Niels Bohr: His Life and Work

Citation preview

NIELS BOHR His life and work as seen by his friends and colleagues

Edited by

S. ROZENTAL

NORTH-HOLLAND PUBLISHING COMPANY - AMSTERDAM

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Contents

First edition 1964 NIELS BOHR Hans /iv og virke fortalt af en kreds af venner og medarbejdere Published by J. H. Schultz Forlag - Copenhagen © Aage Bohr - Copenhagen - 1964

©

r st English edition 1967 Aage Bohr - Copenhagen - 1967 PUBLISHERS:

NORTH-HOLLAND PUBLISHING COMPANY - AMSTERDAM Sole distributors for U. S. A. and Canada: Interscience Publishers, a division of JOHN WILEY & SONS, INC. - NEW YORK

PRINTED IN DENMARK

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Childhood and Youth . . . . . . . . . . . . . . . . . . . . . . . . . . . . LEON RosENFELD AND ERIK RtiDINGER: The Decisive Years I9I I-I9I8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . OsKAR KLEIN: Glimpses of Niels Bohr as Scientist and Thinker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . WERNER HEISENBERG: Quantum Theory and Its Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HENDRIK B. G. CASIMIR: Recollections from the Years I929-I93I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LfoN RosENFELD: Niels Bohr in the Thirties. Consolidation and extension of the conception of complementarity OTTO RoBERT FRISCH: The Interest is focussing on the Atomic Nucleus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . STEFAN RozENTAL: The Forties and the Fifties . . . . . . AAGE BoHR: The War Years and the Prospects Raised by the Atomic Weapons . . . . . . . . . . . . . . . . . . . . . . . . ABRAHAM PAIS: Reminiscenses from the Post-war Years J0RGEN KALCKAR: Niels Bohr and His Youngest Disciples CHRISTIAN M0LLER and MoGENS PIHL: Review of Niels Bohr's Research Work . . . . . . . . . . . . . . . . . . . . . . . . . . VIKTOR F. WEISSKOPF: Niels Bohr and International Scientific Collaboration . . . . . . . . . . . . . . . . . . . . . . . . JOHANNES PEDERSEN: Niels Bohr and the Royal Danish Academy of Sciences and Letters . . . . . . . . . . . . . . . . VIGGO KAMPMANN: Niels Bohr and the Danish Atomic Energy Research Establishment . . . . . . . . . . . . . . . . . . MoGENS PIHL: Niels Bohr and the Danish Community RICHARD CouRANT: Fifty Years of Friendship . . . . . . . . PAUL A. M. DIRAC: The Versatility of Niels Bohr HANS HENRIK KocH: Science and Administration . WILLIAM SCHARFF: Memories of Tisvilde . . . . . . . . . . . . MoGENS ANDERSEN: An Impression . . . . . . . . . . . . . . . . HANS BoHR: My Father . . . . . . . . . . . . . . . . . . . . . . . . . . Open Letter to the United Nations by Niels Bohr . . . . . . Chronological Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Pictures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 II 38 74 94 I09 I I4 I37 I49 I9 I 2I5 227 240 26 I 266 28I 290 30I 306 3 Io 3I 5 32I 325 340 353 354

Introduction

The plan to write a collective book on Niels Bohr was conceived as long as 1 5 years ago, but for various reasons its execution was repeatedly postponed and only now at last has it been possible to carry it out. The aim of the book was to convey to wider circles an impression of the significance of Bohr's work, not only for our knowledge of the atomic world, but also for the theory of knowledge and the philosophy of science. Originally it was hoped to assemble contributions from a number of people who had been close to Niels Bohr, such as members of his family, friends in school and university and associates in his scientific work. These authors who, each at different periods of time, had followed Niels Bohr's life and work at close quarters would together have presented a picture of the development of his thought and his many activities. Such a life story of the man who, for many years, had been a central figure in the development of atomic science, and who inspired the work of many physicists all over the world would have been a firsthand contribution to the history of physics in the last five decades. Unfortunately, several of those who should have been the first to participate in this work are no longer alive. Among these are Niels Bohr's brother Harald, his cousin Paula Strelitz, his friends and colleagues Ole Chievitz, H. M. Hansen, Hans Kramers, Wolfgang Pauli, who originally participated in the planning of the book; there is no adequate substitute for their testimony of the events of the early years. The original plan had therefore to be somewhat modified. The first two sections of the book-the first written by David Jens Adler, the second by Leon Rosenfeld and Erik Riidingerhad to be based on evidence from letters and other documents, on memories of past conversations with the departed friends and on recollections of surviving witnesses of those times. The other authors who have written down their own experiences have also made extensive use of the available source material in order to ensure the greatest possible accuracy.

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INTRODUCTION

An effort has been made to describe the scientific work of Niels Bohr so that it can be followed by lay readers, and although some difficult passages could not be avoided, these are not essential for a general understanding of Bohr's way of thinking and an appreciation of the fascinating interplay between the scientist and the man. For the benefit of those who would like to obtain a deeper insight into Nieis Bohr's achievements in physics, a special section, written by Christian M0ller and Mogens Pihl, has been added. There, the scientific background is presented in a more popular form thus supplementing the presentation in the preceding sections. The contributions covering the various periods of Niels Bohr's life and scientific activity constitute the first part of the book. The second part contains, besides the popular account of the physical problems just mentioned, a number of contributions which may give a picture of Niels Bohr's manysided interests and his activities in fields other than fundamental scientific research. The third part contains a few recollections of a more personal character. The book concludes with a reprint of the Open Letter to the United Nations of 1950. In this document Niels Bohr has set out the ideas which were foremost in his mind in his later years and which are still of great topical importance. Many of the contributors are of course physicists who are present or former members of the Copenhagen Institute and are now living in various countries. The other authors are people who had close relations with Niels Bohr in various fields of activity. Thus, Viggo Kampmann was the Prime Minister of Denmark at the time when the Danish Atomic Energy Commission was founded, and Hans Henrik Koch has-since the foundation of the Commission-acted as the Chairman of its Executive Council. Johannes Pedersen, professor of oriental languages at the University of Copenhagen, and for many years a close friend of Niels Bohr, succeeded him as the President of the Royal Danish Academy of Sciences. Richard Courant, the prominent mathematician, is the contributor who has known Niels Bohr longest. Niels Bohr had many personal friends among artists, and two of the articles have been written by Danish painters: the late William Scharff was a contemporary of Niels Bohr; while Mogens Andersen belongs to the following generation. One of Niels Bohr's sons, Hans, has written the lat section entitled "My Father". The book appeared originally in Danish in the autumn of 1964. The

INTRODUCTION

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editing work was carried out with the co-operation of some of the contributors. The invaluable support which Mrs. Margrethe Bohr gave to this work is also acknowledged with deep gratitude. Apart from minor details, the present English edition is identical with the Danish one. A number of the articles were originally written in English, and one in German. Most of the articles in Danish have been translated by Mr. Robert Gosney, and a few by Dr. J. E. Hooper. Thanks are also due to Professor J. Hamilton for assistance in connection with the translation. The pictures have mainly been chosen from the collections of Mrs. Margrethe Bohr and the Niels Bohr Institute. A number of pictures from the later years have been taken by Gunvor Betting, Hans Bohr, Henrik Clausen, John Durban, George Gamow, Vagn Hansen, J0rgen Kalckar, B0rge Lassen, Knud Meister, Nordisk Presse-Foto, Politikens Presse-Foto, Stefan Rozental, The Weizmann Institute. Especially as regards older pictures and in a few cases of the more recent ones the names of the photographers could not be traced. Stefan Rozental

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ninth year in essentially the same form as it still dominates my life to-day. If I had to describe it more closely, I think it would be best to say it is an instinct; certainly regard for my position in life or the like has not been involved in it; neither was it any definite purpose which obsessed me. It was not until much later in my life that I became grateful that this love made me work along a line-that of scientific research and the spreading of knowledge-which from the ethical point of view I place on the highest level. And I remember well that when this became clear to me I had the most definite conception of what a misfortune it would have been for me if this instinctive urge had not been such, that what was necessary to my nature must lead to an aim that I could respect. I began at an early age to collect objects of natural history and naturally my collection gradually grew to a considerable size. I collected all such objects, especially parts of skeleton, stuffed animals (I did not have many of these because they were so expensive) and specimens in spirit. It must have been my love of systematic scholarship which led me to collect; a passion for collecting as such is very foreign to my nature, and I do not think that I ever collected stamps or anything like that (or only for so short a time that I cannot remember it). Nonetheless I have no aptitude for natural history as such; I lack the ability to recognize the forms of plants and animals, and I have no interest in the determination of species, and later I even had difficulty in seeing its scientific importance." With this background it is not surprising that in the course of his medical studies it was experimental physiology which caught Bohr's interest, nor that in the whole of his later scientific work in physiology it was particularly the physical aspects which became his main field. When only 22 years old, Christian Bohr wrote his first scientific work (The Effect of Salicylic Acid on the Digestion of Meat), and three years later, in r 880, he defended his thesis for the degree of Doctor of Philosophy at the University of Copenhagen, a treatise on "fat globules" in milk. But it was work on the binding of gases to the blood and on respiratory conditions in general which especially came to be the main interest of his scientific life. In this he showed not only a clear sense of the meticulous care required by good experimental work, but he also felt a neverslackening interest in the general interpretation of the results of physiology. This made him one of the most diligent contributors to the annual publi-

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cations of the University, in which his clear descriptions of the problems of physiology became the starting point for far-reaching discussions of one of the main philosophical themes of his time-the schism between the "vitalistic" (or finalistic) theories and the so-called mechanistic conception of the vital processes. There is no doubt that Christian Bohr's interest in such questions contributed to Niels Bohr's preoccupation with biology many years later. These interests brought Christian Bohr into close contact with university colleagues interested in philosophy, and his relationship with scholars like Harald H0ffding and Vilhelm Thomsen was more intimate than one usually sees in the contact between people in such different fields of knowledge. H0ffding in his "Memoirs" described his association with Christian Bohr as follows:"The beginning of the regular meetings from which I gained much pleasure dates roughly from the time I have been speaking about. They started when I used to join Christian Bohr the physiologist after the meetings at the Academy of Sciences and Letters, and we would then carry on the discussion in a cafe. As a physiologist and a disciple of the Leipzig scientist Ludwig he followed the line that requires the strict application of physical and chemical methods to physiology. Outside the laboratory he was a keen worshipper of Goethe. When he spoke of practical situations or of views of life, he liked to do so in the form of paradoxes and these were as a rule improvised. A conversation was given new life when he joined in. Our gatherings at the cafe after the meetings at the Academy soon included a third member, the physicist Christiansen. He and Bohr had many interests in common, as Bohr's physiological method led him to detailed studies in physics. This trio which had been formed soon tired of cafe life, and it was therefore arranged that we should in turn go to each other's home on those Friday evenings when the Society was meeting. A fourth man now joined us, the famous philologist Vilhelm Thomsen." In his memorial lecture on H0ff ding many years later at the Academy Niels Bohr mentioned the profound influence he and his brother Harald had received from their earliest childhood by being permitted to sit and listen to conversations on those evenings when the quartette met at the Bohrs' home. This was not so much a direct influence as an inspiration for a deep understanding of the unity in all human searching for knowledge,

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regardless of the different forms in which it manifests itself in the endeavours of a biologist, a physicist, a philologist and a philosopher. Even in the field of sport Christian Bohr was among the country's most tireless initiators. His interest in everything English made him a supporter of the various ball games, especially Soccer, which in those days was not yet very well known in Denmark. In an obituary, Asmus Diemer (one of the sports correspondents of the Copenhagen press in those days) put it in the following way: "Professor Bohr took a never-failing interest in the students' sports. In the days when "Akademisk Boldklub" (the university football club) laid out its large playing fields at Tagensvej, he supported the leaders of the club in word and deed. He helped in every possible way, and he was the deus ex machina every time the shoe pinched. And when the job was done, and everything went as it should and the whole undertaking made steady progress, then Professor Bohr was the happiest man of all." Christian Bohr was politically a progressive. The story is told that he was glad when his maternal uncle, the Conservative Christian Rimestad, was defeated by the Radical Left candidate, Herman Trier, at the parliamentary elections in r 884. The question of the equality of women and their emancipation was one to which he devoted great energy. Among other things he undertook to prepare a few classes of adult female students for matriculation. In one of these classes was the young Ellen Adler. In her case, however, matriculation did not lead to further studies at the University. Teacher and pupil fell in love and were married in r 88 r. Ellen Adler was the daughter of the banker D. B. Adler, who was wellknown to his contemporaries as a financier by his participation in the foundation of several important financial companies (including the Private Bank together with C. F. Tietgen, the Commercial Bank of Copenhagen and the New Jutland Provincial Credit Association). He was also an energetic politician and was elected a number of times to the Upper House and the Lower House as a member of the National Liberal party, whose left wing he supported. At the side of Christian Bohr the gentle Ellen became the beloved centre of the constantly growing circle of intellectuals who were guests in their lovely home in the old surgical academy in Bredgade. At the time

of her death, Niels Bohr's close friend from his childhood, Ole Chievitz,

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later professor of surgery at the University of Copenhagen, described her: "And Ellen Bohr's lovable personality cast its warm glow over everything, for this was the essence of her nature. It was so great that I can imagine that people who met her for the first time thought it must be an affectation; but one did not have to be with her many times to discover that like everything else about Ellen Bohr it was genuine, honest and strong. It was an unselfishness second to none ... " It is certainly no exaggeration to say that Niels and Harald Bohr grew up in a home which was not only intellectual, but which was also among the most distinguished in outlook and humanity. Christian and Ellen Bohr were to a rare degree able to give their children an education which provided the widest possible scope for their independent development, at the same time as developing their sense of cultural and human values. Harald Bohr was generally regarded as the brighter of the two boys. At a very early stage, however, Christian Bohr took the opposite view; he realized Niels' great abilities and special gifts and the extent of his imagination. His opinion became so firm that at one point he felt that Harald should not become a natural scientist. But it was of course not in his ' ' nature to make up his children's minds for them, and it was an intense pleasure to him that Harald with his thesis for the doctorate in r gr o brilliantly started on a career as mathematician which in the following years made him almost as internationally famous among mathematicians as Niels Bohr was among physicists. Niels, meanwhile, as Christian Bohr expressed it, was "the special one of the family", and from his earliest youth Harald agreed with this. In contrast to his younger brother, in his childhood Niels was very much concerned with using his hands in practical activities. First of all he showed a good knack for woodwork, which was later supplemented by working in metal-a craft whose strict claims on accuracy gave him particular satisfaction. But, of course, mechanical things were included in the scope of his interests. A story about this shows how careful Niels was and also shows his father's understanding of his special abilities. The hub sprocket of a bicycle had gone wrong and in spite of adult protests Niels resolutely took it apart. It was a long time before he began to put it together again, and the adults renewed their protests by suggesting anxiously that Niels should stop trying to mend the cycle and let a mechanic have a look

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at it. But Christian Bohr merely said quietly, "Leave the boy alone. He knows what he is doing!" An after having thoroughly studied the individual parts, Niels finally put the bicycle together so that it was as good as new. This episode also illustrates another characteristic of Niels Bohr as a child, a characteristic which can be recognized to some extent in his later life. Another child, a relation seven years younger, later told the story that even if in fact they were mere spectators, Niels gave them all a feeling of being participants in the work-a feeling that the bicycle was repaired by them all. Another episode, too, serves to illustrate Niels' care and attention to detail. In the primary school, the fifth class had been given the task of drawing a certain house with a garden and fence around it. Niels started drawing, but when he came to the fence he went off and counted the pales; the fence in the drawing must as a matter of course have just as many pales as in reality. (See picture facing this page.) During the years of their childhood, as in many respects also in later life, Niels and Harald were almost inseparable in whatever they did. Therefore is was a great sorrow to both of them that because of the difference in their ages they could not start school at the same time. On the other hand, Niels did not "forget" Harald at school, and this was shown when Niels joined the woodworking class. He got down resolutely to building a puppet theatre for his younger brother, and it was a great disappointment to him when the teacher explained that he could not take home the wood which was intended for the school's woodworking classes, and that as a result he could not complete this private project. (But the puppet theatre was soon constructed, since Christian Bohr presented the boys with both bench and tools, later supplemented with a lathe, when Niels' interest in metalwork came to light.) Little is known of Niels Bohr's schooldays. He was undoubtedly clever at school without being brilliant, but at a very early stage he displayed an ability to see the more fundamental relationships between things. Characteristic in this respect is a little anecdote about Niels when he was around 3 years old. While out for a walk, his father had pointed out a tree and had started to say, as one does to a child, how beautifully the trunk divided into branches, and the branches into even thinner branches, finally to end in leaves. After having listened to this for a while, Niels is said to

A p h otograph fro m childhood.

