitute the light will no longer appear to be states of a hypothetical medium, but rather independent entitites emitted by the sources of light, exactly as in the Newtonian emission theory of light. Exactly as according to the latter theory, a space not permeated by radiation and free of ponderable matter appears to be really empty" (Einstein 1909b, 487). In his Autobiographical Notes Einstein reasoned that reflections that a radiation must possess – a kind of molecular structure – made it clear to him "as long ago as shortly after 1900, i.e., shortly after Planck's trailblazing work, that neither mechanics nor electrodynamics could (except in limiting cases) claim exact validity" (Einstein 1949, 48-49). In 1955 Einstein wrote to Seelig: "I had already previously recognised that Maxwell's theory did not represent the microstructure of radiation and could therefore have no general validity" (Einstein to Seelig February 19, 1955, EA 39-070). While working simultaneously on the quantum problem (a corpuscular conception of light) and the nature of radiation, and on the electrodynamics of moving bodies, the following question naturally arose: Do the energy and frequency of a light quantum transform in the same way in passing from one inertial frame to another? If not, then the relativity principle would be violated. 12) Einstein seemed to have pondered these problems for an extra year, from 1903 to 1904, almost until the spring–summer of 1904. Einstein discussed Fizeau's experiment using emission theory. He demonstrated, by using Fizeau's celebrated experimental result, why the standpoint of emission theories could not hold true. 13) Toward the spring–summer 1904, Einstein dropped emission theory and returned to Lorentz's theory. The assumption that Lorentz's equations should hold in the reference frame of the moving body led to the concept of the invariance of the velocity of light, which, however, contradicts the addition rule of velocities used in mechanics. Einstein questioned why these two concepts contradicted each other. He realised that this was really

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hard to resolve, and spent almost a year in vain trying to modify the idea of Lorentz in the hope of resolving this problem (Einstein 1922a, 46). In the 1920 manuscript, "Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development", a footnote by Einstein explains that, "the difficulty to be overcome lay in the constancy of the speed of light in a vacuum, which I first thought would have to be given up. Only after years of groping did I realise that the difficulty rested in the arbitrariness of the fundamental concepts of kinematics" (Einstein 1920a, 20). In the spring of 1905, Einstein found the final solution; the "step", which solved his dilemma.

8 "The Step" Pais wrote, "When I talked with him about those times of transition, he expressed himself in a curiously impersonal way. He would refer to the birth of special relativity as 'den Schritt', the step" (Pais 1983, 163).49 When was the special relativity theory conceived? Was it in 1895 when Einstein invented the chasing after a light beam thought experiment? Was it in 1900 during his troubles with the conflict between classical mechanics and the constancy of the velocity of light? Did it occur when he propounded the magnet and conductor thought experiment? Or, did it arise when he dropped emission theories and came back to Lorentz's theory? In his Autobiographical Notes Einstein discussed his objections to Newton's theory while he was trying to develop his general theory of relativity. Then, he suddenly addressed Newton directly in one of the most brilliant paragraphs in the Notes (Einstein 1949, 30-33): "Enough of this! Newton, forgive me; you found the only way which, in your age, was just about possible for a man of highest thought – and creative power. The concepts, which you created, are even today still guiding our thinking in physics, although we now know that they will have to be replaced by others farther removed from the sphere of immediate experience, if we aim at a profounder understanding of relationships". Einstein struggled emotionally on two occasions when replacing Newton's concepts: once before 1905, and a second time when he worked on the general theory of relativity. Before 1905, it took Einstein almost five years to replace Newton's concepts. He tried to replace Lorentz first and leave

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Newton intact. Finally, he realised he must replace Newtonian kinematics to arrive at a profounder understanding of the electrodynamics and optics of moving bodies. As mentioned earlier, little is known of Einstein's struggles between 1902 and 1905; however, the previous sections have been an attempt to reconstruct what Einstein, perhaps, could have done during these years. Evidence on Einstein's final step – from May 1905 to June 1905 – toward the breakthrough that led him to the theory of special relativity is available. According to this evidence, it appears that within the five to six weeks after May 1905, Einstein arrived at the solution to his problem above, and was able to complete and submit his paper, "Electrodynamics of Moving Bodies" for publication. Einstein confronted a new problem after he gave up on ether. According to the Maxwell-Hertz equations, there exists one inertial reference frame in which the speed of light is constant regardless of the motion of the light source. If there is no ether to single out this inertial frame, then Einstein’s principle of relativity requires that it must hold in all inertial frames. Einstein realised that the ordinary Newtonian law of addition of velocities was probably problematic ("Newton, forgive me"): In all of his struggles with an emission theory as well as with Lorentz’s theory, Einstein had been assuming that the ordinary Newtonian law of addition of velocities was unproblematic. However, if the Newtonian addition law of velocities was correct then there would only be one inertial frame in which the velocity of light was constant and independent of direction. This violated the principle of relativity and supplied Einstein with the reason to abandon Lorentz’s theory and resort to an emission theory of light. This law of Newtonian mechanics was based on certain tacit assumptions made about the nature of time, simultaneity, and space measurements. In order to solve the contradictions, Einstein had to abandon the Newtonian law of addition of velocities, and with it the tacit assumptions implicit in this law. He accepted a new law of addition of velocities; in so doing he needed to make new kinematical tacit assumptions about space and time. Einstein constructed a new kinematical theory based on the relativity principle and the light principle, thus resolving the apparent conflict between them.

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In making Lorentz's light postulate compatible with the principle of relativity, Einstein very likely realised the reciprocity of the appearances, which does not presuppose the new concept of time.50

9 Einstein's Steps Toward the "The Step" 9.1 Five to Six Weeks between the Discovery and the Relativity Paper On May 18 or 25, 1905, Einstein wrote the famous letter to his friend Habicht telling him about the four or five ground-breaking papers he was producing, "The fourth paper is only a rough draft at this point, and is an electrodynamics of moving bodies that employs a modification of the theory of space and time; the purely kinematical part of this paper will surely interest you" (Einstein to Habicht, May 18 or 25, 1905, CPAE 5, Doc. 27). The Annalen der Physik received the paper on June 30, 1905. Hence, five to six weeks before completing his relativity paper, Einstein had only "a rough draft" of it. Reiser wrote in his biography of Einstein that, only five weeks elapsed between the discovery of simultaneity and the first formulation of the special theory of relativity in the relativity paper (Reiser 1930, 69). In Wertheimer’s book we find similar remarks: Einstein was intensely concerned with his problem for seven years. From the moment, however, that he came to question the customary concept of time, he realised the relevance of simultaneity, and knew this to be the crucial point for the solution; it took him only five weeks to write his paper on relativity (Wertheimer 1916, 169, 183, note 7). In 1952, Seelig asked Einstein: When was the birth of special relativity? In his book Seelig reported Einstein's answer (Seelig 1954, 82, 1956a, 68-69; EA 39-013): 51 "To my question, whether the birth of the relativity theory could be pinpointed to a certain year, as in the case of Planck's quantum theory, Professor Einstein replied to me on March 11, 1952: 'Five or six weeks elapsed between the completion of the conception of the idea of the special relativity theory and the completion of the appropriate publication. This, however, can hardly be considered as a birthday, since previously the arguments and the foundation stones had been prepared over a period of many years, though without bringing the ultimate decision'".

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Thus it would be claimed that five to six weeks before completing his relativity paper, Einstein had a rough draft of the relativity paper. This draft presented a modification of the theory of space and time – very likely the physical definition of simultaneity had already been formulated, and the draft had a purely kinematical part.

9.2 The Einstein-Besso Meeting According to the Kyoto lecture notes Einstein described the final stages of his work on the theory of relativity (Einstein 1922a, 46). Einstein said that by chance a friend of his in Bern (probably Besso, but the notes do not mention his name) helped him out. It was a beautiful day when he visited him with the problem. Einstein started the conversation with his friend: "Recently I have been working on a difficult problem. Today I come here to battle against that problem with you". Einstein and his friend discussed every aspect of this problem. Suddenly, Einstein understood where the key to his problem lay. The next day he came back to him again and, without even saying hello, said "Thank you. I’ve completely solved the problem". An analysis of the concept of time was his solution. "Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity". With this new concept, Einstein could resolve all the difficulties completely for the first time. Within five weeks the special theory of relativity was completed. Toward the end of 1903 a vacancy for a "technical expert second-class" examiner in the Patent Office was advertised. Einstein immediately drew Michele Besso's attention to the role and the latter joined the Patent Office on March 15, 1904. On the same day, Einstein and his wife Mileva gave up their apartment at Kramgasse 49 in the old city centre, and moved to Besenscheuerweg 28 in the Mattenhof district on the city's outskirts. They moved to be closer to Michele Besso and his wife. The two, Einstein and Besso, would walk to and from the Patent Office together. Besso and Einstein were very close friends; Einstein opened his letter to Besso from June 23, 1918, by saying, "When I see your writing I always have a very special feeling, because nobody is so close to me, nobody knows me so well, nobody is so kindly inclined to me as you are" (Einstein to Besso, June 23, 1918 in Einstein and Besso 1971, letter 43). When Besso died (a month before Einstein's death), Einstein wrote to his late friend's family, "Later, the Patent Office brought us together again. The conversations on the way home were of incomparable charm – it was

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as if the 'all-too-human' concerns did not at all exist" (Einstein to Besso's family, March 21, 1955, in Einstein and Besso 1971, letter 215). Seelig wrote: "The first friend to hear of the relativity theory was the engineer, Michele Angelo Besso". Seelig says that since Einstein and Besso went the same way back home, and Besso was always eager to discuss the subjects of which he knew a great deal (sociology, medicine, mathematics, physics and philosophy), Einstein "initiated him into his discovery". What was this discovery? According to Seelig "The main subject of discussion was the discovery of the light quanta". In endless conversations, Besso, in the role of a critical disbeliever, defended Newton's recognised time and space concepts, into which he wove Mach's sensualistic positivism, and his analytical criticism of Newtonian mechanics. This did not bother Einstein, because Besso was the best "sounding-board in the whole of Europe" (Seelig 1954, 85, 1956a, 71). On the contrary, Einstein needed someone to defend the conventional Newtonian time and space concepts; only in this way could he realise that these concepts were to be replaced by new ones.

9.3 The Final Discovery within Five Weeks Let us try to find out what could be Einstein's final steps after he had arrived at "The Step". Einstein was about to formulate a draft of the kinematical part of his relativity paper. He explained the main idea of this section to his colleagues from the Patent Office, particularly to Joseph Sauter. Seelig wrote that as to the electrodynamics of moving bodies, Sauter told him that he could still remember "today" (approximately 1952) how Einstein, in the spring of 1905, explained to him in great excitement his discovery of the relativity theory as they walked home together. He gave him his notes, which Sauter criticised with official severity; Sauter pestered Einstein for a whole month with every possible objection without managing to make him the least bit impatient, until he was finally convinced that his objections were no more than the usual judgments of contemporary physics (Seelig 1954, 87-89, 1956a, 73-75). Perhaps Einstein explained to Sauter his discovery at the beginning of May 1905 (at approximately the same time he wrote to Habicht), and gave Sauter his notes (a rough draft of the kinematical part of the relativity paper) around this time. Sauter pestered Einstein for a whole month until, perhaps, the beginning of June.

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Fifty years later, during a radio broadcast of his memories, Sauter said in Flückiger's transcription from the recording "Comment j'ai appris à connaître Einstein" (How I Came to Know Einstein) (Sauter 1960, 156): "Before any other theoretical consideration, Einstein pointed out the necessity of a new definition of 'synchronisation' of two identical clocks distant from one another; to fix these ideas, he told me, 'suppose one of the clocks is on a tower at Bern and the other on a tower at Muri (the ancient aristocratic annex of Bern). At the instant when the clock of Bern marks noon exactly, let a luminous signal leave from Bern in the direction of Muri; it will arrive at Muri when the clock at Muri marks a time noon + t; at that moment, reflected the signal in the direction of Bern; if on the moment when it returns to Bern the clock in Bern marks noon + 2t, we will say that the two clocks are synchronised'. After having defined what he meant by simultaneity of two instantaneous events produced in two distant points, Einstein defined the two principles on which he based all the calculations of his new physics".

In the same book where Sauter's memoirs are found (Flückiger's Einstein in Bern), Flückiger writes that the first friend to become acquainted with the theory of relativity in Bern was Einstein's colleague Michele Besso. The other two friends from the Patent Office, Dr Sauter and Lucian Chavan were also introduced to the revolutionary discovery. Flückiger also writes that Sauter remembers his joint walks with Einstein, and how excited Einstein was with the new discovery (Flückiger 1974, 102-103).52 After reading Sauter's account, we can conclude that at the beginning of May 1905 Einstein explained his new discovery to Sauter, he then gave him the contents of his notes to read. These were presumably rough drafts of the kinematical part of the relativity paper, and included the definition for distant simultaneity that would appear in Section §1 of his paper. Einstein explained to Sauter the meaning of this definition. Subsequently, he defined the two principles of his new kinematics. We can therefore guess that by the time Einstein spoke with Sauter – and explained to him the thought experiment of two clocks, his definition of distant simultaneity, he had already written the kinematical part of his 1905 relativity paper. This happened sometime in June 1905. We concluded that at the beginning of May 1905 Einstein explained his new discovery to Sauter who said: "Before any other theoretical consideration, Einstein pointed out the necessity of a new definition of 'synchronisation' of two identical clocks distant from one another" (Sauter

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1960, 156). In a letter from April 14, 1952, to Seelig, Solovine includes Poincaré's 1905 La valeur de la science (Value of Science), in a less complete list of the readings of the Olympia Academy (CPAE 2, xxiv). Value of Science was published in March 1905. Value of Science included Poincaré's 1898 paper "La mesure du temps" (The Measurement of Time) (Poincaré 1898a) as Chapter II, but in a revised form. In addition, Poincaré's 1904 Saint Louis talk "L'État Actual et l'Avenir de la Physique Mathématique" (The Present State and Future of Mathematical Physics) (Poincaré 1904) was comprised of Chapters VII to IX of this book (Poincaré 1905a, 41-54, 123-147). In the first paper, Poincaré cited the synchronisation of clocks by telegraphic signals for longitude measurements. In the second paper he gave a physical interpretation of the local time in terms of clock synchronisation by light signals, and formulated a principle of relativity. Could Einstein have read Value of Science before submitting his relativity paper in June 1905, five to six weeks before completing his relativity paper? In 1904, Habicht left Bern; Solovine left a year later. Following Habicht's departure, the Olympia Academy ceased to exist (Hoffmann and Dukas 1973, 38-39). This was most likely the reason why Poincaré's Value of Science was not on the reading list. Einstein could certainly have read Poincaré's book. However, since he did not mention this book he either did not read it or perhaps he read it later.

10 Biographical Sketch of Poincaré Dr Édouard Toulouse describes Poincaré as follows (Toulouse 1909, 140):53 "M. H. Poincaré is a man of size (1.65) And body size (70 kilos with clothes) Medium bent, slightly prominent belly. Coloured face, large red nose. The hair is brown and the mustache is blond".

Tobias Dantzig recalled that he saw Poincaré often between the years 1906 and 1910, as a student at Sorbonne. Dantzig remembered his unusual eyes: myopic, yet luminous and penetrating. He describes Poincaré as a man small in stature, stooped and ill at ease, as it were, in limb and joint. This

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last impression was accentuated by his manner of writing on the blackboard. His penmanship was very bad, and his draftsmanship even worse. Poincaré was ambidextrous, Dantzig recalls a remark of a fellowstudent to the effect that "Poincaré could use either hand with equal ease and dexterity" (Dantzig 1954, 2).54 On October 13, 1910, at a meeting of the Berlin Scientific Association, Poincaré gave a lecture, Die Neue Mechanik (New Mechanics), in the rooms of the institute 'Urania'. Alexander Moszkowski was among the people who attended the lecture (Moszkowski 1921a, 15, 1921b, 1; Poincaré 1910): "An audience of rather meager dimensions assembled. I still see him before me in my mind's eye, a scholar who was snatched away in the prime of his creative period, a man whose external appearance did not suggest the light of genius, and whose carefully trimmed beard reminded one rather of the type of a practicing barrister. He walked up and down the platform, accompanying his speech with gestures marked by an easy elegance. There was no sign of an attempt to force a doctrine. He developed his thesis, in spite of the foreign language, in fluent and readily intelligible terms. It was at this lecture that we heard the name Albert Einstein pronounced for the first time [In diesem Vortrag geschah es zum erstenmal, daß wir den Namen Albert Einstein hörten]".

10.1 A Mathematics Monster Poincaré was born on April 29, 1854, in Nancy, a town in the Lorraine County in France. He was born in the Hôtel Martigny, an apartment building that still exists at the corner of Grande Rue and Rue de Guise. Today, this building has been transformed into a pharmacy. Poincaré had only one sister, Aline, a few years younger than him. Poincaré’s family was well known in Lorraine. His grandfather, on his father's side, Jacques-Nicolas, was a pharmacist. His father, Léon, a neurologist, a professor at the Faculty of Medicine, and his uncle, Antoni, graduated from the École Polytechnique (Polytechnic School). He was an inspector of roads and bridges; he had two sons, Lucian and Raymond. The first was to be a physicist and then a rector of the University of Paris. Raymond was prime minister and minister of foreign affairs and then the president of the French Republic between 1913 and 1920. In 1895, Poincaré’s younger sister married the famous moral philosopher, Émile Boutroux, with whom Poincaré used to discuss philosophical problems. Their son, Pierre, was a mathematician and philosopher. Henri’s mother,

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Eugénie Launois, came from a family of gentlemen farmers in Arrancy. She was twenty-four years old when Henri was born, and he resembled her in several physical characteristics (Toulouse 1909, 15-17; Mawhin 2004, 2). Frédéric Masson states that Poincaré used to say that his family name was in fact Pontcaré (Lebon 1912, 6).55 When Poincaré started to talk at age nine months, his family realised he was a prodigy (Toulouse 1909, 21). Alternatively, it is noteworthy that Einstein's parents were worried because he started to talk comparatively late. Einstein could not tell how old he was at that time, "but certainly not younger than three" (Hoffmann and Dukas 1973, 14). Masson probably heard the following story from one of Poincaré's relatives: One evening, when only nine months old, as darkness fell, Poincaré's eye caught a star and he called his mother's attention to it; as others shone out he espied them and became excitedly intent in his search for others, so much so that he was with difficulty quieted, and brought into a mood for sleep. In this, one may choose to see a presage, writes Alfred Delury (Lebon 1912, 7; Delury 1912, 310).56 On the basis of Masson's report (Lebon's biography) (Lebon 1912, 7-8), Delury continued that at the age of five a serious illness threatened, for a time, to deprive Poincaré of the power of speech; it left him weak, and intensified in him a certain native shyness. Illness had a maturing influence on the child Poincaré (Delury 1912, 310). Dr Toulouse explained that the illness was a serious diphtheria paralysis of the soft palate and paraplegia, which lasted for three months. For two months, as a result of this paralysis, Poincaré had trouble speaking. Two years after the infection, he still felt dizziness when descending stairs (Toulouse 1909, 21-22). At six, Poincaré could read and probably write. Poincaré told Toulouse he believed that at that age he easily learned to count. Masson said: "I was told" that Poincaré was a tender and shy child, he preferred the company of his sister upon playing with other children, and he was never drawn to violent sports. Poincaré used to invent games for his sister and his cousins. He received an emeritus teacher who came home, and was a friend of the family. The private teacher taught Poincaré a few subjects, gave him early mathematical skills, which immediately interested him. Poincaré was asked by his teacher to complete written assignments, and he had conversations with him about everything. This teaching was so

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encyclopedic that it was appropriate to Poincaré's nature (Lebon 1912, 8; Delury, 1912, 310; Toulouse 1909, 23). Einstein, at age five or six, also preferred to play with his sister at home and refrained from joining the boisterous games with children of family and relatives; he occupied himself with quieter activities, and he would play by himself for hours. By apparent contrast to Poincaré, Einstein was not as tender. As stated earlier, at the age of five or six, Einstein – who also received his first instruction at home from a female teacher – once grabbed a chair and stroked it at her. Frightened, she ran away and was never seen again (Winteler-Einstein 1924b, lxvi, 1vii, 1924c, xviii). Stories like these reflect Einstein's rebellious temper and lack of obedience. Poincaré entered the Lycée (secondary and high school) of his native city, Nancy, at the age of nine. He stayed there for eight and half years and finished ninth in 1871. Poincaré came well-prepared on October 1862 to the Lycée, was one of the top students and was superior to his fellow students in all branches, exhibiting unusual ability in mathematics. The Lycée was later renamed the Lycée Henri Poincaré (Delury 1912, 310; Lebon 1912, 8; Toulouse 1909, 23-24). When Einstein was nine, he was not considered extremely talented (of course, he was very likely more talented than the rest of the pupils in his class). Teachers at school did not fully appreciate Einstein because of his lack of obedience and discipline. As a student of languages, he was only mediocre. He hated the burden of so much memorising and did not show the slightest talent for rote learning, which the study of classical languages called for (Frank 1949, 23, 1947, 10; Reiser 1930, 37). Einstein refused to learn topics in which he was weak and did not excel. By apparent contrast to Einstein "in practical life" Poincaré "showed discipline, and this is an essential element of his character" (Toulouse 1909, 140). When Poincaré read a whole treatise of geometry alone, his astonished teacher ran to tell his mother, "Your son will be a mathematician" (Lebon 1912, 8; Delury 1912, 310). Masson's above description of Poincaré was greatly exaggerated by Delury saying that each year of Poincaré's work at the Lycée strengthened the faith in this prediction (Delury 1912, 311). Delury might have heard this and other stories as myths spread among mathematicians in conferences.

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Alternatively, Einstein’s Latin teacher told him that nothing would turn out of him; his other teachers also found his lack of obedience annoying (Seelig 1954, 15, 1956a, 12). One professor Weber thought that Einstein would become a great physicist. Alas, it lasted only a short time. In October 1895, when Einstein sat the entrance examinations for the Zurich Polytechnic, Weber invited him to attend his college physics lectures, provided he remained in Zurich. Fairly soon afterwards Weber was disappointed with Einstein's rebellious character. Poincaré (who showed discipline) enjoyed success quickly, while Einstein's defiance of authority explains why his success did not come so easily (Einstein 1955, 9; Winteler-Einstein, 1924b, 1xv, 1924c, xxii). Early at school Poincaré was attracted to physics and natural sciences, but his gift as a mathematician began even earlier (Toulouse 1909, 28; Lebon 1912, 8). He began to read mathematical books intended for specialists. From childhood, he found arithmetic easy. Early on in school he began reading popular science books, and more serious books later. He took great pleasure in listening to music; he even learned to play the piano, although he was not very good. In writing and drawing Poincaré was unsuccessful. Toulouse asked Poincaré to draw and sketch all sort of things – geometric figures, faces, figures, and so on. He said that Poincaré was not talented in this direction. Indeed, the drawings in Toulouse's book disclose Poincaré's lack of talent (Toulouse 1909, 24, 26, 142). It is a well-known fact that Einstein was a lover of music. Milana Bota (who lodged with Mileva Mariü at the pension) wrote to her parents that Einstein "plays violin beautifully, he is a real artist" (Popoviü 2003, 3-4); but Einstein was not a professional violinist. Further, Einstein was fascinated with popular science books from an early age. Max Talmud gave Einstein, as reading material, Bernstein's Popular Books on Physical Science. Subsequently, Einstein began to read mathematical books intended for specialists; "for mathematics, however, he showed a great predilection" at the age of thirteen and because of this, Talmud gave him Spieker's textbook on geometry (Talmey 1932a, 163, 1932b, 69). Poincaré learned regularly for competitions, and he learned faster than other students. He won first prize in the concours général (a competition between students from all French Lycées). His professor at Nancy is said to have referred to him as a "monster of mathematics" (Toulouse 1909, 24; Dieudonné 1970-1990).

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Unlike Einstein, Poincaré learned languages easily. Toulouse says that he learned German in the Lycée, even though he did not speak it at home. Poincaré learned German during the war and German occupation of Nancy, and also during his three-month stay in Austria in 1887 (Toulouse 1909, 24-25). Delury reports that it was while Poincaré was still in the Lycée that Nancy was occupied by the Germans. During this time Poincaré, aged sixteen, accompanied his father (who was a physician) in his ambulance and assisted him with caring for the sick and wounded. Poincaré learned German during this time by reading German newspapers and bulletins (Delury 1912, 311; Lebon 1912, 9-10). Dantzig also reproduced the same story, which he probably read in Delury's sketch. However, Dantzig added the following anecdote: During the occupation, Poincaré taught himself to read German. In fact, he learned the language so well that he could read German newspapers fluently. In this way, he managed to stay abreast of events and to brief his friends during the period when French journals were banned. In the years to come he kept up his German studies, and it may be said without exaggeration that no Frenchman had a better knowledge of German mathematical and physical literature than Poincaré (Dantzig 1954, 4). One of Poincaré's earliest mathematical achievements was a generalisation of the so-called elliptic functions. He could have called these functions ultra-elliptic, or pan-elliptic: he chose instead to call them Fuchsian, in honour of the German, Lazarus Fuchs, who had indicated their possibility without proving their existence. This homage must have raised many French eyebrows, as evidenced by an epigram which Dantzig heard twenty years later. This would read in free translation: "The only Fuchsian claim to fame is that a French discovery bears his name". These protests did not disturb Poincaré. A few months later he presented the French Academy of Sciences with a new discovery which he called Kleinean Groups, honouring the German mathematician, Felix Klein. There were several similar incidents where, it seemed, Poincaré had been leaning backwards to pay homage to German scientists; the most striking of all occurred at Göttingen in 1909, when Poincaré delivered a series of six lectures, five of these in German. However, the sixth lecture discussing the principle of relativity was delivered in French! (Poincaré 1909, 41-47). By age fifteen Poincaré began to study English. During a visit to England he tried to read signs. Upon his return, he began to methodically learn English, followed later with an English course at the École des Mines (the school of Mines) (Toulouse 1909, 25).

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Poincaré graduated school in November 1871, where he had completed a Bachelor of Letters and Bachelor of Sciences. At age eighteen, he was asked by Dr Toulouse about his opinion on religion. Poincaré replied that he had first believed in religion and then he gradually came to doubt it. By eighteen years old, he had stopped believing in religion. At that stage he was a free thinker, he believed in the right to search and tell the truth, and for that reason he opposed clerical (Catholic) intolerance. There are common points between Poincaré's and Einstein's attitude to religion. When Einstein was twelve-years-old, a deep, religious feeling was awakened in him after he received Jewish religious instruction by a distant relative. However, a year later, he regarded ritual customs as superstitious usages, preventing man from thinking independently. There arose in Einstein an aversion to Jewish Orthodox practices or any other traditional religion, as well as to attendance at religious services, and this he never lost (Winteler-Einstein, 1924b, 1x, 1924c, xx; Frank, 1949, 2829, 1947, 14-15).

10.2 Henri Poincaré and Paul Appell After graduating the Lycée, Poincaré entered a preparation class in mathematics for the concourse examinations to the grandes écoles (French great schools) of Paris. On December 22, 1912, a few months after Poincaré's death, his close friend Paul Appell sat down to write the following memorial sketch on their close friendship in Nancy during the preparation class for the concourse examinations to the grandes écoles of Paris. In this sketch Appell tells in all sincerity his recollections, but his stories often sound like hero-worship to Poincaré, and as such are sometimes exaggerated. In fact, Poincaré was so brilliant in mathematics that his friends exaggerated when telling stories about his mathematical abilities. And so Appell's report reveals that Poincaré's friends were immensely impressed with his exceptional mathematical abilities and knowledge. For instance, Appell said that Poincaré won the first prize in the elementary mathematics concourses competitions; he was the only one to solve the final year problem given by the École Polytechnique (Polytechnic School) (Appell 1912, 190). Paul Appell starts his report by describing the meeting with Poincaré (Appell 1912, 189). After Easter, Paul's mother sent him from Strasbourg to Nancy, to participate in the preparatory class for the École

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Polytechnique. He arrived as an inexperienced, young student to Mr Pruvost's class. In the beginning of October the special class was assigned to one of the most distinguished young professors, Elliot, a mathematician whose value had an effect on all students. From the very first class, one of his classmates, pointing to Poincaré, stated: "This is a very strong type, he will be accepted second to the École Forestière", meaning strong in learning, because the School of Forestry was prestigious among the students of Nancy.57 Appell also recalls that Poincaré's appearance stood out. At first glance, he was not the ordinary type of intelligent student. He seemed to be absorbed in inner thoughts, with his eyes somewhat obscured by reflection. When he spoke, his eyes sparkled with an expression of kindness, which had both a malicious and deep expression. Appell felt drawn to him as they were both outsiders; they exchanged a few words when going out the class. Appell was struck by his manner of speaking: short, a little choppy, and interspersed with long silences. Appell recalls that it was obvious that, from the first questions in class, his superiority appeared to shine. He answered questions by eliminating intermediate explanations, with short and concise answers, answers that the teacher always asked him to develop. The teacher used to tell him: "If you answer this way in the examination, you might be misunderstood". Appell remembers that he and Poincaré used to talk when leaving class, and very quickly became attached to each other (Appell 1912, 190). Einstein's superiority in class also shone, and the students (but not his experimental physics teacher Jean Pernet) immediately appreciated his superiority. Einstein the rebel solved problems by eliminating Pernet's explanations. As mentioned, Margarette von Uexküll, Einstein’s fellow student, gave him her laboratory notes so that he could cook up some better results.58 Appell describes his walks with Poincaré through Nancy's streets back from class to their homes with two additional friends. On their way they used to converse on geometry and philosophy. Appell remembers how much Poincaré had read – Joseph Bertrand's algebra, Jean-Marie Duhamel's analysis, Michel Chasles' higher geometry and the geometry of Eugène Rouché. With great simplicity and loyal friendship Poincaré provided his fellow students all the information and explanations they asked for.

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Poincaré had synthetic distinctions for problems, so when the professor requested the locus of points, where we see an ellipse at a given angle, Poincaré immediately supplied the answer. Likewise, in problems of analytic geometry he often gave very elegant geometric solutions. His composition was not only ranked first among the entire compositions in all departments in Paris, but was especially notified by the examiners. When the examinations approached, Poincaré's teacher showed growing concern that Poincaré would give answers that were too elliptical, which might seem obscure to reviewers. Indeed, Appell reports that, at the École Normale Supérieure's (Normal Superior School) concourse in Paris there was an amusing incident with Poincaré. Qualified applicants were required to sketch geometric descriptions during the oral examinations pertaining to their oral answers. Poincaré was disinterested and bored by tracing mathematical lines and making careful designs, he preferred, after receiving all the data, to search for the equation of the horizontal projection of the intersection of curves. Hence, he found the curves with a perfection unattained by those who used conventional constructions. However, when drawing these on his sheet, something distracted him and he reversed the drawing by 180°. The examiner was very intrigued by this solution, which was both inaccurate and perfect (Appell 1912, 191-194). Appell recalls that this examiner, "already dead today" (in 1912) thought that Poincaré expressed himself badly and that he would not make a good professor, "so he gave him such a low grade that, to our amazement, he was ranked fifth at the École Normale Supérieure; a strange fate for a genius who cannot meet the classifications of ordinary men!" Appell also mentions the story of the famous mathematician, Évariste Galois, who was denied entrance to the École Polytechnique, after arguing with his examiner on logarithms and then producing the right answer (Appell 1912, 193). Einstein's teacher, again Jean Pernet, gave Einstein the lowest possible grade in his course "Introduction to the Practice of Physics – Elementary Practice of Physics". He told Einstein his work lacked capability, physics was difficult, and advised him to study medicine, law or philology instead (Seelig, 1954, 47, 1956, 40-41).59 Between August 4 and 6, 1873, following their oral examinations at the École Normale Supérieure, Appell and Poincaré returned to Nancy to write their compositions for the École Polytechnique. Upon arrival, they found the city in celebration – flags everywhere, on all the houses,

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vehicles, wagons of milk, and vegetable carts. The German troops had left, more specifically, while they went to write their compositions, the first troops from the French army entered Nancy. Poincaré became nervous from excitement and was eager to join his family in Hôtel de Ville (City Hall) where they awaited the arrival of the French troops on the Place Stanislas. As a result of all the excitement, Poincaré fared poorly in his composition, not only was it an exercise in which he did not excel, but he also stuck his paper too quickly and stuck the layers of papers with Chinese ink too rapidly before the previous ones were dry. Appell recalled that while they were preparing for the oral examinations, Poincaré, as a service, was willing to question his friends. He took the sheets of examinations and, while imitating the intonations and habits of the examiners, accidently stuck the sheets with glue. Subsequently, he examined the candidates by providing them with different oral problems and drawings to solve. Appell recounts, "I can still see him saying, tonguein-cheek, to a candidate, a nearby colleague, terrified by this revelation, that the examiner Moutard asked about the properties of the rotation of the Limaçon of Pascal". Finally, after very successful examinations, and a particularly remarkable examination in geometry, Poincaré was accepted to the École Polytechnique – in first place. Appell and Poincaré met again next fall in Paris; Poincaré was at the École Polytechnique, and Appell at the École Normale Supérieure (Appell 1912, 194-195).

10.3 The École Polytechnique The École Polytechnique was created in 1794 and originally called École central des travaux publics (Central School for Public Works). Since its foundation, it was reputed for attracting great mathematicians among its staff. For instance, in 1797 Joseph-Louis Lagrange taught the "Theory of Analytical Functions", Jean-Baptiste Joseph Fourier and Augustin-Louis Cauchy were also professors at the École Polytechnique. When in 1873 the young Poincaré entered the prestigious École Polytechnique, its mathematical tradition resounded throughout Europe. Nevertheless, Göttingen enjoyed the most prestige as a place to study mathematics, thanks to Carl Friedrich Gauss and his students Richard Dedekind and Bernhard Riemann. Still, the École Polytechnique was considered the best institute in France. It produced a fraternity of alumni who were mathematicians and engineers that were called "Polytechnicians"; they received the best education in mathematical physics or mathematical

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technology. After their graduation they joined the highest levels of the state's administrative structure (Bottazzini 2000, 35-36; Galison 2003, 50). At that time, in 1874, the well-known philosopher Émile Boutroux arrived at the University of Nancy. There, he met Poincaré's sister, Aline Poincaré. They married in 1875. Poincaré and Boutroux enjoyed discussing philosophical problems. Boutroux introduced Poincaré to philosophical writings as well as his friends, philosophers, and colleagues. Einstein was also drawn to the mystery of philosophy. At age thirteen he often discussed philosophy with Max Talmud, who also introduced him to Kant's writings (Talmey 1932b, 69). Poincaré was so brilliant in mathematics that people exaggerated his exceptional mathematical abilities; for example, Toulouse wrote that "Poincaré, so it seems, took no notes at all in the courses of mathematics at the the École Polytechnique". Masson tells a similar story: "It is said that you followed your courses, at least in mathematics, without taking notes, without writing anything of what the professors were saying". Hence, this story was probably known among Poincaré's students and colleagues (Toulouse 1909, 99; Lebon 1912, 10). Poincaré’s science professors at the École Polytechnique were Charles Hermite (Analysis), Marie Alfred Cornu (Physics), Louis-Jean Résal (Mechanics), Amédée Mannheim (Geometry), Hervé Faye (Astronomy) and Edmond Fremy (Chemistry). Poincaré's two most influential professors were Hermite and Cornu (Walter 1996, 4). Hermite was a professor at the École Polytechnique for a short time, between 1699 and 1876. He taught Analysis, a first year course, and the first course that Poincaré later gave when he started his academic career in 1879. Hermite also delivered the course on differential geometry, and this topic became one of Poincaré's favourites. In addition, Hermite supervised Poincaré after he graduated (Bottazzini 2000, 36). In lectures given by the young physicist Cornu, Poincaré was exposed to the fundamentals of the wave theory of light, including the problem of ether drag and the solution offered by Fresnel’s drag coefficient. According to a retrospective account, Poincaré designed and executed an optical experiment to demonstrate the translation of the Earth with respect to the luminiferous ether (Walter 1996, 6).

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While a student at the Zurich Polytechnic Einstein also performed an ether drift experiment. Einstein wanted to construct an apparatus to accurately measure the Earth's movement with respect to the ether. However, he was unable to do so because Weber’s scepticism was too great (Einstein, 1982, 46; Reiser 1930, 52). It was thus probably a custom in those days among students to perform such experiments as part of the training in school laboratory. In 1875, Poincaré graduated the École Polytechnique with exceptionally high grades; he ranked second among the hundreds of students. He could have easily finished first if not for his weak drawing skills. Poincaré told Dr Toulouse (as reported by the latter) that he had ranked first when entering the École Polytechnique and then he graduated second (Toulouse 1909, 28; Lebon 1912, 11).

10.4 École des Mines During the second year of his studies, Poincaré chose to continue his studies after the École Polytechnique, at École des Mines (the School of Mines). The top-ranked graduates of the École Polytechnique almost invariably chose to continue their studies at this institution. There they studied three years towards a technical or administrative career in Mines. After three years of learning, graduates of the School of Mines were assured high-profile careers with excellent pay and social advantages; yet those who went on to become mine inspectors did so at great risk (Walter 1996, 4). After graduating with such an impressive rank, Poincaré naturally decided to continue on at the School of Mines. This is curious because Toulouse wrote about Poincaré, "He does not have the gift of mining" (Toulouse 1909, 142). Nevertheless, Poincaré chose this direction and not the competing technical school, École des Ponts et Chaussées (School of Civil Engineering), from which Antoine Henri Becquerel graduated in 1894 (Walter 1996, 4). One of Poincaré's professors at the School of Mines was Alfred Potier. He gave a general physics course to prepare students for the special entrance examinations (Poincaré 1905f, 282). Potier graduated the École Polytechnique like Poincaré, but a few years before him, in 1859. He followed the French tradition and continued straight to the School of Mines. However, unlike Poincaré, Potier was

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attracted to mineralogy, geology and mining engineering. He made numerous field studies in mining and was an inspector general until his retirement. He remained attached to the geological survey. Potier's favourite work, and on which his reputation grew, consisted of mathematical and experimental physics. He studied the theory of heat, the theory of optics, the theory of light, and electricity. In this respect, he had a lot in common with Poincaré. He considered the theoretical aspects of electricity, as well as the industrial aspects of the topic; but Poincaré was also interested in the technical aspects of electromagnetism when writing on Hertz's experiments with his antennas and spark gap detectors and receivers. Yet, even when Poincaré considered the applied aspects of electromagnetism, he did it as a mathematical physicist. On the other hand, Potier was more technical than Poincaré, who was destined to be a mathematician. In 1893, Potier held the chair of industrial electricity at the School of Mines, while Poincaré would later hold the chair of mathematical physics in Paris. By 1881, Potier was also a professor of physics at the École Polytechnique, at the same time that Poincaré was a professor in Paris. Potier died in 1905.60 The study of mathematics was not part of the curriculum at the School of Mines. Poincaré's notebooks from this period are filled with hundreds of doodles, suggesting a certain lack of concentration and interest in the courses (Walter 1996, 4). By contrast, Poincaré studied geology and went on excursions. Masson said that Poincaré inherited a passion for travelling from his father. As a student at the School of Mines he travelled to Austria and Sweden, parts of Europe, Africa and America; during these trips his companions noticed his excellent knowledge – from statistics to history, and even the curious customs and habits of peoples (Lebon 1912, 11). While studying at the School of Mines, Poincaré also received his diploma in mathematics from the Faculty of Science of Paris in August 1876. On March 28, 1879, he graduated the School of Mines. During the last two years at the School of Mines, Poincaré prepared his PhD thesis in mathematics, while studying the works of mathematicians on his own. He defended his thesis on August 1, 1879, at the Faculty of Science in Paris; the jury included Pierre Bonnet, Jean-Claude Bouquet and Jean-Gaston Darboux. Darboux's report was very positive about the results and the methods, but was far less enthusiastic about the clarity of

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the style. In 1879, Poincaré was awarded a doctorate in mathematics from the University of Paris. Poincaré's doctoral thesis was intended to improve a method for solving partial differential equations that had been suggested some years earlier by Cauchy (Walter 1996, 4; Mawhin 2004, 3; Miller 1996, 343).

10.5 An Academic Career: Faculty of Science in Caen Poincaré's academic career started in the Faculty of Science in Caen between August 1879 and October 1881. On April 20, 1881, just before leaving, Poincaré married Louise Poulain d'Andecy. They had three daughters, Jeanne, Yvonne, Henriette, and then one son Léon. Poincaré started to exhibit his talent for writing papers one after the other. He sent more than twenty notes to the Comptes Rendus de l’Académie des sciences de Paris (Proceedings of the Academy of Sciences of Paris), dealing with three completely different topics: the arithmetic of forms, the qualitative theory of differential equations, and Fuchsian functions (Mawhin 2004, 4-5).

10.6 Professor at the Faculty of Sciences in Paris In the fall of 1881, Poincaré moved to Paris; there he stayed until his premature death. His career and fame grew rapidly in France, and gradually worldwide. He was named to the Faculty of Sciences in Paris as Maître de conférences d'Analyse (Senior lecturer in Analysis), and in 1883 the duties of Répétiteur d'Analyse (Lecturer in Analysis) at the École Polytechnique were added. In 1885, he became Chargé du cours de mécanique physique et expérimentale (Lecturer on Physics, Mechanics and Experiment) at the Faculty of Sciences, and the next year, he was appointed to the professorship of mathematical physics and the theory of probability. In the same year, he was also appointed a professorship in celestial mechanics. As professor of mathematical physics, Poincaré, year after year, chose a new subject for his courses and dealt with the outstanding questions in the different branches of physics. His choice of topics included hydrodynamics, thermodynamics and kinetic theory, optics, electrodynamics, Maxwell's theory, and Hertz's experiments (and other topics from the forefront of fin de siècle physical science) (Delury 1912, 313-314).

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Poincaré had taught electromagnetism at the Sorbonne, the École Polytechnique and the École supérieure des Postes et Télégraphes (Superior School of Post and Telegraph). Between 1889 and 1899 he taught the works of Maxwell, Helmholtz, Hertz (the 1884-1890 interpretation of Hertz to Maxwell's equations), Larmor, Lorentz, and others in courses such as, Électricité et optique and Théories électrodynamiques. A favourite topic for Poincaré was Hertz's experiments with sparks; Hertz's detector and transmitter and propagation of electromagnetic waves, and the possibility of wireless telegraphy (Les théories de Helmholtz et les expériences de Hertz) (Poincaré 1889, 1890, 1891b, 1892b, 1894b, 1894c, 1901). Poincaré exchanged many letters with Heinrich Hertz on the topic of radio waves. The first letter to Hertz is dated August 15, 1890. Poincaré was excited by Hertz's experiments, but he found a calculation error in Hertz's paper published in the Wiedemann's Annalen der Physik und Chemie. He wrote to Hertz and explained the error to him (Poincaré to Hertz, August 15, 1890, Walter et al 2000, 184-184, letter 30.1). Hertz immediately replied, "Mister and most distinguished colleague, the error you have discovered is truly unpleasant". Hertz told Poincaré that Oliver Lodge proposed a competing experimental approach to his own method (Hertz to Poincaré, August 21, 1890, Walter et al 2000, 186, letter 30.2). Poincaré approached Hertz again two weeks later on September 11, 1890. He told Hertz that he included his experiments in the volume containing his lessons from 1888, and that this latter volume provided teaching standards (Poincaré to Hertz, September 11, 1890, Walter et al 2000, 187, letter 30.3). This was considered a great honour, because Poincaré's volumes of lessons were indeed the authorised textbooks in France, and they determined the teaching standards in mathematical physics. The lectures were mostly written by Poincaré's students; afterwards, he corrected and edited them. Subsequently, these lectures were published in volumes, and he updated them according to new studies and innovations such as for instance, new information provided by Hertz to Poincaré through their exchange of letters. Poincaré also asked Hertz some questions. Hertz immediately replied to Poincaré on September 22, 1890. Hertz understood Poincaré's questions and actions as an important support for the views of Faraday and Maxwell. Two weeks later, Poincaré replied to Hertz. Poincaré asked additional questions in regard to Hertz's experiments. He wanted to include them in

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the volume of lessons that he was currently publishing – papers on Hertz's experiments – and he was considering the theory of telegraphy, which implemented Hertz's equipment. Poincaré therefore wrote to Hertz: "Will you allow me now to ask additional questions?" He asked Hertz additional technical questions on his experiments (Poincaré to Hertz, October 8, 1890, Walter et al 2000,189, letter 30.5). Hertz sent Poincaré a very long letter answering all his questions. In this letter he explained with sketches the procedure, difficulties at the moment of writing the letter, the errors for which he did not know their causes, and the subtleties of his experiments (Hertz to Poincaré, October 19, 1890, Walter et al 2000, 192-195, letter 30.6). Poincaré and Hertz continued to exchange letters on Hertz's experiments until the end of December 1891. On December 30, 1891, Hertz sent Poincaré the final letter (Hertz to Poincaré, December 30, 1891, Walter et al 2000, 202, letter 30.15). Louis De Broglie recalled in 1951 that all the young people in Poincaré's generation who were interested in mathematical physics (he remembered that there were few), were fed by Poincaré's textbooks. The teaching of mathematical physics at the Sorbonne was also based on Poincaré's books. Paul Langevin did not publish his courses (de Broglie 1951, 45). Like Poincaré, Einstein was also interested in Maxwell's theory. However, in German speaking countries Maxwell's ideas were accepted more slowly. Helmholtz (Weber's mentor) was the first to embrace Maxwell's ideas. In 1896, when Einstein enrolled in the Zurich Polytechnic, Maxwell's theory was not yet on the school's official programme. Einstein, the free-thinker, felt that the most fascinating subject at the time that he was a student was Maxwell's theory (Einstein 1949, 31).

10.7 The Bureau des Longitudes Beginning in January 1893, and until his death in 1912, Poincaré served at the Bureau des Longitudes (Bureau of Longitudes) in Paris. It was a natural continuation to his adventurous love for geological excursions and navigations, which he had undertaken during his studies at the School of Mines. In September 1899, about a year and a half after he published his well-known paper, "The Measurement of Time", Poincaré was elected president of the Bureau, a post he rose to again in 1909 and 1910. One of the main projects of the Bureau of Longitudes was mapping places of areas. Peter Galison reports that the Bureau's publications determining the exact positions of colonies in 1897 were received by Poincaré just before

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he wrote his 1898 paper, "The Measurement of Time" (Galison 2003, 129, 221). Can we compare Einstein sitting in the Patent Office in Bern to Poincaré sitting in the Bureau of Longitudes in Paris? Einstein published his paper "On the Electrodynamics of Moving Bodies" in 1905 (Einstein 1905a) during his tenure at the Patent Office. Poincaré published his paper in 1898, "The Measurement of Time" (Poincaré 1898a) during his term at the Bureau of Longitudes. Galison compares Poincaré and his work at the bureau as a manager, to Einstein's as a clerk at the Patent Office (Galison 2003, 175). Apparently, this comparison is controversial. Martínez says that Einstein might have been inspired by patents of clocks, trains and clock towers that happened to stand within proximity to the Patent Office, as alluded to in Galison's book. However, unlike Poincaré, Einstein himself left no written statement even implying that he became increasingly interested in time because of any timing technologies he may have been exposed to (Martínez 2004b, 226).

10.8 The 1900 Congresses At the turn of the century Poincaré had become one of France's most respected and honoured mathematicians and scientists. His work in mathematical physics was well known and respected in scientific circles. In addition, the general public read his popular publications in science. Poincaré was invited to give keynote lectures in congresses, and whenever people wanted to know the future direction of science they invited him as the sole authority to present a lecture on this topic. He had an unshaken status as the oracle of science, and he won honour and respect from the best universities and received scientific prizes for his contributions. He first filed a request for membership at the prestigious Académie des sciences (Academy of Sciences) in Paris in 1884. However, this was only realised in 1887, and in 1906 he became its president. In 1908 the Académie française (French Academy) opened its doors to him, and he became its president until his premature death in 1912. In 1900 he was already member of 15 foreign academies in Amsterdam, Berlin, Boston, Edinburgh, Stockholm, Copenhagen, Saint Petersburg, Rome, Munich, Washington and the Royal Society of London. Eventually, he became a member of all the principal scientific societies and academies in Europe and the United States (Delury 1912, 311).

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In 1900, Paris hosted a grand event, Exposition Universelle (Universal Exposition). Paris was the centre of art and science in Europe. On April 14, the universal exposition was inaugurated, a grandiose world fair that would last until November that year. Millions of visitors came to this exposition. Governments, industrial firms, entrepreneurs and individual scientists alike participated in the exposition and exhibited and promoted their goods, visions they could offer for other people's futures, and scientific advances. Everything promised enterprise on a scale never before realised. Fair organisers budgeted for a projected sixty million visitors over seven months (Staley 2008, 133). Michelson exhibited his interferometer in the Paris fair. In May 1900, Millikan was dispatched to aid in unpacking, repairing, and setting up Michelson's interferometer. The effort paid off. Michelson was awarded the Grand Prize of the Exposition Universelle Internationale in the University of Chicago exhibit group 1, class 3, Higher Education, Scientific Institutions (Michelson Livingston 1973, 208). As part of the fair, Paris organised hundred and twenty-seven conferences that year dealing with topics such as history of religion, the Second Mathematics International Conference (Poincaré participated in this conference, and was on its organising committee), the thirteenth Medical International Conference, and the International Conference of Electricity (Staley 2008, 167-168). Two additional international congresses that took place during the World Fair that are relevant to this discussion are the congresses dedicated to physics and philosophy. In both congresses, Poincaré was a central figure. The French Physical Society had already begun preparations for the international congress of physics in January 1899 (Staley 2008, 166). The same holds for the other congresses and for that of philosophy. The first international congress of philosophy was held from August 1 to 5, 1900, under the presidency of Émile Boutroux, Poincaré's brother-inlaw, who was at that time professor at the Sorbonne (Lovett 1901, 157). A day after the congress of philosophy ended, Poincaré hurried to the international congress of physics, which took place from August 6 to 12, 1900. The organising committee consisted of Alfred Cornu (the professor from his student days at the École Polytechnique), Louis-Paul Cailletet, Lucien Poincaré (his cousin) and Charles-Édouard Guillaume, and a host of prominent French physicists. At the congress there were many participants from around the world, and there was an exhibition (Staley 2008, 166).

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During the 1900 universal exposition in the philosophy congress, Poincaré's talk, "Sur les principes de la mécanique" (On the Principles of Mechanics) was devoted to mathematics-logic, philosophy and the history of sciences. Poincaré's audience was predominantly mathematicians. The session was directed by Professor Jules Tannery, Boutroux's friend. The papers presented to this section were published a month later in September 1900 in the Revue de métaphysique et de morale and devoted to the congress of philosophy. Among the participants of the session were Bertrand Russell, who spoke on "The Idea of Order and Absolute Position in Space and Time", Giuseppe Peano who talked about "Mathematical Definitions", Jacques Hadamard who spoke about "On Induction in Mathematics", and of course Poincaré who gave the above mentioned talk, "On the Principles of Mechanics" (Lovett 1901, 157-158). On August 6, 1900, Poincaré participated in the International Congress of Physics. He gave the keynote lecture "Sur les rapports de la physique expérimentale et de la physique mathématique" (Relations between Experimental and Mathematical Physics) during the mathematics session. Later that year on December 11, 1900 the twenty-fifth Festschrift anniversary of Lorentz's doctorate was celebrated. Poincaré did not present his Festschrift paper as a lecture but only handed in a manuscript, "La théorie de Lorentz et le principe de réaction" (Lorentz's [Electron] Theory and the Principle of Reaction) (Poincaré, 1900b). Lorentz was offered a collection of papers by friends and colleages, edited by Heike KamerlinghOnnes and Herman Haga. The Festschrift, a special issue of Archives néerlandaises des sciences exactes et naturelles counts 678 pages with 58 contributers by, among others, Ludwig Boltzmann, Max Planck, Henri Poincaré, Lord Rayleigh, Joseph John Thomson and Woldemar Voigt (Kox 2008, 117). In 1900, Poincaré was at his pinnacle; he was the most successful scientist in France, and possible in the whole world. However, Poincaré felt a deep, internal crisis. The contents of his lectures, which he presented at the two international conferences (of physics and philosophy), and the Festschrift paper reveal this crisis as regards to reconciling Lorentz's theory with the principle of relativity and the principle of action and reaction. On September 24, 1904, Poincaré gave a lecture at a congress for arts and science in Saint Louis, titled "L'état actuel et l'avenir de la physique mathématique" (The Present State and Future of Mathematical Physics – later published in Bulletin des sciences mathématiques).

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The astronomer George Ellery Hale (professor at the University of Chicago until 1904) was organizing a world scientific meeting in September 1904 in connection with the International Electrical Congress at the Saint Louis World's Fair. In The Popular Science Monthly Hale described his preparations for the world scientific meeting. He wrote that at the beginning of the twentieth century, the assembling of congresses on various subjects were especially so prominent a feature of great expositions of industry that such gatherings tended to lose interest. The 1904 Saint Louis Universal Exposition decided, at an early stage in their preparations, to make special efforts for bringing together a congress which should be more comprehensive in its scope, of wider interest in its discussions, and of more permanent value as a memorial of the exposition, than the usual conventions of this class. After holding several consultations with eminent scholars, Hale decided that the field of the congress should be as wide as that of science itself. He decided to supplement all the specialties by a discussion of the principles of the more important groups of sciences, and of the methods by which the sciences should be brought together, unified, and made mutually helpful. A general address on the work of the congress was followed by discourses on the inner unity of seven great divisions of knowledge. A necessary condition to success, which was in view from the beginning, was that the leading addresses should be given by the most eminent representative of every branch of science whose attendance at the congress could be secured. This was regarded one of the novelties of the congress, calculated to heighten its interest. Eminent investigators of various countries (one representative of every branch of science) were invited.61 In July of 1904 Michelson received an urgent letter from George Hale: "I sincerely hope you will find it possible to be present […] since it now promises to be a very important [congress …] Poincare is to bring over the views of the French physicists […]". Michelson replied that he would try to come, but September was an inconvenient time. Hale had offered to change the date and place of the meeting to suit him, so important was it, he felt, that Michelson should appear. This was flattering but Michelson thought it unwise to try to change the time or place on his account. Finally, on September 19, 1904, Michelson wrote to Hale that he was exhausted by continued sleeplessness and would not be able to attend the Saint Louis meeting. Hale went to the congress and made the report for him. The meeting proved to be all that Hale had anticipated. Three scientists from the French Academy of Sciences attended the congress: Gaston Darboux, Émile Picard, and Poincaré. It was on this occasion that Poincaré

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told the assembled physicists that, "there are symptoms of a serious crisis, which would seem to indicate that we may expect presently a transformation". He expressed the doubts which the negative result of the Michelson-Morley experiment had created in the minds of many physicists: "Michelson carried precision to its utmost limits; nothing came of it. It is precisely to overcome this stubbornness that today mathematicians are forced to employ all their ingenuity". "Michelson has shown, as I have said, that the methods of physics are powerless to put absolute motion in evidence" (Poincaré 1904, 302, 311, 321; Michelson Livingston 1973, 228-229).

10.9 The End Delury wrote (Delury 1912, 319-320): "While in Rome [April], at the Mathematical Congress of 1908, he was taken seriously ill, and was unable to be present at the later sessions of the meeting. He was, in time, able to resume his work, and his many friends came to feel that, comparatively young, he had many years before him. This, however, was not to be. The ailment returning or persisting, a surgical operation was counselled. For a short time after the operation, all seemed well, but unexpectedly and suddenly the end came".

Poincaré died on July 17, 1912, just as his excitement for the new quantum theory began to take root. He almost won the Nobel Prize after Lorentz and Pieter Zeeman proposed his name for the Nobel Prize in physics in 1910 (Walter, Bolmont and Coret 2000, 260). The Royal Society of London sent as its representative, Sir Joseph Larmor – whose electron theory Poincaré fiercely objected, to Poincaré's Funeral. The following is one of the undated condolences letters sent to Poincaré's cousin, Raymond Poincaré, in French (Einstein, 1989, 256): "Prof. Dr Albert Einstein Member of the Academy of Sciences I desire to present my homage to M. president of the Council on his cousin the grand master Henri Poincaré Albert Einstein"

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11 Poincaré's Possible Influence on Einstein's Pathway toward Special Relativity 11.1 Poincaré's Dynamics of the Electron In 1905, Poincaré elaborated Lorentz's electron theory from 1904 in two papers entitled "Sur la dynamique de l'électron" (On the Dynamics of the Electron) (Poincaré 1905b and 1905c). The first of the two papers (Poincaré 1905b), was a report and an outline of the latter (Poincaré 1905c). The report was presented on June 5, 1905, to the French Academy of Sciences and published in the Comptes rendus hebdomadaires des séances de l'Académie des sciences, Paris. It was four pages long, the usual length of reports published in the Comptes rendus. On July 23, 1905, Poincaré submitted the second paper – published only in 1906 – to an obscure Italian journal by the name, Rendiconti del Circolo Matematico di Palermo. It was not the first time that Poincaré published papers in this journal (Poincaré 1894a). During May 1905 Poincaré sent three undated letters to Lorentz in which he presented the essential elements of his theory. At the same time, however, it is a curious coincidence that Einstein wrote his famous May 1905 undated letter to Habicht, in which he promised him four works. In May 1905, both Poincaré and Einstein possessed drafts of papers pertaining to the principle of relativity. Einstein was developing a new kinematics leading to a theory of relativity, and Poincaré perfected Lorentz's theory, using his mathematical theory of groups, to a stage that one could not disclose absolute motions at all. Yves Pierseaux described the difference between the two theories (Pierseaux 2004, 60). The two famous papers, that of Einstein (1905a) and that of Poincaré (1905b), "contain not only two approaches of SR [special relativity] but two different theories of SR" (Pierseaux 2004, 58). He explains the two different theories as Einstein's principles of kinematics and Poincaré's theory of groups. The "Dynamics of the Electron" is a mathematical physics theory, rather than a theoretical physics one. Louis De Broglie distinguishes between mathematical physics and theoretical physics (de Broglie 1951, 46). The first, according to De Broglie, is the profound and critical examination of the physical theories put forward by the researcher who assesses mathematical speculations in order to improve these theories and in order to render their inherent proofs more rigorous. In contrast, theoretical physics is the construction of theories suitable to serve as an explanation

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of the experimental facts and to guide the work of the laboratory staff. Extensive mathematical knowledge is a pre-requisite, although it is not necessary; it is ordinarily the work of "real" mathematicians. De Broglie explains that theoretical physics requires wide knowledge of the experimental facts, and mainly some kind of intuition in physics, which not all mathematicians have, as did Poincaré. Poincaré, according to De Broglie, was especially destined to engage fruitfully in mathematical physics. De Broglie asserted that Einstein was a scientist of the second type. These definitions stem from the French scientific tradition, and, in respect to Poincaré, was even apparent in the manner in which Poincaré presented his scientific endeavours and the titles of his papers. Below, I first examine Poincaré's three letters to Lorentz followed by a discussion on his paper. The letters reveal the manner and succession in which he originally presented his equations, and can be compared to his paper that was published later (1905b).

11.2 The May 1905 Letters to Lorentz In the first letter, sent sometime in May 1905, Poincaré writes that he had been studying in greater detail Lorentz's 1904 paper for some time, and that he had already mentioned "the main results" at the congress in Saint Louis (Poincaré to Lorentz, May, 1905, Walter et al 2000, 255, Letter Number 38.3).62 What were these main results he was alluding to? In the 1904 lecture, "The Present State and Future of Mathematical Physics", Poincaré explained his physical interpretation of Lorentz's local time by the synchronisation of clocks by light signals. Poincaré starts with two observers who exchange signals; however, knowing that the transmission of light is not instantaneous, they cross the signals. When station B received the signal from the station A, its clock should not mark the same hour as that of the station A at the moment of sending the signal. This hour is augmented by a constant representing the duration of the transmission. Suppose that the station A sends its signal when its clock marks the hour zero, and that the station B perceives it when its clock marks the hour t. The clocks are synchronised if the delay equal to t represents the duration of the transmission. To verify this, station B sends a signal when its clock marks zero. If station A receives the signal when its clock marks t, then the watches are synchronised (Poincaré 1904b, 311).

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To achieve synchonisation using this method both stations must be fixed. If the two stations are moving, then the duration of transmission will not be identical in both directions, since if station A, for example, moves forward to meet the optical perturbation emanating from B, station B would have moved before receiving the perturbation emanating from A. The watches synchronised in that manner do not mark, therefore, true time; rather, they mark local time, so that one of them is slower than the other. It matters little, since we have no means of perceiving it. All the phenomena which happen at A, for example, will be late, but all will be equally so, and the observer who ascertains them will not perceive it since his watch is slow. Already in 1900, Poincaré had suggested a physical interpretation of Lorentz's local time by the synchronisation of clocks using light signals (Poincaré 1900b, 272). Poincaré reasoned that the phenomena in a moving system should be related, not to the true time t, but to a certain local time t’ defined in the following manner. He proposed placing several observers at different points, and synchronising their watches by means of light signals. Using the times of transmissions, they attempt to correct these signals. However, since they are ignorant of the translation motion in which they are moving, and believe as a consequence that the signals are transmitted equally fast in both directions, they are confined to crossing the observations, by sending one signal from A to B, then another from B to A. The local time t' is the time marked by the watches thus synchronised. Poincaré could not require reciprocity of the appearances, i.e., the velocity of the frame "at rest" relative to the moving system is equal and opposite to that of the moving system relative to the system at rest. For Poincaré, in the moving system, an observer measures "apparent" lengths and "apparent" time units; in the ether frame he is measuring "real" lengths and "real" time units. Norton explains that, as opposed to Einstein, before 1905 Poincaré stressed the importance of the method of clocks and their synchronisation by light signals (Poincaré 1898a, 1900b). For Einstein, the synchronisation of clocks by light signals did not play an important role in his process of discovery (See Chapter D and Norton, 2004; 2008). In the first letter, Poincaré also wrote that he agreed with Lorentz on all essential points; however, there were some differences, especially as regards the Lorentz's 1904 transformations for the charge density appearing on page 813 of Lorentz's paper. Poincaré modified these

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equations (Poincaré to Lorentz, May, 1905, Walter et al 2000, 255). Lorentz set (Lorentz 1904, 813): 

ͳ ߩ ൌ ߩᇱ Ǣ݇ ଶ ‫ݑ‬௫ ൌ ‫ݑ‬௫ᇱ ǡ ݈݇ ଷ

Using Poincaré's notation, we can write:H is the constant velocity of translation of the system in the x direction, the speed of light is equal to 1, u is a velocity which an electron has in addition to this, the velocity x component of the electron is ‫ݒ‬௫ ൌ ‫ݑ‬௫ ൅ ߝ and: ݇ൌ

ͳ ξͳ െ ߝ ଶ

Ǥ

Poincaré corrected Lorentz's expression and set (Poincaré to Lorentz, May, 1905, Poincaré Archives Nancy): ሺͳሻ

ͳ ͳ ሺߩሺͳ ൅ ߝ‫ݒ‬௫ ሻ ൌ ߩᇱ Ǥ ଷ ߩሺ‫ݒ‬௫ ൅ ߝሻ ൌ ߩᇱ ‫ݑ‬௫ᇱ ଷ ݈݇ ݈݇

The change seemed necessary to Poincaré because the apparent charge of the electron had to be conserved. Subsequently, Poincaré modified two more equations appearing on page 813 of Lorentz's 1904 paper. Poincaré's second letter to Lorentz was also sent some time during May 1905. In it, Poincaré thanks Lorentz for his kind reply – Lorentz must have answered Poincaré's first letter, but his reply was not preserved (Walter, Bolmont and Coret 2000, 258, note 1). Poincaré reports to Lorentz that he had made some changes to his idea. Poincaré then charged forward to his major discovery: he sent Lorentz the correct coordinate and time transformations (Lorentz transformations). Lorentz wrote the following transformations (Lorentz 1904, 312): ‫ ݔ‬ᇱ ൌ ݈݇‫ݔ‬ǡ ‫ ݕ‬ᇱ ൌ ݈‫ݕ‬ǡ

‫ ݖ‬ᇱ ൌ ݈‫ݖ‬ǡ

‫ݐ‬ᇱ ൌ

݈ ‫ ݐ‬െ ݈݇ߝ‫ݔ‬ǡ ݇

x', y', z', t' are the space coordinates and time coordinate for an observer moving in the ether and x, y, z, t are the space coordinates and the time coordinate for an observer resting in the ether. l and H are two arbitrary constants. Poincaré corrected Lorentz's transformations:

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‫ ݔ‬ᇱ ൌ ݈݇ሺ‫ ݔ‬൅ ߝ‫ݐ‬ሻǡ ‫ ݐ‬ᇱ ൌ ݈݇ሺ‫ ݐ‬൅ ߝ‫ݔ‬ሻǡ ‫ ݕ‬ᇱ ൌ ݈‫ݕ‬ǡ ‫ ݖ‬ᇱ ൌ ݈‫ݖ‬ǡ and wrote to him: "These transformations form a group". This was the first time that Poincaré spoke about the famous Lorentz group. He subsequently demonstrated to Lorentz that this was indeed the case. Poincaré had discovered like Lorentz, but by another route that l = 1. What was this route? From Poincaré's paper (Poincaré 1905c, 146) we know that he used group theory to demonstrate that l = 1. This was a great discovery that paved the way to Poincaré's Lorentz group (Poincaré to Lorentz, May, 1905, Walter et al 2000, 257, Letter 38.4; Kox 2008, letter 127). Poincaré sent Lorentz another letter in May 1905, the third letter. This time he did not send him any equations and mathematical derivations. Instead, he wrote that he was continuing his research and that his results are fully confirmed "in the sense that the compensation is perfect (which prevents the experimental determination of absolute motion) and can only be complete with the hypothesis l = 1" (Poincaré to Lorentz, May, 1905, Walter et al 2000, 258, Letter 38.5; Kox 2008, letter 128). Using group theory, Poincaré managed to demonstrate that the postulate of relativity was fully valid according to Lorentz's theory. Less than a month later, Poincaré reported his discovery to the French Academy of Sciences. The four pages "On the Dynamics of the Electron" were published on June 4, 1905, in the Comptes rendus.

11.3 Introducing the Problems In the extended version of the papers, Poincaré introduces the problems that had occupied him. The introduction explains the motive for undertaking the study: Why did Poincaré write a long paper centred on one postulate, the postulate of relativity (embodied in the Lorentz transformations)? Poincaré began his paper with the aberration of light. He explained Fresnel's idea, Michelson's experiment, and said that it appears that the impossibility to detect the absolute motion of the Earth by experiment is a general law of nature: "We are naturally led to admit this law, which we will call the Postulate of Relativity and admit without restriction. Whether or not this postulate, which up to now agrees with experiment, may later be corroborated or disproved by experiments of greater precision, it is interesting in any case to ascertain its consequences" (Poincaré 1905c, 129).

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Already in August 1900, in the congress of philosophy, Poincaré had formulated the Galilean principle of relative motion during his talk "On the Principles of Mechanics". This formulation was reproduced two years later in the chapters discussing Mechanics in Science and Hypothesis, "The motion of some system has to obey the same laws, whether with respect to fixed axes, or to mobile axes carried by a rectilinear and uniform motion". Poincaré called this the principle of relative motion, and said it is imposed on us, because the most vulgar experiments have confirmed it, and also the contrary hypothesis is singularly repugnant to the mind (Poincaré 1900c, 477, 1902a, 129). Four years later, during the Saint Louis congress Poincaré spoke about the principle of relativity (Poincaré 1904b, 306). "The principle of relativity, according to which the laws of physical phenomena must be the same for a stationary observer as for one carried along in a uniform motion of translation, so that we have no means, and can have none, of determining whether or not we are being carried along in such a motion". It is an added merit of the "Dynamics of the Electron" that in quite a natural manner Poincaré speaks of a Postulate of Relativity. He then speaks about the results of Michelson's ether drift experiments that pointed towards the postulate of relativity (Poincaré 1905c, 129). Following this, an explanation was proposed by Lorentz and FitzGerald, who introduced the hypothesis of a contraction of all bodies in the direction of the Earth’s motion and proportional to the square of the aberration. "This contraction, which we will call the Lorentzian contraction, would explain Michelson's experiment and all others performed up to now": According to Lorentz and Poincaré, all moving bodies experience a contraction in the direction of motion in the ratio: ଶ

ͳǣ ටͳ െ ‫ ݒ‬ൗܿ ଶ . (v is the velocity of translation and c the velocity of light). A body resting in the ether does not experience this contraction. Poincaré said that in order to achieve an agreement with the postulate of relativity, Lorentz complemented the contraction hypothesis by demonstrating that we are able to impress a translation upon an entire system without modifying any observable phenomena, because the equations of an electromagnetic medium are unaltered by certain transformations, which Poincaré called the "Lorentz transformations".

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Poincaré perfected these transformations by which he could show that, "Two systems, one of which is at rest, the other in translation, become thereby exact images of each other" (Poincaré 1905c, 130). Already in 1900, Poincaré objected to the invention of a new hypothesis every time a negative result was received as an outcome of a newly performed ether drift experiment. As far as he was concerned, it was not mere chance that all the experiments had so far led to a negative result; this must have signified a rule of nature, imposed upon them, according to which, in principle, no such experiment could ever give a positive result. Poincaré contemplated his concerns in terms of quandaries (Poincaré 1900a, 1172): "Experiments were performed that should have detected the terms of the first order; the results of which were negative; could it be a mere chance? [...] Then more precise experiments were performed, they were also negative; could this be too a result of chance [?]". Poincaré searched for a perfect compensation that would prevent us from ever detecting motion with respect to the ether, which he considered a convenient hypothesis. During the academic year 1888, Poincaré taught his students in the second semester of 1887-1888 in the faculty of sciences in Paris, Théorie mathématique de la lumière (The Mathematical Theory of Light). Poincaré later organised his lectures (probably transcribed by his students). In the introduction from December 2, 1888, he expressed what he believed to be the matter of metaphysicians (Poincaré 1889, I-II): "It matters to us little whether the ether really exists; it is the matter of metaphysicians; what is essential for us is that everything happens as if it existed and that this hypothesis is convenient for the explanation of phenomena. After all, have we any other reason for believing in the existence of material objects? That too is only a convenient hypothesis; only it will never cease to be so, while a day will come no doubt in which the ether will be rejected as useless".

Two years later, on August 6, 1900, Poincaré participated in the International Congress of Physics in Paris and gave the keynote lecture "Relations between Experimental and Mathematical Physics". In the printed version of the talk he asked: "And our ether, does it really exist"? "We know whence our belief in the ether comes from". Poincaré continues that according to Fizeau's experiment "By the interference of rays that traverse through the air or the water in movement, it seems we watch two different media penetrating each other and yet moving with respect to each

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other. One believes to touch the ether with the finger" (Poincaré 1900a, 1171-1172). It has already been mentioned that Fizeau did not observe any moving ether, and he did not approve the "partial ether" drag hypothesis. Fizeau's original interpretation of Fresnel's result (Fresnel's formula) in his 1851 paper was that it is the waves that are partially dragged by the dielectric medium and not the ether! However, in 1881 Michelson wrote: "According to Fresnel, the ether, which is enclosed in optical media, partakes of the motion of these media, to an extent depending on their indices of refraction. For air, this motion would be but a small fraction of that of the air itself and will be neglected" (Michelson 1881, 120). In 1886 Michelson and Morley divided Fresnel's theory into two parts. In the first part, the ether is supposed to be at rest. In the second part, with respect to the interior of transparent media, it is supposed to move with a velocity lower than the velocity of the medium, as hypothesised by Fresnel. They claimed that upon simple assumptions – that seem to amount to no more than the two hypotheses concerned – is composed a satisfactory theory of aberration. "The second hypothesis notwithstanding its seemingly improbability, must be considered as fully proved, first by the celebrated experiment of Fizeau, and secondly, by the ample confirmation of our own work [1886]. The experimental trial of the first hypothesis forms the subject of the present paper" (Michelson and Morley 1887, 334). Poincaré, however, could only overcome the drawbacks in his (1900a) explanation by writing a professional account. However, he was eager to give popular lectures and explanations. At any rate, popular accounts like the one above could have encouraged readers to ask for more precise information in Poincaré's professional accounts. The French editor, Camille Flammarion, asked Poincaré to collect his papers into a general philosophical volume accessible to the general reader. In 1902 Poincaré combined in his book La Science et l’Hypothèse (Science and Hypothesis) his 1888 and 1900 scientific works, including the comments, which were comprehensible for the general reader, as expressed in the two completely different contexts (Poincaré 1902a, 180, 215). In his book, Poincaré formulated the principle of relative motion and described ether drift experiments. Then, the two paragraphs of 1888 and 1900 formed a coherent line of thought according to which the ether might be useless. However, in professional accounts, as well as in popular ones Poincaré never gave up the ether.