A drawin g Niels Bohr m ade a t an age of 1 1. T h e de tail s are r eprodu ced with great accuracy.

1

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Niels Boh r's parents: Professor Ch ristian Bohr and his wife E llen, nee Adler.

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have exclaimed, "Yes, but if it weren't like that there wouldn't be any tree!" Niels Bohr's "worst" subject was without doubt Danish composition. He simply never quite mastered the incidental formal requirements which were essential to this subject, and there are innumerable anecdotes about Niels' Danish essays. He seemed to have a special difficulty in meeting the requirements that the essay should be given a suitable introduction and a conclusion. This led to the following brief composition on the subject "A walk round the harbour" :-"My brother and I went for a walk round the harbour. There we saw ships loading and landing." Niels, it is said, was himself very enthusiastic about the alliteration in the words "loading" and "landing". But the teacher's repeated demands for an introduction and a conclusion in essays often stimulated Niels' sense of humour, as in one essay on metals, the last line of which runs, "In conclusion I would like to mention aluminium", or as in a cheeky suggestion for an introduction which he discussed with his brother, but which never came under the eye of the teacher. The subject of this essay was "The use of the forces of nature in the home", and Niels' suggestion was that the essay should be introduced with the words "In our home we do not use the forces of nature!" Christian Bohr had no doubt special qualifications for understanding Niels' difficulties in written Danish. For in the memoirs already quoted he hinted at his own poor attitude to this subject as follows:- "While I had an average interest in most of the subjects I was taught, there were two disciplines which I loathed. One was free composition in Danish. I presume that in spite of reading a great deal of fiction I was slow in developing the abilities needed to write a pleasant account of a subject I found difficult to understand. Perhaps, too, the demands on this point were somewhat exaggerated. The title of the essay for matriculation in this subject was "How one is educated in the school of adversity". A 1 7-year-old must have had an unhappy youth or an unusual imagination to produce something plausible on such a subject. The most one could produce was, probably, unnatural and untrue." Apart from Danish essays, Niels was an able and interested pupil, and gradually his gift for natural science came to the fore in subjects such as physics and mathematics. It even reached the point where he started 2

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criticizing various things in the physics text book as being. incorrect. When a worried school-friend asked him what he would do if he w_er.e given one of the "incorrect" passages in the exam, Niels answered as if it were the most natural thing in the world, "Tell them, of course how . . things really are". Niels Bohr's interest, however, was not limited to those subjects m which his special abilities made their mark. He worked. kee~ly ~~th at history and languages, and wrote excellent essays in Latin. ~is dihge.nce in such subjects resulted in Niels being first in his class m the fmal examination. of . h 1 f · d Alb . V . J0rgensen , who remained a close .friend . H is sc oo - nen , Niels Bohr all his life, has reported the following in a few remmiscences of their schooldays:. . "I do not know if now it is the practice to make the pupils recite verses learned by heart, as a part of the teaching of Danish ~~nguage. It. was certainly the case in our day. Niels Bohr had a special ability and aptitude for this art (just as his choice of poetry was unusual and good). He recited the poems in a rather chanting, slow and dreamy ton~. I do not believe that Niels ever tried writing verse himself, but there is no doubt that he had a lyrical sense. . I have the impression that Niels was not ambitious (.he was c~rtamly no "swot"), and was not driven by this virtue ~or vice) to his good performances. Later in life I have realized from his own statem~~ts that his maternal aunt, a headmistress, :tv1iss Hanna Adler, .was a~.bit10us on nt But I do not believe that she "pushed" this ambition, and I . l h is accou . will always be convinced that Niels' ability expressed itself a~ a n~tura and simple thing without any special effort. He was a very qmck thU:ker, and I remember various occasions when his thoughts ran on more qmc~ly than his ability to use the sponge etc. at the blackboard, the result bemg that as his thoughts gradually needed new numbers and symbols he went on to wipe the board with his fingers (and sleeves). Neither he nor the blackboard looked very tidy afterwards." Niels Bohr's class belonged to the last group of students under th~ old system before the Education Act of I 903, and at that tim: the matn~ul­ ation examination gave no indulgence in the form of red~cmg the curn~~­ lum or dropping subjects. Everybody was therefore reqmred to show d1h·

gence and attentiveness, which furthermore was encouraged by a much stricter discipline than is known to-day. Another of Niels' school-friends, Aage Berleme, has reported the following little feature of school life:"The gymnastics teacher Swendsen, a one-time sergeant, fell ill, and Sergeant Petersen was to take his place. Before the first period Petersen took aside Ole Chievitz, the senior in the class, and put the following question to him, "Tell me, Ole, did Swendsen bash you much? Because I'd like to continue the class in the same spirit." This feature of school life, of course, contributed on the other hand to a good corporate spirit in the classes and this was very true of Bohr's class, which gradually concentrated around Niels. Ole Chievitz once expressed this as follows:"! clearly remember how we were all impressed by him as a human being even in those days. It was so decidedly Bohr's manner and personality which set the tone for the class as a whole." Apart from home and school, it was Naerumgaard, his maternal grandmother's country house north of Copenhagen, that was the natural centre of the childhood and youth of Niels and Harald. In 1908 Naerumgaard was presented to the Municipality of Copenhagen for use as a children's home in accordance with the wishes expressed in the will of D. B. Adler and his wife. In the transfer it was decided that, for the first two generations of D. B. Adler's descendants, a representative of the family should be a member of the school board, and it so happened that many years later Niels Bohr filled this office during the last two years of his life. A picture of Niels Bohr at Naerumgaard is given by a relative, Germanborn Paula Strelitz, who spent a great deal of her childhood in Denmark, and who later settled there and grew very close to Niels Bohr and his family:"When one thinks a long way back and tries to remember the world of one's childhood, one sees a number of isolated pictures. A child does not retain the idea of a continuous development. The writer calls to mind mainly the pictures from Naerumgaard, where the Bohr family spent their summer holidays with their maternal grandmother, Jenny Adler, whose great and strong personality, whose uprightness and goodness quite naturally made her the pivot and leader of this large house. She was the beloved ideal of her grandchildren. She sat at one end of the long table in the large 2•

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dining room; I do not remember that there were ever any "impo~tant" guests who were seated next to her. To right and left of her sat ,~he chil~e~ at a good distance from their parents. There was no danger of correction at the table. They were no more well-behaved than other children, but they were confident and happy and ate nicely what she (grandmother o~ Au~t Jenny) gave them. I remember that Niels at one ti~e covered his frmt jelly with an excessively mountainous layer of sugar; it looked wo~derful. But his father whose sharp eyes had taken in the action from a distance, remarked fro~ the other end of the table, "Really, Niels!" Grandmother answered quietly but firmly, "Maybe he needs it." It was perhaps especially at Naerumgaard that Niels and Harald came really close to their Aunt Hanna. Hanna Adler was two y~ars ol~er than Ellen Bohr, and is said to have had a touchingly protective attitude to her younger sister right from her childhood. In the book th~t w~s published in memory of Hanna Adler on the centenary of her birth m 1959, Niels Bohr wrote in the foreword:. . "From my earliest childhood I have vivid memories of her active_ and loving participation in everything concerning her brothers and sisters and their children. Although my brother Harald and I were not , a~ong her pupils at school, we shared with them "Aunt Hanna's" educational influence. When she could spare time from her school work, she took_us on Sundays around Copenhagen's natural history a~d ethnographical exhibitions and art museums, and in the summer holidays at N aerumgaard, where she accompanied us on foot or on a bicycle in the wo~ds and fields of the district, we learned both about nature and human hf e, while she jokingly or seriously talked to us about everything that could catch our imagination." . Niels Bohr retained for the whole of his life a close contact with several of his school friends-Alb. V. J0rgensen and Aage Berleme, who have already been mentioned, and Carl Johan Michelsen. But Niels Bohr was especially close to one of them, namely Ole Chievitz, whose father was professor of anatomy at Copenhagen University and thus a colleague and close friend of Christian Bohr. . Few people could be considered more different in externals than Niels Bohr and Ole Chievitz. Chievitz was impulsive and always eager to take up a detennined standpoint. In a number of spheres it was inevitable

that the points of view of Bohr and Chievitz should be divergent, but it was as if all differences of opinion throughout their lives brought them closer and closer together, and there was never any break in their friendship from its very first beginning when they shared a school desk for the last six years before matriculation in the Gammelholm Grammar School. The deep mutual admiration Niels Bohr and Ole Chievitz felt for one another-and perhaps not least for those traits in each other that were most in contrast-found public expression on a few occasions. When Ole Chievitz died, Niels Bohr spoke at the great service in the Cathedral in memory of his friend, and said among other things:"In his school-days his independence and love of truth won him the spontaneous respect of everybody, as did his ability to get to the root of every matter. By his eagerness to join in any struggle for what he thought was right, Ole often became a subject of dispute among his contemporaries, but we all united in our admiration for his straightforwardness and fearlessness, which together with his enthusiasm and energy made him such a good friend. In many ways Ole Chievitz had something very special about him, but at the same time, and in an extraordinary manner, his whole nature showed those features that characterize the human being who seeks and struggles. However passionate his stand might be and his urge to express it in his actions, he had with all his strength a heart-warming gentleness which he made great efforts to conceal, although often in vain. In him the sense of justice and feelings of kindliness were developed as in few people, but he combined with this the ability of the great personality to recognize without vacillation what the situation required of him at any given moment. It was quite foreign to his nature to strive for agreement; on the contrary, he often enjoyed stimulating controversy by pretending to take some attitude. On such occasions, which always implied a self-examination, one felt perhaps most strongly the depth and warmth of his personality and came to like him, if possible, even more." Barely one year earlier, on the occasion of Bohr's sixtieth birthday, Chievitz in a press interview answered the question "Which characteristic of Niels Bohr do you estimate highest?" by saying "His goodness ... Let us not give examples. Bohr would not care for that. You must be satisfied with my word when I tell you that he is good in big things as well

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as small. Yes, I'm not exaggerating just because it's his birthday when I . . h ld1" . . say that I consider him the best human b emg m t e wor · This mutual friendship and admiration did not prevent Chievitz,who both because of his nature and because of the closeness of comradeship was not easily impressed-from opposing Bohr for fun in ~oth scientific and philosophical discussions and making him the object .of an imaginative and disrespectful wit which Bohr himself was the first to appreciate. One of the most direct pictures of this side ~f the two f~ie~ds' relationship is given by some "log-books" (kept mamly by C~ievitz) from the yacht "Chita'', which he and Bohr bought together with the chemist Niels Bjerrum and the xylographer Holger Hendriksen in 19~6, and in which the four friends went on short trips and long tours durmg the following eight years. The idea was that the log-books should be k.ept for the skipper's (Niels Bjerrum's) sober records of a purely nautical character but very soon it was the mate, Ole Chievitz, and Holger Hendriksen~the ship's "doctor in chief" and the "scientist and philanthropist" as they called each other-who took charge of the book to ~s~ it for. witty and disrespectful fantasies about life on board and the part1c1pants m the crmse. A general picture of Niels Bohr's part in the cruises of the "Chita" has been left by Niels Bjerrum:"With Bohr on board there were always talks and discussions going on, if he were not lying down resting or sleeping in the cabin. Bohr has a remarkable ability to start his companions thinking, so that they feel much more clever than they really are. He also has a remarkable ability of finding problems in everyday observations. When he saw the moon reflected on the water, it turned into a problem to deduce why it became a streak and not merely a large patch. When we tacked into the wind using our sails, it turned into a problem of how it was possible." Niels Bjerrum noticed another striking feature in his friend:"In order to appreciate fully his remarkable nature, one must realize that through the years he retained his boyishness, a boy'.s love of gar:ies and a boy's curiosity, the latter of course being a very important thmg for a natural scientist. Bohr has always been very skilled in throwing stones up high and to a great distance, and at playing ducks and dra~es on the water with stones, and his pleasure in this has not deserted him.

I remember a time when he visited us at Skagen, and we went to see the church buried in sand. Bohr tried to throw a stone over it. As this proved only too easy for him, he started throwing stones up and getting them to fall outside the shutters of the two peepholes in the first and second stories of the tower, but that was also too easy and Bohr, who got keener and keener, started throwing stones through the small holes in the shutters, and when he succeeded, he got the idea of our trying to throw our walking sticks up and make them stand against the shutters, and when this was successful, we had to try to knock them down by throwing stones at them. Finally he got us to try to get the sticks to hang up there with the handles through the holes in the shutters, and this really did succeed. The rest of us then gave up the idea of getting them down again by throwing stones, but Bohr persevered and was delighted when he finally succeeded." But through all the descriptions and reminiscences from Niels Bohr's childhood and earliest youth (and to some extent his later life) there runs like a leitmotif above all else the inseparability that characterized the relationship between the two brothers Niels and Harald Bohr. As children neither of the two brothers could think of doing anythincr without the other. A very early account of this is the story of how Niel: went around the N aerumgaard gardens the whole of one afternoon calling for Harald. When an older cousin finally asked, "What do you want Harald for?" he answered her, "I've been given a bun, and I want to share it with Harald." As already mentioned, Harald, as a child was considered by many to be the brighter of the two brothers, and although Niels was two years older, Harald matriculated the year after him when only seventeen. At the early age of 22 years, in January 1910, he defended his doctor's thesis "Contribution to the Theory of Dirichlet's Series", and this was the prelude to a brillant contribution to mathematics which gained him great international respect. At that time Harald Bohr was by far the more famous of the two brothers, not so much because of his scientific gifts as for the fact that he was among Denmark's best footballers. For a number of years he played half-back in the first team of the AB football club, and he won a silver medal for Denmark at the Olympic Games in London in 1908 (where

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the British sporting press was loud in praise of "the shock-headed" Dane). Niels too was a keen footballer, but he did not get any further than becoming reserve goalkeeper for the AB team, and he took an active p~rt' in o~ly a few games. "Yes, Niels was quite good; but he was too slow m commg out'", teasingly explained his younger brother in later years. In the relationship between the two boys Harald's quick-wittedness showed itself in those days in the way he teased Niels. In Harald Bohr, the profound sense of humour which both brothers retaine~ thro~ghout ~he whole of their life was combined with an altogether sparklmg wit, of which the primary and most favoured butt was Niels. Aage Berleme, their school friend ' has bcriven his version of this in the following words:• • "But the person who teased Niels most and who told the funniest stones about him was Harald, his younger brother. Although every class kept to itself and looked down on all boys in the lower classes, Harald, because he was Niels' brother, was sometimes allowed to come into our classroom during break, or else we deigned to talk to him in the playgrou~d, and then it was his delight-naturally in all friendliness-to tell stones about Niels and his merits. In short Harald loved in all friendliness (for the brothers stuck together through thick and thin) to make fun of Niels"· And however witty Harald could be at Niels' expense, Niels utterly lacked the ability to tease. Harald Bohr himself used to tell the story of how he once persuaded Niels to play at "teasing one another". It was Harald's tum first, but before very long Niels gave in with an imploring, "Oh, oh, stop it, please, no more ... " "Very well", answered Harald mercilessly, "it's your turn then." Niels thought for a long time, and then said in a vain attempt to put a malicious tone into his voice, "You've got a little spot on your coat!" In 1905 a number of students, who knew one another from H0ffding's colloquia in the preliminary course in philosophy, formed a group. The idea was that philosophical and scientific questions should be discussed, and naturally both Niels and Harald were invited to join. The group was called Ekliptika, because the number of members was limited to twelve. Apart from the Bohr brothers there were Peter Skov the jurist (later Danish ambassador to Moscow), Edgar Rubin the psychologist, Poul N0rlund the historian and his brother Niels Erik the mathematician (who with Niels and Harald Bohr went under the name of "the broth-