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Poincaré ended the 1905 "Dynamics of the Electron" introduction by alluding to the method of clocks and their synchronisation by light signals. He asked: "How do we go about measuring? He answered that readers' first responses would be: We transport objects considered to be invariable solids, one on top of the other. However, this is no longer true in his new theory, if we admit the Lorentzian contraction. "In this theory, two lengths are equal, by definition, if they are traversed by light in equal times" (Poincaré 1905c, 131). Like Einstein, Poincaré adopted a definition of distant simultaneity. However, as said earlier, unlike Einstein, Poincaré did not discover the relativity of simultaneity. In 1902, Poincaré wrote a letter to the Royal Academy of Sciences in Stockholm recommending the candidacy of Lorentz for a Nobel Prize in Physics. In trying to persuade the Nobel committee about Lorentz's achievements, Poincaré wrote: "Two phenomena taking place in two different places can appear simultaneous even though they are not: everything happens as if the clock in one of these places retards with respect to that of the other, and as if no conceivable experiment could show evidence of this discordance" (Poincaré 1902b). Poincaré said that everything happens as if the clock in one of the places retards with respect to that of the other. He wrote "as if" because he did not postulate that the speed of light is the same in all inertial frames (did not drop the ether), and did not abandon the basic principles of Newtonian kinematics. John Stachel calls our attention to the fact that the as if has been dropped by Einstein as the conclusion of a reasoning process, because of Einstein's full demonstration from his own procedure of synchronisation for the new physical definition of relative space and time (based on the isotropy of the velocity of light, i.e. the adequation of it with the relativity principle). Hence, his synchronisation is only apparently similar to the one of Poincaré (Stachel 2005b, 217). Although Poincaré did not discover relativity of simultaneity he was the first to question absolute simultaneity and absolute time. In 1900, in a talk at the Paris Philosophy congress, "On the Principles of Mechanics", unlike others, he was genuinely perplexed by the kind of absolutes in mechanics, and declared (Poincaré 1900c, 458-459): "There is no absolute space and we only perceive relative movements; however one expresses most often mechanical facts as if there was an absolute space to which they could be referred. There is no absolute time;

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to say two durations are equal is an assertion which has by itself no meaning and which can acquire one only by convention. Not only do we have no direct intuition of the equality of two durations, but we do not even have it of the simultaneity of two events which are produced in two different scenes; this is what I explained in an article titled The Measurement of Time1".

In a footnote, Poincaré gave an exact reference to this paper. The above 1900 passage reappeared in Poincaré's 1902 book Science and Hypothesis (Poincaré 1902a, 100). In his 1898 paper, "The Measurement of Time", Poincaré propounded new ideas about time and distant simultaneity: "We do not have the direct intuition of the equality of two intervals of time. People who believe they possess this intuition are dupes by an illusion" (Poincaré 1898a, 2). We "do not have the direct intuition of simultaneity, nor anymore of the equality of two durations. If we think we do have this intuition, it is but an illusion" (Poincaré 1898a, 12-13). Poincaré stated that we had replaced the non-intuition of simultaneity and the equality of two intervals of time with certain rules: time should be defined in such a way as to make the equations of classical mechanics, physics and astronomy as simple as possible. On page 92 of the 1904 German edition of Science and Hypothesis (Wissenschaft und Hypothese) Poincaré discusses time and distant simultaneity. On this page there is a footnote redirecting the reader to endnote number 43 on pages 287-289. The footnote refers to Poincaré's paper "The Measurement of Time" and to the journal where it is published: Revue de métaphysique et de morale. Endnote 43 at the end of the book supplies technical background material. It does not discuss Poincaré's 1898 paper "The Measurement of Time" (Poincaré 1904a, 92, 287-289). 63 According to Michel Paty, Poincaré's critiques on absolute simultaneity are made first (up to 1905) with the argument that simultaneity is subjective (Mach's critique was on the same ground), and rejoined his interpretation of the relativity of space (and of geometry) and of the relativity of motion. He always insists on this aspect (up to his last writings). A remark of him (in the 1900 paper) is very significant in this respect, and this subjective aspect dominated Poincaré’s thought. As stated previously, Poincaré imagined several observers are placed at different points, with no relative motion among these points; they all move with the same velocity. According to the principle of relativity the observers do not

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know whether they are moving in uniform translation or are fixed in the ether, so they naturally believe that they are fixed with respect to the ether. As a consequence, they would believe that the velocity of light was constant and the same in all directions (Poincaré 1900b, 272). Poincaré thinks the judgements of simultaneity as being subjective, and he considers (up to 1905 at least) only a subjective correction of clocks and their synchronisation. Similarly he would constantly (and consistently with this view) consider (even after 1905) that the practical effect of the relativity of motion consists in that people who are in relatively moving systems are not aware of their own motion. This would have explained why Poincaré did not make an explicit and direct mathematical derivation of local time through his synchronisation procedures. In order to have this derivation directly done, he (Poincaré) would have had to deal with the constancy of the velocity of light in any direction, a consideration he had not in hands from a physical point of view up to 1906. One can consider that Poincaré's subjective interpretation of simultaneity has been an obstacle to get at the constancy of the velocity of light isotropically from a theoretical point of view. It is only since his 1906-1907 Sorbonne lectures, where he derives both the principle of relativity and the constancy of the velocity of light, that he could consider physically (and no more only subjectively) the velocity of light as constant in any direction. One can consider that Poincarés subjective interpretation of simultaneity has been an obstacle to get at the constancy of the velocity of light isotropically from a theoretical point of view (Poincaré 1906-1907, 217-221). In Poincaré's lectures of 1906-1907, the classical Galilean or Newtonian law of addition of velocities is still used in his synchronisations analysis. The time to be added or subtracted when comparing the paths of the light in both systems in relative motion is defined (in the relative rest system) as the distance versus the velocity, and this last is taken in the classical additive way, c + v, and c – v: ‫ݐ‬ൌ

݀ ݀ Ǣ ‫ݐ‬ᇱ ൌ Ǥ ܿെ‫ݒ‬ ܿ൅‫ݒ‬

Apparently, Poincaré is not aware of the inconsistency of using at the same time the constancy of the velocity of light (which he should know he will get at) and the classical Galilean law of addition of velocities (Poincaré 1906-1907, 217-218).

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In this respect, one could say in a word that in 1905 Poincaré the mathematician wrote down a mathematical expression, the correct relativistic addition theorem for velocities (Poincaré 1905c, 133; see Section 11.4 below). Einstein did not make the calculations, in his synchronisation procedure, in the same way as Poincaré, who used classical Galilean law of addition of velocities (c + v, and c – v). Instead of calculating time from velocities, he formulated velocities as distance/duration, and equated these velocities according to his principle of constancy of the velocity of light (See Chapter D, Section 3.2). The difference between Poincaré's treatments of synchronisations to get at local time before and after 1906 (from a subjective toward a more objective, properly physical, approach) is that he was, since 1905, in full possession of the constancy of the velocity of light, and he knew that after the considerations on apparent motion he would get at the constancy of the velocity of light, and therefore he was able to give to clocks synchronisation an objective physical meaning (Poincaré 1906-1907, 219221): his reasoning naturally could rejoin Einstein's one, which unveils another "mystery" noted by some scholars, without any necessity to speak of influence or borrow. Once it had been decided to proceed through clocks synchronisation one could in a rather natural way use the "material culture" of the time, that of clocks synchronisation to which both Poincaré and Einstein were familiar with. This usual synchronisation was to link distant places, but situated in one single reference frame (that of ether at rest). Poincaré and Einstein developed methods to link systems in relative motion. They did it differently because of their different theoretical presuppositions about the constancy of the velocity of light (real one for Einstein, apparent one for Poincaré). But once the ingredients of synchronisation were settled, the procedure itself was rather straightforward for intelligent and engineer-minded scientists. There is no doubt that Einstein's solution was the more consistent one, and this is related to his particular way to the reform of electromagnetic theory through the regulation by two physical principles, which would be reduced to a single one, the principle of special relativity, after the physical reformulation of space and time, for the constancy of the velocity of light isotropically would then after be automatically given (Paty 1992).

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11.4 The Lorentz Transformations Section §1 and Section §4 of Poincaré's (1905b) "On the Dynamics of the Electron" paper, contain material directly related to the principle of relativity. Sections §6 to §8 discuss the configuration of the electron and present "Poincaré's pressure" theory and Section §9 discusses gravitation. In Section §1 (of 1905b) Poincaré presented the main results as regards to the postulate of relativity. He started with the Maxwell-Lorentz fundamental equations and the equation for the Lorentz force. He then showed that "These equations admit a remarkable transformation discovered by Lorentz" (in 1904). These were the complete Lorentz transformations that Poincaré had written in his second (May 1905) letter to Lorentz (Poincaré 1905c, 132). Poincaré postulated these transformations and did not derive them. He explained that the Lorentz transformation "owes its interest to the fact that it explains why no experiment can inform us of the absolute motion of the universe" (Poincaré 1905c, 132). Poincaré then considered the electron in uniform translation. The Lorentz transformation changes the electron into an ellipsoid. This ellipsoid was in uniform motion. The charge of the electron is invariant under the Lorentz transformations. Poincaré designated the new charge density by U' and wrote the corrected charge density transformations (Poincaré 1905c, 133): ߩᇱ ൌ

݇ ߩሺͳ ൅ ߝ‫ݒ‬௫ ሻǤ ݈ଷ

Poincaré designated the new velocity component by ‫ݒ‬௫ ' ([) and obtained the règle d'addition des vitesses (the addition law for velocities) (Poincaré 1905c, 133): ‫ݒ‬௫ ᇱ ൌ

‫ݒ‬௫ ൅ ߝ ǡ ͳ ൅ ߝ‫ݒ‬௫

where,H is the constant velocity of translation of the moving system in the x direction, the speed of light is equal to 1, u is a velocity which an electron has in addition to this, the velocity component of the electron is ‫ݒ‬௫ ൌ ‫ݑ‬௫ ൅ ߝ and: ݇ൌ

ͳ ξͳ െ ߝ ଶ

Ǥ

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In his first letter to Lorentz, Poincaré described a new expression for the charge density and the corrected charge density transformations. Only in the second letter did he write about the Lorentz transformations. Poincaré did not write in his letters to Lorentz about the addition law for velocities. Writing about this law in the 1905 paper reveals how Poincaré might have originally obtained the corrected charge density transformations. In regard to the presentation in the 1905 paper, it may reasonably be claimed that Poincaré had discovered the Lorentz transformations shortly before he found the new corrected charge density transformations. There are good reasons to ask why he sent Lorentz the corrected charge density transformations first, before sending him the Lorentz transformations. The answer may lie in Poincaré's apparent uncertainty of whether his Lorentz transformations were actually correct. He thus waited for Lorentz's approval for his corrected charge density transformations, after which he sent him the Lorentz transformations. Subsequently, in the (1905b) paper, using the Lorentz transformations Poincaré derived, with "formulae" that "are notably different from those of Lorentz" the transformation for the electric and magnetic fields (Poincaré 1905c, 135): ݂ᇱ ൌ

݇ ͳ ݇ ݂ǡ ݃ᇱ ൌ ଶ ሺ݃ ൅ ߝߛሻǡ ݄ ൌ ଶ ሺ݄ െ ߝߚሻǡ ଶ ݈ ݈ ݈

ߙᇱ ൌ

݇ ͳ ݇ ߙǡ ߚᇱ ൌ ଶ ሺߚ െ ߝ݄ሻǡ ߛ ൌ ଶ ሺߛ ൅ ߝ݃ሻǡ ݈ଶ ݈ ݈

where, f, g, h are the electric field components, and D, E, J, are the magnetic field components. In Section §4, Poincaré demonstrated that the Lorentz transformation forms a group. "We are thus led to consider a continuous group, which we call the Lorentz group". Poincaré elaborated the demonstration he had sent in the second letter to Lorentz, in May 1905. Poincaré described the mathematical properties of the Lorentz group and said that any transformation of this group can always be decomposed into a transformation having the form of a Galilean transformation and a linear transformation, which leaves the quadratic form ‫ ݔ‬ଶ ൅ ‫ ݕ‬ଶ ൅ ‫ ݖ‬ଶ െ  ‫ ݐ‬ଶ unaltered (Poincaré 1905c, 144-146). Poincaré did not associate this quadratic form with propagation of light in order to prove that the principle of the constancy of the velocity of light is compatible with the

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principle of relativity (i.e. to define a null interval) like Einstein or a metric like Minkowski. The physics meaning of the quadratic form was not discussed by Poincaré (Pierseaux 2004, 62), but an additional demonstration in Section §4 follows. In the second letter Poincaré reported to Lorentz that like him, he discovered but by another route, l = 1. In the (1905b) paper, Poincaré quite naturally demonstrated this. The point being made in the (1905b) paper is, briefly, that Poincaré uses group theory to demonstrate that l = 1 (Poincaré 1905c, 144-145; Poincaré to Lorentz, May, 1905, Walter et al 2000, 257, Letter Number 38.4; Kox 2008, letter 127) Section §9 discusses Poincaré's theory of gravitation, extending to his mathematical theory of groups from electrodynamics to gravitation.

11.5 Did Poincaré's Dynamics of the Electron Influence Einstein? On July 16, 1955, at the International Relativity Conference in Bern, Max Born delivered a lecture "Physik und Relativität" (Physics and Relativity), and spoke about Poincaré's influence on Einstein. According to Born, Seelig asked Einstein which scientific literature had contributed most to his ideas on relativity during his period in Bern (EA 39-068). On February 19, 1955, Einstein replied to Seelig's questions (EA 39-070).64 Seelig published this answer in the Technische Rundschau (Technical Review) (N. 20, 47, Bern 6, May, 1955) (Born 1959, 189-190, 1969, 103-104). Seelig heard about the mathematician, Edmund Whittaker's work, History of the Theories of Aether and Electricity 1900-1926, and of the chapter "Relativity of Poincaré and Lorentz" (Whittaker 1953, see also Whittaker 1955). In his letter to Einstein, Seelig wrote "of Poincaré" above the word "Relativity" as if he suddenly recalled having also read the name Poincaré. In this chapter, writes Seelig, Whittaker makes the curious claim that Poincaré and Lorentz are the actual founders of the theory of relativity.65 For Whittaker, says Seelig, the problem seems to be mathematical rather than physical-philosophical. Seelig requested from Einstein an answer to the question: Whether, as Whittaker claims, before 1905 during Einstein's time in Bern, Poincaré in particular had a decisive impact on him. Seelig also asked Einstein whether he remembered working on Lorentz before 1905. Seelig told the aging Einstein that, in the next congress such questions would be raised (EA 39-068).

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Einstein did not live long enough to participate in this conference and answer these questions. Indeed the conference was held in July 1955 (shortly after Einstein died), and Max Born had participated and reported on Einstein's published reply to Seelig's question, in his talk "Physics and Relativity" (Born 1959, 189-190, 1969, 103-104): "There is no doubt that the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905. Lorentz had already observed that for the analysis of Maxwell's equations the transformations which were later known by his name are essential, and Poincaré had even penetrated deeper into these connections. Concerning myself, I knew only Lorentz's important work of 1895 – 'La théorie électromagnétique de Maxwell' and 'Versuch einer Theorie der elektrischen und Optischen Erscheinungen in bewegten Körpern' – but not Lorentz's later work, nor the consecutive investigations by Poincaré. In this sense, my work of 1905 was independent. The new feature of it was the realisation of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell's equations and was concerned with the nature of space and time in general. A further new result was that the 'Lorentz invariance' is a general condition for any theory. This was for me of particular importance because I had already previously recognised that Maxwell's theory did not represent the microstructure of radiation and could therefore have no general validity". This is the published reply as it appeared in Born's book without a line under the word "spezielle" (special). In his letter to Seelig, Einstein put a line under the word "special". Einstein told Seelig that, when developing the special theory of relativity he did not know of Poincaré's studies as regards to the dynamics of the electron (EA 39-070). In September 1907, the editor of the Jahrbuch der Radioaktivität und Elektronik (Yearbook for Radioactivity and Electronics), Johannes Stark, asked Einstein to write a review article on the theory of relativity. On September, 25, 1907, Einstein replied that he would be happy to "deliver the desired report", but he wished to know the date Stark would like to receive the paper (Einstein to Stark, September 25, 1907, CPAE 5, Doc. 58). Einstein told Stark, "Also, I must say that I am not able to acquaint myself with everything published on the subject, because the library is closed during my free time" (from the Patent Office). He said that he was acquainted – in addition to his own works – with only four papers at that time (among them Lorentz's 1904 electron theory paper, and two papers by Planck, with whom Einstein was corresponding). Einstein wrote to

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Stark that he did not know of any other theoretical work relevant to the subject of special relativity. He closed his letter to Stark by saying, "You would therefore do me a great favour if you could bring to my attention other publications, if you know about such". Accordingly, Einstein was still sitting in the Patent Office and was unaware of important papers written by leading scholars.

12 Did Poincaré Explore the Inertial Mass-Energy Equivalence? 12.1. Einstein Explores the Inertial Mass-Energy Equivalence On September 27, 1905, Einstein submitted his paper, "Does the Inertia of a Body Depend Upon its Energy Content?" to the Annalen Der Physik (published on November 21, 1905) (Einstein 1905b, 639-641). A body at rest in an inertial reference frame (x, y, z) sends out – in the line making an angle with the x axis – plane light to both directions with a total energy L: each direction it sends waves of energy L/2. Einstein defines the following terms: E0 – the initial energy of the body at rest with respect to the system (x, y, z) before, and E1 – after emitting the waves. H0 – the energy of the body with respect to the system (x', y', z'), which is moving relative to (x, y, z) before, and H1 – after emitting the waves. H and E are energy values of the same body, referred to two systems of coordinates in motion relative to each other; the body is at rest in one of the two systems, system (x, y, z). The difference H – E can differ from the kinetic energy K of the body, with respect to the other system (x', y', z'), only by an additive constant that does not change during the emission of light. H0 – E0 = K0 + const., H1 – E1 = K1 + const.. Einstein writes:

‫ܭ‬଴ െ ‫ܭ‬ଵ ൌ  ‫ۇ‬

ͳ

ଶ ටͳ െ ˜ ൗ ଶ … ‫ۉ‬

െ ͳ‫ۊ‬Ǥ ‫ی‬

Neglecting magnitudes of the fourth and higher order: ଵ

‫ܭ‬଴ െ ‫ܭ‬ଵ ൌ ଶ

‫ݒ‬ଶ Ǥ …ଶ

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Einstein concluded, "If a body emits the energy L in the form of radiation, its mass diminishes by L/c²" (Einstein 1905b, 641). Einstein ended his paper by saying (Einstein 1905b, 641): "It is inessential that the energy withdrawn from a body turns straight into radiation energy, so we are led to the general conclusion: The mass of a body is a measure of its energy content; if the energy changes by L, the mass changes in the same sense by L/9ǜ1020, if the energy is measured in ergs and the mass in grams".

In 1905, Einstein was only able to show that a change in energy is associated with a change in inertial mass equal to the change in energy divided by c2. Einstein returned to the relation between inertial mass and energy in 1906 – as shown below – and in 1907, he gave more general arguments for their complete equivalence.

12.2. Poincaré 1900 – The "Hertzian Oscillator" Lorentz's theory of the electron violated the principle of action and reaction, but Poincaré believed he could mend this violation (Poincaré 1901). Perhaps because Lorentz was so successful in deriving Fresnel's dragging coefficient in his theory, Poincaré also believed that one could find an explanation that would yield conservation of momentum (for ether and matter) in Lorentz's theory. Poincaré devoted his Lorentz Festschrift paper on December 11, 1900, "The Theory of Lorentz and the Principle of Reaction" to solving this problem (Poincaré 1900b). Poincaré stated that, in the present state (before 1905), Lorentz's theory of systems of ether-and-matter did not respect both principles of action and reaction and of the relativity of motion, contrarily to the systems of matter considered by mechanics. His endeavours were oriented towards the formulation of a better theory which would obey the standards of mathematical physics, restoring these two principles. He did it in an indirect and phenomenological or semi empirical way, using the Lorentz's hypothesis of length contraction and of local time. Poincaré considered a "Hertzian Oscillator", a device like the one used by Heinrich Hertz to create and emit electromagnetic waves. The oscillator emits energy in all directions. Poincaré provided it with a parabolic mirror, as Hertz himself had done with his oscillator, in order to send the energy in a single direction. The device recoils as a result of the energy emitted. Although the recoil is very feeble, it exists and might be verified

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experimentally. No motion of any other material body compensates for the recoil the oscillator undergoes at that moment. If the radiation later encounters some material body, the compensation will be effected on the condition that no energy has been lost on the way. In this manner, the receiving body becomes a perfect absorbent and absorbs all the energy. It is very likely that the compensation will only be partial, because not all the radiation will reach the receiving body; and even if all of it had reached that body, the compensation will not be simultaneous. The compensation is effected by the radiation pressure on the bodies it encounters; if it never encounters any material body, the compensation will never be effected (Poincaré 1904b, 314). An observer carried along with a system moving relative to the oscillator's system is in an "apparent motion", and moving with "apparent velocity" v of the system relative to the oscillator. The "real recoil" measured in the oscillator's system is J/c. The oscillator radiates energy density of amount J with respect to the ether (c the velocity of light). Poincaré asked for the "apparent recoil" measured in the system moving relative to the oscillator. He found that one had to assert that there existed as compensation, "une force complémentaire apparente" (apparent complementary force): െ

‫ݒܬ‬ ܿଶ

Poincaré added: "I put the sign – because the recoil, as its name indicates, takes place in the negative direction" (Poincaré 1900b, 278). Obviously, Poincaré did not explore a relation between inertial mass and energy here. As a result of the oscillator's recoil, in a system moving relative to the oscillator's system, the oscillator generating the electromagnetic energy suffers an apparent complementary force (reaction). In the oscillator's system, there is no complementary force. The principle of action and reaction is thus applicable to matter alone because of the existence of the apparent complementary force, even though the principle is, in fact, also valid for the ether (Poincaré 1900b, 277-278).

12.3. Poincaré 1900 – The Fictitious Fluid In the 1900 Lorentz Festschrift paper, Poincaré considered a small conductor, charged positively and surrounded by ether. An electromagnetic wave is passed through the ether and strikes the conductor. The wave originated from a source where the waves were

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completely detached when they hit the conductor. At the moment the waves reached the conductor, the electric force resulting from the perturbation would act on the charge, causing a pondermotive force to act on the conductor. In accordance with the principle of action and reaction, this force would not be balanced by any other force acting on ponderable matter because all other ponderable bodies are supposed to be far removed, well beyond the scope of the perturbed ether. What is the force that must produce this recoil? What then will happen according to Lorentz's theory? It appeared that the solution could be found only in the ether: if we suggest a detailed mechanistic model for the ether, then the ether would cause the action on the ponderable matter and this would solve the problem. Joseph Larmor, in accordance with the British tradition, had thought of this solution. However, Poincaré objected to Larmor's solution. In 1900, Poincaré explained how Larmor's investigation may have produced an undesirable result: "With Lorentz, we do not know what the movements of the ether are: thanks to this ignorance, we might suppose them such as compensating those of matter". However, "with Larmor, we know the movements of the ether and we can certify that the compensation does not take place. If Larmor has to my mind failed, does that mean that a mechanical explanation" for the ether "is impossible? Far from it: […] as long as a phenomenon obeys the two principles of energy and of least action, it involves an infinite number of mechanical explanations" (Poincaré 1900a, 1173). Poincaré wrote in his lectures on Électricité et optique (Electricity and Optics) that "If, then, a phenomenon involves a complete mechanical explanation, it will involve an infinite of others that will, equally well, report all the particularities revealed by experience" (Poincaré 1891b, xiv). In the 1920 manuscript, "Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development", Einstein explained Poincaré's above reasoning (Einstein 1920a, 3): "Maxwell himself still clung to the conception that all physical events have to be interpreted in terms of mechanics. But his efforts and those of other important theoreticians to devise a mechanical model of electromagnetic phenomena in the ether did not meet with success. Poincaré pointed out that even if the construction of such a picture were accomplished, it would not be a decisive success because such a picture would only be one in an infinite number of possible ones, which, in principle, would be equally justified".

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Poincaré's objections to detailed mechanistic models for the ether were powerful. Hence, in his 1900 Lorentz Festschrift paper Poincaré assumed that he could re-establish the equality of action and reaction in the theory of Lorentz for the phenomena of radiation pressure by other means (Poincaré 1900b, 253-255). Poincaré suggested the following solution to the above problem: We say that the space which the disturbance must traverse in passing to the small conductor (charged positively and surrounded by ether) is not empty, but is filled not only with ether, but with some subtle, yet ponderable fluid; that this matter receives the recoil, at the very moment the energy reaches it, and recoils, when the disturbance leaves it. That would save Newton's principle of action and reaction (Poincaré 1904, 314). Poincaré considered that electrons, on which other far-removed electrons, acted by means of electromagnetic energy transmitted by the ether. The problem was that Lorentz's theory did not satisfy the principle of action and reaction (in Poincaré's terminology, "the principle of reaction"), which means that the sum of the momenta of the ensemble of electrons does not remain constant. The problem was thus beset with many difficulties. When considering electromagnetic forces and the non-electromagnetic collisions (actions due to other electrons), if the principle of reaction is valid for matter (the electrons) alone, one finds in this system that the conservation of momentum is satisfied when there is no electromagnetic field. Poincaré indicated that in order for the conservation of momentum to be satisfied in Lorentz's theory, one has to regard electromagnetic energy as a fluid carrying with it a total momentum. If the momentum is the momentum of the electromagnetic energy, which is localised in the ether, and considered as a mass animated with a certain velocity, according to the ideas of Maxwell, one arrives at the existence of radiation pressure. One then has to agree that the principle of reaction is valid for matter plus the ether (Poincaré 1900b, 278). However, Poincaré believed that any experiment whatsoever conducted for the purpose of confirming this conclusion would always provide a result where the principle of reaction was applicable to matter alone. Poincaré, therefore, defined the fluid as fluide fictif (fictitious fluid) (Poincaré 1895, 392). As regards the fictitious fluid, Poincaré defined it in terms of the mass ௃ density of the fictitious fluid మ, with J the energy density and c the ௖ velocity of light (Poincaré 1900b, 256). The quantity of fictitious fluid ௃ passing through a unit surface per unit time is ‫ ׬‬మ ȉ ‫ݑ‬ ሬԦǡthe inner product ௖

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integral of the mass density of the fictitious fluid and its velocity. This meant that the fluid was destroyed/created per unit volume. The principle of action and reaction may be defined in the following way: The centre of gravity of an isolated system moves in a straight line. Poincaré indicated that, in order for the conservation of momentum to be satisfied, one has to regard electromagnetic energy as a fictitious fluid. However, from the constancy of the momentum, it cannot be concluded that the centre of gravity of the system that is formed of matter and Poincaré's fluid moves in a straight line. Only if there is no destruction or creation of electromagnetic energy anywhere, will the centre of gravity of a system formed of matter and the electromagnetic energy move in a straight line. However, Poincaré's fictitious fluid, representing electromagnetic energy, was not indestructible. The fluid was destroyed/created per unit volume and time by a certain quantity (Poincaré 1900b, 256).

12.4. Lorentz's Response to Poincaré's 1900 Paper On January 20, 1901, Lorentz wrote a letter to Poincaré and responded to the latter's 1900 Lorentz Festschrift paper (Lorentz to Poincaré, January 20, 1901, Walter et al 2000, 253, letter 38.1; Kox 2008, letter 82). Lorentz was especially troubled by the conservation of momentum equation for matter and electromagnetic energy (Poincaré 1900b, 255). Lorentz seemed not to accept Poincaré's idea that, in order for this equation to be valid, one has to regard electromagnetic energy as a fictitious fluid carrying with it a total momentum (Poincaré 1900b, 278). Lorentz agreed with Poincaré that when a body acquires a certain amount of motion, then the mind is satisfied only when we can identify a simultaneous change in another body. Lorentz thought we could also be satisfied when the change was not simultaneous. In this respect, Lorentz referred Poincaré to the equation from his paper, "The conservation of Momentum", which is not satisfied by Lorentz's theory: actions due to other electrons (matter) + electromagnetic energy. Lorentz then told Poincaré that they could simply consider electromagnetic energy to be quantities dependent on the state of the ether, and which are "equivalent" to the momentum. Lorentz concluded that we could just be satisfied with this. Of course Poincaré could not accept this solution. Lorentz added, "I must confess that I cannot change my theory in the way you report that the difficulty disappears".

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It seemed unlikely to Lorentz that Poincaré or anybody would succeed because "the violation of the principle of reaction was essential in all theories that are able to explain Fizeau's experiment". Lorentz realised that he had to choose between Fizeau's 1851 water tube experiment and the principle of action and reaction, and he told Poincaré, "As to the principle of reaction, it does not seem to be a fundamental principle of physics" (Lorentz to Poincaré, January 20, 1901, Walter et al 2000, 253, letter 38.1; Kox 2008, letter 82). Poincaré was well-aware of the problem. He knew he had to choose between Fizeau's experiment and the principle of reaction. In his 1904 Saint Louis talk, he said: "If the energy during its [the fluid's] propagation remained always attached to some material substratum, this matter would carry the light along with it and Fizeau has shown […] that there is nothing of the kind. Michelson and Morley have since confirmed this". He concluded that the principle of reaction "therefore becomes useless" (Poincaré 1904, 314). In 1904 and later in 1908 Poincaré chose Fizeau's experiment, and gave up the principle of reaction (Poincaré 1908a, 570). However, in his lessons at the École supérieure des Postes et Télégraphes in 1911-1912, "The Dynamics of the Electron", posthumously published from the notes of his students and a list of equations left by Poincaré, he returned to the problem of the violation of the principle of reaction in Lorentz's theory and to the fictitious fluid (Poincaré 1913, 26-32).

12.5. Einstein 1906 – Inseparability of Theorem of Conservation of Mass and of Energy In his 1906 paper, "Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der Energie" (The Principle of Conservation of Motion of the Centre of Gravity and the Inertia of Energy"), Einstein solved Poincaré's problem. Einstein mentioned Poincaré's 1900 paper in this regard. He wrote that the simple formal considerations he had used were already contained in Poincaré's work, but he had preferred not to base himself on that work for the sake of clarity (Einstein 1906, 627). Einstein solved the problem by using the assumption that the theorem of the constancy of mass is a special case of the principle of energy. Consider the theorem of the conservation of the motion of the centre of gravity: the centre of gravity of bodies which act upon each other, independently of any exterior action, remains always at rest, or moves uniformly in a straight line. Einstein showed that if the inertial mass E/c2 is associated with the energy E, and on assuming the inseparability of the theorem of

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the conservation of mass and that of energy, then – at least as a first approximation – the theorem of the conservation of the motion of the centre of gravity is also valid for all systems in which electromagnetic processes take place (Einstein 1906, 632-633). Einstein was the first to explore the inertial mass-energy equivalence. Before 1905 (and also afterwards), Poincaré did not explore the inertial mass-energy equivalence. On February 17, 1908, a somewhat aggravated Einstein at the Patent Office in Bern wrote a postcard to Johannes Stark: "I was a little surprised to see that you did not acknowledge my priority regarding the relationship between inertial mass and energy". Stark answered warmly and with regret (Dukas and Hoffmann 1979, 20, 126). Einstein indeed deserved the priority for the relationship between inertial mass and energy.

13. Poincaré's Groups and Conventions 13.1 Poincaré's Conventionalism of Geometry Besides technical works, Poincaré regularly published papers in popular science and philosophy journals. He discussed the role of logic in mathematics, and the foundations of geometry and arithmetic, the foundations of mechanics, and the recent developments in physics. He developed the philosophy of conventionalism of geometry and the conventionalism of the principles of mechanics. In 1887, Poincaré published his first paper discussing the foundations of geometry; in 1891 he published his second paper on the topic, explicitly discussing conventionalism of geometry (Poincaré 1887, 1891a). Poincaré began to entertain conventionalist ideas in relation to geometry when he studied group theory in mathematics. While trying to solve the problems in group theory, Poincaré formulated for the first time the philosophy of conventionalism for geometry at the end of the 1887 paper, "Sur les hypothèses fondamentales de la géometrie" (The Fundamental Hypotheses of Geometry), but without yet speaking of "conventionalism" (Poincaré 1887, in 1934-1953, 90-91). Poincaré assumed a group of movements not altering the distances, and arrived at a conclusion according to which geometry was nothing but the study of a group. Because the existence of one group is not incompatible with that of another group, the truth of Euclidean geometry is not

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incompatible with that of the geometry of Nikolái Ivánovich Lobachevski, for example, and any other non-Euclidean geometry. We choose, out of all the possible groups, a particular group with respect to which we relate the physical phenomena. This is the same as choosing, among the different coordinate systems, three coordinate axes with respect to which a geometrical figure is related. What determines this choice? It is first and foremost the simplicity of the chosen group. There is, however, another reason: there exists in nature remarkable bodies which we call solids, and experience has taught us that the diverse possible movements of these bodies are linked, to quite a great extent, by the same relations as the diverse operations of the chosen group. However, the chosen group is only more convenient than the others. One cannot speak of the Euclidean geometry as true and of the geometry of Lobachevski as false; this is exactly the same as not being able to speak of the Cartesian coordinates as true and the Polar ones as false. Poincaré proposed another geometry, the truth of which was not incompatible with the other geometries; he called it the "fourth geometry". The first time that Poincaré's fourth geometry appeared in print was in his 1891 paper, "Les Géométries non Euclidiennes" (The Non Euclidean Geometries) (Poincaré 1891a, 772). Poincaré said that among the possible geometries, the fourth geometry was one that deserves attention, because we can construct a fourth geometry in addition to those of Euclid, Lobachewski, and Riemann. In an English paper, "On the Foundations of Geometry", published in The Monist in 1898 (an English translation by T. J. McCormack of a manuscript written in French by Poincaré), Poincaré explained Conventionalism for the first time using philosophical language (Poincaré 1898b, 38): "Geometry and Contradiction In following up all the consequences of the different geometrical axioms, are we never led to contradictions? The axioms are not analytical judgments a priori; they are conventions. Is it certain that all these conventions are compatible? These conventions, it is true, have all been suggested to us by experiments, but by crude experiments".

Poincaré summarised the paper and explained that geometry is not an experimental science, because it is in fact a study of a mathematical group (Poincaré 1898b, 41):

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"Experience forms merely the occasion for our reflecting upon the geometrical ideas which pre-exist in us. But the occasion is necessary; if it did not exist we should not reflect; and if our experiences were different, doubtless our reflections would also be different. Space is not a form of our sensibility; it is an instrument which serves us not to represent things to ourselves, but to reason upon things. What we call geometry is nothing but the study of formal properties of a certain continuous group; so that we may say, space is a group".

In 1921, Einstein responded to Poincaré's conventionalism of geometry. Let us see how Einstein interpreted Poincaré. In his talk "Geometrie und Erfahrung" (Geometry and Experience), presented to the Prussian Academy of Sciences on January 27, 1921, Einstein started by implicitly presenting Kant's problem – the axioms of geometry are free creations of the human mind ("Diese Axiome sind freie Schöpfungen des menschlichen Geistes"), and are independent of experience. They thus do not refer to reality, and cannot say anything about reality. Subsequently, Einstein explained that geometry means "geodesy", and geodesics are measurements done with "rigid bodies". He then added a Satz (theorem): "Solid bodies are related with respect to their possible dispositions, as are bodies in Euclidean geometry of three dimensions; then the propositions of Euclidean geometry contain statements about the behaviour of practically rigid bodies". He concluded that geometry thus supplemented is a natural science, and "we can virtually consider it as the oldest branch of physics" (Einstein 1921, 124-125). Poincaré appeared to have in mind something completely different, for he wrote that experience has taught us the diverse possible motions of solid bodies and that these bodies are linked, to quite a great extent, by the same relations as the diverse operations of the chosen group (he chose Euclidean geometry). However, the chosen group is only more convenient than the others (Poincaré 1887, in 1934-1953, 90-91). Notice the difference between Einstein and Poincaré: Poincaré's starting point is group theory, while Einstein's praktische Geometrie (practical geometry), as opposed to "purely axiomatic geometry", does not take this into account when responding to Poincaré's ideas. Question: What is the geometry of the world? For Poincaré this question has no meaning; for him, we choose the geometry group that is more convenient and simple than the others. However, following Einstein's above Satz, within practical geometry this question has clear meaning (Einstein 1921, 125).

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Subsequently, Einstein debated explicitly with Poincaré and his persistent adherence to Euclidean geometry; the pillar that held his geometric conventionalism (Einstein 1921, 126): "If we reject the relation between the body of axiomatic Euclidean geometry and the practically rigid body of reality, we easily arrive at the following view, which should, particularly, be paid homage to the acute and profound thinker, H. Poincaré: Of all other conceivable axiomatic geometries, Euclidean geometry is distinguished by its simplicity".

Einstein did not agree with this standpoint because axiomatic geometry did not contain any statements about reality, and it could not be perceptible and testable, unless it was accompanied by physical theorems. Einstein said that the problem posed by Poincaré was, if experience led to contradictions with the physical laws, then we could always change these and not Euclidean geometry, the simplest of all geometries. If geometry (G) does not say anything about the behaviour of real things, but only geometry together with the epitome (P) of physical laws, then (G) + (P) is subject to the control of experience. Hence, we may choose (G) arbitrarily, and also parts of (P), because all these are conventions. We must choose (G) + (P) together to be in accord with experience. This way we can always choose (the simplest geometry) Euclidean geometry and change (P) (Einstein 1921, 126-127). Michel Paty commented on Einstein's presentation of Poincaré's standpoint: "Actually, this is not exactly Poincaré's point of view, but a translation of it made by Einstein in his own perspective, that is according to his conception of physical geometry. For, in Poincaré's conception, geometry enters in the considerations of physics only through definitions and is not on an equal footing with it" (Paty 1992, 132). Paty is right. Einstein appeared to not fully comprehend Poincaré's geometric group theory, and thus he misrepresented his geometric conventionalism. Let us again call geometry (G) and the laws of optics (P) and weave these into Poincaré's following quotation from Science and Hypothesis: "We could renounce the Euclidean geometry [(G)] or better modify the laws of optics [(P)] and admit that light is not rigorously propagated in a straight line. It is needless to add that everybody would regard this solution as more advantageous. Euclidean geometry [(G)] has therefore nothing to fear from new experiments" (Poincaré 1902a, 95-96). In the above quotation Poincaré suggested two possibilities: 1. If we renounce (G), then according to (P) light propagates in curved lines; or, 2.

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If we accept (G), then we modify (P). Both alternatives (1) and (2) are logically and empirically equivalent. It is not (G) + (P) one unit, but (G) and (P). Poincaré chose the second alternative (2), and he chose the group (G), because it is more convenient and simpler than the groups, nonEuclidean geometry. Einstein then sub specie, and, in essence, agreed with Poincaré (at least with "the Poincaré" that he had presented). However, he did suggest an alternative view to this "Poincaré" (Einstein 1921, 127-128): The question whether the continuum is Euclidean, or according to the general Riemannian scheme, or whether its structure is according to a different geometry, is actually a physical question that must be answered by experience. This is not a question to be chosen by convention as a matter of convenience. Riemann's geometry is valid if the disposition laws of the practically rigid body are transformable into the laws of bodies of the Euclidean geometry; this becomes exact the more the dimensions of space-time in the considered area diminish. Einstein's punch line was that without this alternative view "it would have been impossible for me to develop the [general] theory of relativity" (Einstein 1921, 126). Hans Reichenbach commented on the above text (Reichenbach 1922, 33): "Those who know Einstein's clear and comprehensive way of thinking from personal conversations will understand the significance of this remark. Einstein is not a formal mathematician concerned with developing purely mathematical theories; rather, he thinks analytically, i.e., he is concerned with clarifying the meaning of concepts. Mathematics is, for him, only a means of expressing an intimate process, a process that operates from unconscious sources and for which the formal language is merely the framework".

A year after lecturing on "Geometry and Experience", Einstein visited and lectured in Paris in April 1922. Charles Nordmann, published reports about the visit, discussions and meetings as a paper, "Einstein expose et discute sa théorie" (Einstein Presents and Discusses his Theory). During his stay in Paris, Einstein was asked of Poincaré's influence on his way to his general theory of relativity (Nordmann 1922, 142-143): "Henri Poincaré died and certainly it would have been something deeply moving to see Einstein discuss this powerful spirit which paved the way on so many points. Would he become a partisan of the general theory of

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Since Poincaré's and Einstein's conceptions were so far removed from one another, Nordmann concluded by reporting what Einstein had told him: "Perhaps even more than Poincaré, Einstein admits to have been influenced by the famous Viennese physicist Mach" (Nordmann 1922, 142-143).66

13.2 Conventionalism of Principles At first, scientists were a little sceptical about Poincaré's conventionalism, they were also confused. This was evident in Paul Painlevé's reaction to Poincaré's conventionalism of principles. During the 1900 universal exposition in the philosophy congress, Poincaré read parts of his paper "On the Principles of Mechanics" to the audience; this was the first time that he had presented his philosophy of conventionalism of principles. One of the mathematicians in the audience was the mathematics professor from Princeton, Edgar Odell Lovett. A year later he reported on what he had heard during this congress, including the discussions and responses to the talks (Lovett 1901; Poincaré 1900c). Lovett explained that in reading extracts from his paper, Poincaré elucidated the principles of mechanics. He asserted that the principle of inertia was not an a priori truth; nor was it an experimental law, since it could never be verified; this was similar to the law of acceleration (second law of Newton), which was simply the definition of force. According to the principle of inertia, a material point, far removed from the action of any other material points, moves in a straight line with uniform motion. Suppose we desire to verify this law experimentally. We verify that a material point moves in a straight line with uniform motion with respect to one reference frame. According to Poincaré we can always chose an infinite of other reference frames that will represent the principle of inertia equally well. Hence, we can never verify – experimentally – the principle of inertia.

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The principle of action and reaction may be defined in the following way: The centre of gravity of an isolated system can only have a uniform rectilinear motion. We cannot verify this axiom in question by experiment, because we are not in possession of an isolated system. In order to verify this, it is necessary for an isolated system to exist, but these systems do not exist. Hence the principle of action and reaction is approximately true for systems approximately isolated, but the question of knowing whether it is rigorously true for systems rigorously isolated is devoid of meaning (Lovett 1901, 161). Poincaré, according to Lovett, went on to treat the principle of relative motion. He said that the principle of relative motion seems to impose itself upon the mind and to be confirmed by experience. However, we can demonstrate it neither a priori nor a posteriori. Finally, Poincaré discussed the principle of the conservation of energy, which can be neither verified nor disproved by experience, since it is reduced to this: "There is something which remains constant' which is the very formula of determinism". Poincaré, according to Lovett, concluded that the principles of mechanics (Lovett 1901, 161): "[…] are from one point of view truths founded on experience and, from another, a priori and universal postulates. In a word they are conventions, not absolutely arbitrary, but convenient, that is to say appropriate to experience. Thus is explained the fact that experience can construct or suggest the principles of mechanics, but can never overthrow them".

Lovett's report of Poincaré's talk was succinct. Poincaré probably provided a standard twenty-minute conference talk. He later published this talk, adapted it, and expanded it somewhat, the result being different from Lovett's above report (Poincaré 1900c). According to Lovett, the discussion after Poincaré's talk began with a question by Paul Painlevé "who insisted upon the arbitrary character assumed by the principles of mechanics in M. Poincaré's exposition. They are conventions which experience can never bring to default because as soon as any fact should contradict them we would always find, nolens volens, a means of adapting them to the new fact" (Lovett 1901, 161-162). Painlevé gave as an example for his claim, the law of gravitation. He thought that Poincaré presented Newton's law only as convention that the facts never contradict, because when they seemed to contradict it, we

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invent new facts to justify it. Still, who would dream of replacing Newton's law by the following convention: "Two bodies repel each other proportionally to their distance and inversely as their masses", correcting the divergence between this and experience by means of supplementary hypotheses. Painlevé reasoned, "We feel that the law of Newton is a convention preferable to all others, because it is clearly imposed by the facts". According to Painlevé' this was exactly the case with Euclidean geometry: All the groups were equivalent, but it appeared that one was always preferable, because we could always change the auxiliary hypotheses so as to save it from failing (Lovett 1901, 162). Lovett summarised Painlevé's standpoint: He conceives physical science as a method of successive approximations, oriented initially by empiricism and guided by certain principles of experimental origin. Painlevé reasoned that the "convergence" of this method was not an assured a priori, but well justified by its success, i.e., by the increasingly natural and perfect accord between theory and reality. Poincaré responded that there was really no lack of accord between Painlevé and himself. He himself recognised that science always proceeded and will always proceed by successive approximations. Unlike Painlevé, "he pointed out the series of artifices, more or less conscious, by which the founders of mechanics had succeeded in transforming the first approximation, not into a provisional truth susceptible of correction, but into a definitive and rigorous truth; and this to a great improvement in clearness of statement, and consequently to the benefit of science itself" (Lovett 1901, 162-163). According to Jacques Hadamard, several comments are immediately called for: 1. If we assign as the object of mechanics, not the explanation of the phenomena of motion but merely their description in the simplest and most exact manner, the principles of mechanics, as we state them, are sufficiently justified; and, 2. When we find facts in apparent contradiction with these principles we can suggest that a new force intervene, in place of changing the general principles (Lovett 1901, 163). In a paper published that same year, Poincaré writes about a disk thought experiment that invoked such a force or mechanism, of which the inhabitants of the disk were unaware.67 Pierre Duhem appeared to have objected to this suggestion when he subsequently remarked that it is not a single determinate hypothesis, but

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the ensemble of the hypotheses of mechanics, that we can attempt to verify experimentally (Lovett 1901, 163). Poincaré replied to Hadamard and Duhem (Lovett 1901, 163-164), "I agreed that the experimental sciences can never verify anything but an ensemble of hypotheses. Every experiment furnishes us one equation in a very great number of unknowns. Our science, still imperfect, does not give us a sufficient number of equations; we have fewer than there are unknowns. We can count on new experiments to give us continually new equations, which will diminish the indeterminacy of the problem. But as regards the unknowns introduced by geometry (curvature of space) or by rational mechanics (it's most general principles), there is something more. Not only does experience not give us enough equations to determine them, but it is absurd and contradictory to suppose that it can ever give them; for the reason that these unknowns enter into the experimental problems as auxiliary supererogatory variables. This explains why the hypotheses which one might make relative to these unknowns are neither true nor false".

Duhem responded to Poincaré's talk in his book La théorie physique: son objet, et sa structure (The Aim and Structure of Physical Theory) (Duhem 1906, 349-355, 1914, 212-216). Duhem wrote (Duhem 1906, 355, 1914, 216): "Whatever the nature of the hypothesis is, […] it is never in isolation contradicted by experiment, experimental contradiction always bears as a whole on the entire group constituting a theory without any possibility of designating which proposition in this group should be rejected. There thus disappears what might have seemed paradoxical in the following assertion: Certain physical theories rest on hypotheses which do not by themselves have any physical meaning".

Mathematicians in the audience were not persuaded by Poincaré's answers. Another mathematician protested against Poincaré's scepticism. He held that the laws of mechanics have an objective value, and that they are not creations of the human intellect. The world existed before humanity, and the world will exist after it. It already obeyed, and it will continue to obey, the laws of mechanics. Hence, science is true in the sense that it deals with real existences. According to Lovett, Poincaré did not quite seem to answer his question, and he only remarked that we raise here the question of the reality of the external world, which would be more in place in the first section (metaphysics) of the conference (Lovett 1901, 164-165).

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With this ended the first presentation of Poincaré's conventionalism of the principles of mechanics. In 1902 Poincaré included the extended version of his talk from the philosophy congress (Poincaré 1900c) in his book Science and Hypothesis.

D. THE MEANING OF EINSTEIN'S 1905 SPECIAL RELATIVITY

In 1929, George Sylvester Viereck interviewed Einstein for The Saturday Evening Post. According to Viereck, Einstein said that the meaning of relativity has been widely misunderstood. "Philosophers play with the word, like a child with a doll. Relativity, as I see it, merely denotes that certain physical and mechanical facts, which have been regarded as positive and permanent, are relative with regard to certain other facts in the sphere of physics and mechanics. It does not mean that everything in life is relative and that we have the right to turn the whole world mischievously topsy-turvy". Viereck said he remembered that some years before 1929, when he first met Einstein in New York, Einstein had emphatically resisted the suggestion that he was a philosopher (Viereck 1929, 109).

1 Einstein's Methodology and Creativity 1.1 Invention or Discovery? Alberto Martínez asked in his latest book Kinematics, whether the formulation of the special theory of relativity was a discovery or Erfindung (an invention). Martínez said that, nowadays, many writers call it a "discovery". However, throughout his life, Einstein emphasised the importance of invention when characterising his theoretical contribution (Martínez 2009, 285). It appears that Einstein himself made different statements about the metaphor for the process that results in a new idea. At times he spoke as if the theory of relativity was an invention, rather than discovery – which implies previous existence. On other occasions, he insisted strongly on the feature of discovering the principle of relativity.

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As mentioned in Chapter C, section 11.6 above, on February 19, 1955, Einstein answered Seelig's questions in a return letter (EA 39-070): "Es ist Zweifellos, dass die spezielle Relativitätstheorie, wenn wir ihre Entwicklung rückschauend betrachten, im Jahre 1905 reif zur Entdeckung war" (There is no doubt that the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905). In 1949, in his Autobiographical Notes Einstein said (Einstein 1949, 48-49): "Je länger und verzweifelter ich mich bemühte, desto mehr kam ich zu der Überzeugung, dass nur die Auffindung eines allgemeinen formalen Prinzipes uns zu gesicherten Ergebnissen führen könnte" (The longer and the more desperately I tried, the more I came to the conviction that only the discovery of a general formal principle could lead us to assured results". In the above sources, Einstein did not use the word Erfindung (invention), but rather the words Entdeckung and Auffindung (discovery). At about the same time, Einstein told Besso in 1948 that, he saw Mach's weakness in his belief more or less that science consists in the mere "ordering" of empirical material. Mach, according to Einstein, misjudged the free constructive element in the formation of concepts. He believed that in some sense theories arise by discovery and not invention (Einstein to Besso, January 6, 1948, Einstein and Besso 1971, Letter 153). We should recall that some twenty years earlier in 1921, Einstein said in "Geometry and Experience" that the axioms of geometry are free creations of the human mind (Einstein 1921, 124). Four years later he explained what he meant by free constructive element in the formation of concepts or free creations of the human mind. In an unpublished opening lecture for a course on the theory of relativity that Einstein gave in Argentina in 1925, he explained (Einstein 1925, 453): "Not only are fundamental laws the result of an act of imagination that cannot be controlled, but so are their ingredients, the ideas derived from those laws. Thus, the concept of acceleration was in itself an act of free creation of the mind which, even if supported by the observation of the motion of solid bodies, assumes as a precondition nothing less than the infinitesimal calculus".

Einstein described this creative activity using notions from the chicken realm. On December 12, 1919, Einstein told Besso that in the Patent Office he "hatched" his "most beautiful thoughts" (Einstein to Besso, December 12, 1919 in Einstein and Besso 1971, letter 51). On March 3,

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1920, Einstein wrote to Max Born: "In my spare time I always brood about the problem of the quanta from the point of view of relativity" (Einstein to Max Born, March 3, 1920, Einstein and Born 1969, letter 14). Kollros recalled that before Einstein left Zurich for Berlin, he "accompanied him home that night. He said: 'The Berliner gentlemen speculate that I am an award-winning Chicken-hen, but I do not know if I can still lay eggs!'" (Kollros, 1955, 29-30). In 1921, in a lecture "On the Theory of Relativity" at King's College London, Einstein said that the theory of relativity owes its invention entirely to the desire to make physical theory fit observed facts as well as possible (Einstein 1954, 246). We can say, roughly speaking, that here rather than "discovery" of relativity, Einstein seems to have preferred "invention" of this theory. At the same time as the King's College lecture, Alexander Moszkowski published his book Gesprächen mit Einstein (Conversations with Einstein). In the final chapter of this book, Moszkowski wrote, that at first it staggered him to hear Einstein say that the use of the word "discovery" in itself is to be deprecated. For discovery is equivalent to becoming aware of a thing which is already formed; this links up with proof, which no longer bears the character of "discovery" but, in the last instance, of the means that leads to discovery. According to Moszkowski, Einstein "then stated at first in blunt terms, which he afterwards elaborated by giving detailed illustrations" that "Discovery is really not a creative act!". Moszkowski said that Einstein told him it was not true that fundamental principles occurred to him as a primary thought. If this had been so perhaps it would be justifiable to call it a "discovery". "But the suddenness with which you assume it to have occurred to me must be denied. Actually, I was led to it by steps arising from the individual laws derived from experience". Einstein, according to Moszkowski, supplemented this by emphasising the concept "invention" and ascribed considerable importance to it. Einstein told Moszkowski that the really valuable factor is intuition (Moszkowski 1921a, 100-101, 1921b, 94-96).

1.2 The Significance of Music for Einstein Einstein characterised the process of his creativity using the words: freie Schöpfungen des menschlichen Geistes (free creations of the human mind) (Einstein 1921, 124). Free creations of the human mind are theoretical scientific ideas and musical sonatas, both enhancing one another.

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Einstein wanted to invent and create; he compared the inventive science to music; music was also an inspiration for his scientific inventions. Einstein explained to Heinrich Zangger that he found the idea intolerable of having to apply his inventive ability to everyday life matters and all for dreary money-making: "Thinking for its own sake, as in music!" (Einstein to Zangger, April 22, 1918, CPAE 8, Doc. 514). Music and science both lay outside the material world and money-making practices. Moszkowski said Einstein told him he believes that there is an unfathomable connection between his musical instinct and his nature as a research scientist (Moszkowski 1921a, 232, 192b, 235). In an interview with the BBC in 1966, Einstein's elder son, Hans Albert, recounted that Einstein often told him that one of the most important things in his life is music. He explained that whenever Einstein "felt that he had come to the end of the road or into a difficult situation in his work, he would take refuge in music, and that would usually resolve all his difficulties" (Whitrow 1967, 21).68 In 1929, Viereck interviewed Einstein and wrote: "Professor Einstein looks more like a musician than a mathematician. 'If,' he confessed to me, with a smile that was half wistful, half apologetic, 'I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music'" (Viereck 1929, 113). Indeed, Einstein always took his violin with him, and was constantly eager for a chance to play. In his first visit to the home of his friend, Max Born, Born's wife Hedi thought that her husband had picked up just another young street musician. Einstein pulled out the violin from the case, threw the case to the corner, and started to fiddle. At that time he liked to play the sonatas of Joseph Haydn. Einstein serenaded Born's wife to the meal in their house with a fine verse, which started with the following words (Born 1959, 239-240): Mr Newton once said, momentum conservation Teach "einStein" acceleration If it is in empty space, moving straight on a trace, And flies, never to return, then nothing remained of it again. Your teaching will be happier there: Space bends forwards and towards the rear, "einStein", he thinks is hurtling across, It is deflected by matter of course…

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And then the rhyme finished with the verse: Don't let a whole year from March to pass too vast, Until we see you again, you must! As a Haydn-missioner you will appear Within a brief Einstein year!

Banesh Hoffmann's favourite anecdote about Einstein is about the violin street player. In his first year in Princeton, on Christmas Eve, so the story goes, some children sang carols outside his house. Having finished, they knocked on his door and explained they were collecting money to buy Christmas presents. Einstein listened, then said: "Wait a moment". He put on his scarf and overcoat, and took his violin from its case. Then, joining the children as they went from door to door, he accompanied their singing of "Silent Night" on his violin (Hoffmann 1968). .

Frank tells the following story (Frank 1949, 299, 1947, 172). In 1921, Einstein travelled to Prague with his best companion, the violin. He gave a lecture on the theory of relativity before the Urania, Prague's German Society. He liked the city where he had once been a young professor, working on his gravitation theory and playing chamber music until dawn. It was Einstein's first popular lecture that Frank heard, and he spoke as simply and clearly as possible. After his lecture, he was expected to speak as guest of honour at a reception. He then announced, "It will perhaps be pleasanter and more understandable if instead of making a speech I play a piece for you on the violin", and so he did. It was easier for him to express his feelings this way. He performed a sonata by Mozart, and was probably enthusiastically applauded by an audience that was grateful perhaps not to have to cope again with the theory of relativity. Admittedly, we cannot put Einstein's music on a par with his science. Einstein loved music and played the violin better than many an amateur. However, in music he could not be compared to his favourite composer, Mozart; in science, he was comparable to Newton, whom he revered (Hoffmann and Dukas 1973, 7). Hoffmann recalled playing duets with Einstein on the violin and Hoffmann at the piano. One day, Einstein surprised Hoffmann by saying that Mozart was the greatest composer of all. Beethoven created his music, but the music of Mozart was of such purity and beauty one felt he had merely "found" it. It had always existed as part of the inner beauty of the universe, waiting to be revealed. Hoffmann wrote about Einstein that, it was "this very Mozartean simplicity that most characterised Einstein's methods" (Hoffmann 1968).

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Although Einstein's music was not comparable to Mozart, Mozart's simplicity and genius most characterised Einstein's methods in physics. Professional musicians seldom enjoy making music with amateurs, but Einstein was an exception. To play with Einstein flattered even the greatest professional violinists, who often also commented on Einstein's skills. One day, the story goes, Einstein said, "He plays well. I play badly. He believes he is getting publicity by playing with me". This anecdote perfectly suited Einstein's sense of humour, honesty and rebelliousness.69 Brigitte Fischer, the musical daughter of publisher, Samuel Fischer, became aware of Einstein's unwillingness to accept criticism when she played with him. She wrote in her autobiography: "Occasionally I even made music with Albert Einstein, who is known to have been no great musician. He was a great music lover and an impassioned violinist, but he couldn't endure any criticism of his playing and could fly into a rage when something didn't turn out right". Fischer recalls, on one occasion, playing the Bach Double Violin Concerto with herself at the piano, accompanied by Einstein and an excellent, professional violinist, Gerhart Hauptmann's daughter-in-law, Eva Bernstein. Einstein suddenly broke off and shouted furiously at his partner, whose playing was drowning him out: "Spielen Sie doch nicht so laut!" (Don't play so loud!). Fischer thought Einstein was still charming even when he was angry, but remarked of the event: "I think he got more excited about that than he ever did in a scientific dispute" (Fischer 1986, 10).70 During his final years, Einstein was forced to give up playing the violin. Robert Shankland who interviewed him on February 2, 1952, wrote (Shankland 1963, 54): "As I left Einstein, I realised that he seemed much older. His eyes still had the deep smile but were not as keen as before. His hands were a little feeble, and when I asked him if he still played the violin (a Brahms' score was on his desk) he said, 'No my fingers don't work anymore'".

1.3 The Significance of a Wonder for Einstein At the age of four or five, young Einstein experienced a life-changing wonder when his father, Hermann, showed him a compass. He recounts this experience in his Autobiographical Notes (Einstein 1949, 7-9): "I have no doubt that our thinking goes on for the most part without use of signs (words) and beyond that to a considerable degree unconsciously. For

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how, otherwise, should it happen that sometimes we 'wonder' quite spontaneously about some experience? A wonder of this kind I experienced as a child of four or five years when my father showed me a compass. That this needle behaved in such a determined way did not at all fit into the kind of occurrences that could find a place in the unconscious world of concepts (efficacy produced by direct 'touch'). I can still remember – or at least believe I can remember – that this experience made a deep and lasting impression upon me".

Einstein also told this story to Moszkowski in 1916 (Moszkowski 1921a, 219, 1921b, 221), "His father once showed the infant, as he lay in his cot, a compass, simply with the idea of amusing him – and in the five-year-old boy the swinging metal needle awakened for the first time the greatest wonderment about unknown cohesive forces, a wonderment that was an index of the research spirit that was still lying dormant in his consciousness. The remembrance of this physical event has a significant meaning for the Einstein today".

Being able to "wonder" was integral for Einstein, who felt it provided him with the ability to keep the child alive in the man. Holton wrote that the folkloric image of Einstein is that of the wisest of old men, who looked as if he had even witnessed the Creation itself; but, at the same time, he also seems almost childlike. Holton stressed that Einstein once remarked that he was brought to the formulation of relativity theory in a good part because he kept asking himself questions concerning space and time that only children wonder about (Holton 1988, 374). The famed Swiss child psychologist and historian of science, Jean Piaget, analysed children's questions concerning space and time in his talk "Genetic Epistemology" at Columbia University (Piaget 1968). According to Piaget, Einstein, whom he first met in 1928, encouraged him to study the origins of children's notions of time, in particular, their notions of simultaneity. Piaget raised the following question: "How is it that Einstein was able to give a new operational definition of simultaneity at a distance? How was he able to criticise the Newtonian notion of universal time without giving rise to a deep crisis within physics?" Piaget arrived at the conclusion that "if we look at two objects moving at different speeds, and they stop at the same time, we do not have an adequate perception that they stopped at the same time. Similarly, when children do not have a very exact idea of what simultaneity is, they do not conceive of it independently of the speed at which objects are travelling".

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Einstein's second experience of a "wonder" involved a Euclidean geometry book. His first wonder involving the compass was non-verbal and imaginative, while the Euclidean wonder was conscious and verbal: "At the age of twelve I experienced a second wonder of a totally different nature: in a little book dealing with Euclidean plane geometry, which came into my hands at the beginning of a school year" (Einstein 1949, 10). On his seventy-fourth birthday Einstein was asked the following by reporters: "It is said that you were decisively influenced at the age of five by a compass, and at twelve by a book of Euclidean geometry. Did these things really have any influence on your life work?" Einstein replied: "I myself think so and I believe that these outside influences had a considerable influence on my development. But man has little insight into what goes on within him" (Seelig 1954, 249-250, 1956a, 211).

1.4 Einstein's Sounding Boards John Stachel argues that, according to Einstein, the process of thinking consists of two stages. The first stage "invention", is a solitary activity, primary non-verbal in nature. Many of the crucial thought experiments Einstein later reports confirm the existence of this stage of the thinking process, utilising visual and muscular imagery (e.g., chasing a light ray at the speed of light, and the magnet and conductor thought experiment). At a secondary stage, it was necessary for him to transform the results of this primary process into forms communicable to others. This led Einstein to search throughout his early life for people to act as "sounding boards" for his ideas. These people were capable of understanding the concepts he explained to them and of asking intelligent questions that could help Einstein develop his own ideas, but were not capable of any creative effort of their own. Einstein moved back and forth between the two stages in the course of the development of his ideas. Einstein first had a non verbal image of him chasing a light beam, and later he needed to put ideas into a communicable form. This led Einstein to discuss his ideas with his close friends, Mileva Mariü, Michele Besso and others, who functioned as sounding boards. This brought him to formulate his intuitive ideas in terms of verbal ideas (Stachel 2005a, xxxv, xxxviii). 1.4.1 Mileva Mariü On March 27, 1901, Einstein wrote to Mariü about bringing "our work on relative motion to a successful conclusion!" (Einstein to Mariü, March 27, 1901, CPAE 1, Doc. 94). This sentence and the publication of the love

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letters brought several people to ask: Did Mileva Mariü assist Einstein in writing his 1905 path breaking papers? Various people speculated about Mariü's role, especially in the development of the theory of relativity. Feminist scholars quickly entered the game; for instance, Senta TrömelPlötz wrote: "We see in the two life stories the familiar patterns that lead to the construction of success for men and the deconstruction of success for women. It is not surprising that the editors of the Collected Papers of Albert Einstein have nothing more to say about Mileva Einstein-Mariü than: 'Her personal and intellectual relationships with the young Einstein played an important role in his development'".71 The debate began when Abram Fedorovich Ioffe, a member of the Soviet Academy of Sciences, and later in life an assistant to Wilhelm Conrad Röntgen from 1902 until 1906, saw the original manuscript, "On the Electrodynamics of Moving Bodies", and noted that it was signed "Einstein-Marity". "Marity" is a Hungarian variant of the Serbian "Mariü", Mileva's maiden name. Ioffe wrote: "In 1905, three articles appeared in the 'Annalen der Physik', which began three very important branches of twentieth century physics. Those were the theory of Brownian motion, the photon theory of light, and the theory of relativity. The author of these articles – an unknown person at that time, was a bureaucrat at the Patent Office in Bern, Einstein-Marity (Marity the maiden name of his wife, which by Swiss custom is added to the husband's family name)". Thus it was claimed that Mileva Mariü-Einstein's name was left out of the published article. Only Albert Einstein's name appears in the journal as author. Suppose Mariü's name had been on the relativity manuscript, who from Annelen der Physik erased it? The Annelen had no policy against papers published by women, claims Stachel. Röntgen was an experimentalist and there was no reason why a theoretical paper like the relativity paper would be given to him as a referee. The members of editors in the Annalen, Max Planck and Paul Drude, were leading theoreticians and could certainly referee the paper. In September 1906, Röntgen requested an offprint of the 1905 published paper, presumably because he was preparing a lecture on the equations of motion of the electron. If Röntgen read the paper in 1905 he would not need the offprint a year later (Stachel 2005a, lviii-lix). Harris Walker claims in his letter, "Did Einstein Espouse his Spouse's Ideas?" to Physics Today from 1989: "In February 1919, the marriage of Albert and Mileva ended in an amiable divorce. Mileva received custody of the children, child support and alimony. In an added clause of the

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divorce decree, Albert Einstein agreed to pay Mileva every krona of any future Nobel Prize he might be awarded. He could keep the glory, but (in a settlement that would make an LA divorce lawyer blush) she got the prize". After LA lawyers blushed, Walker concluded, "I find it difficult to resist the conclusion that Mileva, justly or unjustly saw this as her reward for the part she had played in developing the theory of relativity". In 1916 Mariü, who did not want to grant Einstein a divorce, was on the verge of a physical and mental breakdown and was under the delusion that they would get back together. By 1919, Germany had lost the First World War and he did not have enough German money to give her. Nonetheless, everybody knew he would win the Nobel Prize sooner or later. A settlement promise to give Mariü the prize money helped finalise the divorce. Fifty-four letters between Einstein and Mariü were found. We are, however, disappointed by the small number of letters from Mariü, only ten out of the fifty-four. Walker also raises the following claim: One may wonder if the ten letters from Mariü to Einstein "were not so carefully retained" i.e., if Einstein had not destroyed other letters, and that is the reason for why only ten of Mariü's letters to Einstein from 1902 or earlier have come to light, compared to the forty-three of his. Walker "cannot help but see Mileva and Albert Einstein working as a team, hoping together to achieve the kind of husband-and-wife recognition that came to Marie and Pierre Curie".72 In general, Einstein hardly saved any early letters; later, other people tended to save his, for obvious reasons. Nevertheless, none of Mariü's surviving letters to Einstein touches on any substantive point in physics, while his letters to her are packed-full of substantive comments on physics books and articles as well as his own theoretical ideas and experimental proposals.73 Stachel has been engaged in a long polemic with Walker and feminist scholars. Walker and Trömel-Plötz claimed that the words "our work" in Einstein's letter to Mariü of March 27, 1901, is evidence for the claim that Mariü solved Einstein's mathematical problems and assisted in solving his physics problems. According to Stachel, the letter was written in 1901, whereas the special theory of relativity was not finished until 1905. Physics aroused emotions in Einstein that, during the early stage of their courtship, in discussing his work he slipped easily into the "we" mode. His few references to "our work" were penned at difficult moments in their

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relationship, amid reassurances of his love and devotion. Hence, the words "our work on relative motion" were written in the "emotional context", because there is no similar reference in any other letter to Mariü; in fact, Einstein always refers to his work (Stachel 1996, 46-47). Further, Stachel claims that there is "no evidence that Mariü was particularly gifted mathematically, while there is some evidence that she was not". She did not become a physicist or a mathematician, after she failed her final examinations. Indeed, the "conference of examiners" at the Polytechnic awarded diplomas to Einstein, Grossmann and two other candidates in Division VI of the School for Specialized Teachers in the Natural Science, but not to Fräulein Mariü (CPAE 1, Doc. 67).74 Stachel compares the couple, Marie Skáodowska and Pierre Curie to Einstein and Mariü and adds Paul Ehrenfest and Tatyana Afanasyeva to the list. All three wives were Slavs with a higher education. All three husbands came from secular backgrounds: Einstein and Ehrenfest were Jews, raised in south German urban environments (Munich and Vienna, respectively), who had yet to establish their careers when they married. In the case of the Curies and Ehrenfests, there is evidence of the importance of the women's roles in their joint works, and both wives pursued scientific careers after their husbands' deaths. Mariü, of course, did not pursue a scientific career either before or after her separation from Einstein (Stachel 1996, 48). The crucial thing, according to Stachel, is that the letters suggest that the most important role Mariü played in their intellectual relationship during these years was of "a sounding board" for Einstein's ideas. Einstein had a strong need to clarify and develop his ideas in dialogue with others, a role also played on accession by his friends Besso and Conrad Habicht, after he moved to Bern. Mariü was the first of a series of "sounding boards" that Einstein needed in order to help him put the fruits of his research, carried out alone and with the aid of non-verbal symbolic systems, into a form that could be communicated to others (Stachel 1996, 44-45, 2005, xxxv). 1.4.2. Marcel Grossmann No one was better than Einstein at sharing his thoughts with close friends than when he worked on his relativity theory. In 1915, he explained that his friends guided him, but contributed nothing of substance to the results of his relativity theory.

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Financially, the position of an associate professor at the University of Zurich was not very attractive. Einstein's income there was no larger than it had been at the Patent Office, and he had to spend money for things from which he derived no pleasure for life, but which were only required for his position. Although Einstein loved Zurich, he found little time to undertake any decent research because he was occupied with regular teaching, administrative duties, and financial problems. In 1911, Einstein was offered a full professorship at the German University in Prague (Frank, 1949, 130-131, 1947, 75). During the months he worked in Prague, he published two papers discussing the theory of the static gravitational field. Grossmann, Einstein's loyal friend from the Zurich Polytechnic (now called Eidgenössische Technische Hochschule [ETH], Swiss Federal Institute of Technology) was the dean of the Department of Mathematics and Physics at ETH. He assisted Einstein again and persuaded his colleagues to offer Einstein a professorship at the ETH. In November 1911, Henri Poincaré and Marie Curie were asked to write letters of recommendation for Einstein. The last sentence of Poincaré's letter read: "The role of mathematical physics is to ask the right questions, and experiment alone can resolve them. The future will show more and more the worth of Mr Einstein, and the university intelligent enough to attract this young master is certain to reap great honour" (Seelig, 1954, 163, 1956, 134-135). In winter 1911-1912 the decision was made, and Einstein left Prague after teaching there for less than two years. In July 1912, he returned to Zurich, the place he loved so much, to the school of his youth, and there he remained a professor until he left for Berlin in the spring of 1914. Einstein recognised that the gravitational field should not be described by a variable speed of light as he had attempted to do in Prague, but by the metric tensor field; a mathematical object of ten independent components that characterises the geometry of space and time. Sometime upon Einstein's arrival at Zurich, he spoke about his concern with Grossmann and told him one day, "Grossmann, you have to help me, or I shall go crazy!" Grossman managed to show Einstein the mathematical tools he needed (Kollros 1955, 27). Grossmann searched the literature, and brought the works of Riemann, Gregorio Curbastro-Ricci, Tullio Levi-Civita and Elwin Bruno Christoffel to Einstein's attention. Einstein struggled with the new mathematical tools Grossmann brought him in a small blue notebook – named by scholars the Zurich Notebook (CPAE 4, Doc. 10). Einstein became fascinated with Riemann's calculus,

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and he filled forty-three pages of this notebook with calculations. He continued to receive new mathematical tools from Grossmann, whose name he jotted in the notebook to indicate which tensors were received from him. Grossmann's name is written on top of one of the pages, where Einstein considers candidate field equations with a gravitational tensor that is constructed from the Ricci tensor; an equation Einstein would return to in his November 4, 1915, paper on general relativity. Einstein's collaboration with Grossmann led to two joint papers: the first of these was published before the end of June 1913, and the second, almost a year later. Einstein and Grossmann's first joint paper entitled, "Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation" (Outline of a Generalised Theory of Relativity and of a Theory of Gravitation) is called by scholars the Entwurf paper (Einstein and Grossmann 1913). Grossmann wrote the mathematical part of this paper and Einstein wrote the physics part. The paper was first published in 1913 by B. G. Teubner (Leipzig and Berlin). It was reprinted with an added "Bemerkungen" (remark) in the Zeitschrift für Mathematik und Physik in 1914. The remark was written by Einstein and contained the well-known Lochbetrachtung (Hole Argument). Einstein left Zurich in March-April 1914; this ended his collaboration with Grossmann. Einstein wrote in the introduction to his November 4, 1915, general relativity paper that he completely lost trust in the field equations of his Einstein-Grossmann collaboration (1913-1914) Entwurf theory. He therefore returned to the demand for a broader, general covariance for the field equations, from which he parted with a heavy heart in 1912 when he worked together with his friend Grossmann (Einstein 1915, 778). On July 15, 1915, Einstein provided the clearest statement about Grossmann's role in the development of the Einstein-Grossmann Entwurf general theory of relativity, in a letter to Arnold Sommerfeld: "Grossmann will never claim to be considered a co-discoverer. He only helped in guiding me through the mathematical literature, but contributed nothing of substance to the results" (Einstein to Sommerfeld, July 15, 1915, CPAE 8, Doc. 96). Einstein thus explained that the Einstein-Grossmann Entwurf theory was his own theory; three months later he took full responsibility, and eventually he blamed only himself, when the Entwurf field equations collapsed. Einstein thus explained that Grossmann guided him, but contributed nothing of substance to the results of his relativity theory. Hence, and according to Einstein, it appears that Marcel Grossmann was a sounding board for Einstein's ideas.