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25

ers"), Vilhelm Slomann the art-historian, Kaj Hanriksen the entomologist (later Keeper of the Zoological Museum), Einar Cohn, later permanent under-secretary, Lis Jacobsen the etymologist, Viggo Brnndal the philologist in Romance languages, and Astrid Lund who later became Lunding by marriage. It was of course mainly questions of philosophy and epistemology on the basis of H0ffding's colloquia that were discussed. During the winter term they met several times a month at the a Porta or similar cafes, where they discussed the evening's introductory lecture and questions arising from it far into the night. Nobody remembers today whether Niels or Harald ever gave an introductory lecture, but they seem to have been very active in the discussions. And here-no doubt for the first time in a wider circle-the close relationship between the two brothers was expressed in their way of thinking. In an article on the occasion of Niels Bohr's 7oth birthday in 1955 Vilhelm Slomann described in retrospect these Ekliptika evenings as follows:-"When the discussions were beginning to tail off, it often happened that one of them said a few general words about the lecture and continued in a low voice, at a furious pace and with vigorous intensity, but was often interrupted by his brother. Their way of thinking seemed to be co-ordinated; one improved on the other's or his own expressions, or defended in a heated yet at the same time good-humoured manner his choice of words. Ideas changed their tone and became polished; there was no defence of pre-conceived opinions, but the whole of the argument was spontaneous. This way of thinking a deux was so deeply ingrained in the brothers that nobody else could join it. The chairman used to put his pencil down quietly and let them carry on; but when everybody moved in closer to them he might say ineffectually, "Louder, Niels'"'. This picture of the evening meetings of the Ekliptika calls to one's mind the method of work which later became so characteristic of Niels Bohr. While Harald as a rule preferred to work alone, conversation was the way by which Niels Bohr developed his thoughts. The basis of this method of working was not merely that the other people taking part in the conservation became acquainted with the scientific problems or what ever else was being discussed, but also that Niels Bohr felt, to use a modern expression, on the same "wavelength" as the person he talked to. Agreement or difference of opinion or definite views were in this context obvi-

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ously of minor importance; but it was necessary for Niels Bohr to feel on common ground with those who in this way became his most intimate collaborators in solving scientific and social questions, or in the development of his thoughts. Niels Bohr simply could not work if he did not find in his closest environment the most complete harmony and understanding. The brothers wrote quite frequently to each other when they were away from home, especially in their earliest youth. This correspondence is extant and dates from about 191 o. Apart from showing the unique relationship which we have tried to indicate, this correspondence is also delightful because it gives a picture of the brothers in those years ( 1909-1911 ) when they both became masters of science and doctors of philosophy. In the spring of 1909 Harald Bohr had already obtained his master's degree, while Niels was preparing for his. To have peaceful surroundings for his studies Niels had gone on holiday to the vicarage at Vissenbjerg on Funen where the father of Christian Bohr's young assistant Bolger M0llgaard' was vicar. On March 7th, 1909, Niels wrote to Harald from Vissenbjerg : "Please don't be disturbed at receiving three cards all at once, but I promise not to be guilty of such "laxity" again; but when I suddenly realized to my horror that the other card to you just contained "idle chatter", it seemed to me that it was necessary to give some facts about my life here in the vicarage. Everything is fine in every way. I eat and sleep a tremendous amount to the satisfaction of mother (sorry to talk nonsense, I meant to my own satisfaction); but I also get quite a lot done. I have now finished . . . . dynamics and have read most of what Abraham has to say about vector calculus (very interesting), and I have begun Christiansens's manuscript.*) I am enjoying it and the dynamic introduction contains many interesting things, but it makes not the slightest attempt to comply with the requirements which you (and I as well) would expect from a properly founded theory of motion ... " The next day Niels wrote again:"Many thanks for your letter. I am so looking forward to the time when we can do a lot together, and I hope that we shall both gain much pleasure from it. You do not know how much you have taught me. Your *) Presumably the manuscript of the text-book on physics published by Professor C. a few years later.

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way of dealing with Jordan*) was a surprise to me, and it taught me that it is a far too complex and completely unnecessary procedure (for anyone, for example for the great mathematician) to regard all questions as a thick fog which can be met with a larger or smaller degree of "tact" (popularly called incontestable logic). But surely there is to be found in mathematics a fairly firm basis, on which one "perhaps"? can build, partly by one's own work and partly with very welcome help from the aforesaid mathematician. Love to the whole family from your brother who is looking forward to seeing you again soon." ' Niels Bohr's admiration for his brother is also expressed in a letter during the latter's examination in March 1909. "It was extremely nice to hear that things are going well with your examination, although it was not entirely unexpected. In any case I could not know beforehand how many solutions you would give to every single problem ... " Directly after the end of the examination in April 1909 Harald Bohr went to Gottingen to study with the great German mathematician Edmond Landau, and on April 20th Niels wrote: "Hearty congratulations. Th~s time it is not an ordinary birthday, but the beginning of something entirely new. I shall be so pleased for your sake if you do really well at Gottingen both in developing your mathematical personality and also with regard to yourself. I am sending you herewith (besides what Mother is so go~d as to send.you in my name) Kierkegaard's "Stages on Life's Journey". It is the only thmg I have to send; but I do not believe that it would be very easy.to ~ind anythin~ better. In any case I have had very much pleasure in readmg it, I even thmk that it is one of the most delightful things I have ever read. I am looking forward to hearing your opinion of it sometime. I am doing very well in Vissenbjerg. It is lovely now the spring is really here and the first wood anemones have already come out. As you know I have had the first proofs. The treatise**) appeared after all in the Transactions was ~eautiful!y pr~ted and so carefully checked over (there was not a :ingle figure prmted mcorrectly) that it was easy for me to finish it. W eber·H·-:-:·) :~ Jor~an:

Cours d'Analyse---:a "'.ell-knwn. text book on mathematical analysis. ) Niels Bohr alludes to his first scientific work "Determination of the Surface ~ns~on of Wate;- by t~e ~ethod of Jet Vibration"-an English publication of the prizewfmSm?g paper with which m 1907 he won the gold medal of the Royal Danish Academy o ciences and Letters. *** ) Proceedings of the Royal Society (London ) . T

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was kind enough to send me a copy of the "Abstract" that had been in the Proceedings*). It proved to be my Conclusions, so that was very nice. My studies are going well and I am beginning to look forward to the examination, and especially I look forward to the last months of the autumn, when I shall finish. We shall have a fine time together. When I am alone I think of all the many things I am looking forward to talking to you about. This has not been a real letter, and far from what I wanted it to be. But the trouble is that I am sitting here hurrying to get it finished and sent off in time; I started it so late, as I wanted to finish off the Stages before sending it to you. If it is any consolation, I shall be sending another letter in a few days time. So I will end this time by wishing you very many happy returns of the day. P. S. The whole of the M0llgaard family send their good wishes for the Master's birthday." Although young Niels Bohr was excited at reading Kierkegaard's "Stages on Life's Journey'', neither at that time nor later did he agree completely with Kierkegaard's ideas, which is indicated in another letter to Harald, in which he says:"Many thanks for your long letter. It is really terribly nice to hear from you. Mother was kind enough to send your letters on to me, and as I know that it is no easy job to write letters when one has a lot to do, I do not expect letters from you, except when you feel the urge to relieve your mind about your work, and this, you know, is very welcome to me. At the moment I am wildly enthusiastic about H. Lorentz's (Leyden) electron theory. When you have finally read the "Stages", and there is really no reason why you should hurry with it, you shall hear a little about it from me. I have written a few notes about it (not in agreement with K), but I do not intend to be so banal as to attempt, with my poor nonsense, to interfere with your impression of so nice a book. I am getting on fine and I am looking forward more than I can say to the lovely time I shall spend in Copenhagen when I have finished my examination, before I go abroad ... " But the correspondence between the two brothers was not one-sided, of course, and it seems natural at this point to quote a little from Harald's letters from Gottingen:* ) S. Th. Holst Weber was one of Niels Bohr's fellow-students. He was given his Ph. D. in 1916 and later became Danish Consul General in Holland.

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29

"Wh~n I. come home and have relaxed a bit, I am also looking forward to delvmg mto mathematical physics a little, so that I can really follow your ideas and especially what you have already got hold of regarding the small electrons. I have no': to start on the thesis for my doctorate. The last few days I have been m a state of indecision as to whether I should start at the beginning, at the end, or in the middle, and so I have not started at all. Landau has lent me a proof copy of the bibliography to the book on "The distribution of Prime Numbers and Dirichlet's Series". It contains 8oo diff~rent arti:les, .~~st of which I must look through. I am thinking of staymg here m Gottmgen at least until the beginning of September (the term ends August 3rd-4th). Perhaps I shall not come home until after I h~ve been to Stockholm, but you won't escape having me properly home agam after that. When do you think of finishing your examination, Christmas. or before? I am not going to overdo it the first few days, but am lookmg forward to reading a few good books. Yesterday I got hold of ~offman~'s Tales and already last evening I proceeded to lose myself in his amazmg world of fantasy, and am looking forward to this afternoon when I intend to find my way back to it again.-! have read a bit here and t~ere in Kierkegaard. Whether it is because, at the moment or perhaps m general, I do not have the right attitude to K, I must say that although naturally I have to admire his great art and superior gifts yet I do not feel really drawn to him. When, for example, I read Wilhelm Meister af~erwards-where in so many instances one can easily detect obvious, one might almost say, faults-it is as if I were revivified, because everything is so much more human, great and comprehensive. No doubt, too, all the muddle I am in and all the bustling around I have had to do recently as a result, has made me need to read something different from K." And as a touching expression of the strong family feeling inherent in both brothers, Harald concludes his letter:"It would really be delightful if, when I come home, we could read something really good together, could for example sit with Mother in the sitting-room around the gilded "piece" with the three legs, and one or other of us read aloud to the others ... " At the beginning of July Niels Bohr had finished the written work for the Master's degree and he writes to his brother:-

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"Many thanks for all your cards. Now I have luckily finished with all the writing. That is very nice indeed, although I cannot say, like a certain master did, that I am fully satisfied with the result. The problem was so broad and my pen so easily runs away with me that I had to be content with treating just a few parts of it. But I hope the examiners will let it go through, as I think I have put in a few minor details which are not dealt with anywhere else. These details were mostly of a negative kind (you know I have the bad habit of thinking I can find mistakes in others). On the more positive side I think I have given some indication of the reason why, and this is perhaps a fact less well known to you, alloys do not conduct electricity as well as the pure metals of which they are composed. I am now very excited about hearing what Christiansen will say to it all; I shall go up and have a talk with him to-morrow, and will let you know how it all went off . .. " However fluent Niels Bohr's letters to his brother appear from these extracts and however easily they alternate from gentle self-irony to touching admiration for his brother and enthusiasm for books he has read and which he wants to share with Harald, every single sentence has probably cost Niels Bohr tremendous effort. Even for private letters of his youth, such as those quoted here, he wrote many rough drafts. One day Harald found on Niels' desk a letter which Niels should have sent off long before for some particular purpose (to whom the story does not mention) . The letter seemed to Harald to be completely finished and therefore he asked his brother why it could not be sent off. "Oh no, that is just one of the first drafts for a rough copy!" was Niels' answer. And when at a later date Niels was putting the finishing touches to the thesis for his doctorate (again in the vicarage at Vissenbjerg), he one day had to write an imploring letter home asking them to understand that he no longer had time to answer all the many letters he received from home. Both Harald and his parents understood him, all the more so as Niels' mother at that time had already begun to write for Niels at his dictation, just as his wife and his colleagues did later. Letters from Harald to Niels often end with, "Let Mother write to say how things are going with you!" or with, "Don't bother to answer !" Nevertheless Niels' urge to keep in contact with those closest to him was so strong that he remained an industrious writer of letters throughout

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31 the whole of his life, including those times when he was alone on his many tri~s abroad. After his marriage to Margrethe Nr21rlund (see below) she was mamly the one who shared thus in his experiences and ideas. In the spring of I 9 Io Niels Bohr was already writing his thesis for his doctorate. The letters to Harald from this period reflect both the pleasures and the disappointments in this work, just as did later letters from Cambridge and Manchester to his brother and to Margrethe. But this correspondence lies outside the present context. Studies at the University of Copenhagen in those days were not organized alon~ such strict lines as we know them to-day and especially the few candi~ates for t~e master's examination in physics were very much left to their own devices, almost without any fixed lectures and with very little compulsory laboratory work. Niels Bohr's sailing companion of later years, Niels Bjerrum, became in 1905. his teacher in a course of inorganic analytical chemistry. He said later that m all the I 2 years he was assistant in the laboratory, he had never had a pupil whose bill for broken glass was anything like Niels Bohr's. One of the contemporary students at the laboratory has told how one day the whole labor~to~ was rocked by violent explosions. "Oh, that must be Bohr", Bjerrum is said to have remarked. And it turned out that Bohr with his impatient curiosity to see a certain reaction had exceeded the safety regulations. One of Bohr's student friends, Helga Lund, who later became a headmistress in Odense, has given the following glimpse from the lectures of the professor of astronomy, T. N. Thiele :"! began to study mathematics at Copenhagen University three years after I had matriculated, those three years being spent as a teacher in my native town of Silkeborg. The first lecture at the university was on the calculation of probabilities with Professor Thiele. I saw a young fellow with his heavy, bent head and a sort of school satchel in his hand come and sit at the other end of the bench where I sat, and I ~hought."He can't be studying mathematics". The professor explained that m the first term we should work, in groups of two, to calculate a function so as to find out whether it was periodic or not. By chance this young fellow and I were given the same initial figure. The result was that at the Technical University, where in those days we did the first two years with

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the engineers, we always sat together to compare the figures we had calculated. We then went on together to Thiele's next lecture, and as there was a free period between the two, we went to the Student's Union opposite the Cathedral and together studied Thiele's book, which for most of us was fairly enigmatic. This was a great help to me, but after a month I noticed that he was thinking on a completely different plane, and grew somewhat afraid that if this was the standard for the examination I just wouldn't get through. Well, it was soon apparent that it was he who was above standard. The rest of us listened impressed when he and Thiele discussed the problems ... " While Niels Bohr's school-friends in general seem to have regarded him as a normally able pupil, his fellow-students were obviously very early aware of his unique talents. Helga Lund wrote this in a letter to a Norwegian cousin as early as December r 904 : "Apropos genius. It is wonderful to know a genius, and I do, and am even with him every day. His name is Niels Bohr, and I have told you about him before. He is showing himself more and more exceptional. But at the same time he is the kindest, most modest young person you can imagine. He has a brother who is now at the university and who is just as bright; he is studying mathematics. The two are inseparable. I have never known people to be as close as they are. They are quite young, r 7 and r 9, but I hardly ever talk to any other students except those two because they are so nice." In experimental physics the university did not offer much in the way of facilities for candidates for the M.Sc., but Bohr had a special advantage in his father's physiological laboratory, where much work, as we saw, was concentrated on purely physical questions, and where over long periods Bohr often helped his father with experiments. With this background it is not surprising that Bohr's first scientific work was of an experimental nature, although even this work proclaims its originator's special pleasure and ability at working theoretically on problems. In 1905 The Royal Danish Academy of Sciences and Letters had offered a prize in physics for a closer investigation of jet vibrations with the view to determining the surface tension of liquids. Two papers were submitted, both of which were rewarded with the golden medal. One

The brothers Harald a nd Niels Bohr at three periods of th eir life.

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A photograph of his class at the G a mmelholm Gy mnasium . N iels Bohr is third from th e left in th e front row.

After m a tricu la tion in 1903. Stan ding, from N iels Bohr, O le C h ievitz.