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In October 1914, Einstein completed a summary review on the Entwurf theory, titled, "Die formale Grundlage der allgemeinen Relativitätstheorie" (The Formal Foundation of the General Theory of Relativity). Einstein wrote the equations for the conservation of energy-momentum for matter, and established a connection between these equations and the components of the gravitational field. He showed that a material point in gravitational fields moves on a geodesic line in space-time, the equation of which is written in terms of the Christoffel symbols. By November 4, 1915, Einstein found it advantageous to use for the components of the gravitational field, not the previous equation, but the Christoffel symbols. In addition, he corrected the 1914 equations of conservation of energymomentum for matter.75 Even though in 1912 Einstein already possessed the gravitational field equations, he had still not recognised the formal importance of the Christoffel symbols as the components of the gravitational field, and could not obtain a clear overview. He then "fell into the jungle" for three years, together with Grossmann until 1915 (Einstein to Lorentz, January, 1 1916, CPAE 8, Doc. 177). In his first November paper (November 4, 1915) on the general theory of relativity, Einstein wrote the Lagrangian form of his gravitational field equations. In the fourth November paper (November 25, 1915) on general relativity, Einstein added a trace term of the energy-momentum tensor on the right-hand side of the generally covariant field equations. Remember that in 1915 Einstein used for the components of the gravitational field the Christoffel symbols, and thus corrected the Entwurf equations of conservation of energy-momentum for matter. Considering the energymomentum conservation equations for matter, an important similarity between equations suggests that this equation could have assisted Einstein in obtaining the final form of the field equations (the November 25, 1915 ones) that were generally covariant in the final November 25, 1915, paper on the general theory of relativity. Hence, on November 4, 1915, Einstein had already explored much of the main ingredients that were required for the formulation of the final form of the field equations of November 25, 1915. The interesting history of the derivation of the final form of the field equations was inspired by the exchange of letters between Einstein and his friend Paul Ehrenfest in the winter of 1916 and by Einstein's derivation of the November 25, 1915, field equations in his 1916 paper, "Die Grundlage der allgemeinen Relativitätstheorie" (The Foundation of the General Theory of Relativity).76

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1.4.3 Michele Besso According to Stachel, Einstein brooded or ruminated on his ideas ("grübeln", Grübelei"). While studying at the Polytechnic, he studied the works of great physicists and often used his friends as sounding boards for the development of his ideas. Einstein's best friend, Michele Besso, was one such friend (Satchel 2005, xl). Martínez objects to characterising Besso as a "sounding board" for Einstein's ideas. Martínez writes that this description was "first used by Einstein but repudiated by Besso as downplaying his role in their discussions and collaborations" (Martínez 2003, 354). Einstein ends his 1905 relativity paper by saying (Einstein 1905a, 921): "In conclusion, I note that when I worked on the problem discussed here, my friend and colleague M. Besso faithfully stood by me, and I am indebted to him for several valuable suggestions. Bern, June 1905 (received June 30, 1905)".

What could Besso's valuable suggestions have been? In a letter of August 3, 1952, Besso recounted (Besso to Einstein, August 3, 1952 in Einstein and Besso 1971, Letter 188): "Another little fairy tale of mine concerning my view that I had participated in [the formulation of] the special theory of relativity. It seemed to me, as an electrical engineer, I must have brought up, in conversations with you, the question, within the context of Maxwell's theory, of what is induced in the inductor of an alternator; depending on whether it is at rest or rotating, there is induced in the inductive part an electromotive [i.e., a magnetic] force or a [purely] electric one, as a peculiarly practical anticipation of the relativistic point of view […]. That this somehow still resonates emotionally within me is demonstrated by the confusing sentence structure. May Spinoza and Freud watch over me".

Besso first studied mathematics and physics at Trieste, and then at the University of Rome (1891-1895), where he may have learned Maxwell's theory, but there is no evidence for this. On the advice of his uncle David, who taught mathematics at the University of Modena (Italy), he left for Zurich and enrolled in October 1891 in the mechanics department of the Federal Zurich Polytechnic School. After four years of study he obtained his diploma in mechanical engineering and, soon afterwards, a position in an electrical-machinery factory in Zurich. However, he could not have

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been acquainted with Maxwell's theory from his studies at the Polytechnic (Speziali 1979, 263-264). Weber did not teach Maxwell's theory at the Polytechnic. Sauter, Weber's assistant and later Einstein's colleague at the Patent Office, recalled that "this theory [Maxwell's] was not yet on the official programme of the Zurich Polytechnic School" (Sauter 1960, 154). Therefore, it was probably through Einstein's self-reading about Maxwell's theory, that he was able to explain it to Besso. Only after such an explanation could Besso, "within the context of Maxwell's theory", refer to his technical work and speak with Einstein or remind him about induction (of which Einstein had already read about in Joseph Krist's book) (Krist 1891, 94). As already stated, although he never mentioned Föppl on his reading list, Einstein had probably also read about induction in Föppl's book (Reiser 1930, 49; Frank 1949, 38). Seelig wrote that later Besso used the following analogy (Seelig 1954, 85, 1956a, 71): "Einstein the eagle has taken Besso the sparrow under his wing. Then the sparrow fluttered a little higher: 'I could not have found a better soundingboard in the whole of Europe' [Einen besseren Resonanzboden hätte ich in ganz Europa nicht finden können], Einstein remarked when the conversation turned one day to Besso. In this way, Einstein and Besso became inseparable".

According to Besso's letter to Einstein from 1952, Besso and Einstein discussed Faraday's induction within the context of Maxwell's theory. While Einstein considered Besso a sounding board Besso felt he had participated in the formulation of the special theory of relativity. Nonetheless, Besso wrote to Einstein that this was "Ein anderes Märchenklein" (another little fairy tale) of mine. Even in 1913, Besso was still Einstein's sounding board. In June 1913, Besso visited Einstein in Zurich and actively participated in solving the Einstein-Grossmann Entwurf gravitation equations with Einstein. They both tried to find solutions to the problem of the advance of Mercury's perihelion in the field of a static sun. Their joint work is known as the Einstein-Besso manuscript. Besso was inducted by Einstein into the necessary calculations. The Entwurf theory predicted a perihelion advance of about 18'' per century instead of 43'' per century. As chance would have it, in the same month Einstein had another visitor. In June 1913, Paul and Tatyana Ehrenfest travelled from Leiden to Zurich. They stayed at a pension in Zurich, but

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spent a great deal of time with Einstein and his family. It was during this time that Ehrenfest met Besso (Klein 1970, 294). Einstein was thus in the company of Besso and Ehrenfest while he attempted to resolve the Einstein-Grossmann Entwurf field equations and solve the problem of the precession of Mercury's perihelion. Besso collaborated with Einstein on the wrong gravitational theory, and their calculation based on this theory provided an incorrect result (CPAE 4, Doc. 14, 1-14). Towards the end of 1915, Einstein abandoned the Einstein-Grossmann Entwurf gravitational theory; he transferred the basic framework of the calculation from the Einstein-Besso manuscript, and corrected it according to his new 1915 generally covariant field equations. With his new 1915 general relativity theory, he achieved the correct precession quickly by applying the methods he had already worked out two years earlier with Besso ("The Einstein-Besso Manuscript on the Motion of the Perihelion of Mercury", CPAE 4, 349-351). However, Einstein did not acknowledge his earlier work with Besso, and did not mention Besso's name in his 1915 paper explaining the anomalous precession of Mercury. It appears that Einstein did not mention Besso because he still considered him a sounding board, even though Besso undertook calculations with Einstein in Zurich. Indeed when Einstein wrote a series of letters to Besso between 1913 and 1916, and described to him, step by step, his discoveries of general relativity, Besso once again functioned as the committed sounding board (Speziali, Letters 9 to 14). After completing the 1915 general theory of relativity, Einstein sent Besso his 1915 general relativity papers, and told his good friend that his wildest dreams have now come true: general covariance and the perihelion of Mercury (Einstein to Besso, December 10, 1915, CPAE 8, Doc. 162). In 1942, Besso's youngest sister Bice travelled all the way from Europe to visit Einstein in Princeton. After she had finished hearing all about her brother's health and his many grandchildren, Bice seemed suddenly to recall an extremely urgent matter – as if, indeed, it were the very reason she had flown all the way over to Princeton from Europe. "Herr Professor," she asked Einstein in German, "this I really meant to ask you for a long time – why hasn't Michele [Besso] made some important discovery in mathematics?" Einstein said, laughing, "Aber, Frau Bice, this is a very good sign. Michele is a humanist, a universal spirit, too interested in too many things to become a monomaniac. Only a monomaniac gets what we commonly refer to as results." He giggled happily to himself.77

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Einstein explained this further in 1926. Einstein's friend in Zurich, Heinrich Zangger heard that Besso's position in the Patent Office was in jeopardy. On December 12, 1926, from Berlin, Einstein wrote in favour of his best friend: Besso's strength is an exceptional intelligence and unlimited devotion to the professional and moral duties. By contrast, his weakness is the low ability to make decisions. His success in life is disproportionate to his brilliant abilities and his extraordinary knowledge in purely and technical scientific fields. This explains why few official documents bear his name. Everybody in the office who requested advice in engineering matters consulted him. He understands very quickly the technical and legal aspect of every patent case. Einstein went on to say that Besso was most valuable as a consultant, and his withdrawal from the office would be a grave mistake. Einstein tried to save his position (Flückinger 1974, 151-152), although, some twenty years earlier he had admitted: "It's true, Michele is an awful schlemiel [clumsy]" (Einstein to Mariü, March 27, 1901, CPAE 1, Doc. 94). Besso was irreplaceable to Einstein, and the above traits were necessary for Einstein when he communicated with Besso and described his new ideas to him. Above all, Besso possessed wide knowledge in physics, mathematics and philosophy, and he was able to discuss the philosophical foundations of physics with Einstein (Einstein to Besso, March 6, 1952, in Einstein and Besso 1971, 464-465).

1.5 Poincaré's Creativity versus Einstein's Creativity Dr Toulouse examined Poincaré in 1897. However, Toulouse only published his book in 1909. He explained that he hesitated for many years to publish the notes, but finally decided to do so after he had found things he had not seen before (Toulouse 1909, 8-9, preface): This was after Poincaré had published his 1908 paper dealing with the process of his invention, "L'invention mathématique" (Mathematical Invention), quoted in Toulouse's book on pages 183-186 (Poincaré 1908b). Toulouse realized that his own analysis from 1897 of Poincaré's process of creativity, which reflected the way he had arrived at his new ideas and created scientific papers, fitted Poincaré's own description from 1908. He thus re-examined his notes and wrote the above said conclusions that appear on pages 186187. Toulouse then said that he was able to organise his notes and publish the book. As already stated, in 1916 the Gestalt psychologist Max Wertheimer interviewed Einstein, in much the same way as Toulouse interviewed

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Poincaré. Like Toulouse, Wertheimer hesitated to publish the interviews with Einstein and his analysis of Einstein's creativity. It took Wertheimer a long time to publish the interviews with Einstein: Wertheimer died on December 10, 1943, and Wertheimer's book, Productive Thinking, was published posthumously in 1945.78 Jacques Hadamard wrote in the introduction to his 1945 book, The Mathematical Mind, in which he also analysed Poincaré's 1908 paper, "Mathematical Invention" (Hadamard 1945, Forward): "This study, like everything which could be written on mathematical invention, was first inspired by Henri Poincaré's famous lecture before the Société de Psychologie [Psychological Society] in Paris".

Both Hadamard and Toulouse knew Poincaré personally: Hadamard's acquaintance with Poincaré was collegiate, both were mathematicians; and Toulouse the psychiatrist interviewed Poincaré, who revealed many personal details about himself. Poincaré was inspired to develop Fuchsian functions by the work of his school teacher, Charles Hermite. Many years later, in 1908, Poincaré presented his famous talk, "Mathematical Invention", to the Psychological Society of Paris at the Institut Général Psychologique (General Institute of Psychology). In this lecture, Poincaré disclosed his own scientific approach, and how, in 1881, he solved the problem with the Fuchsian functions, known today as automorphic functions. Poincaré thus revealed in this talk the process of his scientific creativity (Poincaré 1908b, 7-8). For fifteen days Poincaré attempted to demonstrate that any function could exist, similar to what he called Fuchsian functions. Nonetheless, he felt very ignorant. Every day he sat at his desk and spent an hour or two trying many combinations, without any solution. One evening, contrary to his habit, he drank black coffee, and could not sleep; ideas rose in crowds, and he felt them come against him, until two of them were clinging to form a stable combination. In the morning he had established the existence of a class of Fuchsian functions. He had only to write the results, and this took him a few hours. At this time, he left Caen, where he was then living, to take part in a geologic excursion conducted by the School of Mines. The events of the trip made him forget his mathematical work; having arrived at Coutances, he entered an omnibus; the moment he put his foot on the step, the idea

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came to him, without anything in his former thoughts seeming to have prepared him for it – the transformations he had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. Poincaré did not verify this, because he did not have time to, since, upon taking his seat in the omnibus, he resumed the conversation already started, but he felt a perfect certainty. On his return to Caen, he verified the result. Then it seems that the same happened with arithmetic. Poincaré turned to the study of arithmetic questions, apparently without much success. He was disgusted with his failure, and went to spend a few days at the seaside. One day, while walking on the cliff, the idea arose, with just the same characteristics of brevity, suddenness and immediate certainty as before. He realised that the undefined arithmetic transformations of quadratic forms were identical with those of non-Euclidean geometry. Hadamard, who translated and analysed Poincaré's above lecture at the Psychological Society in Paris, said "that extraordinary fact of watching passively, as if from the outside, the evolution of subconscious ideas seems to be quite special to Poincaré" (Hadamard 1945, 15). Hadamard once asked Einstein questions about his creativity and the process by which his ideas developed, and published the answers. Hadamard wanted to know what kind of "internal world" (i.e. what internal or mental images) mathematicians make use of, whether they are motor, auditory, visual, or mixed, depending on the subject they are studying (Hadamard 1945, 140). Einstein replied that, "The words or the language, as they are written or spoken, do not seem to play any role in my mechanism or thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined". Einstein spoke about a certain connection between the above elements (certain signs and more or less clear images) and relevant logically connected concepts. He explained to Hadamard that, "The above mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will" (Hadamard 1945, 142-143). Hadamard mentioned Max Wertheimer's interview with Einstein. Einstein told Wertheimer that his "thoughts did not come in any verbal formulation.

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I very rarely think in words at all. A thought comes, and I may try to express it in words afterward". Wertheimer remarked to Einstein that many people report that their thinking is always in words; Einstein only laughed (Wertheimer 1916, 184). Einstein first used images (anchored in the unconscious) to solve problems in science; for instance, he first imagined thought experiments. Words, as they are written or spoken, came later, when he expressed his discoveries through the language of logical connections. According to Viereck, Einstein said: "I am enough of the artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world" (Viereck 1929, 117). At about the same time that Hadamard interviewed Einstein, Einstein wrote a letter to the art historian Paul M. Laporte (in German on May 4, 1946). Laporte had sent Einstein a manuscript on cubism and relativity, which was based on attempts at popularisations of the theory of relativity. Einstein replied to Laporte that a work of art is evaluated differently than a work of science: "In science, the principle of order which creates units is achieved through logical connections while, in art, the principle of order is anchored in the unconscious" (Laporte 1966, 246).79 Fairly soon after writing in the Autobiographical Notes that he came to the conviction that, only the discovery of a universal formal principle would solve his problems, Einstein explained his chasing after a light beam thought experiment. He said it appeared to him intuitively clear that, judged from the standpoint of an observer, who pursues a light beam with a velocity c, everything would have to happen according to the same laws as for an observer who, relative to the Earth, was at rest. "For how should the first observer know, or be able to determine, that he is in a state of fast uniform motion?" (Einstein 1949, 50-51). Einstein wrote, "Intuitively clear". Judged from the point of view of Einstein's creativity, he told Hadamard that his primary thinking process involved visual and tactile images. It was intuitively clear to Einstein that there should be no such thing as a frozen light wave on the basis of his ability to think in images, thought experiments, and entertain non-verbal images. He sensed that his thought experiment created a difficulty to the ether theory, even if this thought experiment could not yet be formulated in terms of words. Both Einstein's and Poincaré's initial work was undertaken in their unconscious minds. Einstein's first stage was non-verbal and visual, while

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Poincaré's first stage was verbal and included non-visual mathematical signs (as we shall see from Toulouse's explanation of Poincaré's story). Einstein's second stage was communicating his non-verbal images to his friends at the Patent Office, while Poincaré's second stage was solitarily writing his results. Dr Toulouse remarked on the same text from Poincaré's 1908 talk: "This method of work is not common in science matters, and constitutes a very special character of mental activity of M. H Poincaré" (Toulouse 1909, 187). Indeed, in his 1908 talk Poincaré reflected on the way his unconscious arrives at his ideas (Poincaré 1908b, 9). "Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable". Poincaré therefore does not sit at the table for too long. He takes a break and then returns, because most of the work is done by his unconscious mind; as he had explained before, "but I was very ignorant, and every day I sat at my desk. I spent an hour or two, I tried many combinations and I came to no results" (Poincaré 1908b, 7-8). Dr Toulouse analysed the above 1908 trip and omnibus story detailing Poincaré's resolution of the problem with Fuchsian functions. He explained that indeed Poincaré did not sit at the table for too long (Toulouse 1909, 144-145): "Mr H. Poincaré works every morning from 10:00 to 12:00, and in the afternoon from 5:00 to 7:00, and never in the evening after dinner. He cannot work more than two fruitful consecutive hours. If he works more time it will not produce more. During the holidays he takes a complete intellectual rest. He also suffers from long sitting".

Toulouse compared Poincaré's observations from his 1908 paper to his own interviews with Poincaré from 1897. He arrived at the following conclusions regarding Poincaré's creativity, after quoting Poincaré's article on "Mathematical Invention" from 1908 on pages 183-186: "From all these facts, it appears that M. H. Poincaré's intellectual activity is especially spontaneous and automatic". And, "Mr H. Poincaré is not visual". That is, according to Toulouse, Poincaré did not have a good visual memory (Toulouse 1909, 14, 101, 103, 187). Nevertheless, he did have a good memory, and he had a good verbal memory. Poincaré had a logical memory.

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By apparent contrast, the elder Einstein said that his principal weakness was a poor memory, especially for words and texts (Hoffmann and Dukas 1973, 19-20). It seems that Toulouse exaggerated when he said that Poincaré did not invent facts and that he was not visual because, like Einstein, Poincaré invented thought experiments. In Science and Hypothesis and his other general books Poincaré proposed multiple thought experiments. For instance, he presupposed that an individual is transported to a planet, the sky of which is constantly covered with heavy and thick clouds so that he can never see the other stars. He would live on that planet as if it were isolated in space. But this individual would notice that the planet revolves, for example by repeating the experiment of Foucault's pendulum. The absolute rotation of this planet may be clearly demonstrated in this way (Poincaré 1902a, 100). Unlike Einstein, Poincaré's first stage apparently did not consist of inventing non-verbal and visual thought experiments. Although Poincaré had a good verbal memory, Toulouse said that he was not a great orator (Toulouse 1909, 124). When discussing Einstein's childhood, it was mentioned that in 1954, the elderly Einstein recounted "Also, I never exactly became an orator later" (Hoffmann and Dukas 1973, 14). Poincaré spoke correctly, but with a shyness that he was aware of. He therefore avoided speaking unprepared in public, except in circles of scientists. Dr Toulouse explained that he wrote his speeches in advance, by preparing a number of sentences that he pronounced and practiced aloud to himself, usually at the beginning of his speech. When Poincaré spoke it went smoothly, but he never wrote down the entire speech and did not learn it by heart. Poincaré primarily sought clarity before correctness, and often repeated his words so that they would be clearer (Toulouse 1909, 124). According to Hans Albert, Einstein always liked to improvise. When Einstein had to give a talk he never knew ahead of time exactly what he was going to say. "It would depend on the impression he got from the audience in which way he would express himself and into how much detail he would go" (Whitrow 1967, 19). Toulouse described Poincaré's working habits: Poincaré makes daily interruptions for two to three hours, and sleeps every night from ten to

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seven in the morning. He tries to get seven hours of sleep (Toulouse 1909, 142). Einstein was a bohemian and could not be fitted into any pattern. As mentioned, he often informally discussed his lectures with students late into the evening at Café Terrasse (Seelig 1954, 15, 121, 1956a, 13, 101102). Leopold Infeld described the older Einstein (Infeld 1941, 293):80 "One of my colleagues in Princeton asked me: 'If Einstein dislikes his fame and would like to increase his privacy, why does he not do what ordinary people do? Why does he wear long hair, a funny leather jacket, no socks, no suspenders, no collars, no ties?' The answer is simple and can easily be deduced from his aloofness and desire to loosen his ties with the outside world. The idea is to restrict his needs and, by this restriction, increase his freedom"

Toulouse writes that Poincaré did not write his papers according to plans (Toulouse 1909, 186). We can readily admit that the way Poincaré works is unusual. "As a preparation he takes a few notes. Often there is no big plan. Or he simply writes a few ideas on a paper that he would develop. Usually, he starts from memory, without his mind knowing the solution beforehand, before developing the problems that he would address. The beginning is usually easy and he is then led by his work. Then, it is difficult to distract him". Poincaré would become distracted when not involved in science, and his family and associates would recognise his distraction. There is proof of this, for example, during one of his travels, he put a sheet of white paper in an envelope instead of a letter; on another occasion he packed a sheet instead of a shirt. Alternatively, he did not suffer these distractions when involved in scientific endeavours (Toulouse 1909, 145, 145, 27). Einstein also enjoyed a tremendous ability to concentrate. As already stated, when Einstein was 16 years old his sister reported that he already had this remarkable power of concentration that even in a large, quite noisy group, he could withdraw to the sofa, take pen and paper, and lose himself so completely in a problem that the many voices stimulated rather than disturbed him (Winteler-Einstein 1924b, 1xiv, 1924c, xxii). Dr Toulouse wrote that when Poincaré searched for something, he often automatically wrote a formula to see if it stimulated any ideas. If the start of the process was very painful, then Poincaré did not persist; he did not have patience. In some of his works, Poincaré proceeded by blows, taking and abandoning the subject. During the intervals he assumed that his

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unconsciousness continued the work of reflection. Stopping the work was difficult if there was not a strong enough distraction, especially if this work was not considered complete. For this reason, Poincaré did nothing important in the evening to avoid his sleep being disturbed (Toulouse 1909, 145-146). Poincaré was aware of his ability to arrive at mathematical innovations, abruptly, with sudden strokes, during geological excursions and visits to mines or other trips, his great love from the days he used to study at the School of Mines. He did not need more than two hours of work per day. Most of the work was done unconsciously during other activities, and Poincaré could exploit his hobbies and adventurous aspirations. His uniqueness was the ability to combine mathematics and adventure within his creative, unconscious mind.

2 Kinematics of a "Rigid Body" – No Such Thing In 1905, Einstein wrote in his relativity paper, "On the Electrodynamics of Moving Bodies": "The theory to be developed here is based, like all electrodynamics, on the kinematics of the rigid body, since the assertions of any such theory concerns with the relations among rigid bodies (coordinate systems), clocks, and electromagnetic processes". Einstein defined position by "means of rigid measuring rods and using the methods of Euclidean geometry" (Einstein 1905a, 892). Further, Einstein considered "a rigid sphere" at rest relative to the "moving system" k, with its centre at the origin of the system k. The sphere has a radius of R in k. He wrote the equation of the surface of the sphere moving relative to the system k with a velocity v. The equation of the same sphere measured from the perspective of the "system at rest" K, that is expressed in the coordinates x, y, z at the time t = 0 is different, because the x direction is contracted, while the y and z coordinates remained unaffected. Einstein concludes (Einstein 1905a, 903): "A rigid body which, measured in a state of rest, is in the form of a sphere, therefore, has in a state of motion – viewed from the system at rest [K] – the form of an ellipsoid of revolution. […] Thus, whereas the Y and Z dimensions of the sphere (and therefore of every rigid body no matter what shape) do not appear modified by the motion, the X dimension appears contracted in the ratio ͳǣ ඥͳ െ ‫ ݒ‬ଶ Τܿ ଶ , so the greater the value of v, the greater the contraction".

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Einstein remarked that it was clear that the same results hold well for bodies at rest in the rest system K, viewed from a system in uniform motion k. In Einstein's theory, the Lorentz contraction does not "really" exist – in the sense that it can be detected by physical means – for an observer moving with the object. However, it does exist – in the sense that it can be detected by physical means – by a non-co-moving observer. Einstein reasoned that for v = c all moving objects as viewed from K contract into plane figures. Therefore, "For velocities greater than that of light [superluminal velocities] our considerations become meaningless; we shall find in the considerations that follow, that in our theory the velocity of light physically plays the role of infinitely great velocities" (Einstein 1905a, 903). Einstein spoke above about a "rigid body", "contraction" and mentioned that according to special relativity information cannot travel faster than the speed of light; and so he arrived at a contradiction. There can be no rigid body or rigid sphere, which is possible in classical mechanics where forces are transferred at infinite speeds. A rigid body moves in a rigid manner, no matter what forces are imposed on the body. In fact, rigid motions can be defined without any contradiction in special relativity, even though a rigid body does not exist in the special theory of relativity. Einstein spoke about a rigid body because in 1905 he did not realise that the concept of the rigid body was incompatible with the special theory of relativity, and had to be replaced by the concept of rigid motions. At the eighty-first meeting of the German Society of Scientists and Physicians in Salzburg in September 1909, Max Born presented a paper in which he first analysed this problem and showed the existence of a very limited class of rigid motions in special relativity; although one cannot have rigid bodies in special relativity, one can move the measuring rod rigidly; for this, Born provided a Lorentz invariant definition. Born explained that, "measuring rods that maintain their length at uniform translation in the co-moving coordinate system, suffer a contraction in the direction of their velocity when viewed from the system at rest. Therefore, the concept of the rigid body is dropped [fällt], at least in its form adapted to Newtonian kinematics" (Born 1909a, 2). Arnold Sommerfeld commented on Born's talk "Über die Dynamik des Elektrons in der Kinematik des Relativitätsprinzips" (On the Dynamics of the Electron in the Kinematics of the Relativity Principle) in a Diskussion

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(discussion) following the paper (Born 1909b, Sommerfeld 1909a): "Über die Zusammensetzung der Geschwindigkeiten in der Relativtheorie. Diskussion" (On the Addition of Velocities in Relativity Theory). Born noted in a later paper that he had discussed the subject with Einstein and they were puzzled that the rigid body at rest can never be brought into uniform motion (Born 1910). Born discussed the problem of rigid bodies in the theory of relativity. In 1911, Max Laue responded to Born's paper about the necessity to admit the possibility of shape changes of a body, in his paper titled "Zur Diskussion über den starren Körpern in der Relativitätstheorie" (On the Discussion of Rigid Bodies in the Theory of Relativity). Laue wrote that this was also explained by the example Einstein gave in his conversation with Born, which was communicated to him during a discussion at the meeting of natural scientists in Königsberg by Sommerfeld (Laue 1911, 86). Laue gives the following example: Consider a measuring rod at rest. In the beginning a second measuring rod is also at rest. At one end A of the first rod – an intersection point between the two rods – an event happens. The second rod is immediately set into motion. Then the other end B would have to go into motion immediately or simultaneously as a result of the event that happened at A. Laue explains that if the end B goes into motion immediately as a result of the event that happens at A, then the transmission of information from A to B (the impulse that brings the rod into motion) takes place with superluminal speed V. But special relativity says that no signal can be transferred beyond the fundamental velocity of light c. Therefore, the concept of a rigid body contradicts this consequence of special relativity (Laue 1911, 86). According to special relativity the second measuring rod, which is brought into motion by an impulse emanating from A, doesn't remain straight but gets shortened in A (i.e., it does not remain constant in length). The previous conclusion, V > c, only holds for motions at which the measuring rod remains straight, i.e. when the measuring rod is a rigid body (Laue 1911, 87). In June 9, 1952, Einstein wrote an appendix to the fifteenth edition of his popular 1917 book On the Special and the General Theory of Relativity. In this appendix he wrote (Einstein 1952b, 142-143):

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D. The Meaning of Einstein's 1905 Special Relativity "The subtlety of the concept of space was enhanced by the discovery that there exist no completely rigid bodies. All bodies are elastically deformable and alter in volume with changes in temperature".

3 Distant Simultaneity 3.1 Definition of Distant Simultaneity In 1905 Einstein had given meaning to the space coordinates by the system of rigid rods at rest in a coordinate system (in a state of inertial motion), and now the question was how to give meaning to the time coordinate. Providing a definition of simultaneity was necessary, because all judgments in which time was involved are always judgments of simultaneous events (Einstein 1905a, 892-893). Einstein defined measurement conventions using clocks and measuring rods and adopted a definition of distant simultaneity.

3.2 1905: Definition of Distant Simultaneity with Reference to Synchronised Clocks Let us first see how Einstein proceeded with the aid of rods and synchronised clocks to define distant simultaneity. In Section §1 Einstein says, "As we know from experience". Einstein implicitly tells his reader: you have been on trains, looked at the hands of clocks. "If for instance, I say, 'That train arrives here at seven o'clock', I mean something like this: 'This pointing of the small hand of my watch to seven and the arrival of the train are simultaneous events" (Einstein 1905a, 893). Einstein substitutes "the position of the small hand of my watch" for "time". This is reasonable when we want to define time for the place where the watch is located. Einstein uses the train and clock example to exemplify to his readers some experience from his daily life. However, we must not infer from such examples that this and other similar thought experiments could indicate that Einstein might have been inspired by patents of clocks, trains and clock towers that happened to stand near the Patent Office he used to work at in Bern. Einstein himself left no written statement even implying that he became increasingly interested in time because of any timing technologies at the Patent Office (Martínez 2004b, 226). Immediately after this intuitive presentation, Einstein explains that we might be satisfied with evaluating the time of the events determined by an observer (standing at the origin of the coordinates) together with the clock, and assigning the corresponding positions of the hands to light signals,

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given out by every event to be timed, and reaching him through empty space. Why is this scheme not proper? Einstein refers again to experience; we know from experience that this coordination has the disadvantage of not being independent of the position of the observer equipped with the clock. Next, Einstein tells his readers that it is possible to evaluate the time of events that are remote from the clock, but it is not convenient. This sounds reasonable as well, but it is a leap of thought (Einstein 1905a, 893). Einstein introduces a synchronisation procedure (Einstein 1905a, 893894). There is a clock at the point A in space, and an observer at A can determine the time of events in the immediate vicinity of A by finding the positions of the hands of the clock, which are simultaneous with these events. There is a clock at point B of space– the clock at B, in all respects, resembles the one at A. It is possible for an observer at B to determine the time values of events in the immediate vicinity of B. Einstein explains: "But it is not possible, without further assumption, to compare, the time of an event at A with the one at B". Einstein had so far defined only an "A time'' and a "B time,'' but not defined a "common time'' for A and B. Einstein needed a "further assumption" to the two principles of his theory, a definition. The common time can now be defined "by establishing by definition distant simultaneity that the 'time' required by light to travel from A to B equals the "time'' it requires to travel from B to A". The definition is as follows (Einstein 1905a, 894): "Let a ray of light go from A to B at a time tA, at B time tB it is reflected from B towards A, and arrives again at A at a time t'A. By definition the two clocks are synchronous if tB – tA = t'A – tB."

Einstein then assumes two additional hypotheses that are generally valid (Einstein 1905a, 894): 1) Additivity: if the clock at B runs synchronously with the clock at A, the clock at A runs synchronously with the clock at B. 2) Transitivity: if the clock at A runs synchronously with the clock at B as with the clock at C, then the clocks at B and C also run synchronously relative to each other.

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Subsequently, Einstein tells the reader, "With the help of certain (imagined) physical experiments, we have defined what is to be understood by synchronous clocks at rest relative to each other located at different places, and obviously obtained a definition of 'simultaneous' and 'time'". Also, the definition: "The 'time' of an event is the reading that is given simultaneously with the event by a clock at rest, which is located at the place of the event, this clock for all times is synchronous with a specified clock at rest" (Einstein 1905a, 894). Einstein refers again to experience: "In agreement with experience", we further stipulate the quantity: ʹ‫ܤܣ‬ ൌ ܿǡ ‫ݐ‬Ԣ஺ െ ‫ݐ‬஺ be a universal constant (the velocity of light in empty space)". Einstein defined time by means of clocks at rest in a system at rest, and he called it "the time of the system at rest".

3.3 Definition of Distant Simultaneity without Reference to Synchronised Clocks In his popular 1917 book, On the Special and the General Theory of Relativity, Einstein defined distant simultaneity with respect to a given frame of reference without any reference to synchronised clocks. Five years earlier, Vladimir Variþak criticised Einstein (as discussed in Section 4 below). Einstein responded by suggesting a thought experiment that does not require the use of synchronised clocks in order to verify the Lorentz contraction. In 1917, Einstein considered two bolts of lightning that strike points A and B respectively. The interval AB is measured, and an observer is placed in the middle M of the interval AB. The observer is provided with a device (for example two mirrors inclined at an angle of 90° to each other) that allows him simultaneous view of both places A and B. If he perceives the two strokes of lightening simultaneously, then they are simultaneous. Einstein first says that the two optical signals from A to M and B to M both proceed at the same speed. However, the speed could only be defined if we already had at our disposal the means of measuring time. Einstein then adopts a definition of simultaneity, "That light requires the same time to traverse the path A arrow M as for the path B arrow M". Only after

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defining distant simultaneity does Einstein proceed on to the definition of "time", which does involve clocks (Einstein 1917, 14-15, 1920b, 25-28).81

3.4 On the Relativity of Lengths and Times In 1905, in order to evaluate remote events Einstein needed to formulate the two heuristic principles of his theory; these would guide him in his search for the solution to the problems (Einstein 1905a, 895): "1. The laws by which the states of physical systems change are independent, whether these changes of state are referred to the one or the other of two systems of coordinates in uniform motion of translation. 2. Any ray of light moves in the coordinate system 'at rest' with the definite velocity c, independent of whether the ray is emitted by a body at rest or in motion. Here: Velocity = light path/time interval".

Where "time interval" is understood in the sense of the definition of distant simultaneity given in Section §1 for clock synchronisation in one system: the time required by light to travel from A to B = time it requires to travel from B to A. With the aid of the two principles and the definition of distant simultaneity, in Section §2 of the 1905 relativity paper, Einstein presents the principal result of his kinematics: relativity of simultaneity. Let there be a theoretical rigid rod at rest. Its length is l as measured by a measuring rod which is also at rest. Einstein imagines the axis of the rod lying along the X axis of the coordinate "system at rest" (K). The rod is then set into uniform parallel motion of translation (with velocity v) along the X-axis in the direction of increasing x. Einstein asks: What is the length of the moving rod? Einstein defines its length in two different ways by implementing his two heuristic principles (Einstein 1905a, 895-896): 1) First there is an observer who moves together with the rod to be measured and with the measuring rod. He measures the length of the rod directly by superposing the measuring rod, in just the same way as if the three were at rest. 2) The observer in K ascertains, as required by Section §1, using synchronous clocks at rest, at what points of K the two ends of the rod to be measured are located at a definite time t. "The distance between these

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two points, measured with the rod used before, but now at rest, is also a length, which may be designated the 'Length of the Rod'". Einstein was guided by the principle of relativity and thus calls the length by operation 1) – the length of the rod in "the moving system" k. This length is equal to the length l of the rod at rest. Einstein calls the length of the rod by operation 2), "the length of the (moving) rod in the system at rest" K. Since, according to Einstein, one could give preference to either of the two observers, as the one was in motion and the other was at rest, this latter statement laid down the following definition: the length of a body in its rest frame is uncontracted. This length was first named by Einstein in 1907 "the geometrical form" of the body, and then later called the body's "proper length" (length l in the above example). An observer in the rest frame of a body measures its geometrical form. Einstein's terminology was required to emphasise that the contraction is kinematical rather than dynamic in nature (as it was for Lorentz and Poincaré). Since the contraction is kinematical, each observer measured the other observer's lengths as being contracted; this is complete reciprocity: each observer measured the other observer's "kinematical form" (Einstein 1907b, 417). Both concepts, "geometrical" and "kinematical" form, comply with Einstein's principle of relativity: All inertial systems and observers are equivalent, and there is no real distinction between quantities referred to by a fixed observer in the ether, and apparent quantities referred to moving observers relative to each other. This form of the principle stems from Einstein's desire to unify mechanics and electrodynamics under the principle of relativity. By contrast, the Lorentz-Poincaré's real contraction was perfectly suited to their conception of the theorem of corresponding states and the principle of relativity: a principle that only serves to prevent us from ever discovering motion with respect to the ether. This principle of relativity was thus transferred from mechanics to electrodynamics as a paramount principle, with no intention of unifying both fields. Einstein was going to demonstrate the relativity of simultaneity by using both his principles: the relativity and the light postulate (Einstein 1905a, 896): Suppose the rod moves with a uniform velocity v along the x axis of the "rest system" K. At the two ends A and B of the moving rod, clocks are placed, which are synchronous, however, with the clocks of K. With each clock there is a moving observer. Remember that observer A can determine the time of events immediately near clock A, and B can do the

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same near clock B. Now we want the two clocks to be synchronised according to the procedure in §1 and so the observers exchange signals. Imagine again the observer 2) in K who ascertains, as required by §1 the kinematical length of the moving rod. The clocks of the observer in K are synchronous with the clocks of the observers A and B of the moving rod. He sees the two observers A and B exchanging light signals. In the moving system a ray of light is sent from A at time tA, there it is reflected from B at time tB, and arrives back at A at time t'A. The observer in K uses the definition of distant simultaneity from §1 (Einstein 1905a, 896-897). The result found by him shows that observers moving with the rod will thus find that their clocks are not synchronous, while observers in K will declare the clocks to be synchronous (Einstein 1905a, 897): "We thus see that we cannot ascribe any absolute meaning to the concept of simultaneity, but that two events, which are simultaneous as viewed from a system of coordinates, can no longer be considered simultaneous events when observed from a system which is moving relative to that system".

4 Challenges to Einstein's Connection of Synchronisation and Contraction Einstein showed the connection between the contraction of the moving rod as observed from reference frame K ("the system at rest") and the relativity of simultaneity. From this connection Vladimir Variþak suggested in 1911 the following interpretation to the contraction of lengths: Einstein's contraction should be regarded as an apparent phenomenon, produced by the manner in which our clocks are synchronised and lengths are measured. It results from measuring lengths using synchronised clocks. This contraction is thus connected with the relativity of simultaneity. A state is considered real only when it can be determined in the same way in all reference frames. However, the Lorentz contraction in Einstein's sense is apparent – because an observer in K will see the rod contracted, while an observer in k (comoving with the rod) will see the rod without contraction. Variþak thus asked: Is the Lorentz contraction observable? The contraction is a subjective phenomenon since it is only observable from the standpoint of a non-co-moving observer. It depends on an observer being present in order to measure length using synchronised clocks. On the other hand, Lorentz’s

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contraction is an objective phenomenon; for it occurs whether an observer is present or not (Variþak 1911, 169). Variþak sent Einstein the draft of his paper. On March 3, 1911, Einstein replied: "I cannot understand how you can draw support of your opinion from this. I want to justify my opposite opinion explicitly". Einstein asked Variþak if he could inform him about his publication plans (Einstein to Variþak, March 3, 1911, CPAE 5, Doc. 257a): "If you are going to publish your note, it is my duty to also express my own point of view publicly, because my silence might be interpreted as agreement, and because I believe that your note could create confusion. I therefore ask you to let me know whether you still want to publish it, and in which journal I should publish my response".

Indeed, Variþak published his paper and Einstein responded. On May 18, 1911, Einstein submitted his paper, "Zum Ehrenfestschen Paradoxon. Bemerkung zu V. Variþaks Aufsatz" (On the Ehrenfest Paradox. Comment on V. Variþak’s Paper) to Physikalische Zeitschrift, in which he replied to Variþak’s comments (Einstein 1911, 509-510). Einstein wrote that the question of whether the Lorentz contraction exists or does not exist in reality is misleading. It does not exist "in reality" insofar as it does not exist for an observer moving with the object. However, it does exist "in reality", in the sense that it could be detected by physical means by a nonco-moving observer. Einstein ended his reply to Variþak’s comments by suggesting the following thought experiment that does not require the use of synchronised clocks to verify the Lorentz contraction (Einstein 1911, 510; Pauli 1921, 27 [557], 1958, 12-13): Consider two rods A'B' and A''B'' of the same proper length. The two rods move parallel to the x-axis with respect to the system K with equal and opposite large constant velocity v: they pass each other with A'B' moving in the positive, and A''B'' in the negative direction of the x-axis. The endpoints A' and A'' of the rods meet at a point A* on the x-axis of K, while the endpoints B' and B'' meet at a point B* of K. The distance A*B* as measured by measuring rods at rest in K will then be contracted with respect to the proper length of either of the two moving rods. Therefore, the Lorentz contraction is not a property of a single measuring rod taken by itself, but a reciprocal relation between two such rods A'B' and A''B'' moving relatively to each other, and this relation is in principle observable.

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In 1916, Einstein used his definition of distant simultaneity with respect to a given frame of reference without any reference to clocks and suggested the famous train thought experiment to exemplify the relativity of simultaneity in his 1917 popular book, On the Special and the General Theory of Relativity (Einstein 1917, 16-17, 1920b, 30-33): We suppose a very long train travelling along the rails with constant velocity v relative to the Earth. People travelling in the train consider events in reference to the train. Einstein considers two events, strokes of lightning A and B, and says that these are simultaneous with respect to the railway embankment, i.e., the Earth frame. He asks, are these also simultaneous relatively to the train? He shows they are not. When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean that the rays of light emitted at the places A and B – where the lightning occurs – meet each other at the midpoint M of the embankment at the same moment of time. But the events A and B correspond to positions A and B on the train. Let M' be the midpoint of the length AB on the travelling train. When the flashes of lightning occur, as judged by an observer on the embankment, M and M' coincide, and then M' moves towards the right with velocity v. If an observer sitting in the position M' in the train did not possess this velocity, then he would remain at M and the light rays emitted by the two flashes of lightning A and B would reach him simultaneously, and they would meet him where he is seated at the same moment. In reality the observer at M' is rushing towards the light signal coming from B, while he is riding on ahead of the beam of light coming from A. It means that the light signal from A traversed a greater distance to reach the observer at M'. The light beam from the place B traversed a lesser distance. Since the velocity of light is constant, the observer at M' sees the beam of light emitted from B before he sees that emitted from A. Einstein thus concludes: Observers who take the railway train as their reference frame must therefore arrive at the conclusion that the lightning flash B took place earlier than the lightning flash A.

5 Derivation of the Lorentz Transformation 5.1 The Lorentz Transformations Derived by the Principle of Relativity and the Light Postulate

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In Section §3 of the 1905 relativity paper, Einstein derived the Lorentz transformations (the transformations of the coordinates and times) in the following way: He defined two systems, the first, a rest system K, and a second, system k moving with a constant velocity v in the direction of increasing x of the other system K. Einstein defined the two systems of coordinates and time of a specific event one with respect to the system K and the other with respect to k. Einstein defined the two systems in the following manner (Einstein 1905a, 897): "Let there be in the space 'at rest' two systems of coordinates, i.e. two systems, each of three rigid material lines, perpendicular to one another, and originating from a point. Let the X-axes of the two systems coincide, and their Y- and Z-axes respectively be parallel. Each system shall be provided with a rigid measuring-rod and a number of clocks, and let both measuring-rods, and all the clocks of the two systems, be in all respects identical".

Now impart to the origin of one of the two systems (k) a (constant) velocity v in the direction of the increasing x of the other system (K) "at rest", and let this velocity be communicated to the axes of the coordinates, the relevant measuring-rod, and the clocks. To each time t of the system K there will correspond a definite position of the axes of k, and from "reasons of symmetry" we are entitled to assume that the motion of k may be such that the axes of k are at the time t (of K) parallel to the axes of K. Einstein imagined that space was measured from the system K at rest by means of a measuring-rod at rest, and from the moving system k by means of the measuring-rod moving with it. The coordinates obtained by this way are: x, y, z and ȟ, Ș, ȗ, respectively. The time is determined by means of light signals in the manner indicated in Section §1 of the relativity paper: there are clocks at many points in system K and observers exchanging light signals between these points at which the clocks are located – the time t is determined for all these points in K where there clocks are. The same method is used in system k, with clocks at rest relative to system k, and time IJ is determined for k. To any system of values x, y, z, t, which completely define the place and time of the event in the system K at rest, there corresponds a system of values ȟ, Ș, ȗ, IJ, determining that event relative to the system k. Einstein's task was to find the system of transformation equations – connecting these quantities. The derivation of the Lorentz transformation, or as Einstein calls them in 1905, the transformations of coordinates and time, in Section §3 of the relativity paper – the equations connecting the two systems of quantities x, y, z, t and

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ȟ, Ș, ȗ, IJ – was very cumbersome. It was based on synchronising clocks (Einstein 1905a, 897-898). The final form of Einstein's transformation equations for the coordinates and time (the Lorentz transformations) is: ߬ ൌ ߚ ቀ‫ ݐ‬െ ߚൌ

‫ݔݒ‬ ቁ ǡ ߦ ൌ ߚሺ‫ ݔ‬െ ‫ݐݒ‬ሻǡ ߟ ൌ ‫ݕ‬ǡ ߞ ൌ ‫ݖ‬ǡ ܿଶ

ͳ ඥͳ െ ‫ ݒ‬ଶ Τܿ ଶ

Ǥ

The derivation uses the two guiding principles and "the rule given in §1" "and applying the principle of the constancy of the velocity of light in the rest system", and "expressing in equations that light (as required by the principle of the constancy of the velocity of light in combination with the principle of relativity) is also propagated with velocity c when measured in the moving system" (Einstein 1905a, 899, 902). Einstein obtained the transformation equations for the coordinates and time (the Lorentz transformations), and he was about to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if this is the case in the system at rest. According to the "light postulate" defined in Section §2 any ray of light moves in the coordinate system K with the definite velocity c, independent of whether the ray be emitted by a moving or a body at rest. In Lorentz's theory of the electron (not mentioned in the kinematical part), this was indeed the case in the system at rest – with respect to the stationary ether – which is superfluous in Einstein's theory. Einstein now needs to prove that light is also propagated with the definite velocity c as measured in the system k, because he renounced the ether. He writes, "For we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity". Einstein gave the proof of the compatibility. He had struggled for five years with the solution to the problem of the incompatibility between the Galilean principle of relativity and the principle of the constancy of the velocity of light (as shown when discussing Einstein's route to special relativity, see Chapter C) the result of which is presented here; and the proof: consider the equation of a spherical wave propagating with the velocity c in system K: x2 + y2 + z2 = c2t2. Transforming this equation with the aid of the equations of transformation gives: ȟ2 + Ș2 + ȗ2 = c2IJ2.

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Einstein thus concludes, "The wave under consideration is also a spherical wave with velocity of propagation c when it is observed in the moving system. This demonstrates that our two fundamental principles are compatible" (Einstein, 1905a, 900-901). According to John Stachel, Einstein's elaboration culminates when he got at this solution, conciliating his two chosen principles (relativity and constancy of light velocity) through a redefinition of space and time. The part of Einstein's 1905 relativity paper dealing with this redefinition is fundamental for Einstein's own intelligibility (and ours), and for the consistency of his theory. He reforms the concepts of space and time by making them physical, by submitting them to the two physical principles he enunciated. This aspect has been overlooked by most scholars, who insist on the process of measurement with rods and clocks, which is, actually, only the means of submitting space and time to the two principles, with the intention, as an effect, of the deduction of the Lorentz transformation formulas. The essential in it is the role played by the constancy of the velocity of light, admitted for all directions in space, i.e., in agreement with the principle of relativity and worked out in a fully consistent way. Clocks synchronisation, in Einstein’s hands, includes explicitly and wholly the principle of constancy of the velocity of light. By contrast, this was not Poincaré's conception, as he had not specified to which extent the velocity of light was constant, and relied, in his clocks synchronisation, on the length contraction hypothesis (Paty 1992). Hence, the question of an eventual Poincaré's influence on Einstein, and the proposed very conjectural scenario for it, looses any attractiveness and appears as a purely peripheral matter; for suppose that Einstein had been influenced by Poincaré's critical attitudes about absolute simultaneity and time. To say it in one word: Einstein's way of synchronising clocks puts in the first place the constancy of the velocity of light (in any direction, i.e. consistently with the principle of relativity), whereas Poincaré, before 1906, does it inconsistently, because he used other properties.

5.2 Lorentz Transformations Derived without the Light Postulate In 1910, the Russian physicist Vladimir (Waldemar) Ignatowski showed that the special theory of relativity does not require the light postulate. In order to construct a theory of relativity without light, and to derive

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Lorentz-like transformations from the relativity principle alone, one needs to assume several additional hypotheses (Ignatowski 1910, 1911): 1) The requirement of reciprocity: the velocity of system K relative to system K' is equal and opposite to that of K' relative to K; the contraction of lengths at rest in K' and observed in K is equal to that of lengths at rest in K and observed in K' (Pauli 1921, 25-26 [555-556], 1958, 11). 2) Isotropy and homogeneity of space and time. It has already been mentioned here that, Einstein also needed additional hypotheses that were generally valid, transitive and additive (Einstein 1905a, 894). Ignatowski proved that Lorentz-like transformations follow from such assumptions, with one parameter, which can be either finite or zero (Pauli 1921, 26 [556], 1958, 11). Ignatowski's derivation was based on the group structure of the transformations linking two inertial frames. The general solution contained both the Lorentz group and the Galilean group as a singular limit of the former. A group depends on one free parameter, easily interpreted as the maximal velocity that a frame can have with respect to another one (Darrigol 2014, 139). Hence, the parameter can be identified with the reciprocal of the maximum possible speed in inertial frames; if we apply these Lorentz transformations to the Maxwell equations, then the parameter is the speed of light. Ignatowski thus claimed he proved that the second postulate of Einstein's theory was superfluous. On the other hand, Einstein's conclusion, repeatedly demonstrated in the 1905 paper from a few points of view that the speed of light, the upper limit on the velocities in inertial systems, was required in Ignatowski's formalism. However, one could claim that Ignatowski was forced to recourse to electrodynamics in order to include the speed of light, and thus indeed the second postulate of Einstein was necessary. In 1910, Ignatowski assumed the principle of relativity, isotropy and homogeneity of space, and the reciprocity of the transformations. One year later in 1911 Philipp Frank and Hermann Rothe accomplished Ignatowski's task by confining themselves to only two even more restricted postulates (Frank and Rothe 1911). Max Jammer, however, claimed that neither Ignatowski nor Frank and Rothe were able to identify

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the invariant velocity contained in the resulting transformations with the velocity of light (Jammer 2006, 146). Roberto Torretti found inconsistencies and contradictions in Ignatowski's additional hypotheses 1) and 2), and that his derivation required, after all, the additional hypothesis of the invariant velocity of light (Torretti 1996, 298-299). From then until today numerous other derivations of the Lorentz transformations or their equivalents have been proposed without invoking the light postulate or any reference to the concept of simultaneity (for instance, Mermin 1984). In 1935, Einstein apparently addressed Ignatowski and all others who were trying to derive Lorentz-like transformations without the light postulate. As he stated it: "The question as to the independence of those" mechanical concepts and their relations "is a natural one because the Lorentz transformation, the real basis of the special relativity theory, in itself has nothing to do with the Maxwell theory". The special theory of relativity grew out of the Maxwell electromagnetic equations. Hence, even in the derivation of the mechanical concepts and their relations the consideration of those of the electromagnetic field has played an essential role (Einstein 1935, 223). Einstein took the constancy of the velocity of light from Maxwell's electromagnetic theory. He distinguished, says Stachel, on one side, factual evidence, from optics experiments and astronomy observations, as an indication for the principle of relativity, at variance with the general interpretations; these were in terms of the generality of the constancy and isotropy of the velocity of light. On the other hand, the theoretical necessity of the constancy of the velocity of light was thus raised at the rank of a general principle, as the core of Maxwell’s theory, because of the role of electromagnetic waves in it, but restricted to the ether reference frame. Factually, both propositions were in agreement, this is evident in the introduction of Einstein's 1905 relativity paper, whereas theoretically they were apparently in contradiction, for in Maxwell-Lorentz's electromagnetic theory the velocity of light was constant only in the etherin-absolute-rest system. Einstein never gave up the light postulate, and apparently he did not accept alternative ways to develop the special theory of relativity that exist and are independent of the light postulate. Accounts of the kinematics of the special theory of relativity tended to follow Einstein's lead (Stachel 1995, 277-278).

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6 Relativistic Addition Theorem for Velocities and Superluminal Velocities In Section §5 of the 1905 relativity paper, Einstein obtained the relativistic addition theorem for velocities (Einstein 1905a, 905-906).82 ܷൌ

‫ݒ‬൅‫ݓ‬ Ǥ ͳ ൅ ‫ݓݒ‬ൗܿ ଶ

After presenting the relativistic addition theorem for velocities Einstein concluded, "It follows from this equation that from a composition of two velocities which are smaller than c, there always results a velocity smaller than c. It also follows that the velocity of light c cannot be changed by composition with a velocity less than that of light". The composition of two velocities is always equal to c for anything moving with speed c (Einstein 1905a, 906). It soon turned out that Einstein's argument concerning the addition theorem for velocities led to the discussion of superluminal velocities. From the summer of 1907, in six letters to Prof. Wilhelm Wien, Einstein discussed the occurrences of velocities exceeding the speed of light in dispersive and absorptive media. Einstein tried to answer the question whether such phase velocities in dispersive and absorptive media are the physically meaningful signal velocities relativity theory requires to be less than or equal to the velocity of light. Three years earlier Wien defended the impossibility of superluminal speeds in a debate with Max Abraham. Abraham assumed that rigid spherical electrons kept their spherical form at any velocity. His spherical electron seemed to permit superluminal velocities, because it was a rigid spherical electron and could be accelerated indefinitely. Lorentz assumed that the moving electron was contracted in the direction of motion, and according to Lorentz's theory it would require an infinite amount of energy to accelerate his deformable electron to the speed of light. Therefore, Lorentz's model of the electron did not allow superluminal speeds at all. Wien was thus a supporter of Lorentz's electron. Einstein's 1905 relativity theory also did not allow superluminal speeds at all. By this time in his June 1907 review article on the theory of relativity, "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen" (On the Relativity Principle and the Conclusions Drawn from It) Einstein

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had developed an argument against superluminal velocities that was quite distinct from those featured in the 1905 relativity paper (Einstein 1907b). In his June 1907 review article, Einstein wrote, "The addition theorem for velocities also yields the interesting conclusion that there cannot exist an effect that can be used for arbitrary signaling and that is propagated faster than light in a vacuum" (Einstein 1907b, 423). Einstein used the relativistic addition theorem for velocities to show that a signal propagating superluminally from cause to effect in the rest frames of those two events will propagate from effect to cause in another frame moving relatively to the first. Einstein explained: If, as we have assumed, the velocity of propagation of a body relative to a system S is W > c, the velocity of light, one can always choose v such that the time T < 0. "This result means that we would have to consider as possible a transfer mechanism whereby the achieved effect would precede the cause. Even though this result, in my opinion, does not contain any contradiction from a purely logical point of view, it conflicts with the character of all our experience to such an extent that this seems sufficient to prove the impossibility of the assumption W > c" (Einstein 1907b, 424). It is not unlikely that Wien had read Einstein's June 1907 paper and this aroused his interest in the question. Wien could not accept superluminal velocities and wrote Einstein a letter in which he used the standard expression for the group velocity in dispersive media. The fundamental impossibility of superluminal speeds became controversial because it became clear that in dispersive and absorptive media the phase velocity of a plane wave and even the group velocity of a superposition of waves could exceed the speed of light. Thus Maxwell's theory seemed to have contradicted relativity. Einstein was confronted with a new challenge: Was his 1905 new relativistic addition law of velocities applicable to group velocity in dispersive media? He tried to present Wien with an expression for group velocity in dispersive media, based on his relativistic addition law of velocities, he claimed was valid for absorptive media, and so superluminal velocities would be incompatible with Maxwell's theory ("Einstein on Superluminal Signal Velocities", CPAE 5, 57-58). Subsequently, Einstein recognised that his expression needed an amendment and correction. He wrote to Wien that, in his opinion, there was a contradiction with the principle of relativity in conjunction with the

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principle of the constancy of the velocity of light in the vacuum, if, for a specific metal and specific colour, the phase velocity exceeded the velocity of light in a vacuum. Obviously, the propagation of an electromagnetic signal with superluminal velocity was also incompatible with Maxwell's theory of electricity and light. This follows from the results of a study by Emil Wiechert that was published in the 1900 Lorentz Festschrift special issue of Archives néerlandaises des sciences exactes et naturelles. Einstein then proposed an expression according to Wiechart's theory. Some thought went into this expression, but it also contradicted Maxwell's theory. Einstein wrote to Wien: "As I have now recognised the letter I sent you yesterday is in need of an amendment and a correction. We must stick with the [standard] relation", and Einstein came back to the standard expression of the group velocity of the waves, which Wien had originally proposed (Einstein to Wien, August 23, 25 or July, 1907, CPAE 5, Doc. 49, 50). Einstein was finally confused (Einstein to Wien, July 29, 1907, CPAE 5, Doc. 51): "Unfortunately, almost everything that I reported to you, all too rashly, in my previous letters proved to be false upon closer examination. In fact, the only thing that is to be retained as correct is that Maxwell's theory rules out the possibility of the propagation of a signal with superluminal velocity. For the case of non-absorbing bodies or non-absorbing regions of a body, the expression for the group velocity is also, in my opinion, correct".

Einstein told Wien that it is in general difficult to retain the concept of "group velocity" for absorptive bodies if the absorption coefficient depended on the frequency. We can readily admit that Einstein was confessing to Wien that his reasoning was faulty. Einstein was confused because he did not have the correct expression for group velocity in dispersive media. However, he knew that one thing was correct: "According to Wiechart's results it is beyond doubt that our electromagnetic theories of dispersion can never yield superluminal velocity for the propagation of an optical signal" (Einstein to Wien, July 29, 1907, CPAE 5, Doc. 51). He vacillated between the classical expression that Wien wrote to him and his own expression, which was based on his relativistic addition law for velocities. Finally, Einstein gave up the whole project. He explained to Wien that extremely complicated investigations would be needed to calculate the

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propagation velocities of optical signals in metals; small wonder that in 1907, Wien was not convinced by Einstein's arguments. He remained concerned with the problem of superluminal velocities (Einstein to Wien, August 26, 1907, CPAE 5, Doc. 55, "Einstein on Superluminal Signal Velocities", 58-59). Many years later, Einstein vigorously objected to the coordinate "Schwarzschild singularity" because no material object can travel faster than light (because of superluminal velocities). In 1915 Karl Schwarzschild found a spherically symmetric, static and exact solution of Einstein's full non-linear gravitational field equations (the so-called "Schwarzschild black hole solution"). The solution has a coordinate singularity (a "region" in which the Einstein field equations break down) at a radius R, the "Schwarzschild radius". Schwarzschild investigated a spherical star of incompressible liquid. He found that the density must go to infinity as the star shrank toward the critical Schwarzschild radius. In 1939 Einstein said that the concept of an incompressible liquid was not compatible with the special theory of relativity as elastic waves would have to travel with infinite velocity. It would be necessary, therefore, to introduce a compressible liquid whose equation of state excluded the possibility of sound signals with a speed in excess of the velocity of light. However, one could not be sure that no assumptions had been made that contain physical impossibilities. Einstein considered as a field-producing mass, a great number of small gravitating particles that move freely under the influence of the field produced by all of them together. This is a system resembling Schwarzschild's spherical star. Hereby we may proceed as if the field, in which the particles are moving, were produced by a continuous mass distribution of spherical symmetry, corresponding to the whole of the particles. Einstein demonstrated that the particles would need to be moving at the velocity of light before reaching the Schwarzschild radius. Hence, Einstein concluded that there was no way a Schwarzschild singularity could ever be possible: "[…] the 'Schwarzschild singularities' do not exist in physical reality. […] The 'Schwarzschild singularity' does not appear for the reason that matter cannot be concentrated arbitrarily. This is due to the fact that otherwise the constituting particles would reach the velocity of light". Hence, Einstein objected to the Schwarzschild singularity: "The problem quite naturally leads to the question, answered by this paper in the negative, as to whether physical models are capable of exhibiting such a singularity" (Einstein 1939, 922, 936).

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In 1935, Einstein and his assistant Nathan Rosen proposed a new solution, free from singularities. The four-dimensional space was described mathematically by two sheets. A bridge (also known as "wormhole"), spatially finite, which connects these sheets, characterises the presence of an electrically neutral elementary particle (Einstein and Rosen 1935, 75). In the 1970s, physicists raised the idea that faster-than-light particles, tachyons, could be accommodated by special relativity: tachyons falling radially inwards never reach the Schwarzschild singularity. Instead, they are bounced back at the Schwarzschild radius. Maybe, if ordinary matter was dropped into a black hole and converted to tachyons inside the Schwarzschild radius, some of the resulting tachyons may re-emerge.83

7 Laue's Derivation of Fresnel's Formula The famous Michelson-Morley second order in v/c ether drift experiment was not mentioned in the 1905 relativity paper; curiously, Einstein did not mention the result of Fizeau's 1851 experimental result in this paper either. This is puzzling in light of the importance of the experiment in Einstein's pathway to his theory. Einstein only mentions and derives stellar aberration in the relativity paper. Einstein presented in the kinematical part the new relativistic addition law for velocities, but he did not derive Fizeau's experimental result from this law. Apparently, Einstein did not recognise that the result of the Fizeau experiment could be obtained using this law. He did not derive stellar aberration in a similar manner either. In Section §7 of the 1905 relativity paper Einstein derived the latter result from the same transformation equations of the wave normal that gave the Doppler effect without mentioning the relativistic addition law for velocities. In his 1907 paper, "Die Mitführung des Lichtes durch bewegte Körper nach dem Relativitätsprinzip" (The Entrainment of Light by Moving Bodies According to the Principle of Relativity), Max Laue obtained Fresnel's coefficient (Fizeau's result) from Einstein's relativistic addition law for velocities. The result was rather complicated in 1907, and was mathematically equivalent to Lorentz's derivation of 1895 (see Chapter B, Section 2.4). In his 1913 paper, "Das Relativitätsprinzip" (The Principle of Relativity), Laue simplified it when he considered that the direction of the light ray coincides with that of the motion of the observer relative to the medium (Laue 1913).

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In 1907, Laue wrote to Einstein that, he came across an article in the Annalen by Laub, "Zur Optik der bewegten Körper" (Optics of Moving Bodies) (Laub 1907), which derives the dragging coefficient in Fresnel's formula from the relativity principle. Unfortunately, Laub's paper contained two errors and one inconsistency in the reasoning, namely an interchanging of group and phase velocity. Therefore, Laue, also deriving the dragging coefficient in the same way, did not withdraw his derivation; "rather", he wrote, "it will appear in one of the next issues (Laue to Einstein, September 4, 1907, CPAE 5, Doc. 57). As mentioned in Chapter C Section 6.3, before 1905 Einstein tried to discuss Fizeau's experiment "as originally discussed by Lorentz" in 1895. According to the 1922 Kyoto lecture notes Einstein said (Einstein 1922a, 46): "Then I tried to discuss the Fizeau experiment on the assumption that the Lorentz equations for electrons should hold in the frame of reference of the moving body as well as in the frame of reference of the vacuum as originally discussed by Lorentz". However, Einstein was still under the impression that the ordinary Newtonian law of addition of velocities was unproblematic. Finally, Einstein failed to notice the kinematic nature of Fresnel's formula, resulting from direct application of relativistic addition law for velocities. It might seem surprising that Einstein could derive this addition law for relative velocities in his 1905 paper (§5) without recognising that the result of the Fizeau experiment was an implementation of this law (Norton 2004, 93). In 1905, Einstein wanted to show, heuristically, that optical phenomena could be derived from the transformation of the waveform and not derived from the relativistic addition law for velocities. He wanted to demonstrate that the optics of moving bodies problems could be solved using his new kinematics (§3) – the principle of relativity and the light postulate, and the Maxwell equations. Einstein wrote in his relativity paper that all problems in the optics of moving bodies could be solved by the heuristic method employed here (Einstein 1905, 916). In order to derive Fizeau's result from the transformation of the wave he probably needed a complicated calculation. It appears that he could not simply derive the Fizeau result from the transformation of the waveform. In later papers he followed a different path and derived aberration and Fizeau's result by means of the relativistic addition law of velocities – following Laue's derivation.

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8 Einstein's Clocks and Langevin's Twins In 1905 Einstein presented the clock paradox, and in 1911 Paul Langevin expanded Einstein's result to human observers, the "Twin Paradox". The crucial difference between Einstein and Langevin is explained below.

8.1 Time Dilation In the relativity paper Einstein derives the time dilation formula (Einstein 1905a, 904). Imagine clocks that can mark the time t when at rest relative to the rest system (K), and the time IJ when at rest relative to the moving system (k). A clock is located at the origin of the system k, and is adjusted to mark the time IJ. What is the rate of this clock, when viewed from the rest system K? According to the Lorentz transformation equation for the time: ߬ ൌ ߚ ቀ‫ ݐ‬െ

‫ݔݒ‬ ቁǡ ܿଶ

where, x = vt and: ߚൌ

ͳ ඥͳ െ ‫ ݒ‬ଶ Τܿ ଶ

Ǥ

Einstein obtains: ߬ ൌ ‫ݐ‬ඥͳ െ ‫ ݒ‬ଶ Τܿ ଶ ൌ ‫ ݐ‬െ ቀͳ െ ඥͳ െ ‫ ݒ‬ଶ Τܿ ଶ ቁ –Ǥ The time marked by the clock (viewed in K) is slow byቀͳ െ ඥͳ െ ˜ ଶ Τ… ଶ ቁ seconds, or to first order, by

ଵ ୴మ ଶ ୡమ

seconds.

8.2 Clock Paradox From this Einstein derived an eigentümliche Konsequenz (peculiar consequence) (Einstein 1905a, 904-905): "If at the points A and B of K there are clocks at rest which, considered from the system at rest, are running synchronously, and if the clock at A is moved with the velocity v along the line connecting B, then upon arrival of this clock at B the two clocks no longer synchronise, but the clock that

250

D. The Meaning of Einstein's 1905 Special Relativity ଵ ୲୴మ

moved from A to B lags behind the other which has remained at B by ଶ ୡమ sec. (up to quantities of the fourth and higher order), where t is the time required by the clock to travel from A to B".

The above "peculiar consequence" came to be known as the clock paradox. Einstein proposed an experimental test for the clock paradox: "From this we conclude that a balance-wheel clock located at the Earth's equator must run very slightly slower than an absolutely identical clock, subjected to otherwise identical conditions, that is located at one of the Earth's poles" (Einstein 1905a, 904-905).84

8.3 Twin Paradox Einstein spoke of clocks, while in 1911 Paul Langevin extended Einstein's clock paradox to human observers and the aging effect. Human observers, "twins", come instead of Einstein's clocks, and Langevin spoke of the twin paradox. Einstein did not present the so-called twin paradox, but did continue to speak about the clock paradox. Einstein might not have been interested in the question of what happens to the observers themselves. The reason for this could be that he dealt with measurement procedures, clocks and measuring rods and he considered his theory as "a theory of measuring rods and clocks". In 1946 Einstein wrote in his Autobiographical Notes that the insight fundamental for the special theory of relativity is this: The light postulate and the principle of relativity are compatible if the Lorentz transformations are postulated for the conversion of coordinates and times of events. "With the given physical interpretation of coordinates and time, this is by no means merely a conventional step but implies certain hypotheses concerning the actual behaviour of moving measuring rods and clocks, which can be experimentally confirmed or disproved" (Einstein 1949, 5657). Einstein's observers were measuring time with clocks and measuring rods. Einstein might not have been interested in so-called biology of the observers, whether these observers were getting older, younger, or whether they had undergone any other changes; these changes appeared to be out of the scope of his "principle of relativity", or kinematics.

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In Paul Langevin's talk, "L'Evolution de l'espace et du temps" (Evolution of Space and Time) given on April 11, 1911, Langevin imagines two arbitrary events in the history of an element of matter. Their time interval is measured by observers in non-uniform motion who have constantly moved together with the element. This time interval will be shorter than the one for a uniformly moving reference system. This latter reference system can be such that the two events considered could be situated at the same point, relative to which an element of matter has moved in a closed path, exactly as it is in Einstein's original clock paradox, and returns to its original position, due to its non-uniform movement. Langevin proves that, for observers at rest relative to that element of matter, the time that has elapsed between the beginning and end of the path, the proper time in Minkowski's sense of the element of matter, will be shorter than for the observers in the uniformly moving reference system (Langevin 1911, 48). In other words, concludes Langevin, the element of matter will have aged less between the beginning and end of its path than if it had not been accelerated, if it had instead remained at rest in a uniformly moving reference system. It follows from the result stated above, that the observer having aged less is the one whose motion during the separation was furthest removed from uniform motion, the one most strongly accelerated (Langevin 1911, 48-49). Immediately after this explanation Langevin describes the famous twin paradox (Langevin 1911, 50): "This remark gives a way, for any of us, who is willing to devote two years of his life, of knowing how the Earth will be in two hundred years' time, to explore the future of the Earth, by hopping forward in the history of the latter, of two centuries, corresponding in his own life to only two years; but without any hope of return, without the possibility to come and inform us of the result of his journey, because any similar attempt can only throw him further and further into the future. It is sufficient for this that our traveller agrees to shut himself up in a projectile, sent away from the Earth, with a speed sufficiently close to that of light, although less, which is physically possible, arranging that an encounter occurs with, for example, a star, after one year in the life of the traveller, that sends the spaceship back towards the Earth with the same speed. Returning to Earth, having aged by two years, he will climb out of his vehicle and find our globe aged by at least two hundred years, if his speed had stayed within an interval of less than twenty-thousandth of the speed of light. Solidly established experimental facts of physics allow us to state that the situation will really be as the one just described".