33

(under the motto "Preparations are the worst") was written by a candidate for the master's degree (later professor) P. 0. Pedersen, the other (with the laconic fJ y £5) by Niels Bohr. Some two years later Niels Bohr had his paper published in the "Philosophical Transactions of the Royal Society of London". The problem was meant purely as an experimental one, and the theory of the English physicist Lord Rayleigh was to be used in the analysis of the vibrations of jets of various liquids. In contrast to P. 0. Pedersen, who determined the surface tension of a large number of liquids by an effective method, Bohr only succeeded in analyzing the behaviour of water jets, because the method he decided upon, which aimed at very exact measurements, required a great deal of time. On the other hand, Bohr was able to begin his paper with a thorough, and quite unexpected extension of Lord Rayleigh's theory. According to this theory, it was possible to determine the surface tension of a liquid from the length of the waves formed on the surface of a jet with known speed and cross-section . Bohr, however, showed that for a quantitative determination of the surface tension, it is necessary to extend the theory so as to take into account the viscosity of the liquid as well as the final amplitudes of the vibrations of the jets of liquid and the effect of the surrounding atmosphere. After such a comprehensive extension of the theory Bohr went on to give an account of his experimental work. To obtain sufficiently long and stable jets Bohr chose to run water through long glass tubes. But to make waves on the surface of the jets of water is was also necessary for the cross-section of the tubes not to be completely circular. Bohr chose an elliptical cross-section, and in his paper he remarks on the effort which merely this preliminary work on the production of the tubes involved:"The orifices of the glass tubes employed were given an elliptic section by specially heating the tubes on two opposite sides before drawing them out. Twisting of the glass tubes would produce a rotation of the jet about its axis, and the planes of vibration would not preserve the same direction at different distances from the orifice; to avoid such results it was necessary during the heating and drawing-out to have both ends of the tube fastened on slides which could be displaced along a metal prism. When the glass tubes were drawn out and cut off, they were examined 3

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34 under a microscope, and only those whose orifice had a uniform elliptic section were used . . . " With the same care Bohr explained the other elements in the experi. mental arrangement required by the research. The prolonged experiments which this method required even f~r a smgle result were carried out (preferably at night to exclude any disturbance of the stability of the jets) in his father's physiological laboratory. The paper itself was written at Naerumgaard, wh:re Christian Bohr almost forced his son to go and finish it and not contmuously to make new and time consuming corrections. The conclusion of the Academy is summarized as follows: "A single determination according to the method of the author requires constant work over many hours. For tha~ .reason .the jet must. be maintained over a long period under stable conditions; this length of time limits the application of the method for liquids which change their ~ature in contact with air and also requires a relatively large quantity of liquid ... Although this work does not really solve the problem as ~ompletely as the first, as it deals only with a single liquid, namely water, its author on the other hand deserves considerable merit for having furthered the solution on other points, so that we feel justified in suggesting that this paper too should be rewarded with the Society's gold medal." . . . The deep insight into the problems of the surface tension of hqmds ~hi~h Niels Bohr gained through his work on the prize essay. l~ter stoo~ him m good stead in a most unexpected way. When in the thirti~s he discovered that many of the fundamental characteristics of the atomic nucleus could be explained by analogy with liquid drops (see page 256) h:r.e too he had far more detailed basic knowledge than his fellow physicists, who for ;he most part had never come into direct contact with problems of this type. . Another subject which occupied him as a student and which was later to become an important subject for his research, was the phenomenon of radioactivity. There exists a manuscript of a lecture given by Niels Bohr around 1905 with the title "Lecture on radioactive transformations". The lecture which was given in a series of seminars organized by Professor Christiansen does not reflect any independent experimental or theoretical

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35

work, but-as such student colloquia should-gives a survey of the latest discoveries and theories in that special field. However, it provides many examples of the care with which Niels Bohr even then (although little more than some twenty years old) tried to put forward the different points of view and results, and the strict clarity with which they are set out. As a characteristic example we quote young Bohr's discussion of a feature which became very important in later nuclear physics, but which at that time must have appeared strange:"That there is any meaning at all in speaking of an average lifetime without indicating a definite time for the starting point, lies in the fact that atoms as it were do not grow older before they break down, so that the chance of breaking down is just as great at any point in their lifetime." As has already appeared from the correspondence quoted here between Harald and Niels Bohr, the subject of Niels Bohr's master's thesis, which took six weeks to write-the same as for his doctor's thesis two years later -was the interpretation of the different physical properties of metals, such as electric and thermal conductivity, magnetic properties and the thermoelectric phenomena, on the basis of the electron theory, which at that time had been developed especially through the work of Lorentz in Roland, Drude in Germany and J. J. Thomson and James Jeans in England. These investigations were based on the assumption that the characteristic metallic properties are associated with the presence of electrons which are able to move approximately freely through the metal, colliding from time to time with the stationary molecules of the metal. One attempted to test this assumption by pursuing its consequences and comparing these with the observed properties of metals. An important part of Niels Bohr's thesis for his master's degree is devoted to a clarification of the assumptions employed by the various workers in the field. And although Niels Bohr himself-as far as can be seen from his letters to Harald-felt a little worried at not having been able to "include much in it", in the introductory paragraphs one is struck by the enormous number of publications the young candidate for the master's degree not only succeeded in reading, but also in analyzing in great detail. It is Niels Bohr's critical and logical faculties which dominate 3*

CHILDHOOD AND YOUTH this work, his sense for seizing on the fundamental features or consequences of a theory and comparing them with the assumptions or experiences on which the theory is based. A single example will serve to illustrate the above-mentioned critical and logical approach and the strict clarity with which the argument is built up, finally to be compared with its starting point. The comment deals with one of Lorentz's assumptions:"There seem to be certain, at least formal, flaws in the ideas put forward by Lorentz, which derive from the fact that the law whereby metal molecules and electrons are assumed to interact does not lead to thermal equilibrium. Thus one might ask whence the electrons receive their velocities, which vary according to the temperature at the different places in the metal; indeed, they only collide with metal molecules, and these can, according to the law on which the calculation is based, neither give energy to, nor take it from the electrons." Directly after receiving his degree Niels Bohr started work on his doctor's thesis, which represents an extension of the electron theory of metals and which also contains a clear recognition of those points at which the theory encountered difficulties in principle. The assumptions of the theory are formulated on as general a basis as possible, and the consequences are pursued in great detail. For a number of metallic properties the results were found to be in rather good agreement with the observations, but at certain points, whose nature Niels Bohr carefully defined and described, fuudamental difficulties seemed to arise. In connection with the magnetic properties of metals Niels Bohr states straight out that an explanation within the existing scope of the electron theory does not seem feasible. That Danish physicists of those days found it difficult to understand the thesis, emerges in an amusing way from a report in a daily paper, which deserves to be quoted in full:"Yesterday the late Professor Bohr's other son defended his doctor's thesis, Studies in the Electron Theory of Metals, for the doctorate of philosophy. "This was the 26 year-old master of science Niels Bohr, who after only one and a half hours was able to leave the University as a Ph. D. Professor Heegaard was his first opponent. He dealt with the linguistic side of the thesis and had nothing but praise for the erudite treatise. Professor

CHILDHOOD AND YOUTH

37 Christiansen continued with a more specialized opposition, but it can be called such only in the most figurative sense of the word. "Professor Christiansen spoke in his usual pleasant way, told little anecdotes an~ went so far in his praise of Niels Bohr's work as to regret that the treatISe had not appeared in a foreign language. Here in Denmark there was hardly anybody enough informed about the electron theory of metals to be able to judge a thesis on the subject. "Dr. Bo~r, a pale and modest young man, did not take much part in the proceedmgs, whose short duration is a record. The little auditorium III was overflowing, and people were standing right out in the corridor of the university." In I 9 Io, a very short time after receiving his master's degree, Niels Bohr had met Margrethe N0rlund, a sister of Harald Bohr's student friend Niels Erik N0rlund and daughter of Mr. and Mrs. N0rlund of Slagelse. In I I I 9 they became engaged, and on August Ist, I9I2, a few days after Niels Bohr had returned home from his first short period of study with Rutherford they got .n_iarried. The honeymoon was spent in England, where the youn~ couple v1s1ted Rutherford after spending a week in Cambridge. Niels Bohr took with him a fairly long paper on the stopping of alpha particles which he had started shortly before returning to Denmark. It must of course remain outside the scope of this present account to describe the happiness Niels Bohr found in his marriage with Margrethe ~0rlund. What these two came to mean to each other cannot be put mto words and those occasional references to their married life, which lasted over 50 years, given by several people in some of the following pages, can but give a very slight idea of its unique character. Not only ~y the streng.th o.f he~ great personality and by her knowledge and ability m so many d1ffermg fields, but especially by her devotion, Margrethe Bohr became the perfect and indispensable support to her husband.

THE DECISIVE YEARS

The Decisive Years 1911-1918

by Leon Rosenfeld and Erik Riidinger

The period of Niels Bohr's life with which we shall deal in the following takes the young, promising but unknown physicist into the centre of world physics. These years saw the foundation of those ideas on the structure of the atom which were to bring about the decisive break with classical physics as well as the development of the point of view, known as the correspondence principle, which was to lead to quantum mechanics, and which contained the germ of the revolution in epistemology characterized by the word complementarity. It is all the more to be regretted that the following pages cannot be in the form of personal reminiscences. Nevertheless, by drawing upon the extensive correspondence, fortunately still extant, from this decisive period in the development of physics-and thus letting Bohr himself, as well as other physicists of the day, tell the story in their own words-we hope to have been able to give a faithful picture of these important years in Niels Bohr's life. The very first document from that time betrays a characteristic feature of Bohr's way of working with which all his later collaborators came to be well acquainted. In a copy of his doctor's thesis he introduced with the greatest care countless corrections of varying length, obviously meant to be included in an English translation of the thesis. It was planned that in September 19II Bohr, then 25 years old, should go to Cambridge for a year on a scholarship from the Carlsberg Foundation, and he wanted to take with him a translation for publication in an English journal. But he had to finish it in a hurry, and most of the corrections were left out. The translation was made with the help of a friend from the neighbourhood, Carl Christian Lautrup, who had lived for some time in England. As his physics was weak, and Bohr lacked familiarity with English, there

39

were a number of amusing blunders. For example, as Bohr would humorously relate, wherever the Danish expression for electric charge occurred, they translated it literally as "electric loading". It was only with difficulty that the translation was finished before Bohr left, and he even had to spend the first few days in Cambridge inserting the formulae. Before we turn to Bohr's period of study in England, there is an event from the summer of 19 11 which deserves mention-namely Bohr's meeting with the Swedish physicist Carl W. Oseen, to whom he had sent his thesis. Oseen later played an important part in the development of physical research in Sweden, and made contributions especially to hydrodynamics which won him universal recognition. When quite young he became a professor in Lund University and in 1909, at the age of 30, occupied the chair of physics in Uppsala University. He met the brothers Bohr in the late summer at the congress of Scandinavian mathematicians in Copenhagen, where both he and Harald Bohr gave lectures, and a friendshi)... grew up between him and the two brothers which through the years provided occasion for an abundant and valuable correspondence. Oseen seems to have been one of the first physicists to recognize Bohr's rare abilities, and many of his letters testify to this. Indeed, after their very first meeting in Copenhagen he writes to his young friend: "I beg you to accept my warm thanks for all the kindness you and your brother showed me during the mathematicians' congress. Getting to know the two of you was one of the greatest benefits I gained from the congress. I think that it will have an important bearing on the whole of my life. I have learnt much from you and still have much to learn. I shall always follow your progress with warm interest .... " It was with great expectations that Niels Bohr arrived at Cambridge at the end of September 19 II. It was not just the name and traditions of this old university that excited the aspiring physicist, for here were gathered several of the most famous physicists of the time, Larmor, Jeans and especially J. J. Thomson, famous for his discovery of the electron. Thomson had been pursuing important work on the electron theory, the subject Bohr had considered so critically in his thesis. He had there dealt with many points that Thomson had also treated and in several cases corrected the latter's results. The possibility of discussing such ques-

LEON ROSENFELD AND ERIK RUDINGER

tions with J. J. Thomson himself was undoubtedly the main motive for Bohr's choice of Cambridge for his projected studies. The first letters to his fiancee are indeed filled with youthful enthusiasm: "After my arrival the first thing I did was to pay my respects to Thomson. He was extremely pleasant, and we had a little talk during which he said he would be interested in seeing my treatise when it was finished. You can imagine how happy I was when I left, and I looked forward to getting the formulae written in quickly. I am so anxious to learn what he will think of the whole thing and also of all the criticism. . .. " and ". . . I found myself rejoicing this morning when I stood outside a shop and by chance happened to read the address "Cambridge" over the door .... "A few days later he writes to his brother: "Oh Harald! Things are going so well for me. I have just been talking to J. J. Thomson and explained to him as well as I could my ideas about radiation, magnetism etc. If only you knew what it meant to me to speak to such a man. He was extremely nice to me, we talked about so much, and I even believe that he thought there was some sense in what I said. He is now going to read the book, and he invited me to have dinner with him in Trinity College on Sunday. He is then going to talk to me about it. Believe me, I am so happy .... " Before Bohr could get started on work in the laboratory there were, of course, various practical things that had to be arranged. With the help of the physiologist A. V. Hill he succeeded in finding two rooms on the outskirts of the town where he remained even after becoming a student of Trinity College. For the young Dane it must have been a great change indeed to enter English academic life with its unusual traditions, its many involved conventions and its visits, and he tells about them with humour in his letters to his mother: " ... my time is taken up with arrangements, visits and dinner parties (what do you think of that?) . . . I have received a whole book from my tutor about what I am permitted to do and what I am not ... " To his fiancee he writes: " ... and now comes the remarkable thing, you should just hear how I can converse, I who used to be so silly about such things, but it is none of my doing, the English ladies are absolute geniuses at drawing you out .... " Lack of familiarity with the mysteries of the English language did not make things easier for Bohr, but he immediately set out to remedy his deficiency by reading "David

THE DECISIVE YEARS

41

Copperfield", and, with his characteristic thoroughness, looking up every single word of whose Danish equivalent he was not entirely certain. The red dictionary Bohr bought for this purpose followed him throughout the whole of his life and even in the writing of his latest papers was the final authority in all cases of doubt. Nor was it an easy matter to get on with the work at the Cavendish laboratory. J. J. Thomson had suggested to Bohr an experiment on positive rays, and he describes his initial difficulties in a letter to his mother: ". . . but you must not think that everything is going all that smoothly. You have no idea of the confusion reigning in the Cavendish laboratory, and a poor foreigner, who does not even know what the different things that he cannot find are called, is in a very awkward position ... " Then he goes on to say that the next day he is going to "bring the dictionary along". He writes to Oseen that he often has occasion to remember Bjerknes' phrase, that "a state of molecular chaos prevails" in the Cavendish laboratory. That he was not dismayed by these difficulties appears from a letter to his brother, in which about a month later he writes that he has " ... in any case learnt during this time among other things how to set up glass apparatus, and I am very pleased about this. . .. " Eventually it turned out that nothing would come of the experiment after all. When it is realized that he also attended lectures by Larmor, Jeans and J. J. Thomson, about which he was very enthusiastic, though not uncritical, it will be clear that there was a limit to the amount of time left over for theoretical studies. The main worry on Bohr's mind, however, was how to get his doctor's thesis published in English. A young physicist named Owen helped him to improve the language, and it was arranged with J. J. Thomson that the thesis should be submitted to the Cambridge Philosophical Society for publication in their Proceedings. In the middle of November Bohr gave a brief account of the contents before the Society, but it was not until May that he received the disappointing intimation that the thesis was too long and thus too expensive to print. If it could be cut down to half, however, its publication would be considered. Bohr first thought of complying with this requirement, and then of publishing the whole privately. Finally he gave up both plans, with the result that the thesis was never published in any of the main languages. This was a serious loss for all those working on the electron theory. Bohr's thesis was

42

LEON ROSENFELD AND ERIK RUDINGER

a continuation of the classical electron theory of metals formulated by H. A. Lorentz. Under very general assumptions, by a systematic application of the methods of statistical mechanics, Bohr had deduced a number of results, which by their very generality were of the greatest importance. One of the main results was, as we shall see in the following, that there were certain phenomena for which no explanation could be given within the framework of this theory. It was a great disappointment to Bohr that J. J. Thomson, partly because of pressure of work, partly because he had apparently lost interest in these questions, never got down to reading the thesis, so that Bohr never had the opportunity of discussing it properly with him, nor, consequently, of raising the points he had critized in Thomson's own work. Bohr's disappointment shows up in several letters. Thus he writes at the beginning of December to Oseen: " ... - Thomson has so little time. I gave him the thesis when I came, but he has not yet read it, and I have only had the opportunity to talk to him about a few details, and I still do not know whether he will agree with me or not ... " That Bohr did not lose heart for this reason we see from a letter to his fiancee, in which he states with his wonderful optimism: " ... I am getting on so well, not really better with Thomson, but personally. I am in such good heart and have so many plans.... " Of the physicists Bohr came to know during his stay in Cambridge the only one with whom he managed to discuss the questions that were on his mind was a lecturer in Birmip.gham, S. B. McLaren. McLaren was nine years older than Bohr and did highly original work on fundamental problems of physics; he was killed in the first world war. Earlier in the year he had published a paper in which he had demonstrated that any attempt, as for example that suggested by Jeans, to explain the radiation phenomena on purely classical grounds without introducing Planck's quantum must of necessity lead to contradictions. Bohr had come to the same conclusion; while working on the thesis, especially on the problems of radiation and magnetism, he had clearly realized that a fundamental revision of classical physics was required if atomic phenomena were to be explained. Just because his assumptions were so general, it was clear to him that the discrepancies between theory and experiment would not disappear if only details in the calculations were changed, but that it was the very basis of the theory, classical mechanics itself, that was inadequate. McLaren was ap-