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8.4 Clock Paradox and Superluminal Velocities Soon after Langevin's paper, Max Laue discussed the clock paradox thought experiment. In December 1911, Laue gave a modification to the paradox in his paper entitled, "Zwei Einwände gegen die Relativitätstheorie und ihre Widerlegung" (Two Objections to the Theory of Relativity and its Refutation). Laue meant two authors raise one objection to the theory: That Einstein's clock paradox and Langevin's version of it as a twin paradox brought scholars to think that it might violate special relativity; because they thought that Einstein's peculiar clock consequence might enable superluminal signal velocities. Laue wrote the paper in order to answer the critics and explain to them why there can be no superluminal signal velocities. Yet Laue adhered to Einstein's original version, clocks and not human observers: A group of equivalent clocks, which were physically exactly the same, were moving in uniform velocity toward the same direction. The clocks moved so close to one another that they could be regarded as being simultaneously together at the same point. They all measured the proper time in Minkowski's sense on their corresponding world line. At a given moment, they took separate paths and, after a certain time they came back together again to the same starting point in space. Afterwards, they again went through a common movement as before. At the meeting point (between the places of separation and clock reunification), the clock that stayed in a "non-legitimate" frame of reference (not always inertial) lagged behind the other clock. This contradiction, says Laue "had recently prompted two authors at this point to raise one objection" (Laue 1912, 118-119). Recall that Einstein had mentioned Emil Wiechert during the 1907 discussions with Wilhelm Wien on the occurrences of velocities exceeding the speed of light in dispersive and absorptive media (Einstein to Wien, August 23 or July, 1907, CPAE 5, Doc. 49). Wiechert had been troubled with this issue for a long time and in his 1911 paper "Relativitätsprinzip und Äther" (Relativity Principle and Ether) he was still occupied by superluminal velocities (Wiechert 1911, 689- 707). Wiechert thought that if superluminal velocities were possible within the scope of the "relativity principle" then all reference systems could not be equivalent. The systems of reference are equivalent insofar as they dealt with a theory in which superluminal velocities are forbidden. If superluminal velocities were possible within the scope of the "relativity principle", then Wiechert saw in Einstein's clock paradox, or Langevin's

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version of Einstein's 1905 clock paradox, a contra example to the regular order of cause and effect. This is so because if velocities exceed the speed of light, then some frames of reference see the returning twin younger, while the others may see him older. Wiechert thought there can be no agreement among the different clocks in the group in Laue's thought experiment. This was not permissible in a theory in which velocities do not exceed that of light. The relativity principle should absolutely deny the occurrence of superluminal velocities, thus all systems should be completely equivalent. Max Laue explained that Einstein and Langevin cancel the possibility of superluminal velocities, because cause comes before effect. All agree that the returning twin is younger, and the twin who stayed at home is older. That is the crux of Einstein's "peculiar consequence" (Laue 1912, 119).85

8.5 Anti-Semites Against Clock Paradox The clock paradox was also an excuse for anti-Semites to blame the theory of relativity as an anti-German science and to blame its author. After 1916 in Berlin, Ernst Gehrcke, Philipp Lenard, and Paul Weyland advocated an anti-relativity propaganda campaign (Rowe and Schulmann 2007, 11). In November 1918 Einstein answered the first two by a Galilean dialogue between a relativist and a critic of the theory of relativity, "Dialog über Einwände gegen die relativitästheorie" (Dialogue about Objections to the Theory of Relativity).86 Einstein's imaginary character, "Kritikus", raises as claims against relativity the original clock paradox and not the twin paradox (Einstein 1918). Kritikus considers a Galilean coordinate system K in the sense of the special theory of relativity, that is, a frame of reference, relative to which isolated, material points move in straight lines and uniformly. Also, U1 and U2 are two identical clocks (Uhr) that are free from outside influences. These run at the same pace when they are in close proximity and also at any distance from each other, if they are both at rest relative to K. Let us look at the following "well-known thought experiment": Let A and B be two distant points of the system K. A is the origin of K, and B is a point on the positive x-axis. The two clocks are initially at rest at point A. They run at the same pace, and the positions of the hands are the same. We now impart a constant velocity in the positive direction of the x-axis to clock U2, so that it moves towards B. At B we imagine the velocity reversed, so that clock U2 returns to A. As it arrives at A, the clock is

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D. The Meaning of Einstein's 1905 Special Relativity

decelerated so that it is once again at rest relative to U1; clock U2 lags behind U1. On this basis Kritikus makes the following statements. According to the principle of relativity, the entire process must occur in exactly the same way if it is represented in a coordinate system K', that is co-moving with clock U2. Then relative to K' it is clock U1 that is moving, with clock U2 remaining at rest. It follows that U1 should finally run behind U2, in contradiction with the above result. Kritikus then says that this result entails serious consequences. Even the most devout adherents of the theory cannot claim that of two clocks, resting side by side, each is late relative to the other. Kritikus thought that all the difficulties are removed by merely returning to classical theory. Relativist: Your last assertion is, of course, incontestable. The entire line of reasoning is not legitimate because according to the special theory of relativity the coordinate systems K and K' are not equal. Indeed, this theory claims only the equivalence of all Galilean (non-accelerated) systems, i.e., coordinate systems relative to which sufficiently isolated material points move uniformly in straight lines. The coordinate system K has certainly been such (a system), but not the temporarily accelerated system K'. One can therefore conclude that the clock U2, after leaving U1 does not contradict the basis of the theory. Kritikus realizes that the theory of relativity may have no internal contradictions; but he still says that this is not sufficient to take it into serious consideration. He just cannot see why one should be willing to take on such horrible complications and mathematical difficulties merely for the sake of an intellectual preference, namely for the idea of relativity. Unfortunately, the above statement failed, and Einstein provided the most convincing disproof of Kritikus' claims by referring to experience (Einstein 1918; Rowe and Schulmann 2007, 96): "Relativist: For several reasons we must willingly accept the complications to which the theory leads us. […] The following counterexample will show how inadvisable it is to appeal to so-called common sense as an arbiter in such things, Lenard himself says: So far no pertinent objections have been found to the validity of the special principle of relativity (i.e., the principle of relativity between uniformly translational motions of coordinate systems). The uniformly moving train could as well be seen 'at rest' and the tracks, including the landscape, as 'uniformly moving'. Will the 'common sense' of the locomotive engineer allow this? He will object that he does

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not go on to heat and grease the landscape but rather the locomotive, and that consequently it must be the latter whose motion shows the effect of his labour".

9 The Magnet and Conductor Thought Experiment Einstein began his 1905 relativity paper with the magnet and conductor thought experiment (Einstein 1905a, 891): "It is well known that Maxwell's electrodynamics, as usually understood at present, when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the electrodynamic interaction between a magnet and a conductor".

Einstein explained in his relativity paper the magnet and conductor experiment in the following way: If the conductor is at rest and the magnet is moved with a given velocity, a certain electric current is induced in the conductor. If the magnet is at rest, and the conductor moves with the same relative velocity, a current of the same magnitude and direction flows in the conductor. The ether theory gives a different explanation for the origin of this current in the two cases. In the first case, an electric field is supposed to be created in the ether by the motion of the magnet relative to it (Faraday’s induction law). In the second case, no such electric field is supposed to be present since the magnet is at rest in the ether, but the current results from the motion of the conductor through the static magnetic field (Lorentz’s force law). This asymmetry of the explanation of the interaction between a magnet and a conductor is foreign to the phenomenon, because the observable phenomena (the current in the conductor) depend only on the relative motion of the conductor and the magnet. According to this experiment, observable electromagnetic phenomena should depend only on the relative motions of ponderable matter. Einstein started his electromagnetic section of the relativity paper again with Faraday's induction. He was then led to solve the conflict with which he opened the kinematical part of his relativity paper. In the electrodynamic section, he intended to discuss the problem of asymmetry in electromagnetism. In order to discuss induction Einstein first obtained the transformation equation for the electric and magnetic forces (fields), using the Lorentz transformations that he had obtained in Section §3 of the

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kinematical part, and the principles of relativity and that of the constancy of the velocity of light (Einstein 1905, 907-909): 1) Einstein first assumes the Maxwell-Hertz equations for empty space are valid for the system K. He writes the components of the electric field vector with respect to the x, y, z axes in K in the form (X, Y, X) and the components of the magnetic field vector as (L, M, N). 2) He applies to the Maxwell-Hertz equations in K the Lorentz transformations for the special and temporal derivatives, i.e.: μ μ μ μ ՜ ǡ ՜ ǡ ݁‫ ܿݐ‬ǥ μ– μɒ μš μɌ by referring the electromagnetic processes to the system of coordinates moving with velocity v relative to K; he obtains the transformed MaxwellHertz equations as they appear when written in k. 3) Next Einstein refers to the principle of relativity: "The principle of relativity requires that if the Maxwell-Hertz equations for empty space are valid in system K, they are also valid in system k" (Einstein 1905, 908). Therefore, the electric and magnetic field vectors – (X', Y', Z') and (L', M', N') – in the moving system k satisfy a set of Maxwell-Hertz equations of the same form as in K. This implies the transformation equations for (X, Y, Z), (L, M, N). 4) Einstein requires that the two systems of equations found for k (in step 2 – by applying the Lorentz transformations, and the transformation equations in step 3, when guided by the principle of relativity) take the same form as the Maxwell-Hertz equations for the system K in step 1). Einstein thus arrives at the equations corresponding to Lorentz's transformations of the coordinates, equations of transformation for electric and magnetic fields (in Einstein's original notation): ܺ ᇱ ൌ ܺǡ ܻ ᇱ ൌ ߚ ൬ܻ െ

‫ܰݒ‬ ‫ܯݒ‬ ൰ ǡ ܼ ᇱ ൌ ߚ ൬ܼ ൅ ൰ǡ ܿ ܿ

‫ܮ‬ᇱ ൌ ‫ܮ‬ǡ ‫ܯ‬ᇱ ൌ ߚ ൬‫ ܯ‬൅

‫ܼݒ‬ ‫ܻݒ‬ ൰ ǡ ܰ ᇱ ൌ ߚ ൬ܰ െ ൰Ǥ ܿ ܿ

(X, Y, Z) – components of the electric field and (L, M, N) – components of the magnetic field.

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Einstein now returned to the experiment by which he opened his paper, the magnet and conductor thought experiment. He was convinced that there should be an electric field acting on the conductor, even if it was moving. To show that, he needed the equations of transformation for electric and magnetic fields, which proved that the magnetic field components in the transformations for the electric field can be interpreted as an electric field in the rest frame of the conductor. In his handwritten (German) corrections in a letter written in English in honour of Michelson's hundredth birthday (dated December 19, 1952), Einstein wrote that his direct path to the special theory of relativity "was mainly determined by the conviction that the electromotive force induced in a conductor moving in a magnetic field is nothing other than an electric field" (quoted in Norton 2004, 49-50). In 1920, Einstein suddenly recalled that the situation with electrodynamics and the magnet and conductor experiment were somewhat similar to gravitation. He invented a new thought experiment, a man falling freely from a roof under the influence of gravity. While still sitting in the Patent Office, Einstein started to think about the problem of gravitation. Einstein published his first paper on the topic on December 4, 1907 (Einstein 1907b, 411-462). It is interesting, however, to look at the path of Einstein's invention. While writing this paper, Einstein suddenly arrived at a breakthrough, which boosted his research toward the general theory of relativity. It appears that Einstein arrived at this breakthrough sometime during November 1907.87 In the 1920 unpublished draft of a paper for Nature magazine, "Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development", Einstein recounted that in 1907, when he was sitting in the Patent Office he was busily writing the comprehensive summary of his work on the special theory of relativity for Stark's Jahrbuch. He was also attempting to modify Newton's theory of gravitation in such a way that its laws fitted into the special theory of relativity (Einstein, 1920a, 265). Einstein was ruminating on special relativity. The case that first made him brood upon the topic of gravitation was the "magneto-electric induction". In his 1905 relativity paper he showed that the electric and magnetic fields do not exist independently of the state of motion of the coordinate systems; hence, the asymmetry in the introduction of the relativity paper "disappears" upon consideration of the magnet and conductor thought experiment (Einstein, 1905a, 910).

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D. The Meaning of Einstein's 1905 Special Relativity

In the manuscript from 1920, Einstein recounted that he used this idea to develop an analogy of gravitation: "The gravitational field is considered in the same way and has only a relative existence, like the electric field generated by magneto-electric induction" (Einstein, 1920a, 265). While Einstein was contemplating the electromagnetic field, he was struck by an incredible idea (which happened sometime during November 1907). Einstein imagined an observer free falling from the roof of an house. During the descent there was, at least in the immediate vicinity, no gravitational field. It seemed to Einstein remarkable that if an observer releases bodies, they remain relative to him, in a state of rest or uniform motion, regardless of their particular chemical and physical nature. "The observer is therefore justified in interpreting his state as being 'at rest'" (Einstein, 1920a, 265). According to Galileo's experimental law, all bodies fall in the same gravitational field with the same acceleration. In 1907, Einstein's thought experiment added new depths to this law. In reference to experience, Einstein suggested the possibility that if one object fell differently in a gravitational field from all the objects, the observer could use it to recognise that he was in a gravitational field and that he was falling in the latter. Einstein supposed that, "if such a thing does not exist –as experience has shown with great precision – then there is no objective reason for the observer to regard himself as falling in a gravitational field". Perhaps Einstein thought of all the reasons that might cause the observer to think that he was in motion, but he concluded: "Rather, he has the right to consider his state at rest with respect to gravitation, and his environment as field-free" (Einstein, 1920a, 265). Einstein's November 1907 breakthrough was to consider Galileo's principle of free fall as a powerful argument in favour of expanding the principle of relativity to systems moving non-uniformly relative to each other. Einstein realized that he might be able to generalise the principle of relativity when guided by Galileo's principle or law, according to which all bodies in a gravitational field have the same fall; for if one body fell differently from all others in the gravitational field, then with the help of this body an observer in free fall (with all other bodies) could find out that he was falling in a gravitational field.

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In the 1907 review article, "On the Relativity Principle and the Conclusions Drawn from It", Einstein presented a new gravitation theory, a coordinate-dependent theory, reminiscent of the 1905 relativity paper. Guided by Galileo's principle, Einstein postulated the Aequivalenzprinzip (principle of equivalence), and with physical reference systems and measuring rods and clocks, he arrived at new results. When no complicated mathematics entered into the theory, the extension of the principle of relativity turned out to be quite natural and simple. Four years later, in June 1911, Einstein published another paper in the Annalen der Physik "Uber den Einfluȕ der Schwerkraft auf die Ausbreitung des Lichtes" (On the Influence of Gravitation on the Propagation of Light). Einstein was guided by Galileo's law of free fall towards formulating a more mature equivalence principle. He still did not leave the comfortable framework of a coordinate-dependent theory, including the physical frame of reference and the system of measuring rods and clocks that gave physical meaning to points in space-time (Einstein 1911). Einstein extended his 1907 crude equivalence principle and formulated an heuristic guiding equivalence principle. I mentioned earlier Einstein at the age of twelve or thirteen, reading Aaron Bernstein's The People's Natural Science Books. Bernstein might have inspired Einstein when he worked on his 1911 gravitation theory. Bernstein imagined a picturesque way of expressing the situation regarding Bradley's measurements of the velocity of light (a thought experiment) (Bernstein 1880 8, 141-142). Imagine a wagon, the walls of which are punched on both sides by a bullet. The bullet is shot through the wagon. The man who shot the bullet directed his gun so that the bullet would be shot directly across the wagon. Investigations of the holes punched in the wagon show that the bullet was shot not exactly across the wagon in a straight line, but slightly oblique. The holes punched through the walls of the wagon, show that the bullet entered slightly forward. However, anyone who had seen this shot from inside the wagon would have claimed that the shot must have been impossible: he would claim that the bullet was deliberately shot obliquely, and not to the front. Yet, it was a straight shot, and the bullet was fired to the front, although it was seen to go through the wagon in an oblique direction. Bernstein provides an explanation for this: The wagon was moving while the bullet pierced the first wall, and it continued to move while the bullet passed through the wagon until it penetrated the next wall. During the time that the bullet was passing from the first wall to the next, the wagon

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moved slightly ahead. Thus, the shot at the opposite wall could not be the same as it would have been were the wagon at rest. This is aberration. Einstein propounded the following thought experiment. Consider a great elevator at rest at the bottom of a building much higher than any real one. Someone outside has fastened a rope to the elevator and is pulling, with a constant force, in an upward direction toward the top of the building. Imagine that a light ray enters the elevator horizontally through a side window and reaches the opposite wall after a very short time. Let us see how two observers – an observer K on the Earth (in the Earth’s gravitational field) and an observer K' inside the elevator – would predict the path of the light. The outside observer, believing in accelerated motion of the elevator, would argue that the light ray enters the window and moves horizontally along a straight line, at a constant velocity toward the opposite wall. But the elevator moves upwards and during the time in which the light travels toward the wall, the elevator changes its position. Therefore, the ray will meet a point not exactly opposite its point of entrance, but a little below. The difference will be very slight, but it exists nevertheless. The light ray travels, relative to the elevator, not along a straight line but along a slightly curved line. The difference is due to the distance covered by the elevator during the time the ray crosses the interior. The inside observer, who believes that the gravitational field is acting on all the objects in his elevator, would say that there is no accelerated motion of the elevator, but only the action of the gravitational field. A beam of light is weightless and, therefore, will not be affected by the gravitational field. If the beam of light is sent in a horizontal direction, it will meet the wall at a point exactly opposite to that at which it entered. We thus have two observers, K and K’ and two opposite points of view: the phenomenon is different for the two. There would be no equivalence of K and K' and from the behavior of the light ray we could say that K' is in absolute motion: whenever an observer finds a bent light ray he knows that the reference frame under consideration is in absolute motion. In 1911 Einstein solved the problem concerning the light rays in the following way. According to the inside observer a beam of light is weightless and therefore, the gravitational field will not affect it. He demonstrated that according to the ideas of the special theory of relativity, a beam of light carries energy and energy has mass. But every inertial mass is attracted by the gravitational field, as inertial and gravitational masses are equivalent, the increase in gravitational mass is equal to E/c2, and therefore equal to the increase in inertial mass as given by the special

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theory of relativity. A beam of light will bend in a gravitational field exactly as a body would if thrown horizontally with a velocity equal to that of light. Thus the reasoning of the inside observer is incorrect, because he did not take into account the bending of light rays in a gravitational field. Therefore, by taking into account this reasoning the inside observer’s results would be exactly the same as those of an outside observer. The essential assumption needed for this conclusion is the equivalence of gravitational and inertial mass incorporated in the principle of equivalence (Einstein 1911, 900-903; Einstein and Infeld, 1938b, pp. 218-221).88 Indeed Einstein's theory of gravitation abounded in creativity, even if it took him more than a year to abandon the comfortable framework of the coordinate-dependent theory model of the special theory of relativity. In 1912, Einstein began studying Minkowski's four-dimensional reformulation of the special theory of relativity in earnest and searched for a gravitational theory, and gravitational field equations (See Chapter D, Section 1.4.2).

10 Relativity and the Light Quantum In his Autobiographical Notes, Einstein explained that while working simultaneously on the quantum problem and the nature of radiation, and on the electrodynamics of moving bodies, he came to the conviction that only the discovery of a general formal principle, the relativity principle, could lead to assured results (Einstein 1949, 48-49). Before submitting his 1905 special relativity paper, Einstein submitted the light quantum paper – the only one of his 1905 papers he considered truly revolutionary. "On a Heuristic Viewpoint Concerning the Generation and Transformation of Light" was sent to the Annalen on March 17, 1905, and received by the publication a day later (Einstein 1905c, 132-148). As already stated, Einstein wrote to Habicht in May 1905 that this paper "deals with the radiation and energy characteristics of light and is very revolutionary" (Einstein to Habicht, May 18 or 25, 1905, CPAE 5, Doc. 27). This paper extended the range of application of Planck's 1900 quantum hypothesis. In order to explain his law of black body radiation, which had been well-verified empirically, Planck was forced to assume that oscillators interacting with the electromagnetic field could only emit and/or absorb energy in discrete units, which he called quanta of energy. The energy of these quanta was proportional to the frequency of the

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oscillator: E = hQ. Planck believed, in accord with Maxwell's theory, the energy of the electromagnetic field itself could change continuously. Einstein now showed that if this formula were extended to the electromagnetic field energy itself, a number of phenomena involving interactions between matter and radiation, otherwise inexplicable classically, could now be simply explained with the help of these light quanta. Einstein worked concurrently on his relativity paper; so the following question naturally arose: If the equation E = hQ holds in one inertial frame of reference, would it hold in all others? If not, then Einstein's relativity principle would be violated. Since h, the so-called quantum of action, is a universal constant, the question is reduced to: Do the energy and frequency of a light quantum transform in the same way in passing from one inertial frame to another? This is just what he demonstrates in his relativity paper. Einstein applies the Lorentz transformation and transformation equations for electric and magnetic fields to the equations of the plane electromagnetic wave with respect to K. He obtains a new set of equations, from which he deduces new transformation equations for the frequency Z and direction cosines of the wave normal n'; he obtains the Doppler principle and the equation that expresses the law of aberration. If an observer is moving with velocity v relative to an infinitely distant source of light of frequencyȣ, the frequency ȣ' of the light perceived by the observer is (Einstein 1905a, 911): ᇱ

ɋ ൌ ɋඨ

ͳ െ ˜Τ… ͳ ൅ ˜Τ…

Einstein then finds the amplitude of the waves as it appears in the system k; the amplitude of the electric or magnetic waves A or A', respectively, as it is measured in the system K or in the system k. Einstein thus gives the equation for the square of amplitude, intensity‫ ן‬A2 (Einstein 1905a, 911): ᇱଶ ͳ െ ˜Τ… ൌ Ǥ ଶ ͳ ൅ ˜Τ…

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Einstein then obtains the transformation of the energy of light rays. We expect that the ratio, A'2/A2 would be the energy of a given light complex "measured in motion" and "measured at rest", if the volume of a light complex were the same measured in K and k. If light per unit volume ‫ ܧ‬ൌ ஺ᇱమ

൫ா మ ା୆మ ൯ ଼గ

஺మ

଼గ

is equal to the energy of

measured in K, then according to the

principle of relativity would be the energy of light per unit volume as ଼గ measured in system k. However, says Einstein, this is not the case. Einstein thus instead considers a spherical surface of radius R moving with the velocity of light (a, b, and c are the direction-cosines of the normal to the light in the system K) He is interested in the light energy enclosed by the light surface. No energy passes outside through the surface of the spherical light surface, because the surface and the light wave both travel with the velocity of light. He calculates the amount of energy enclosed by this surface as viewed from the system k, which will be the energy of the light complex relative to the system k. The spherical surface – viewed in the system k – is an ellipsoidal surface. If we call the energy of the light enclosed by this surface E when it is measured in system K, and E' when measured in system k, we obtain the equation that relates between E and E' (Einstein 1905a, 913-914): ᇱ ͳ െ ˜Τ… ɋᇱ ൌඨ ൌ  ͳ ൅ ˜Τ… ɋ In the relativity paper, Einstein obtained the above formula that ୉ᇲ

஝ᇲ

corresponds to that of the light quantum hypothesis, namely, ൌ . ୉ ஝ Einstein explains, "It is noteworthy that the energy and the frequency of a light complex vary with the observer's state of motion according to the same law" (Einstein 1905a, 914). Einstein's aim was to show that the equation E = hQ which he used in the quantum paper takes the same form in any inertial frame. E = hQ is transformed to E' = hQ' and thus the relativity postulate is not violated. In hindsight, this supplies extra evidence for the light quantum hypothesis. As John Stachel explains, in the 1905 relativity paper Einstein used the notion, Lichtkomplex (light complex). He did not invoke his novel Lichtquanten (quanta of light) heuristic with respect to the principle of relativity (Einstein 1905c, 145). He chose the language "light complex" for

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which no clear definition could be given. Not wanting to introduce a discussion of his still-quite-speculative light quantum hypothesis into a paper, which he regarded as simply an extension of well-accepted classical ideas from mechanics to electromagnetism and optics, he confined his proof to the classical level. Instead of "light quanta", in his proof he introduced the rather awkward term "light complex", a term he soon dropped. Planck was the first scientist to notice Einstein's relativity paper. Einstein's paper on relativity, received by the Annalen der Physik at the end of June 1905 was already in print by September 26. As early as November 1905, Planck had reported favourably on it (Hoffmann and Dukas 1973, 83-84). However, Planck disliked the idea of light quanta. He was co-editor of the Annalen, and he accepted Einstein's "heuristic" paper on light quanta for publication, even though he objected to its basic concepts. Einstein later told his friend Laub that Planck had one fault: He is clumsy finding his way about in foreign trains of thought. It is therefore understandable when he makes quite faulty objections to his latest work on the light quantum (Seelig 1954, 102-103, 1956a, 87). In 1906, Planck's assistant, Laue, wrote to Einstein about obtaining the preprints of the 1905 light quanta paper (Laue to Einstein, June 2, 1906, CPAE 5, Doc. 37): "When at the beginning of your last paper, you formulate your heuristic standpoint to the effect that radiant energy can be absorbed and emitted only in specific finite quanta, I have no objections to make; all of your applications also agree with this formulation. Now, this is not a characteristic of electromagnetic processes in a vacuum, but rather of the emitting or absorbing matter, and hence radiation does not consist of light quanta as it says in §6 of your first paper; rather, it is only when it is exchanging energy with matter that it behaves as if it consisted of them".

Laue ended his letter to Einstein by saying: "By the way, I have never discussed your heuristic point of view with my boss. It is possible that there are differences of opinion between him and me on this question". The boss, who actually did agree with his assistant, wrote to Einstein on July 6, 1907 (Planck to Einstein, July 6, 1907, CPAE 5, Doc. 47): "In any case, I do not believe that this difference in our opinion is of a fundamental nature. Things may have been different when it came to the

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following question: Does the absolute vacuum (the free ether) possess any atomistic properties? Judging by your remark […] that the electromagnetic state in a [finite] portion of space is determined by a finite number of quantities, you seem to answer this question in the affirmative, while I would answer it, at least in line with my present view, in the negative. For I do not seek the meaning of the quantum of action (light quantum) in the vacuum but at the sites of absorption and emission, and assume that the processes in the vacuum are described exactly by Maxwell's equations".

Bernard Cohen, who interviewed Einstein in April 1955, two weeks before he died, reported that he asked Einstein whether Planck had ever fully accepted the theory of photons, or whether he had continued to restrict his interest to the absorption or emission of light without regard to its transmission. "Einstein stared at me for a moment or two in silence. Then he smiled and said: 'No, not a theory. Not a theory of photons', and again his deep laughter enveloped us both – and the question was never answered" (Cohen 1955, 222).

11 Kaufmann's Experiments: "Kugeltheorie" and "Relativtheorie" 11.1 The Mass of the Electron Since 1901, Max Abraham assumed that inertia was created by the electromagnetic field in the ether. Therefore, in order to obtain the law of variation of mass with velocity, one had first to calculate the electromagnetic momentum from the electron's self field. Using the usual definition of the second law of Newton, in the quasi-stationary approximation, Abraham replaced the electromagnetic momentum in the second law of Newton, and converted it into the following definition: acceleration times mass = force. He obtained the law for the variation of mass with velocity, while assuming rigid spherical electrons, keeping their spherical form at any velocity. Accordingly, one distinguishes between the longitudinal mass and the transverse mass, where the total apparent mass is not the same when the actual force applied to the electron is parallel with its velocity and tends to accelerate its motion, as when it is perpendicular to the velocity and tends to alter its direction (Abraham 1903, 152). In his 1904 paper, "Electromagnetic Phenomena in a System Moving With any Velocity Smaller than That of Light", Lorentz also calculated the electron's mass from its electromagnetic momentum. Lorentz assumed that

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the moving electron was contracted in the direction of motion. He obtained equations for longitudinal mass and the transverse mass (Lorentz 1904, 820). A third law for the variation of mass with velocity was proposed by Alfred Bucherer in 1904. This law, like Abraham's, was also compatible with a completely electromagnetic electron theory (Bucherer 1904, 57-58). Langevin had independently proposed the same hypothesis as Bucherer about the shape of a moving electron (Langevin 1905). Before Einstein published his 1905 paper, Max Abraham had opposed Lorentz's expression for the variation of mass with velocity, because Lorentz's electron would need to rely upon non-electrical internal forces to sustain it. This did not satisfy Abraham's desire for a wholly electromagnetic basis for dynamics. Abraham admitted that Lorentz's expression of the variation of the mass with velocity of the contracted electron was much simpler than his from a mathematical perspective; however, simplicity was not yet a reason for preferring a mathematical expression unless the simple expression was confirmed through experiment. Abraham adhered to a rigid electromagnetic foundation for a theory of the electron, and also chose a rigid spherical electron. In his 1905 relativity paper Einstein obtained expressions for the longitudinal and transverse masses, using the principle of relativity and the constancy of the velocity of light. Einstein considered a charged particle (an electron) in motion in an electromagnetic field. For its law of motion, he wrote: F = mass times acceleration. Einstein assumed that at the moment we observe the electron, it was at the origin of the coordinates and was moving with velocity v along the x axis of the system K. Therefore, at the given moment t = 0, the electron was at rest relative to another system of coordinates k, which was moving in parallel motion with velocity v along the x axis of K. Assume this, the electron is instantaneously at rest in k, and the same definition of Newton's second law "the force acting on the electron is called" (F = mass times acceleration) is valid according to the principle of relativity for both K and k. Acceleration is measured in the system K. Einstein mentions that we can assume this without any loss of generality. (Einstein 1905a, 917-919). Einstein then writes the equations of motion relative to k. By using the Lorentz transformations for coordinates and time, and the transformations

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for the electric and magnetic fields, and applying them to K, Einstein obtained the expressions for longitudinal and transverse masses. He then took "the ordinary point of view" and wrote the "longitudinal" and the "transverse" masses of the moving electron. Einstein remarked that his results were also "valid for ponderable material points, because a ponderable material point can be made into an electron (in our sense of the word) by adding an arbitrarily small electric charge to it" (Einstein 1905a, 919). For Einstein, ponderable matter was uncharged matter; thus, he declared that the ether was superfluous, although he still used the conventional "ether-based" notions. This was the language he could communicate with to his colleagues (as much as he could find them while writing the relativity paper as a patent clerk). There is much more to Einstein's last conclusion; Einstein tried to explain to his readers something very important: His results concerning the electron (the mass of the electron and the pondermotive force acting on the electron) are also valid for material points. Einstein was thus not only presenting another model for the electron. In Section §10, he laid down the starting point for a dynamics of a slowly moving material point – although he himself did not develop a relativistic dynamics. Later, in a 1913 reprint, Einstein appended a note to the word "called" in the sentence "the force acting on the electron is called" (Einstein 1905a, 919): "The definition of force given here [mass times acceleration = force] is not advantageous as was first noted by M. Planck. It is instead appropriate to define force in such a way that the laws of momentum and conservation of energy take the simplest form" (CPAE 2, 309-310, note 41). In 1906, Max Planck inaugurated relativistic dynamics, although Planck still remained within the confines of electrodynamics. Planck defined Newton's second law of motion in terms of the rate of change of a new relativistic momentum, in his paper, "Das Prinzip der Relativität und die Grundgleichungen der Mechanik" (The Principle of Relativity and the Equations of Mechanics). Planck imagined a mass point, a particle, placed at the origin of the coordinate system K. He asked, what are the equations of motion of this particle? He considered a new reference system k, moving with the same velocity as the mass point along the x axis of K, with a constant velocity v, the components of which are, vx, vy, vz.

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The particle moves with finite velocity of size q and parallel to x. The particle moves according to the regular Newtonian equation of motion for a free mass point (mass times acceleration = force). However, Planck defined the force as the electromagnetic force, and thus the mass point moves under the action of an electromagnetic field. He transformed the Newtonian equations of motion to another reference system k' whose xaxis coincides with the direction of the velocity q, that is, relative to which the mass point moves with the velocity q relative to k. This is actually the system K. The particle moves in an electromagnetic field with a velocity q in a system K according to the following equations: ୶ ൌ

݀ ݀‫ݐ‬

݉‫ݒ‬௫ ଶ ටͳ െ ‫ ݍ‬ൗ ଶ ܿ

ƒ†•‘‘Ǥ

If q is small compared to the velocity of light c, the equations reduce to the Newtonian equations of motion. Planck extended Einstein's 1905 derivation and defined the second law of Newton as the rate of change of momentum in order for the principle of relativity and the Lorentz transformations to hold well for both systems k and k'. By defining the second law in this way, it would have been natural for Planck to invoke the relativistic momentum (Planck 1906a in 1958 II, 118-119). Einstein adopted Planck's relativistic momentum in 1907: ݉‫ݒ‬௫ ଶ ටͳ െ ‫ ݍ‬ൗ ଶ ܿ

Ǥ

He said that Planck's equations of motion "do not have a physical meaning, but are rather to be understood as defining equations of force" (Einstein 1907b, 433-435). Planck's equations later led to a single expression for the mass variation with velocity: ‫ܯ‬ൌ

݉ ଶ

ටͳ െ ‫ ݒ‬ൗ ଶ ܿ

Ǥ

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Although mass could be split along the direction of motion and normally to it, scientists thought it would be conceptually preferable to look upon mass as one quantity. Einstein did not obtain a single expression for mass, neither in 1905, nor in 1907. In later years, at least, Einstein did not talk about a variation of mass with velocity, but only of the new definition of momentum and energy. After 1907, he even seemed to have rejected a single expression for the mass. Einstein might have, as early as 1907, rejected or disliked the concept of a single expression for the variation of mass with velocity and therefore did not obtain such an expression.

11.2 Kaufmann's Experiments From 1900 onward heralded an especially interesting period of experimental research conducted by Kaufmann that repeatedly confirmed Max Abraham's theory of electrons, at least until 1905. These and other experiments led to the discovery of cathode corpuscles in the beta radiation of radium – corpuscles that emitted and moved in velocities close to that of light. The beta particles' velocity was substantially faster than that of ordinary cathode rays. Scientists understood that these velocities were fast enough to ascertain whether, and to what extent, the inertia of these particles changed with velocity. In 1901 and 1902, Kaufmann's experiments led to the mathematical expression Abraham had predicted, with the aid of some radium chloride, which the Curies had given to Kaufmann. This confirmed Abraham's prediction, according to which the particles owed all their energy to the fact that they were electrified. In 1902, Kaufmann wrote: "The mass of electrons in Becquerel rays depends on the velocity; the dependence is exactly represented by Abraham's formula. The mass of electrons is accordingly of purely electromagnetic nature" (Kaufmann 1902, 56). In 1905, Kaufmann concluded that his results "speak against the correctness of Lorentz's, and also consequently of Einstein's fundamental hypothesis. If one considers this hypothesis as thereby refuted, then the attempt to base the whole of physics, including electrodynamics and optics, upon the principle of relative movement is also a failure" (Cushing 1981, 1142, 1148). In 1906, Kaufmann concluded his paper, "Über die Konstitution des Elektrons" (On the Constitution of the Electron) by stating that Abraham had proven that the Lorentzian electron required the concept of work; therefore, in order to avoid a conflict with the energy law it was necessary

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D. The Meaning of Einstein's 1905 Special Relativity

to assume the existence of an "internal potential energy" of the electron. In contrast, the existence of a pure electromagnetic basis for the mechanics of the electrons that would apply to mechanics as a whole would be proven as being impossible. This was so even if one contemplated the existence of a universal external pressure, as Poincaré did in his theory "Dynamics of the Electron" (1905b), instead of the work due to an unknown internal energy. Poincaré’s pressure maintained the electron's equilibrium when at rest. When the electron was in motion, the pressure caused the electron to undergo a contraction. Therefore, Kaufmann again concluded that his measuring procedures were not compatible with the elementary hypothesis posited by Lorentz-Einstein (Kaufmann 1906). Kaufmann concluded, from 1905 onwards, that the mathematical expression proposed by Alfred Bucherer could also be in accord with his measurements and that one could not definitively decide between that expression and that of Abraham as it was derived from his experiments. In the same paper, Kaufmann noted that the two theories of Lorentz and Einstein yielded the same equations of motion for the electron, and he gave the first clear account of the basic theoretical difference between Lorentz's and Einstein's views (CPAE 2, 267, note 80). In the annual general meeting of the German Society of Scientists and Physicians in Stuttgart, on September 19, 1906, a discussion was held of three world pictures, the electromagnetic theories of Abraham, Bucherer, or the other picture based on Lorentz and Einstein's "principle of relativity". A discussion revolving around the foundations of physics was held after Planck's lecture. The participants in the discussion were, among others, Kaufmann, Planck, Bucherer, Abraham, Sommerfeld and others. Scientists did not yet distinguish between Lorentz's theory and Einstein's theory. There were two main theories relating to the electron: Abraham's and Lorentz-Einstein's. An inclination towards Einstein and Lorentz's theories, on the part of scientists such as Planck and Laue, was evident. Einstein was absent from the Stuttgart meeting due to work commitments at the Patent Office; he therefore did not participate in the Kaufmann discussion. Planck sent Einstein a report of Kaufmann's results and of the ensuing discussion, but added that this was not the updated results. Planck wrote to Einstein on November 9, 1907: "In response to your request, I am sending you by the same mail my 'Postscript to the Discussion of Kaufmann's Deflection Measurements' together with the 'discussion' itself'". Planck told Einstein that Kaufmann subsequently carried out a calculation of the influence that ions produced by the E-rays exert on the

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electrical field between the condenser plates, from which it follows that the electrical field is extraordinary close to being homogeneous. Kaufmann repeated his experiments and validated his results (Planck to Einstein, November 9, 1907, CPAE 5, Doc. 64). Einstein immediately commented on the situation in the review article, "On the Relativity Principle and the Conclusions Drawn from It", in 1907 that he submitted a few weeks later to Stark's Jahrbuch der Radioaktivität und Elektonik. As explained in Chapter D, Section 9, on November 1, 1907, Einstein wrote to Stark: "I have now finished the first part of the work for your Jahrbuch; I am working diligently on the second [part] in my, unfortunately, rather scarce, free time". The first part dealt with the special theory of relativity. After Einstein had obtained Planck's letter on November 9, 1907, he immediately added a new section dealing with Kaufmann's results. Einstein estimated that the whole paper would be forty printed pages long. He told Stark that he hoped he would send him the manuscript "by the end of this month" (Einstein to Stark, November 1, 1907, CPAE 5, Doc. 63). The paper was published on December 4, 1907. Einstein, like Planck, was sceptical and he wrote in the paper: "Only after a more diverse body of observations becomes available will it be possible to decide with confidence whether the systematic deviations are due to a not yet recognised source of errors, or to the circumstance that the foundations of the theory of relativity do not correspond to the facts". Einstein added (Einstein 1907b, 439): "It also should be mentioned that Abraham's and Bucherer's theories of the motion of the electron yield curves that are significantly closer to the observed curve than the curve obtained from the theory of relativity. However, the probability that their theories are correct is rather small, in my opinion, because their basic assumptions concerning the dimensions of the moving electron are not suggested by theoretical systems that encompass larger complexes of phenomena".