THE DECISIVE YEARS

43 parently one of the few other physicists to whom it was equally obvious at that time how radical a change was needed. Bohr went to Birmingham to talk with him. He mentioned the visit in the letter to Oseen previously quoted; he also wrote of McLaren's paper with great enthusiasm and ended with the remark: " ... I think we agreed on most things .... " In October, however, things had already taken a decisive turn, when Bohr at the yearly Cavendish dinner saw for the first time Ernest Rutherford, who four years earlier had become professor of physics at Manchester. Bohr himself has spoken in his Rutherford memorial lecture of Ig58*) of the great impression that Rutherford's personality immediately made on him, although he did not come into personal contact with him on this occasion. We can imagine the prospects that opened before him at the thought of working for a time in the Manchester laboratory, which under Rutherford's leadership had come to great prominence. At the beginning of No~ember Bohr went to Manchester, where he had the opportunity of talkmg to Rutherford at the home of one of his father's colleagues. How much was decided then, however, we do not know, and Bohr no doubt wanted to discuss the whole question of his going to Manchester with his brother, who was to visit England at the beginning of January. At least he wrote shortly after New Year to his fiancee: " ... In any case I shall stay another term at Cambridge, and I am so much looking forward to it, but it is best to wait until Harald returns home to tell you all about it." We shall limit ourselves to giving a few short extracts from his letters during this therm, in which Bohr completely devoted himself to theoretical studies. To his financee he writes at the beginning of the term: " ... This term I am not going to the laboratory, but I am only going to lectures, and will read, read, read (and perhaps make some calculations and think) . . .. " A bit later on in the term after talking about lectures by Jeans and Larmor he says: " ... I sometimes think, as for example to-day at the two lectures, that there is so much, whole worlds that one has a chance of getting a glimpse of, and I am so small and incompetent-more incompetent than you or anybody else imagines ... " A lecture by Thomson *) Published in the Pr?ceedinp of the Physical Society 78, ro83 (196 1 ) and in Essays 1958-62 on Atomic Physics and Human Knowledge, John Wiley & Sons New York (1963). '

44

LEON ROSENFELD AND ERIK RUDINGER

on the motion of a golf-ball made him very enthusiastic, and he writes of this to his brother: " ... You cannot imagine how delightful and enlightening it was, and what fine experiments he demonstrated and with what crisp, sparkling humour it was done. That was really something for me, you know I am myself a little crazy about such things. . .. " The only scientific publication from Bohr's hand during this period at Cambridge is a comment on a paper in the Philosophical Magazine by O. W. Richardson (who later became a close friend of Bohr's) dealing with the electron theory of metals. Bohr points out an error in Richardson's article, leading him to a result differing from that Bohr himself had found in his thesis. Of this he writes to his brother: " ... It was not so easy to find out what was wrong. I would probably never have done it if I had not known my own work. . .. " However, the editor of the Philosophical Magazine, W. Francis, misunderstood the situation; he believed that Bohr was raising a question of priority. It was not until after a fairly copious exchange of letters between Bohr and Francis, in which we find an unusually sharp letter from Bohr, and after Richardson had published another paper on the subject, in which he referred to Bohr's thesis, that Bohr's note was published in the June issue. Richardson's second paper merely led Bohr to add a postscript pointing out that similar objections could as well be raised against the calculations in the latter paper. This little description of Bohr's life in Cambridge would be incomplete if we did not mention the many hours he spent out of doors, either in sporting pursuits such as football and skating, or walking in the countr~, something he had learnt early in life to value greatly. We see his enthusiasm for this, for example, in this fine little description of nature, which he sent to his fiancee after an autumn walk: " ... and then I went on the loveliest walk for an hour before dinner across most beautiful meadows along the river, with the hedges flecked with red berries and with isolated wind-blown willow-trees-just imagine all this under the most magnificent autumn sky with scurrying clouds and blustering wind ... " Immediately after his brother's visit Bohr had written to Rutherford, and in the subsequent exchange of letters it was arranged that Bohr should bo- 0 to Manchester in the middle of March. Plans were discussed in more detail during a visit that he paid Rutherford at the end of February.

THE DECISIVE YEARS

45

One difficulty was that the latter would be away for most of April, but during that time Bohr was to attend an experimental course in radioactive technique' as, an introduction to the work. This he did conscientiously for a month and a half, as is testified by a notebook with carefully drawn graphs of the measurements undertaken. After his visit to Rutherford Bohr writes the following interesting impressions to his fiancee: " ... Rutherford is a really first-class man and extremely capable, in many ways more able than Thomson, even though perhaps he is not so gifted. J. J. Thomson is a tremendously great man, and I have learnt such an enormous amount from his lectures; I like him so much, and I shall be telling you more about him before I leave Cambridge.... " About his departure from Cambridge and his expectations of the future he goes on as follows: " ... I think they have all lost confidence in me, for they just cannot understand why I am leaving Cambridge, but I have such an inclination to try, and I shall have wonderful conditions in Manchester. ... " The laboratory where Niels Bohr spent the next four months had become, since Rutherford had been given a professorship there in I 907, a centre for radioactive research where Rutherford had collected together a number of the best physicists of those days, among them H. Geiger, W. Makower, E. Marsden, E. J. Evans, A. S. Russell, K. Fajans, H. G. J. Moseley, G. Hevesy, J. Chadwick and C. G. Darwin. During those years a number of epoch-making investigations were carried out there, culminating the year before in Rutherford's discovery that nearly the whole of the atom's mass is concentrated in a nucleus of minute extension compared to the size of the atom. This was a great step towards the establishment of a model of the structure of the atoms. Even though the sign of the nuclear charge was not finally determined, it was natural to imagine that the nucleus was positive and that the negative electricity was carried by electrons which under the influence of the attraction by the nucleus circled around it according to laws similar to those controlling the motions of the planets around the sun. Since that time this model has been called the Rutherford atomic model Throughout his life Bohr maintained a close contact with many of the physicists he first met during his stay in Manchester. Of special importance to him, not merely during this stay, but also in later years, was his relation-

LEON ROSENFELD AND ERIK RUDINGER

ship with Rutherford himself and with George Hevesy. The latter was of the same age as Bohr and at that time had already spent a year at Rutherford's laboratory. We have seen above how Rutherford's striking personality made a deep impression on Bohr. After he had come into closer contact with Rutherford at the laboratory, he described him thus to his brother: " ... Rutherford is a man you can rely on; he comes regularly and enquires how things are going and talks about the smallest details.... Rutherford is such an outstanding man and really interested in the work of all the people who are around him .... " Yet, as has often been pointed out, it is hardly possible to imagine two more different physicists than Rutherford, the great experimental scientist, who was deeply anchored to the more "robust" British tradition and Bohr ' ' the theoretician (although he had shown himself to be a clever experi, mental physicist as well), who, with his roots in the tradition of physics developed especially by French and German physicists, was ready with inexorable rigour to draw the full logical conclusions from every new hypothesis. (Bohr himself often emphasized the fortunate circumstance that he, born in a small country without national pretensions, had received in his youth the best of both worlds, both the "continental" theoretical tradition and English empiricism.) Notwithstanding all differences, Rutherford seems to have soon developed a great respect for Bohr; thus Hevesy relates that when he once asked Rutherford from which part of the atom a certain type of radiation emanated, Rutherford immediately answered: "Ask Bohr!" On a later occasion, when Rutherford was asked how it could be that his attitude to Bohr was so different from his attitude to other theoreticians generally, he is said to have replied: "Bohr's different. He's a football player!" However, as we shall soon see, Rutherford was simply not prepared to draw such far-reaching conclusions from his own atom model as Bohr did. The Hungarian George Hevesy was the one to whom Bohr was closest, and when the Institute for Theoretical Physics in Copenhagen was opened nine years later he was one of the first foreigners to come to Denmark and work there. (He had in fact already come to Copenhagen at Bohr's invitation the previous year, in I 920.) In Manchester it was to a large extent Hevesy who drew the rather shy Bohr into the life of Rutherford's laboratory, and Bohr liked remembering later how this "young Hungarian aristo-

~: ·•

THE DECISIVE YEARS

47

crat" and man of the world had made such a great impression on him by his skill in conversation with the opposite sex at parties. From a professional point of view, too, he became the one who meant most to Bohr, since his unusually extensive chemical knowledge was what Bohr needed most at that stage. Bohr had, as it were, taken Rutherford's atom model more seriously than most of the others at the laboratory, including Rutherford himself, in the sense that he soon saw that it was not merely a useful model for the explanation of certain experiments with radioactive substances, but that in fact it offered a basis for a comprehensive theory of the properties of atoms. He at once recognized that Rutherford's model permitted a sharp distinction between, on the one hand, the chemical and the usual physical properties of the elements which must be determined by the way in which the electrons are bound to the nucleus, and therefore only depend on the mass and charge of the nucleus, and, on the other hand, radioactivity which must be determined by the structure of the nucleus itself. From this point of view many other things presently became clear to him. For a long time he had been interested in the periodic system and he now saw that it must be the nuclear charge and not the atomic weight that determines an element's place in the system, and that this explained why such substances as potassium and argon had to be transposed when an attempt was made to arrange them according to ascending order of atomic weight. Furthermore he soon came upon the concept of isotopes, expressing the fact that several subsdmces with different radioactive properties can be chemically identical an~ have the same atomic number because they have the same nuclear chawe. As a direct consequence of these considerations Bohr also came to understand the relations which were later called the radioactive displacement iaws. But he did not always express himself very clearly; thus Hevesy relates \ hat Bohr might say, for instance, that "argon is the wrong argon". If Bohr did not publish these ideas, which were put forward, shortly afterwards, in a rather incomplete form by Fajans, Soddy and van den Broek, it was mainly because Rutherford hesitated to draw such conclusions from his atomic model. Rutherford thought that a greater amount of experimental material was required and did not understand the strict logic in Bohr's line of argument. However, there is very little doubt that

LEON ROSENFELD AND ERIK RUDINGER

Bohr had reached a full understanding of these questions, and we have a testimony to this in a letter from Hevesy to Rutherford of October 14th, r 9 r 3, in which, after discussing the problems mentioned, which had by that time been clarified, he writes: " ... Though Russell was already interested in the problem and I started the valency experiments when Bohr came to Manchester, no doubt he encouraged us both very much and if , we trace the origin of the above ideas to their origin, we will find them in Bohr's mind, as pointed out to me by himself in his usual modest way." Naturally these questions were discussed among the Manchester group, but it must be realized on the one hand that Rutherford was at that time very much taken up with his great book "Radioactive Substances and their Radiations", and on the other hand that in the Manchester laboratory each person concentrated his attention almost exclusively on the investigation, mostly experimental, with which he was particularly concerned. It is therefore difficult to decide how much direct influence discussions in Manchester had on the development of Bohr's ideas and conceptions. While it was undoubtedly stimulating for him to be in a group whose work centred upon Rutherford's model of the atom, it appears that the interest of those around him in the fundamental theoretical problems was rather small. In a letter to his brother late in May he complains, in connection with the electron theory, that " ... I have nobody here who is really interested in such things. . .. " At the beginning of July, however, Bohr tackled a more concrete task, and now the tone has changed to optimism: ". . . Things are not too bad at the moment; a few days ago I had a little idea about understanding the absorption of alpha rays (it so happened, that a young mathematician here, C. G. Darwin (the grandson of the great Darwin) has just published a theory on this question and it seemed to me that it was not only not quite right mathematically (this was however rather trifling) but quite unsatisfactory in its basic conception), and I have worked out a little theory about it, which, however modest, may perhaps throw some light on a few things concerning the structure of atoms. I consider publishing a little paper about it. You can imagine it is fine to be here, where there are so many people to talk with (my last complaint concerned the more general theoretical questions), and indeed with those who know most about these things ... "

~:

,

A draft of a letter to Rutherford mentioned in the contribution to this book deali ng with the years 191 1- 1918.

Marg re the N01·lund and N iels Bohr "' when they were engaged .

~

A go ld en wedd ing photograph ( 1962 ).

THE DECISIVE YEARS

49

The letters home give an impression of the enthusiasm with which Bohr threw himself into the new task of providing a theory for the deceleration of alpha particles when they pass through matter. Thus he writes at the beginning of July to his fiancee: " .. . It doesn't perhaps look so hopeless with those little atoms, even though the outcome of the calculations has its ups and downs ... " and about a fortnight later to his brother: " ... Things are going rather well, for I believe I have found out a few things; but to be sure I have not been so quick to work them out as I was so stupid to think. I hope to have a little paper ready and to show it to Rutherford before I leave, and I am therefore so busy, so busy ... " and with a touch of irony: " ... It is not of lack of plans I am suffering at the moment ... " While Bohr was working out the paper on alpha particles, he did not, however, lose sight of the fundamental problems of the structure of the atom that Rutherford's discovery had raised. On the contrary this paper, although Planck's constant only appears in a small calculation in it, gave him the first clue to the solution of these problems. The very first indication that he has hit upon important relationships we find in an interesting card he sent to his brother as early as July 19th, quite soon after he had started work on the paper. It says: "It is possible that I have perhaps found out a little about the structure of the atom ... ", which perhaps is " ... a tiny little bit of the reality.... " He adds the important remark that " ... It has all grown up out of a little idea I got from the absorption of alpha rays ... " The decisive point Bohr insisted upon was the impossibility in principle of explaining within the framework of the theories of classical physics the stability of atoms on the basis of Rutherford's atom model. The electrons, which were assumed to circle around the positive nucleus, would according to classical theory quickly lose their energy by emission of radiation and would end up by being captured by the nucleus. Thus the atom would be unstable, and in fact Rutherford's model did not contain any element that could determine its radius. The limitations of the classical theory had already been demonstrated at the beginning of the century, particularly by the work of Planck and Einstein on the interaction between radiation and matter, and Bohr was, as mentioned above, early convinced that a fundamental revision was needed. He now saw that the quantum of action which Planck had introduced to explain the phenomena of radiation had 4

LEON ROSENFELD AND ERIK RUDINGER

the required dimension and magnitude for use as the stabilizing quantity fixing the distance and velocity at which the electrons would move around the nucleus in orbits which for the sake of simplicity were considered circular. He here made use of a hypothesis whose form was inspired by an earlier application of the quantum of action to the thermal properties of solids. In the course of June and July Bohr, on this basis, worked out his ideas about the structure of atoms and molecules in their normal or "ground" state. These ideas include many of the concepts which were to be elaborated in the second and third parts of his famous paper on the structure of atoms and molecules, and they also contain the first germs of the theory he developed in the first part of the paper, although, as we shall see he still lacked an essential link. He wrote down his considerations to show 'them to Rutherford, and fortunately the main part of this valuable document is still in existence. What has been said gives an idea of the tremendous amount of work Bohr did in the course of these few months. As we can see, it was hardly an exaggeration when he wrote to his fiancee at the beginning of June that he was working "day and night". When it is added that his friends are reported to have said of him at that time that they only saw him when he needed to "come up to breathe", we have a striking picture of those days which anyone who has seen Bohr absorbed in his work will easily recognize. At the end of July, Bohr returned to Denmark where he was married on August Ist. Actually the young couple had thought of spending their honeymoon in Norway, but Bohr had not been able to finish his paper on alpha rays, and they therefore went to England instead. Bohr completed the paper in Cambridge, after which he went up to Manchester and delivered it to Rutherford. It was published in the Philosophical Magazine for January I9I3.

When Bohr returned home, Martin Knudsen had succeeded Christiansen in the chair of physics. The lectureship Knudsen had held, and for which Bohr would have been the obvious candidate, had been discontinued and was only re-established the following year, when Bohr took it over. In the autumn of I9I2, however, Bohr gave a series of free lectures on the mechan-

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ical foundations of thermodynamics, and at the Danish Physical Society he gave an account of his results concerning the absorption of alpha rays. One of those who attended the lectures in thermodynamics, Mrs. Kirstine Meyer, commented on them in a letter to Bohr thus: " ... I have admired the clarity and conciseness with which you have arranged the difficult material and the good style in which you have lectured to us .... " In the course of the autumn term Bohr was also able, with the help of his wife (many manuscripts and drafts of letters from this and the following years are in her handwriting), to progress somewhat further in his considerations on the part played by the quantum of action in the structure of atoms. However, in a letter to Rutherford at the beginning of November, he mentions some difficulties he has encountered in the calculations. Rutherford reassures him by saying that there is no need to hurry, as there does not seem to be any one else working on the same subject. Still, as time goes on he becomes more and more impatient and on February 5th he writes to Oseen, whom he has just visited: " ... I am afraid I must hurry, if it is to be new when it comes; the question is such a burning one . ... " In the foregoing we have seen that in the course of the summer and autumn of 19 r 2 Bohr had succeeded, starting from the discoveries of Planck and Rutherford, in making models of atoms and molecules in their ground state. Not until early February 19I3, however, did he come upon the third and decisive piece in the jig-saw puzzle, namely a formula that had been proposed by the Swiss mathematician Balmer about 30 years earlier. This formula accounted for the colours-the spectral lines-of the light emitted by hydrogen-the so-called optical spectrum of hydrogen. When asked about the surprising fact that for so long it had not been generally recognized that this formula and related ones, proposed especially by the Swedish physicist Rydberg-all so different from what was otherwise known in physics-could conceal fundamental regularities, Bohr would say: "They were looked upon in the same way as the lovely patterns on the wings of butterflies; their beauty can be admired, but they are not supposed to reveal any fundamental biological laws." Bohr has told us that it was his student friend H. M. Hansen who first drew his attention to Balmer's formula and the simple regularities in the optical spectra which Bohr up to then had not dared to deal with. He 4•

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promptly looked it up in Stark's book "Prinzipien der Atomdynamik". He himself later said: "As soon as I saw Balmer's formula, everything became clear to me", and the material we possess fully confirms the truth of this statement. From letters to Rutherford of January 31st and to Hevesy of February 7th, 1913, it distinctly appears that Bohr at this point had not yet studied Balmer's formula, and this is also indicated by a letter from Oseen to Bohr of November r 1th of the same year, to which we shall return. To Rutherford Bohr wrote explicitly: " ... I do not at all deal with the question of calculation of the frequencies corresponding to the lines in the visible spectrum .... " Thus we here witness an almost incredible process of creation in which, as soon as the last piece was put into the jig-saw puzzle, all the knowledge Bohr had formerly gathered, all the ideas of atomic structure he had thought out, suddenly fell into place, giving him the complete view of the whole. This made it possible for him in less than a month to work out the famous first part of the paper on the structure of the atom which he sent to Rutherford on March 6th, and in which the interpretation of the optical spectra had now become the comer-stone of the edifice. The fundamental new feature now included in the theory is the idea of extending the concept of ground state to a whole series of "stationary states", as Bohr called them, in which the electron is assumed to move at a fixed distance around the nucleus without giving off energy through radiation. The different spectral lines are assumed to be produced by the electron jumping from one stationary state to another with emission of light of a definite colour. This is the conception expressed by Bohr's two famous postulates. We shall now try to explain briefly why it is the formulation of these postulates-rather than the previous fundamental work of Planck and Einstein-that can rightly be said to mark the decisive break with classical physics. According to classical physics, an electron moving around a nucleus should continually emit light of a colour determined by the period of the motion, that is the time the electron needs to make one circuit around the nucleus. Therefore the colour-in contradiction to all experimental evidence-should continually change as the electron, emitting energy, comes nearer to the nucleus, and thereby revolves more and more quickly. In the first place the occurrence of "stationary states" is thus completely precluded

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by the classical theory of electrodynamics. Secondly, it is clear that according to Bohr's theory, in which light is emitted when the electron jumps from one orbit of definite period to another with a quite different period, there cannot be the relation between colour and period required by the classical theory. The condition Bohr enunciated for the determination of the colour of the light, the so-called frequency condition, thus differed in principle completely from the classical one. It was this above all that so much disturbed the physicists of the time-that the colour of the light should not correspond to the period of the electron seemed to them completely inconceivable-and it required the courage of a genius to break with such a firmly anchored conception. It must not be forgotten that a large number of earlier experimentse. g. with radio waves-had confirmed most conclusively the classical relation between the period of the waves and that of the electric currents producing them. It was then natural to ask: how could it be possible to reconcile the assumptions of the new theory with the knowledge obtained from the previous experiments? Bohr was able to answer this question. If one considers larger and larger orbits-which satisfy more and more closely the conditions under which the classical theory should be valid-the periods of two neighbouring orbits approach more and more a common value. And if one determines the colour of the light which according to Bohr's formula is emitted in a jump between two such orbits, one finds that it approaches more and more the colour which classical theory would associate with this common period. Thus even though the mechanism of the emission of light is always completely different from the classical one, the results obtained approximate more and more to the classical ones, the closer the conditions are approached in which the latter are known to be valid. Bohr's theory, so to speak, contains within itself the results of the classical theory: it is a generalization of it, or «corresponds,, with it. Bohr could even show, by imposing this correspondence as a condition, that a certain constant, which he had first introduced somewhat hypothetically, must have the value }'2. This kind of argument is the first indication of the fruitfulness of this conception of correspondence, or analogy as he at first called it-a clue that Bohr himself was to follow up and make use of so successfully in the following years, and which finally was to become the key to quantum mechanics. It is thus with pride that Bohr writes to Rutherford that he

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finds " ... the most beautiful analogy between the old electrodynamics and the considerations used in my paper.... " Although contemporary physicists seem to have been more impressed by Bohr's success in obtaining a close agreement between the experimental value of the so-called Rydberg constant and that calculated on the basis of his theory, one may rightly say that the correspondence argument constitutes the essence of this wonderful paper, which has few parallels in the history of physics. Bohr sent the paper with a letter to Rutherford on March 6th. In Rutherford's answer his difficulties in grasping the new ideas and their scope came out clearly; it was, however, a more practical question which was to be the main problem for Bohr in the coming weeks. In his answer Rutherford repeated no less than three times that he thought that Bohr's paper was too long and ought to be cut down, the last time in the following postscript: "P. S. I suppose you have no objection to my using my judgment to cut out any matter I may consider unnecessary in your paper? Please reply." When one knows Bohr's care in working out his papers, one can imagine his horror at the thought of such an interference; moreover when he received this letter he had already sent Rutherford some additions to the paper. Under these critical circumstances he set off posthaste for Manchester to "fight it out" with Rutherford, as he himself would express it. We can only surmise Rutherford's amazement at the young Dane's initiative, but in any case he never forgot this meeting, when Bohr, after hours of discussion, stuck to his point that every single word in the manuscript had to remain unchanged. Twenty years later Rutherford still told the story: "I could see that he had weighed up every word in it, and it impressed me how determinedly he held on to every sentence, every expression, every quotation; everything had a definite reason, and although I first thought that many sentences could be omitted, it was clear, when he explained to me how closely knit the whole was, that it was impossible to change anything." Nobody who knows the weight Bohr placed upon the importance of argumentation can doubt that he fought not only to retain the formulation he considered the only correct one, but just as much to convince Rutherford by the weight of his arguments that it was really the only possible formulation. Anyhow, the result was that only purely linguistic changes were made.

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After these hectic weeks Bohr worked incessantly on the second and third parts of the paper, the main points of which, as we have stated, were already worked out, but which now had to be gone over and revised in accordance with the new basic idea. Besides considerations about the structure of more complicated atoms and molecules, they contain an attempt to give a more detailed account of the periodic system by means of electron rings, as well as sections on X-rays and radioactive phenomena. Bohr also contemplated including a section on magnetism, in which the new considerations should be connected with the magneton concept introduced by Weiss, and applied to the treatment of the splitting of spectral lines in a magnetic field, known as the Zeeman effect. Here, however, Bohr met with many difficulties of principle which were not cleared up until later, and he gave up the publication of this section, of which only drafts are extant. On May 1 oth he returned the proof of the first part to Rutherford, together with a letter which among other things reports slow progress with the second part because of "troublesome numerical calculations" concerning the stability of systems of electron rings. Some of Bohr's papers dealing with this question are extant, and they testify to the work he had put into it and the care with which all calculations were carried out. During the spring and summer Bohr finished the second and third parts of the paper and sent the manuscripts to Rutherford as they were completed. After the first part had come out in the July issue of the Philosophical Magazine Bohr again went to Manchester, taking time off to visit London and Cambridge.

Bohr no doubt awaited with eager anticipation the reception of the new ideas by the world of physicists. One of the earliest reactions to the first paper was a postcard from Sommerfeld in Munich, who was one of the leading theoretical physicists in Germany. This postcard is so interesting that it deserves reproduction in full:

4. IX. 13 Dear Colleague, I thank you very much for sending me your extremely interesting work, which I had already studied in the Phil. Mag. The problem of expressing the Rydberg-Ritz constant by Planck's h has been for some time in my

LEON ROSENFELD AND ERIK RUDINGER

thoughts. A few years ago I talked about it to Debye. Although I am for the present still rather sceptical about atom models in general, nevertheless the calculation of this constant is indisputably a great achievement. Incidentally, the numerical agreement becomes even better with the new value of Planck's constant h = 6.4 · 10- 21 • Are you also going to use your atom model for the Zeeman effect? I wanted to work on it. Perhaps I can hear of your plans in greater detail through Mr. Rutherford, whom I hope to see in October. Yours sincerely, A. Sommerfeld. Later on Bohr loved to make humorous remarks on Sommerfeld's initial scepticism about "atom models in general". However, it is not very easy to infer from this card to what extent Sommerfeld had really accepted the radical break with the classical conceptions which formed the basis of the new ideas. Interesting evidence of Sommerfeld's attitude is given by the French physicist Brillouin. He reports that he remembers coming into Sommerfeld's office when the latter had just seen the issue of the Philosophical Magazine with Bohr's article in it. "There is a most important paper here by N. Bohr'', said Sommerfeld, "it will mark a date in theoretical physics." In Gottingen, whose faculty of mathematics and natural science had an outstanding reputation in scientific circles, the reception was cooler. We have information about this from the mathematician Richard Courant, a close friend of Harald Bohr's, who was also to become a close friend of Niels' after they had met in Cambridge in September 1913. As Courant relates, everybody at Gottingen had great respect for Harald, who at that time was a frequent visitor there; and Harald assured them that "since Niels says so, and considers it so important, I know that it is really a great progress in physics." Nevertheless some of the leading scientists, for example Runge, of spectroscopic fame, took up a very sceptical attitude to the new theory. According to Bohr's recollection, it was mainly the previously mentioned factor 1'2, though justified by a strict correspondence argument, that prevented the Gottingen people from taking the theory seriously. Years later-when Bohr had been awarded the Nobel Prize-Courant wrote in a letter of congratulation, after recalling how Bohr had told him

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in Cambridge about his ideas: " ... Thanks to a forewarning through Harald, who had so often told such amazing things about his brother, I was then at once prepared to believe that you must be right; but when I reported these things at Gottingen, they laughed at me for taking such fantastic ideas seriously; thus, as it were, I became a martyr to Bohr's model. ... " As early as the beginning of August, Hevesy, to whom Bohr had sent his manuscripts, expressed his recognition of Bohr's work in a finely appreciative letter. After reflections on the profound satisfaction that scientific research can give us, Hevesy writes in his charming English (which we render in the original spelling) : "You will understand now why the reading of your papers has been a source of pleasure for me. I look forward with very much interest to the result of your more elaborated calculations. So far everything is so clear, the behaviour of hydrogen and helium as described by the theorie, so truefull that nobody can avoid to be struck by reading it." A testimony from another close friend is found in a letter from Oseen, sent in November after the third and last part of the paper had appeared. This letter, as already mentioned, shows that Bohr, when he visited him at the beginning of February, was not yet on the track of the spectral laws. This devoted friend expresses his admiration thus: " ... What I first should like to tell you is that, although I already knew the orientation of your thoughts and even some of the results it had led you to, I was on one point surprised by the beauty of your result. This was the relationship between h and the Balmer-Rydberg constant. So far as one can see, you have on this point reached beyond the region of the hypotheses and theories to the truth of facts. Higher no theorist can hope to come and I congratulate you with all my heart." We get an impression of Bohr's own attitude about this time from an interesting remark on a card he sent to McLaren in September. The latter, in answer to a letter from Bohr which is unfortunately lost, had written in February that he himself was " ... inclining to the belief that the old mechanical notions are past mending." As late as July lst, influenced by the apparent implications of an experimental investigation by J. J. Thomson, Bohr had written to Rutherford: "I have for a few days been in a terrible doubt as to the validity of the foundation for the [whole]

LEON ROSENFELD AND ERIK RUDINGER

(crossed out in the draft) theory .... " But we see from the card to McLaren how certain he now feels that he is on the right road: ". . . In the necessity of new assumptions I think that we agree; but do you think such horrid assumptions, as I have used, necessary? For the moment I am inclined to most radical ideas and do consider the application of the mechanics as of only formal validity." If as yet we have not discussed at all the reactions in England, it is because the first occasion on which a large forum of experts was presented with Bohr's theory was the yearly meeting of the British Association for the Advancement of Science, which was held in Birmingham in the middle of September. In May Rutherford had suggested that Bohr should be invited to participate in the discussion on the problems of radiation which was to take place at this conference. As late as September I st, about a week before the beginning of the conference, Bohr wrote that he would not be able to leave Copenhagen. At the last moment, however, after being informed by Rutherford that among others the great Dutch physicist Lorentz would be present, he changed his mind, and the meeting was for him a great experience, which he often referred to later. That already at this stage, when the second part of his paper had just been published, Bohr's theory had attracted attention in England, is shown by the fact that it was not only discussed at the conference by Rutherford and Jeans, but was also mentioned in Sir Oliver Lodge's opening speech. It was Jeans who presented a survey of the radiation problems, and during this he gave a detailed account of Bohr's theory which was introduced with the following words: " ... Dr. Bohr has arrived at a most ingenious and suggestive, and I think we must add convincing, explanation of the laws of spectral series." On Bohr's bold postulates Jeans commented as follows: ". . . The only justification at present put forward for these assumptions is the very weighty one of success." Of his impression of Jeans' attitude to the theory, Bohr says a week later in a letter to his wife: " ... For the present, things are going as well as I could ever have expected. Jeans, who introduced the discussion on the problem of radiation with quite a magnificent lecture, gave a very fine and kind account of my theory. I think he is convinced that there is at least some reality behind my considerations ... " The older physicists, however, were more reticent. Thus Bohr has told

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in his Rutherford lecture how Lord Rayleigh avoided any commitment by a witty statement to the effect that in his younger years he was convinced that a man over sixty should not take part in a debate on new problems; and even though he no longer held this view so firmly, still he held it firmly enough not to want to take part in this discussion. The complete proceedings of the discussion have unfortunately not been recorded, but we know that in connection with Bohr's contribution Lorentz raised the question of the logical relationship between Bohr's postulates and classical theory. Bohr limited himself to answering that this part of the theory was not yet complete, but if the quantum theory were accepted, some such scheme as he had used was necessary. That he did not leave it at that, but continued to explain his ideas to Lorentz after the meeting appears from a letter which Lorentz some years later wrote to Bohr, and in which he alluded to " ... the theories of which you gave me a first exposition in Sir Oliver Lodge's garden ... " During the Birmingham conference an important point of the theory was the subject of discussion in "Nature". In his paper Bohr had come to the conclusion that certain spectral lines, which up to then had been believed to belong to hydrogen, must really be ascribed to helium. Already in the letter which he sent to Rutherford with the first part of the paper he had touched upon this point and asked whether it was possible to undertake experiments to check it at Manchester. These were carried out by Evans during the summer, and his results, which supported Bohr's assertion, were published in "Nature" on September 4th. The outstanding English spectroscopist A. Fowler, who had himself discovered some of the spectral lines in question, was, however, not yet convinced: he pointed to a small but real discrepancy between the experimental results and the values found by a simple application of Bohr's formula. Now, since Bohr's assertion was based on a correspondence argument, such a disagreement, however small, would in fact mean the breakdown of the whole basis for his theory. In the subsequent discussion in "Nature" Bohr showed, however, that Fowler's objection could be answered by taking into account the motion of the nucleus around the centre of gravity of the atom. By this more exact calculation Bohr was not only able to demonstrate the finest agreement between the calculated and the observed spectral lines, but he could also predict that a series of other spectral lines from helium,

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so far unobserved, which according to the simple theory would coincide with some of the Balmer lines, should in fact appear very slightly displaced in relation to these. The lines were discovered the following year by Evans at the places predicted. It is interesting that it was Evans' experiment that was decisive for Einstein's attitude. We know this from two letters which Hevesy sent to Bohr and Rutherford respectively after he had told Einstein of the outcome of these experiments at a congress in Vienna at the end of September. To Bohr he wrote with touching sincerity: ". . . than I asked him [EinsteinJ about his view on your theorie. He told me, it is a very interesting one, important one if it is right and so on and he had very similar ideas many years ago but had no pluck to develop it; I told him than that is established now with certenety that the Pickering-Fowler spectrum belongs to He. When he heard this he was extremely astonished and told me: "Than the frequency of the light does not depand at all on the frequency of the electron"-( I understood him so??) And this is an enormous achiewement. The theory of Bohr must be then wright. I can hardly tell you how pleased I have been and indeed hardly anything else could make me such a pleasure than this spontaneus judgement of Einstein." And the letter to Rutherford finishes thus: " ... When I told him about the Fowler Spectrum the big eyes of Einstein looked still bigger and he told me "Then it is one of the greatest discoveries". I felt very happy hearing Einstein saying so." We earlier emphasized that Bohr's hypotheses were only of a provisional character inasmuch as they presented a "mixture of Planck's ideas with the old mechanics", as Rutherford somewhat disrespectfully had described them. Nobody was aware of this situation more than Bohr himself, and during the following years, when many physicists believed that they were beginning to get firmer ground under their feet, he used every opportunity to stress this lack of theoretical foundation. Thus, in a lecture on the new theory which he gave to the Danish Physical Society in December 1913·*) - and which he himself rightly considered one of his best and clearest *) Published in Fysisk Tidsskrift 1914; in English in The The~ry of Sp ~ ctra. a!'ld Atomic Constitution, Cambr. Univ. Press 1922 (2nd ed. 1924 ) (this translat10n 1s maccurate, however, just at the important place quoted).