The 1906 discussion following Planck's lecture focused on Planck's idea, which demonstrated that Kaufmann's results had indicated the need for a rapprochement to the principle of relativity, and towards Abraham or Bucherer's models, which were not based on the principle of relativity. Planck re-examined Kaufmann's experiments and data analysis, but did not find anything seriously amiss in Kaufmann's interpretation of his data. Nevertheless, Planck believed that Kaufmann's data was not a definitive verification of Abraham's theory or a refutation of Lorentz's.

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The first participant in the discussion to comment on Planck's idea was Kaufmann. Kaufmann thought that it would be best if he were the one to comment on Planck's suggestion, because he had performed the experiments, and felt he was in a position to evaluate Planck's attempts to argue that neither Lorentz's theory nor Abraham's theory agree with the experiments. Kaufmann said that Lorentz's theory finds even less accordance than Abraham's theory. The deviations of Lorentz's theory are so great that nowhere is it possible to explain them by follow-up mistakes. Kaufmann concluded that as far as no principled mistake occurred in the follow-up, "Lorentz's theory is invalidated" (Planck 1906b, 759-760). To this Planck replied, "We would be able to approach Lorentz's theory closer than Abraham's theory. Depending on the fact that the deviations in one theory are fewer than in the other, we could not determine which one was preferable" (Planck 1906b, 760). At the 1906 meeting Planck spoke of Relativtheorie (relative theory). Planck demarcated between two models: "Abraham's, according to which, the electron has the shape of a rigid sphere, and the Lorentz-Einstein's, according to which the 'principle of relativity' obtains precise validity. For abbreviation, I will refer to the first theory as a 'Kugeltheorie' [sphere theory], and the second 'Relativtheorie'" (Planck 1906b, 756). In the discussion afterwards this soon became Relativitätstheorie (relativity theory). In his arguments with other physicists and his comments on their work, Einstein was progressively, and reluctantly, drawn into this new terminology. However, in headings and in the text of his own publications he continued to speak of the "relativity principle". In the 1906 discussion following Planck's lecture, Bucherer was probably already vacillating towards the relativity principle. He said after Planck during the discussion in 1906 that he followed the results and reached a few conclusions concerning Kaufmann's measurements (Planck 1906b, 760): "Relying on the theory of relativity we arrive at the conclusion that other forces will operate when the rays of Becquerel are not directed any more in parallel, but towards the plates of the condenser. From here it is easy to test the principle of relativity theory, depending on Maxwell's equations, by operating Becquerel's rays in inclination towards the electric or magnetic field. Surprisingly, in a perpendicular movement the same forces are received as with Lorentz. I have already thought that perhaps creating an angle caused the deviation in Kaufmann’s measurements".

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Bucherer was almost prepared to give up his model (Planck 1906b, 760). He said he wished to repeat Planck's comment that his theory of the electron was not sufficiently developed in order to continue discussing. "I have engaged in it and in its conclusions very intensively and I have found that it does not give a more significant contribution than the previous and the later theory of Lorentz". Bucherer said that his model, the electron theory distorted in fixed volume, and the distorted system accordingly makes almost the same contribution as the new Lorentz theory. By expanding Planck's calculations on his electron he was unable to conclude what would follow on from these calculations regarding his electron. It was clear, however, that all the theories until then, including Bucherer's own theory, did not answer all the requirements. Bucherer, however, understood this. After 1906, Bucherer renounced his electron model that had led to his expression for the variation of mass with velocity, and began to gravitate towards the Lorentz-Einstein model. In 1908, he conducted experiments on the beta rays of radium. These were more precise than those of Kaufmann, and demonstrated that the Lorentz's model (and that of Einstein's also) was a better representation of the experimental variation of the mass of the cathode rays with their velocity. Bucherer concluded his paper by stating that the experimental results of his experiments showed that scientists should incline towards the LorentzEinstein theory and that "this result is the confirmation of the principle of relativity" (Bucherer 1908, 760). Bucherer wrote to Einstein on September 7, 1908. "First of all I would like to take the liberty of informing you that I have proved the validity of the relativity principle beyond any doubt by means of careful experiments. The experimental design might be known to you from my note in the Physikal Zeitschrift". Bucherer explained in his letter to Einstein how he undertook the test. He then wrote, "I have thereby definitively disproved my own principle" (Bucherer to Einstein, September 7, 1908, CPAE 5, Doc. 117). Bucherer told Einstein, "I think I can rightly claim that I attained substantially greater precision in all measurements than did Kaufmann […]. I am enclosing a photograph of one of my radiograms, from which you will immediately recognise the superiority of my method, i.e., if you have seen Kaufmann's radiograms. Kaufmann has a great many sources of error in his experimental setup, and I have already told him about one of them" (Bucherer to Einstein September 9, 1908, CPAE 5, Doc. 119).

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Planck's opinions in 1906 might have influenced Bucherer when he conducted his experiments confirming Lorentz's theory. Max Born was already thinking about the rigid body problem when he entered into polemics with Abraham on his model for the mass of the electron (Born 1978, 134). Born returned to Göttingen in 1908 and frequently came into contact with Abraham. He was well informed about his controversy with Lorentz. Abraham was anti-relativist and objected to Lorentz's derivation. Born also doubted it, and Abraham's derivation. Both proceeded by calculating the self-energy of a charged rigid body in uniform motion (Lorentz with contraction, Abraham without it) as a function of velocity. They used this energy to obtain the equations of motion. This procedure assumes that the energy calculated for constant velocity also holds for accelerated motion. Born's doubts were concerned with this point, and he decided to derive the equations of motion for an accelerated electron in accord with the principle of relativity. By doing so, Born discovered that this led at once to a great difficulty. For, if a body is accelerated, then different points of it have different velocities, hence different contractions. Therefore, the idea of rigidity is broken down. Born's first problem was devising how far the concept of a rigid body could be preserved in relativity. Rigidity means lack of deformation. Born worked out a mathematical expression for the deformation of a moving body on relativistic principles. The main result was a confirmation of Lorentz's formula for the electromagnetic mass as a function of velocity, and its dependence on acceleration. Born worked on this investigation throughout the winter and spring of 1909; he even applied to the Mathematical Society and given permission to provide a report on his pursuits. Born recalled that after the lecture Abraham joined in the debate to tell him that his knowledge of physics seemed to be just as scant as that of mathematics. He was annoyed because Born's theory led to Lorentz's formula for the electromagnetic mass and not to his (Born 1978, 135).

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12 The Principles of Relativity as Heuristic Principles 12.1 Einstein's Reply to Ehrenfest In 1907, Einstein's friend, Paul Ehrenfest, wrote a paper (Ehrenfest 1907). Ehrenfest thought that Einstein's deformed electron could have been obtained from Lorentz's theory, if we only used the method of deduction. If this was so, Ehrenfest understood that Einstein's theory was nothing but a reformulation of the electrodynamics of Lorentz; Einstein's 1905 solution appeared to Ehrenfest very similar to Lorentz's solution: "In the formulation in which Mr Einstein published it, Lorentzian relativity electrodynamics is treated rather generally as a closed system" (Einstein 1907c, 206). Einstein commented on Ehrenfest's paper. His 1907 reply, "Bemerkungen zu der Notiz von Hrn. Paul Ehrenfest: 'Die Translation deformierbarer Elektronen und der Flächensatz'" ("Comments on the Note of Mr Paul Ehrenfest") is important for the demarcation between his theory of relativity and Lorentz's ether-based theory. Lorentz's theory and the descendants of Lorentz's theory are not theories of relativity. Einstein characterised his work as a theory of principle, and reasoned that beyond kinematics, the 1905 ein heuristisches Prinzip (heuristic principle) could offer new connections between non-kinematical concepts (Einstein 1907c, 206-207): "The principle of relativity, or more exactly, the principle of relativity together with the principle of the constancy of the velocity of light, is not to be conceived as a 'closed system', in fact, not as a system at all, but merely as an heuristic principle which, when considered by itself, contains only statements about rigid bodies, clocks, and light signals. The theory of relativity provides something additional only in that it requires relations between otherwise seemingly unrelated regularities".

In his 1917 popular book, On the Special and the General Theory of Relativity, in the chapter "Der heuristische Wert der Relativitätstheorie" (The Heuristic Value of The Theory of Relativity), Einstein wrote, "the theory becomes a valuable heuristic aid in the search for general laws of nature" (Einstein 1917, 29, 1920b, 51).

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Eherenfest's query dealt with the structure of the electron. Eherenfest thought that, Lorentz's theory in Einstein's formulation must also be able to provide, deductively, an answer to the question posed by transferring Abraham's problem from the rigid electron to the deformable one (Einstein 1907c, 206). Einstein answered Ehrenfest's query by saying that the theory of the motion of an electron was obtained as follows: One postulates the Maxwell equations for vacuum for space-time coordinate systems. By applying the space-time transformation (the Lorentz transformation) derived by means of the system of relativity, one finds the transformation equations for electric and magnetic fields. Using the latter, and applying the Lorentz transformation, one arrives at the law for the acceleration of an electron moving at arbitrary speed from the law for the acceleration of a slowly moving electron, which is assumed or obtained from experience (Einstein 1907c, 207). Einstein explained to Ehrenfest, "We are not dealing here at all with a 'system' in which the individual laws are implicitly contained and from which they can be found by deduction alone, but only with a principle that (similarly to the second law of the thermodynamics) permits the relation of certain laws to others" (Einstein 1907c, 207). It was the first time that Einstein compared the relativity principle to the laws of thermodynamics (CPAE 2, 412, note 8). In 1949, Einstein explained this further still: "Gradually I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more desperately I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results. The example I saw before me was thermodynamics". Einstein said that the general principle was given in the second law of thermodynamics. He then asked how such a universal principle could be found (Einstein 1949, 48-49).

12.2 Theories of Principle and Constructive Theories After 1907, Einstein made a distinction between theories of principle, such as thermodynamics, and constructive theories, such as statistical mechanics. He characterised the special theory of relativity as a theory of principle, and considered it to be basically complete when the two underlying principles of the theory (the principle of relativity and that of the constancy of velocity of light) were established. All later work would

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involve the development of constructive theories compatible with these basic principles. In his paper, "What is the Theory of Relativity?" written at the request of the London Times and published on November 28, 1919, for the first time Einstein formulated his views in a systematic manner (Einstein 1954, 228) (The London Times, November 28, 1919): "We can distinguish various kinds of theories in physics. Most of them are constructive. They attempt to build up a picture of the more complex phenomena out of the materials of a relatively simple formal scheme from which they start out. […] Along with this most important class of theories there exists a second, which I will call 'principle theories'. The advantages of the constructive theory are completeness, adaptability, and clearness; those of the principle theory are logical perfection and security of the foundations. The theory of relativity belongs to the latter class. In order to grasp its nature, one needs first of all to become acquainted with the principles on which it is based".

It should be remembered that Einstein wrote this article after developing the general theory of relativity. When he spoke about the theory of relativity and the principle theory he probably meant both special and general relativity, because he did not explicitly write the word "special". In 1912 Einstein searched for a gravitational theory, and a gravitational field equation, that would satisfy some heuristic requirements. Einstein had to cope with new mathematical tools, and at the same time he was guided by few heuristic principles: the principle of relativity, the equivalence principle, the correspondence principle and the principles of conservation of energy and momentum. In the Zurich Notebook Einstein first tackled relativity and equivalence and arrived at general covariance, and then moved on to correspondence and conservation. Afterwards it was just the other way round. He first tackled correspondence and conservation and then relativity and equivalence, and lost general covariance. The interplay of the four heuristic principles with the new tools of absolute differential calculus of 1912 that Einstein was exploring governed the form of the field equations he was finally left with at the end of the Zurich Notebook. Hence, at the end of the day Einstein's conditions over determined his research between 1912 and 1913. Jürgen Renn and Tilman Sauer formulated the heuristic principles that played a role in Einstein's search and rejection of generally covariant field

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equations between 1912 and 1913. They explain that each of Einstein's heuristic principles against which constructions would have to be checked could be used either as a construction principle or as a criterion for their validity. At the end the match between the correspondence principle and the conservation principle was achieved at the expense of the generalized principle of relativity. At some stage, thus, Einstein appeared to somewhat forgot a little from the generalized principle of relativity; the starting point of his research project. Meanwhile he had developed many tools that would finally lead him to the goal of generally covariant equations. However, at this stage he was not quite sure about the most important principles his novel theory should fulfill. He found it difficult to establish a match between the equations and the principles. During 1912-1913, Einstein gradually created the tensorial framework for his future general relativity. It appears that Einstein's long vacillating between general covariance and the correspondence principle is a symptom of his fixation on the older 1912 paradigm of the (coordinatedependent theory of) static gravitational fields. He needed an extra two years to gradually and mentally switch into the new paradigm of differential calculus; yet he would always envision Riemann's calculus in terms of his heuristic principles. The 1912 Zurich Notebook shows that Einstein already considered the field equations of general relativity about three years before he published them in November 1915. Thus Einstein first wrote down a mathematical expression close to the correct field equation and then discarded it, only to return to it more than three years later. Why did Einstein discard in 19121913 what appears in hindsight to be essentially the correct gravitational field equation, and what made his field equation acceptable in late 1915? Why did he reject equations of much broader covariance in 1912-1913? Accepting the correct mathematical expression in 1912 required abandoning a few heuristic principles that Einstein could not yet reconcile with his field equations of 1912 (Renn and Sauer 2007, 123-125, 225).

13 The Dayton Miller Experiments 13.1 Einstein is Willing to Give Up his Theory of Relativity if Miller is Right The negative result of the Michelson-Morley experiment stimulated many repetitions of this experiment over the next fifty years, especially in light

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of the implications of Einstein's special theory of relativity. All trials of this experiment yielded a null result within the accuracy of the observations. However, one repetition of the experiment performed by Dayton Clarence Miller appeared to be perplexing. Miller observed very small fringe displacements, being on average only about 1/13 of those predicted by the ether theory for the 30 km/sec average velocity of the Earth in its orbit (Shankland, McCuskey, Leone, and Kuerti 1955, 167). Einstein expressed his opinion about the Miller experiments on numerous occasions. In an interview with the BBC in 1966, Karl Popper told an anecdote about Einstein: When Miller, who had always been an opponent of Einstein, announced that he had overwhelming experimental evidence against special relativity, Einstein at once declared that if these results should be substantiated he would give up his theory. At the time some tests, regarded by Einstein as potential refutations, had yielded favourable results, and for this and other reasons many physicists were doubtful about Miller's alleged refutations. Moreover, Miller's results were regarded as quantitatively implausible. They were, one might say, neither here nor there. Yet Einstein did not try to hedge. He made it quite clear that if Miller's results were confirmed, he would give up special relativity, and with it, general relativity (Whitrow 1967, 26-27). It turns out that different sources present a similar reaction by Einstein to Miller's experimental result. In a statement from January 19, 1926, on Miller's experiments, "Meine Theorie und Millers Versuche" (My Theory and Miller's experiments), when Einstein himself appreciated that the results of the Miller experiments might be confirmed, he declared that relativity theory could not be maintained, since the experiments would then prove that, relative to the coordinate systems of the appropriate state of motion (the Earth), the velocity of light in a vacuum would depend upon the direction of motion. With this, the principle of the constancy of the velocity of light, which forms one of the two foundation pillars on which the theory is based, would be refuted. Einstein thought that, "There is, however, in my opinion, practically no likelihood that Mr Miller is right". Einstein then gave a clear-cut warning: "If you, dear reader, wanted to use this interesting scientific situation to make a bet, I recommend you bet that Miller's experiments will prove faulty, or that his results have nothing to do with an 'ether wind'. I myself would be quite happy to put my money on that" (Einstein, 1926; Hentschel 1992, 605-607). Klaus Hentschel reasons that Einstein vigorously insisted on the validity of his theories in their original form. Hentschel found some Einstein

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articles and interviews in the daily press of the mid-twenties that illustrate his unwillingness to modify his theories. Rather, he was prepared to give them up completely in the case of irrefutable contrary empirical evidence. Hentschel asks: Why did Einstein make these risky bets on the unaltered theory instead of searching for small modifications, as many of his contemporary colleagues did whenever experiments appeared to come in conflict with his predictions? (Hentschel 1992, 594). The answer is that since special relativity is an heuristic system of two principles, and it is not a constructive theory like the ether-based electron theory, then one cannot modify principles without giving up the whole theory. However, a theory of principle has a solid theoretical basis, and therefore there is little chance that experiments like that of Miller's (and also like that of Walter Kaufmann's) would turn out to be right.

13.2 Miller's Experiments Miller performed his first observations during April 8-21, 1921, when Einstein first visited America with Chaim Weizmann, president of the World Zionist Organisation. They both raised funds for the Hebrew University of Jerusalem. In May 1921, Einstein delivered four lectures on relativity theory at Princeton University, and received a honourary degree. While he was there, word reached Princeton that Miller had found a nonzero ether drift during preliminary experiments performed in April at Mount Wilson Observatory. Upon hearing this rumour, Einstein produced one of his classical aperçus: "Raffiniert ist der Herrgott, aber boshaft ist er nicht" (The Lord God is subtle, but malicious he is not) – and this is the title of Abraham Pais's 1982 book. Nevertheless, on May 25, 1921, shortly before his departure from the United States, Einstein paid a visit to Miller in Cleveland, as discussed below (Pais 1982, 113). In March 1921, Miller set up his interferometer on Mount Wilson, on the grounds of the Mount Wilson Observatory. Miller made numerous observations during the period April 8-21, 1921. The data indicated a possible small periodic effect, with an average second harmonic amplitude of about 0.04 fringe: "The first observations of sixty-seven sets consisting of 350 turns gave a positive effect such as would be produced by a real ether-drift, corresponding to a relative motion of the Earth and ether of about ten kilometers per second" (Miller 1933, 217-218). However, Miller suspected that temperature effects or magnetostriction in the steel base of the interferometer as it rotated in the Earth's magnetic

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field might be the cause for this effect: "Before announcing such a result, it seemed necessary to study every possible cause which might produce a displacement of fringes similar to that caused by ether-drift". In order to test, Miller first covered the metal parts with cork, performed sets of observations, and the data indicated as before a small periodic effect; therefore Miller concluded that radiant heat is not the cause of the observed effect. He continued to perform ether-drift experiments until 1925-1926 (Miller 1933, 218). Miller suspected that thermal effects might be important, but he ruled out this possibility. According to Miller, after 1921, an extended series of experiments was undertaken to determine the influence of temperature inequality in the interferometer room and of radiant heat falling on the interferometer. Several electric heaters were used, of the type having a heated coil near the focus of a concave reflector. Inequalities in the temperature of the room caused a slow but steady drifting of the fringe system to one side, but caused no periodic displacement. Even when two of the heaters, placed at a distance of three feet from the interferometer as it rotated, were adjusted to throw the heat directly on the uncovered steel frame, there was no periodic effect that was measurable. When the heaters were directed to the air in the light-path that had a covering of glass, a periodic effect could be obtained only when the glass was partly covered with opaque material in a very non-symmetrical manner, as when one arm of the interferometer was completely protected by a covering of corrugated paper-board while the other arms were unprotected. Miller felt that these experiments proved that under the conditions of actual observation, the periodic displacements could not possibly be produced by temperature effects (Miller 1933, 220). Evidently it would have caused Miller great embarrassments had he merely continued to perform ether-drift experiments without studying every possible perturbation, which could produce a displacement of fringes similar to that caused by ether-drift. Shankland said, "Undoubtedly the greatest incentive to continue the experiments came from Professor Albert Einstein who visited Miller at Case on May 25, 1921, and urged that further trials be made to remove any possible doubts concerning the earlier results obtained in this experiment" (Shankland, McCuskey, Leone, and Kuerti 1955, 167-168). On April 14, 1921, a month before Einstein had visited his laboratory (Pais 1982, 113), Miller wrote in his notebook: "Sun is shining full on side of house. There was a very large drift which seems to be in the direction of the sun;

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indicating possibility that the entire effect is due to temperature!" (Shankland, McCuskey, Leone, and Kuerti 1955, 174). In his meeting with Einstein Miller probably expressed his concerns about the effect of temperature. Einstein was very likely convinced that a temperature difference could certainly explain Miller’s result: a decrease in temperature (i.e., thermal effects) led to changes of the optical paths' lengths of the interferometer arms in Miller's experiment, this led to the shift in the position of the interference fringes. Between Shankland’s first two conversations with Einstein in 1950, Shankland and other Case researchers planned to re-analyze Miller’s observational data. In April 1955, the very month in which Einstein passed away, the Reviews of Modern Physics published a paper on Miller's experiments by Shankland with three colleagues from the Case Institute of Physics. In this paper Shankland summarised a 1954 research, which checked a proposal that could have sprang from Einstein. In their 1950 conversations, Shankland possibly heard from Einstein his opinion that the effect was due to temperature. Shankland demonstrated that "Miller's extensive Mount Wilson data contain no effect of the kind predicted by the aether theory", because in the laboratory tests the electric heaters were placed at the level of the mirrors and about three feet from the circle travelled by them. The altered refractive index of the heated air and the thermal effects on the mirror supports change of the optical path lengths of the interferometer, and when these are affected unequally in the two arms, the fringes shift in position. On the assumption that the four arms of the interferometer all have the same thermal insulation, a localised temperature gradient across the room will produce the required effect as the instrument rotates, similar to that anticipated for an ether drift (Shankland, McCuskey, Leone, and Kuerti 1955, 174). On August 31, 1954, Einstein sent Shankland a letter expressing his appreciation for his 1954 work (AE): "I thank you very much for sending me your careful study about the Miller experiments. Those experiments, conducted with so much care, merit, of course, a very careful statistical investigation. This is the more so as the existence of a not trivial positive effect would affect very deeply the fundament of theoretical physics as it is presently accepted. You have shown convincingly that the observed effect is outside the range of accidental deviations and must, therefore, have a systematic cause. You

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made it quite probable that this systematic cause has nothing to do with 'ether-wind', traversed by the two light bundles which produced the bands of interference. Such an effect is indeed practically inevitable if the walls of the laboratory room have a not negligible difference in temperature. It is one of the cases where the systematic errors are increasing quickly with the dimension of the apparatus".

13.3 Einstein Returns to the Ether In May 1921, word reached Einstein that Miller had found a non-zero ether drift during preliminary experiments performed in April at Mount Wilson Observatory. Einstein made it quite clear that if Miller's results were confirmed, he would give up special relativity, and with it, general relativity (Whitrow 1967, 26-27; see Section 13.1). A year before Miller's April 1921 experiments, Mach's ideas influenced Einstein to return to the Ätherhypothese (ether hypothesis) in May 1920, an ether which he named Machsche Äther (Mach’s ether). Why did Einstein come back to the ether and what did he mean by "ether"? In order to answer these questions, we need to get to the core of Einstein's cosmological ideas. In 1917, Einstein added an ad-hoc term to the 1916 field equations of the general theory of relativity. He introduced into his general theory of relativity a cosmological term with the coefficient O. The purpose of this cosmological constant was to ensure that the theory should yield a static model universe (McCrea 1988, 53-56). At that time Einstein's general theory of relativity remained without empirical support. World War I had not yet finished. Although all scientific contact with foreign nations was disrupted by the war, Einstein maintained contact with the so-called "enemy scientists" among the allies, and with those from neutral countries through his link with his colleagues and best friends Lorentz, Willem De Sitter, and Ehrenfest in Leiden. Einstein was eager to check his general theory of relativity as quick as could possible. He thought that his theory also required this so-called cosmological term, which neither changed the covariance of the field equations nor any other predictions of the theory. Einstein wanted to eliminate what he called the erkenntnistheoretischen Schwächen (epistemological weakness) of Newtonian mechanics, the absolute space, from physics. He invented a world – a finite and spatially closed static universe, bounded in space – according to the idea of inertia, with its origin in an interaction between the mass under consideration and

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all of the other masses in the universe, which he called "Mach's ideas" (obviously not Ernst Mach's ideas as has been generally recognised and as Mach himself pronounced them). This would later be called by Einstein Machsches Prinzip (Mach's principle) (more precisely Mach-Einstein principle). Physically then, the cosmological constant O > 0 implies the existence of cosmic repulsion, Einstein's static universe being one in which this repulsion counterbalances gravitational attraction everywhere. Einstein envisaged his cosmological model because the components of the metric tensor gPQ were all determined by the field equations, of which the stress-energy tensor depends on matter. Thus, matter also appears as the source of the gPQ, i.e. of inertia. However, the problem was (and De Sitter discussed it with Einstein): Can we say that the whole of the gPQ is derived from these sources? The field equations determine the gPQ apart from boundary conditions, which can be mathematically defined by stating the values of gPQ at infinity. Einstein hesitated and finally decided to abolish the boundary conditions and invoked a finite and spatially closed universe, bounded in space. De Sitter objected to this solution because of the "world-matter" density in Einstein's universe, which was related to the cosmological constant; ordinary matter density included nebulae (galaxies in later terminology), stars, and so on. De Sitter proposed a vacuum solution of Einstein's field equations with the cosmological constant and with no world-matter. De Sitter's world was thus empty. In De Sitter's vacuum solution of the modified field equations the cosmological term did not depend on any world-matter that was of course not present in his universe. De Sitter proposed a solution by assuming that world-matter density equals zero. In this sense his solution was an empty universe. De Sitter's world was spherical in its space dimensions, but open towards plus and minus infinity in its time dimension (if real time was used), like a hyperboloid. De Sitter became aware of the experimental work by Vesto Melvin Slipher possessing the radial velocities of twenty-five spiral nebulae. Yet in 1917, De Sitter knew of only three of them. He then proposed a redshift effect in his hyperboloid world. In order better to compare his own model with Einstein's solution, De Sitter wrote his solution in a static form. He compared both models, which he called A (Einstein's) and B (De Sitter's), using spherical polar

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coordinates. De Sitter explained that in solutions A and B threedimensional space has constant positive curvature, and the system B is the four-dimensional analogy of the three-dimensional space of the system A. In B the time is entirely relative, and completely equivalent to the other three coordinates. However, Einstein's whole world A is filled homogenously with matter, and at infinity t' = t, and thus system A introduces "a quasi-absolute time". In addition, the system A only satisfies the postulate of relativity if the latter is applied to three-dimensional space. The world-matter thus takes the place of absolute space in Newton's theory. It was hard for Einstein to give up Mach's principle; he tried instead to demonstrate that De Sitter's solution contained a singularity, and thus argued that De Sitter's model was actually not matter-free. According to general relativity, the closer clocks are to a material source, the more slowly they run; Einstein thus reasoned that, clocks slowed down as they approached the equator of De Sitter's solution in the static form, and all matter (world-matter) of De Sitter's world was concentrated there. Einstein concluded that De Sitter's solution contained an intrinsic singularity indicating that hidden matter exists at the equator. In May 1920, Sir Arthur Stanley Eddington satisfied the curiosity of the general reader as well as the needs of the serious student by publishing his then "latest" book, Space, Time, and Gravitation, which was "excellently adapted to serve both classes".89 Eddington was known as "the foremost champion of Einsteinismus in English". He explained the problem with De Sitter's model (Eddington 1920, 159-164): "Spherical space-time, that is to say a four-dimensional continuum of space and imaginary time forming the surface of a sphere in five dimensions, has been investigated by Prof. de Sitter. If real time is used the world is spherical in its space dimensions, but open towards plus and minus infinity in its time dimension, like an hyperboloid. This happily relieves us of the necessity of supposing that as we progress in time we shall ultimately come back to the instant we started from! History never repeats itself. But in the space dimensions we should, if we went on, ultimately come back to the starting point. […] Owing to curvature in the time dimension, as we examine the condition of things further and further from our starting point, our time begins to run faster and faster, or to put it another way natural phenomena and natural clocks slow down. The condition becomes like that described in Mr H. G. Wells's story 'The new accelerator.'

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D. The Meaning of Einstein's 1905 Special Relativity When we reach half-way to the antipodal point, time stands still. Like the Mad Hatter's tea party, it is always 6 o'clock; and nothing whatever can happen however long we wait".

Felix Klein demonstrated to Einstein that the equator in the static form of the De Sitter solution is an artifact of the static form: The equator can never be reached, because the coordinate system in which the De Sitter world is static covers only part of the entire De Sitter space-time. The singularity at the equator can be transformed away and does not indicate the presence of matter. In the end Einstein was convinced that the De Sitter solution was indeed a solution to his modified field equations, but he still believed that it was not a physically possible world, because he held that any acceptable cosmological model would have to be static. Einstein accepted a "special" visiting professorship at the University of Leiden in February 1920. Ehrenfest proposed to Einstein that he travel to Holland in the second half of April and hold his inaugural lecture on May 5, 1920. Einstein therefore finished work on his lecture in early April and scheduled a trip to Leiden for around May 1. Ehrenfest replied in midApril with detailed instructions for the title page: "The Dutch title will necessarily have to be as follows: Down with the ether superstition!! – Lecture delivered at the assumption of the duties of special professor at the University of Leiden by A. Einstein". Einstein arrived in Leiden on May 7. However, Einstein still could not deliver his much-anticipated inaugural lecture in May, because the approval of his chair had not yet materialized. Finally, Queen Wilhelmina issued a decree that appointed Einstein to the newly-created special chair in Leiden and Einstein now at last could hold his inaugural lecture on the "Aether und Relativitätstheorie" (Ether and the Theory of Relativity) at 2 p.m. on October 27, 1920 in the large auditorium of the University of Leiden (van Dongen 2012, 7, 10, 13; Ehrenfest to Einstein, April 13, 1920, CPAE 9, Doc. 373). In this talk, however, Einstein introduced Mach's Ether. The world-matter of Einstein's world was equivalent to an ether, a Machian substance that was needed as a carrier of the effects of inertia. The world-matter was certainly essential because modern physicists do not believe they can accept action at a distance; rather, they return (if they follow Mach) to the ether, which has to serve as medium for the effects of inertia: "But this conception of the ether to which we are led by Mach's way of thinking differs essentially from the ether conceived by Newton, by Fresnel, and by

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Lorentz. Mach's ether not only conditions the behavior of inert masses, but is also conditioned in its state by them" (Einstein 1920c, 11-12). Einstein was of the opinion that, according to the field equations of general relativity, the gravitational field produced by some source contains energy and hence, by special relativity, mass; and this mass in turn is itself a source of gravitational field. Therefore, the gravitational field is coupled to itself. Also: "The metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration". Therefore, "the ether of the general theory of relativity is a medium, which is by itself devoid of all mechanical and kinematical qualities", but the state of it "is at every place determined by connections with the matter and the state of the ether in neighboring places" (Einstein 1920c, 12). This situation excludes action at a distance, and brings back the ether in its new form (Mach's ether) as the general relativistic spacetime. Mach's ether is thus identical with the inertio-gravitational field. In 1914 Einstein introduced the inertio-gravitational field. Inertia and gravitation are the same in essence (the equivalence principle), and are represented by a single inertio-gravitational field. Einstein adopted the metric tensor as the mathematical representation of the inertiogravitational field and interpreted Mach's idea as the requirement that the metric field be entirely determined by its sources – that is the stress-energy tensor. Einstein said that the inertio-gravitational field reminded him of the ursprünglichen spezielleren Relativitätstheorie (original special theory of relativity) "in that the motion of an electric mass in a magnetic field, acted upon by a pondermotive force, can also be regarded as the effect of that electric field, which exists from the standpoint of the moving reference system of the mass, at the location of the mass" (magnet and conductor thought experiment) (Einstein 1914, 1032). Einstein explained this further in 1920. In the manuscript, "Fundamental Ideas and Methods of the Theory of Relativity, Presented in Their Development", Einstein recalled that the situation with electrodynamics and the magnet and conductor experiment were somewhat similar to gravitation. Einstein recounted: "The gravitational field is considered in the same way and has only a relative existence, like the electric field generated by magneto-electric induction" (Einstein, 1920a, 265; discussed in chapter D, section 9).90

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Just as the Lorentz transformation mixes special and temporal coordinates – so John Stachel explains – the equations of transformation for electric and magnetic fields mix the electric and magnetic components. That is why, for Einstein, there was one electromagnetic field. This is the true unification of the two fields. Their breakup is relative to the inertial frame. For Einstein the two fields mix and not just interact. With Maxwell they interact, but they do not mix. Maxwell did not know about Einstein's take on the electromagnetic field. The main difference between the gravitational field and the electromagnetic field is in their breakup: For the gravitational field, the breakup is into inertia and gravitation relative to the acceleration; in the magnetic field the breakup is into electric and magnetic fields relative to the velocity. One cannot have unification of inertia and gravitation because they depend on acceleration. A year later, in April-May 1921, Einstein joined Chaim Weizmann's tour of the United States to gain support among American Jewry for the Zionist cause. His role was to raise funds for the establishment of the Jerusalem University. Princeton University arranged five lectures on the theory of relativity from May 9 to 13, 1921, the subject of these lectures, which were delivered in German, were special relativity and general relativity. The last lecture given the afternoon of May 13 dealt with general relativity and cosmology. Einstein's Princeton Lectures were published in 1922 as a book, The Meaning of Relativity. Einstein explained in The Meaning of Relativity: "In the first place, it is contrary to the mode of thinking in science to conceive of a thing (the space-time continuum) which acts itself, but which cannot be acted upon. This is the reason why E. Mach was led to make the attempt to eliminate space as an active cause in the system of mechanics" (Einstein 1922b, 59).91 This was one of the reasons why Einstein introduced Mach's ether. By the time Einstein gave his Princeton lectures in 1921, he had clearly made virtue out of necessity. Einstein had come to see the interactive nature of the metric field as a blessing in disguise (Brown and Lehmkuhl 2013, 13). In De Sitter's 1917 solution, gravitation is negligible compared with cosmic repulsion, thus predicting the recession of galaxies. In 1922-1923 Eddington and Hermann Weyl independently indicated that Einstein's cosmological term was related to a non-static element in De Sitter's world. They found support for De Sitter's model in Slipher's observed radial velocities of spiral nebulae. On the basis of Slipher's experimental observations, Weyl rejected Einstein's model and supported De Sitter's; he obtained a relation between redshift and distance in De Sitter's universe,

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established using "Weyl's principle" (stars lie on a "bundle" of geodesics that diverge from a common event in the past). In 1923 Einstein sent a postcard to Weyl in which he disagreed with the cosmological problem. He stated that according to De Sitter two points are in a motion of recession, and if there is no quasi-static world then the cosmological term should be discarded (Einstein to Weyl, May 23, 1923, ETH-Bibliothek Zurich). The cosmological problem that Einstein did not agree with was probably the De Sitter spectral shift effect. In 1917, Einstein claimed that small velocities of the stars (with respect to the velocity of light), v