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lectures-he emphasized this aspect of the problem in the following fine conclusion: "Before closing I only wish to say that I hope I have expressed myself sufficiently clearly so that you have appreciated the extent to which these considerations conflict with the admirably coherent group of conceptions which have been rightly termed the classical theory of electrodynamics. On the other hand, I have tried to convey to you the impression that just by emphasizing this conflict, it may be also possible in the course of time to discover a certain coherence in the new ideas." In the autumn of 1g1 3 there appeared two very important papers directly connected with Bohr's theory. In the first Moseley published the results of the experiments he had carried out in Manchester, in which for a number of consecutive elements of the periodic system he had measured the wavelengths of "spectral lines" of the so-called characteristic X-radiation, which is outside the visible region. Moseley's experiments supported Bohr's ideas beautifully: the lines were found to shift regularly from element to element, in such a way that a certain quantity changed by one unit from one substance to the next, and this quantity could only be the charge of the nucleus, or, what is the same, the number of electrons in the neutral atom. The interpretation of the occurrence of the characteristic lines of the X-radiation on the basis of Bohr's model was, however, first given the following year by the German physicist W. Kossel, who assumed that they occur when an electron has been removed from one of the inner orbits and an outer electron jumps into the empty place, emitting radiation according to Bohr's formula. The other great advance during this autumn was the discovery by the German physicist Stark that a spectral line is split up into several lines when the atoms from which the line is emitted are placed in an electric field, in analogy with Zeeman's earlier discovery of the corresponding effect for a magnetic field. Stark published his paper in November, and it was Rutherford who drew Bohr's attention to it in a letter to him at the beginning of December in which he said: "Just a note to draw your attention to the recent discovery of Stark, that an electric field produces separation of lines of hydrogen and helium very similar to the Zeeman effect .... I think it is rather up to you at the present time to write something on the Zeeman and electric effects, if it is possible to reconcile them with your theory."

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Bohr started on this work straight away, and his theory had now become so well known that several other physicists also tried to use it for the explanation of the Stark effect. With a speed unusual for Bohr he published his results in the March issue of the Philosophical Magazine. In the introduction to this paper Bohr puts forward a new formulation of the foundation of his theory. This is a characteristic feature, which we find again in all the later papers, that by a constantly more refined analysis of the basic assumptions he tries to obtain an ever clearer understanding of their implications. As for the two problems to which the article was directed, the theory was not yet sufficiently developed to account for the phenomena, and in the case of the Zeeman effect Bohr was even led by apparently cogent reasons to modify his frequency condition. Later, when Sommerfeld in I9l5-16 had developed the theory further, and the correspondence principle was refined, it turned out that these reasons were invalid, and the frequency condition could be retained in its original form . In the case of the Stark effect the theory was able to explain the broader features and provide certain qualitative statements, but here, too, it was not until after Sommerfeld's extension of the theory that one had a glimpse of a real explanation. Another point that was to remain an enigma for a couple of years yet, and which was to become the key to the next great advance, was that the hydrogen lines proved to be double. Bohr first suggested that the phenomenon might be a splitting-up due to a Stark effect in the discharge tube in which the spectrum was produced, and during the spring of I 9 l 4 he started experiments with H. M. Hansen to examine this point, but they produced a negative result. At the same time he gave a series of lectures on his old speciality, the electron theory of metals, and at the Danish Physical Society he spoke on the new work on X -rays. At the beginning of the spring, efforts were seriously resumed to provide an independent teaching post for Bohr, an idea which had previously been put forward in lg l I but had been abandoned, amongst other reasons because of resistance to it in the university. As a result, Bohr had had to sacrifice much valuable time in working as an assistant, particularly in teaching medical students. To give an idea of Bohr's worries during these years, we shall just reproduce a passage of a letter to Oseen of March I9I4, which precedes a request for a recommendation in support of his

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petition for the establishment of a chair in theoretical physics: " ... There is in fact no laboratory belonging to my position, for the one Prof. Knudsen had when he was a lecturer was transferred to the professor when I was appointed. I have only the task of giving the medical students instruction in physics and have nothing to do with advanced teaching in physics, and have thus no chance of getting pupils or assistants. I am therefore working on getting a teaching post in theoretical physics established (you perhaps remember that after my doctor's thesis there was some talk of this), but I don't suppose there is much hope of success, since the faculty still does not favour the establishment of such a post." The matter was allowed to drag on, and when Rutherford shortly afterwards offered Bohr the Manchester readership which had become vacant after Darwin left, he therefore accepted it. Rutherford first cautiously indicated the possibility in a letter he sent in May: " ... I daresay you know that Darwin's tenure of the Readership has expired, and we are now advertising for a successor at £zoo. Preliminary enquiries show that not many men of promise are available. I should like to get a young fellow with some originality in him." In June Bohr went to Manchester and made final arrangements with Rutherford to take over the readership for the university year I 9 I 4-1 5, for which period he was granted leave of absence from the University of Copenhagen. In July, before he went to England, Bohr went on a walking tour in the Alps with his brother and on the way through Germany he took the opportunity of visiting Wiirzburg, Gottingen and Munich, and in the last two places he gave an account of his results. While Harald, who joined him in Gottingen, was already well acquainted with the circle there, it was the first time that Niels had an opportunity of talking to the German physicists about his theory, and naturally he used this opportunity to explain his ideas to Debye, Born, Wien, Sommerfeld, Kossel and others. From letters home to his wife we get an impression of these conversations and particularly of the attitude to his theory in Gottingen. Runge, as expected, seemed impossible to persuade, he " ... belongs to the old school ... ". Debye, on the other hand, for whom Bohr had great admiration, " ... has always taken a favourable view of my speculations, but I think I succeeded in persuading him that perhaps all this can lead to more than he had imagined .... " It is noteworthy that Bohr reports scepticism

LEON ROSENFELD AND ERIK RUDINGER

in the case of Born, who was only a few years older than he, and who was later to make such important contributions to quantum theory: " ... To begin with he had taken an entirely negative attitude to my theory, but I believe that I succeeded in making him realize that it was not altogether as wild as it looked at first sight .... " Bohr also spent much time with the Gottingen mathematicians, with whom he went walking and played tennis. He gave his impressions of his stay in Munich in a letter to his mother, but unfortunately this letter seems to have been lost. The walking tour itself took place in the Bavarian and Austrian Alps, where the two brothers wandered from hut to hut, and from here Bohr sent enthusiastic descriptions of nature home to his wife. On one occasion when he had climbed to the top of a mountain he wrote of the view: " ... I cannot describe how lovely it was up there; on three sides as far as the eye could see there was nothing but snow-covered mountain tops, and on the fourth you could look down into a grassy valley which opened out into a wide plain, and it was funny to see how the mountains suddenly grew up, as it were, out of the plain ... " And later, when fog and rain had prevented a projected day's walk: " ... It is impossible to describe how amazing and wonderful it is, when the fog on the mountains suddenly comes driving down from all the peaks, initially as quite small clouds, finally to fill the whole valley ... " That the two brothers were in quite good form we realize when we hear that they walked as much as 22 miles a day. The brothers had planned to come home on August 6th, but in the meantime the war broke out, so they had to return in a hurry and only just managed to get through Germany before the frontiers were closed. The war disrupted regular sea traffic with England, and Bohr was very doubtful whether he should go to England under these circumstances. After having contacted the laboratory in Manchester by telegraph, he made up his mind to go nevertheless, and together with his wife he arrived in England at the beginning of October, having crossed by ship direct from Copenhagen round the north of Scotland. The following spring Bohr decided to ask for another year's leave from Copenhagen, and his stay in England was thus extended to the summer of 191 6. During that time Bohr gave lectures on thermodynamics, kinetic theory, electromagnetism and electron theory and, of course, continued his

Niels Bohr's theory o n a tomi c constitu tion is hased on two fu nda m enta l discoveries : in 1goo Max Planck introduced th e q uantum of action a nd in 191 r E rn est R u therford d iscovered the atom ic nu cleus. T h e upper p h otograph was taken duri ng a visit by Pl a n ck to Copenhagen in 1930; th e lower duri n g one of Bohr's visits to Rutherford in Camb rid ge. Rutherfo rd and Bohr are seen sitting back to back during an excursion to the university rowing races.

In his cou ntry house at T isvilde N iels Bohr used much of his spare tim e for wo rkin g in the garden. H e is seen, together with coll eagues from the Institu te, fe lling trees and sawing up logs.

Over a number of years N iels Bohr, with a group of friends, took par t in excursions in the yach t

"Chita". From the left: Nie ls Bohr, Niels Bjerrum, Ole Chievitz.

THE DECISIVE YEARS

work on the atomic theory as well as on the theory of the deceleration of charged particles. Furthermore he found occasion for experimental work. In I g 14 the two German physicists Franck and Hertz had made a very important discovery, which in the following years was to play a large part in the development of quantum theory, and for which about ten years later they received the Nobel prize. They found that mercury atoms bombarded with electrons absorb the energy in quanta: the electrons do not give off their energy to the mercury atoms if it is below a certain critical value, but easily give it off if it is above this amount. These experiments eventually provided further essential support for Bohr's theory, since what happens is that the colliding electron raises the outermost electron in a mercury atom from its ground state to the next stationary state, and the energy required for this process has just the value found by Franck and Hertz. It is, however, interesting that this possibility did not occur to Franck and Hertz themselves, who in the paper reporting their experiments did not mention Bohr's theory at all, but on the contrary considered that they had completely removed the outermost electron from the mercury atoms, that they had ionized them. Thus they believed that it was the ionization energy that they had measured, and they in fact observed that ionization took place. This, however, would be completely incomprehensible on the basis of Bohr's theory and would create a great difficulty for it, since it should require much more energy to ionize an atom than the amount which Franck and Hertz had measured. Bohr, who soon found the right explanation, came to the conclusion that the ionization observed must be the result of a side-effect. It was with a view to clarifying this important point that he started an experimental investigation, together with Makower. How this had to be abandoned, because their apparatus caught fire, and because the German glassblower who had constructed it had in the meanwhile been interned, is humorously described in Bohr's Rutherford lecture. It is worthy of note that as late as I g 1 6 Franck and Hertz were still talking of the critical energy value as an ionization energy, and not until after Davis and Goucher, working in New York, had finally shown in 1g1 7 that the ionization was a secondary effect, did they accept Bohr's explanation. Bohr's theoretical work in these years was aimed mainly, of course, at developing the atomic theory further, and he published an article on this 5

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subject in September 1915. Here, together with a carefully elab~rated survey of the fundamental assumptions, one finds among other t~mgs a discussion of the Franck-Hertz experiment with its correct explanat10n, as well as an account of Moseley's experiments on the basis of Kossel's explanation. (In August 19 15 Moseley had been killed in the war at the age of 27, a loss that was deeply regretted by physicists al~ over the world.) At the same time Bohr continued, as already stated, his work on the theory of the deceleration of charged particles passing through .matter, which he refined by the use of statistical methods, and he published a paper on this in October 19I5. Bohr had also contemplated dealing wi~h the apparent contrast between the classical principles which ar: used m these calculations and the principles which formed the basis of the quantum theory of the atom, but he was afraid that the paper would become too long, and gave this up again. One of the most interesting papers which Bohr wrote in these years is, however, quite a short note phrased as a letter to the Philosophi:al Magazine and commenting on a paper by H. S. Allen. In thi~ not~, which was published in February 1915, Bohr mentions for the first time the correction which is introduced in his formula for the hydrogen spectrum when the theory of relativity is applied to the orbits of the electron in the hydrogen atom. In the case of elliptical orbits, one finds that the ellipse will turn as a whole, so that the electron will describe a series of "loops" around the nucleus, and Bohr now suggests that this rotation could be the cause of the doubling of the hydrogen lines which had already preoccupied him so much the previous year. This was indeed, as we shall soon see, just the direction that the next great advance was to take. Bohr, however, does not go any deeper into the problem, but merely adds that it is hardly worth the trouble to take up a detailed treatment of the question before more exact measurements of the splitting-up of the spectral lines are available. Such measurements were undertaken at the same time by Evans in Manchester and the German physicist Paschen in Tiibingen. While Evans came up against various experimental obstacles, Paschen succeeded during I 9 1 5, by a brilliant series of measurements, in determining a numb:r of the required values with great accuracy. It was then Sommerfeld, m close contact with Paschen, who was able to make the next decisive step forward. Sommerfeld followed the very line of approach indicated by Bohr, by

THE DECISIVE YEARS

applying the relativity theory to elliptical orbits. At the same time, however, he added a fundamentally new feature to the theory by finding a way of determining the stationary states of the system which was more general than the one Bohr had used. Thus, while Bohr had only been able to deal with periodic motions of electrons, i. e., motions which are exactly repeated after one revolution, Sommerfeld's theory was also applicable to many types of non-periodic motion, which naturally meant a great advance. It allowed Sommerfeld to account for the double lines of hydrogen, and he could further show that other spectral lines must be split up into components, that is have a so-called fine structure; in the case of ionized helium he found excellent agreement with Paschen's measurements. Shortly after Sommerfeld's theory had been put forward, Epstein and Schwarzschild were able to account for the Stark effect of the hydrogen atom on the new basis. Sommerfeld had presented his theory to the Munich Academy of Sciences in December I9I5 and January I9I6. He sent his papers to Bohr, who received them in March I 9 I 6, when he was finishing a paper on " The Application of the Quantum Theory to Periodic Systems", which was already in proof. Bohr welcomed Sommerfeld's work with enthusiasm and immediately wrote a letter to him in which he said: "I thank you so much for your most interesting and beautiful papers. I do not think that I ever have enjoyed the reading of anything more than I enjoyed the study of them, and I need not say that not only I but everybody here has taken the greatest interest in your important and beautiful results .... ", and he wrote to Oseen that " ... This paper has quite changed the present state of the Quantum theory ... " In consequence he wanted to revise his own paper in accordance with the new ideas, but when this proved impossible he decided to withdraw it. It was not until two years later that there appeared in an entirely different form the first part of a long treatise "On the Quantum Theory of Line Spectra".

In March I 9 16 Bohr got word from Denmark that it finally looked as if a professorship in theoretical physics would be established for him. The official notification came at the beginning of May. While the previous year an approach to the Ministry had been turned down, we now read in 5*

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the recommendation of the Ministry to the Treasury: ". . . With regard to theoretical physics, it must be emphasized that this subject, in accordance with the proposal of the faculty for a change in the arrangement of the degree examination, will be given more importance, and that there is just now a scientist particularly suitable for filling the post, namely the present lecturer Niels Bohr, Ph.D., who has shown himself outstandingly able in the field of theoretical physics. . .. " But this decision did not remove all difficulties, since the lectureship Bohr had held up to then was discontinued, so that he was still to have, as professor, " ... the duty, until further notice, of continuing the teaching which until now has rested on him as lecturer in physics.... " After his return, however, Bohr succeeded in getting an assistant for this work, and he finally ceased to have responsibility for it when the lectureship was re-established in r 9 r 8. Among those who congratulated him was, of course, Bohr's old teacher at the university, Professor C. Christiansen, who formerly had expressed fear that Bohr would remain abroad, and who now sent a letter of congratulation in which he gave an excellent characterization of his pupil: " ... I know you from your young days; I have never met anybody who was as thorough in everything as you are, who had the energy to carry things through, and who at the same time was generally interested in life as a whole ... " At this point Bohr's fame had also reached America, and in February he had received an invitation from Professor G. N. Lewis to spend a term and give a series of lectures at the University of California. Bohr seriously considered this proposal, but on the one hand the war was an obstacle, and on the other it would have been difficult, if not impossible, for him to obtain leave of absence the first term after his appointment as professor. At any rate the idea was abandoned, and seven years elapsed before Bohr paid his first visit to America. Shortly before the beginning of the autumn term something happened which was to be of great importance for Bohr in the following years. A 2 r -year-old Dutch physicist, Hendrik Anthony Kramers, who had studied with Lorentz and Ehrenfest in Leyden, came to Copenhagen. As he relates in a letter to Bohr, it was rather by chance that he had come to Denmark; he merely wanted to study abroad for a time, and as Denmark was neutral, it was natural for him to go there. In this letter he introduces himself to

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Bohr: "To begin, let me introduce myself, by telling that I am a Dutch student in physics and mathematics.... ", and he continues: "Of course I should like very much to come in acquaintance with you in the first place, and also with your brother Harald .... " After seeing Bohr he expressed the wish to be his assistant. Bohr has told how his brother whose ' that advice he asked in this as in so many other questions, had answered if the young Dutchman was really so keen, he might as well be given a chance. That is what Bohr did, and it succeeded beyond all expectations: Kramers worked as Bohr's assistant for the next ten years and did not leave Denmark until he was given a professorship at Utrecht in I 926. He was the first scientific assistant to join Bohr in the newly-established Institute for Theoretical Physics in I92I, and he was an invaluable source of inspiration for those working at the Institute and thus for physics in Denmark generally. In the autumn of r 9 r 6 Bohr took up his duties as a professor, and in the years immediately following he gave lectures on such varied subjects as mechanics, the theory of elasticity, thermodynamics, electron theory, and atomic theory. Also he held colloquia in which he made the students report on the most important recent papers. He further conducted examinations, at which he carefully entered in a notebook his assessmentssometimes very critical-of the students' performances. He gave several lectures on atomic theory at the Danish Physical Society, of which he was chairman during the period 1916-19. In r9I7 he was elected a member of the Royal Danish Academy of Sciences and Letters, of which he was later the president for many years. For his own work Bohr had only a room next to the library at the Technical University, and in a letter to Sophus Weber he complained in I9I 7 that he had no room at all for experimenting. Energetic as he was, he did not leave it at that, but in the same year applied to the government for permission to set up a laboratory. For various reasons, one being the rise in prices during the following period, he had to apply in 19 r 9 to the Carlsberg Foundation for a further grant, an application which was supported by Rutherford and Sommerfeld. Already before the end of 19 r 7, however, on the initiative of his school friend Aage Berleme, a sum equivalent to £4000 had been collected privately in order to obtain a piece of land on the Blegdamsvej. Soon afterwards a start was made with

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the building of the University Institute for Theoretical Physics, which was ' to fulfil so completely the wish expressed by Sommerfeld in his recommendation to the Carlsberg Foundation: "May in the future, as was the case at the Radium Institute in Vienna, scientists from all countries meet for special studies in Copenhagen and pursue common cultural ideals at the Bohr Institute for Atomic Physics." Together with Kramers, who was especially familiar with the mathematical formulation of classical mechanics, Bohr worked out in these years the great treatise "On the Quantum Theory of Line Spectra", the core of which was a further development of the correspondence principle on the basis established by Sommerfeld. As we have pointed out in our previous account of Bohr's treatment of simple circular orbits, this principle enunciates the fundamental, purely logical requirement that the new theory, since it is a generalization of the classical one, must "contain" the results of the latter in the sense that the calculated quantities, such as the colours or strengths of the spectral lines, must approach the values calculated by classical methods when the state of the system gets closer and closer to the range of validity of classical physics. Many of the more complicated motions of the electrons may in principle be decomposed mathematically into simpler "partial motions". According to classical theory each of these partial motions will correspond to a definite part of the light emitted, which will be all the more predominant the more important the partial motion in question is in the total motion. Now in Bohr's correspondence principle each transition from one stationary state to another corresponds to one of these partial motions. When larger and larger orbits are reached, the colours of the spectral lines predicted by Bohr's formula do indeed approach, as they must, the values which the classical formula gives for the partial motions corresponding to the transitions in question. The profound difference in the mechanism for the emission of light according to the classical theory and Bohr's theory is illustrated perhaps even better by this example than by that previously mentioned. While it is clear that according to the classical theory all colours are emitted at one and the same time, since the decomposition into partial motions is a purely mathematical device, it is just as obvious that according to Bohr's theory only one component is emitted at a time, corresponding to a definite jump of an electron. Only the collective result of all the electron jumps in a large number of

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atoms will approach the classical distribution of light in the correspondence limit. The point was now that from the classical analysis of the motion Bohr could draw conclusions about the probability of an electron jumping between two of the inner orbits, which are far from the classical conditions, and deduce from this the main properties of the light which according to the quantum theory should be emitted in such a transition. We may mention as an important example that if a certain partial motion was completely lacking in the classical description, Bohr could conclude that the corresponding jump of an electron between two orbits just could not take place, and by this entirely general argument he was able to explain a number of the experimentally found "selection rules", expressing the fact that many transitions between stationary states do not occur at all. To-day it is difficult to realize how the far-reaching character of this correspondence argument could have escaped so many of the physicists of the time. Yet this is apparent for example in the exchange of letters between Sommerfeld and Bohr. In I 920 Sommerfeld thus writes that he " ... must ... admit that the origin of your principle, which is so alien to the quantum theory, still disturbs me ... ", and as late as r 92 2 Bohr writes to Sommerfeld: " ... In the later years I myself have often felt very lonely as a scientist because I had the impression that my endeavours to develop the principles of the quantum theory systematically to the best of my ability were received with very little comprehension. For me it is not a matter of petty didactic details, but a serious attempt to reach such an inner coherence that there could be a hope of obtaining a more secure foundation for further constructive work .... " In fact the correspondence principle contained the germ of the decisive epistemological advance expressed by the principle of complementarity-that however much a physical theory may evade our imagination, it is nevertheless necessary in principle to describe its results in the language applied to the macroscopic world. As time went on the treatise grew in bulk, and Bohr finally decided to publish it in parts. It came out in the Transactions of the Royal Danish Academy, the first part in March and the second in December 1918. By this time the two following parts were also worked out, but Bohr wanted to revise them. Finally, however, he gave up this revision and in 1922 published the third part in its original form with an appendix dealing

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with later developments. The fourth part was never published. In the years 1916-18 Kramers applied the theory to the fine structure and the Stark effect of the hydrogen spectrum, which he treated in full mathematical detail. His paper was also published in the Transactions of the Royal Danish Academy and formed the thesis for his doctor's degree in Leyden in the spring of 19I9. Already in the autumn of 1916 Bohr and Kramers had developed a detailed theory of the helium atom which is mentioned in many of Bohr's letters for a number of years following, but which was never published. Although at one stage they apparently believed that they had solved this problem, it finally turned out that the helium atom could not be treated on the basis of the early theories; for example, these gave too low a value for the ionization energy. Thus, the helium atom became one of the problems which most strongly pointed to the necessity of more radical changes. This was very early foreseen by Bohr: in a letter he sent to Oseen after his return from Germany in I 9 I 4, while writing of the difficulties encountered in dealing with systems containing more than two particles, he added the following, almost prophetic remark: ". . . I am inclined to believe that the problem presents extremely great difficulties which can only be circumvented by deviating very much further from the usual considerations than has been necessary up to now, and that success so far has been exclusively due to the simplicity of the systems considered. . .. " This conviction, however, was far from being shared by all physicists. Sommerfeld especially was inclined to take the early theories more literally than Bohr considered justified. A characteristic remark in this respect is found in one of Sommerfeld's letters to Bohr from I9I8, in which after discussing Rubinowicz' more "lucid" way of deducing some of the selection rules, he adds the following comment: " ... Your method certainly goes further, but the conception indicated above seems to me physically more instructive .... " Yet it was the view expressed by Bohr that was to bring success. Thus in I g I 6- 1 7 Einstein, by applying statistical considerations to Bohr's stationary states, but without using any special ideas of electron orbits, succeeded in arriving at a surprisingly simple deduction of Planck's radiation formula. This fundamental approach, in combination with the correspondence principle, eventually became the starting point of a development which, especially by the decisive contributions of Bohr's young

•

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collaborators, Kramers and above all Heisenberg, was to lead to the solution of the essential problems. In this solution-a mathematically consistent formalism called quantum mechanics-the concept of distinct electron orbits is completely abandoned, whilst all the requirements of the correspondence principle are fulfilled. It must have been hard in the early years, with all the patent success of the rather primitive atom model, to shake off unfounded optimism regarding the fruitfulness of the orbit conception and to accept the necessity of a description renouncing in principle such pictures, but based merely on the correspondence principle. This is vividly shown in a letter Bohr sent to Oseen in January Ig26, very shortly after the new theory was put forward. Let us therefore conclude the sketch we have tried to give by letting Bohr himself cast a glance back on the journey now accomplished: " ... We are slowly progressing, I hope, but in every result lurks the temptation to stray from the right path. This is so true in atomic theory that at the present stage of the development of the quantum theory we can hardly say whether it was good or bad luck that the properties of the Kepler motion could be brought into such simple connection with the hydrogen spectrum, as was believed possible at one time. If this connection had merely had that asymptotic character which one might expect from the correspondence principle, then we should not have been tempted to apply mechanics as crudely as we believed possible for some time. On the other hand it was just these mechanical considerations that were helpful in building up the analysis of the optical phenomena which gradually led to quantum mechanics .... "

G/LIMPSES OF NIELS BOHR AS SCIENTIST AND THINKER

Glimpses of Niels Bohr as Scientist and Thinker by Oskar Klein

Being the oldest survivor of the circle of young physicists who came to Niels Bohr from different countries when his fundamental papers began to be noticed in physical literature, in this contribution to the memorial volume in addition to such glimpses of his work and manner of working, which I can give from my own experience in those years, I shall also touch on some features of his development before that time. These I learned partly from him and partly from some of those who were closest to him. Thereby I shall alternately, just as he used to do, go from philosophy to physics anc.l from physics to philosophy. Niels Bohr himself and his brother Harald, the brilliant mathematician, liked to give examples of the innocently credulous-and at the same time resolute-way in which as a child he accepted what he saw and heard. They also spoke of geometrical intuition he developed so early, as witnessed by his astonishingly sure judgement of the capacity of vessels, an ability which particularly amused his father, the eminent physiologist and original thinker. The first feature appeared for instance in believing literally what he learnt from the lessons on religion at school. For a long time this made the sensitive boy unhappy on account of his parents' lack of faith. When later, as a young man, he began to doubt, he did this also with unusual . resolution, and thereby developed a deep philosophical bent similar to that which seems to have characterized the early Greek natural philosophers. While Harald H0ff ding's objectivity and free search for harmony in existence seems to have been significant for his development, he had otherwise little in common with the prevailing philosophical trends of this time. It might be said that his original, innocently credulous way, and his power

75

of doubting, entered his philosophy as complementary features-to use his later favourite expression. With his strong and subtle logical intuition, as a young student and later as a scientist, Bohr would already pay the greatest attention to logical stringency, without, however,. finding much interest in formal logiceven if such considerations would at times amuse him. I remember how once he tried to explain Russell's "logical calculus" to us young people by proving that, when we were in the room and the room in the house, then we would also be in the house. I don't believe he succeeded, in any case it caused him some exertion. His engagement in the old fundamental problem of ethics, concerning the freedom and limitation of will was however much deeper, just as later he was to become involved in the problem of the relation between biology and physics. Behind his concern with these problems, there was more than scientific curiosity, namely the desire for harmony without sacrificing either the claims of logic or those of experience. While most people tend to notice the differences between similar things, it was natural for him to see what was common to apparently different ones. With his strong feeling for truth, his early concern with the problem of will helped him to be on his guard against cheap generalizations, and to be aware of features of irrationality, arising from the very nature of investigation, in any non-trivial problem. This trend of his had nothing in common with the kind of mysticism, which fills the holes in our attempts towards a rational philosophy with mythological ideas taken literally-i.e. with quasirational concepts-but it may well be called religious, when that word is used in its essential meaning. At the same time this trend had a characteristic mixture of humour and poetical understanding. Anyone who has followed the scientific work of Niels Bohr will see how accurately this basic inclination fell in line with the problems presented by physics, when he started as a scientist. It was well known to his early friends that he had this inclination long before it was expressed in his physical research. He was amused, when one of these-to whom he talked, in the later twenties, about his work concerning complementarity- remarked that this was just what Bohr had always thought, a statement he himself, of course, took as an enormous exaggeration. Still, we his earliest pupils could witness that it contained quite a lot of truth.

OSKAR KLEIN

When in May I 9 I 8 I first came to Bohr, my intention was, of course, to learn physics. He was then, in active co-operation with his Dutch assistant Hans Kramers, who had come to him in the autumn of I 9 I 6, eagerly busy with the elaboration of the program he had sketched in his first paper on atomic theory of I 9 I 3; the first part of his great paper in the Reports of the Royal Danish Academy on the theory of spectral lines had just appeared. But this did not prevent him from talking about many different things in his enthusiastic way either in his room in the Technical University at S0lvtorvet or in his home in Hellerup, where he and Mrs. Bohr received us young people with great hospitality, or (not least) on walking tours. I remember particularly one rather long walk in the north of Zealand in the summer I 9 I 8, where among many other things he mentioned his father's idea that teleology, when we want to describe the behaviour of living beings, may be a point of view on a par with that of causality. This idea was later to play an essential role in Bohr's attempt to throw light on the relation between the biologist's and the physicist's way of describing nature. Something similar may be said about his considerations on the problem of will, which he also talked about in this connection. He stressed very strongly the danger of unconsciously changing, from one sense to another, such words as will and purpose, when one does not realize that thinking about the process of thinking is a singular point in our consciousness. A later development of such considerations-which at that time he seemed to regard merely as germs of thought-became the very basis of his epistemology, as he stated it many years later in his contribution to the celebration volume in honour of the jubilee of Planck's doctorate. Bohr's scientific work in these years was mainly concerned with what, some years later, he called the correspondence principle. From this basic point of view he was able to get order into the complex of problems arising from Planck's discovery of the quantum of action and Rutherford's discovery of the atomic nucleus. The first and second part of the paper mentioned above contain a lucid presentation, strongly supported by many new examples, of the ideas which already had led him in his early papers to such decisive results as the connection between the empirically discovered laws of Rydberg and the quantum-theoretical treatment of the nuclear

model of the atom. In conversation, however, he preferred to take up the

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77

unsolved problems around which his thoughts moved incessantly. In particular, there was still the quantum paradox: how the classical mechanical and electrodynamical description of nature, with the old rule that "nature makes no jumps", could be reconciled with the discontinuous way in which energy is exchanged between the atom and the radiation field. It is true that in the paper mentioned above Bohr had made an important advance by means of the correspondence viewpoint in showing that-in spite of the abyss, whose depth he never ceased to emphasize, between the quantumtheoretical mode of description and that of classical physics-a detailed correspondence is exhibited between these two modes of description, so that their results coincide in the limit where Planck's quantum of action is very small compared with the actions to be described. In this work he had built on a new derivation by Einstein of Planck's radiation law, the very origin of quantum theory. Einstein obtained this result by formulating probability laws for the transitions of an atom from one stationary state to another. I well remember Bohr's great admiration for Einstein arising equally from this great scientist's contributions to statistical molecular theory, to quantum theory and to relativity theory. Bohr, however, could not reconcile himself to Einstein's concept of light quanta, which had been further elaborated in the work I have just mentioned. Bohr's objections came from his thorough familiarity with the wave theory of light, and, when these things were mentioned, he used to emphasize the fantastic accuracy and completeness of this theory in accounting for the many experiments on the propagation of light. Especially he underlined that the definition of the frequency of a light quantum, which determines its energy, is itself derived from the wave theory. Einstein, on the other hand, believed that a true theory of light must in some way combine wave and particle features, so that light energy is concentrated within smal regions; and he looked for experiments, through which deviations from the superposition principle might be discovered. How deep a revision of our accustomed ideas Bohr was already prepared to accept, appeared in his remark that perhaps one would have to give up the rigorous validity of the energy principle. Many years later he returned to this idea, which, however, was refuted by direct experiments. But already before that happened he had come to regard this idea as too cheap a way of overcoming the quantum paradox. While Einstein's too literal concepts

OSKAR KLEIN

of light quanta were disproved by experiments, these were later to come to their right in Bohr's clarified concept of the relation between the quantumtheoretical and the classical description of physical phenomena. But, the time was not yet ripe for this viewpoint, which was to arise as the main result of many years of work by Bohr himself and a number of other physicists. The fact that more scientists had entered the field of research, which Bohr had opened up, meant both new inspiration and a gradually heavier burden for him, because he could not help submitting to his own viewpoint every progress, experimental or theoretical. This put its characteristic mark on his work on the great paper mentioned; the first version had already been in proof ready for printing more than two years earlier, but was withdrawn by Bohr, when he learned of some new work by the distinguished German physicist Sommerfeld. Knowing Bohr's way of working it was, indeed, little less than a miracle, that the long papers with their great abundance of thoroughly cogitated points of view and examples studied in every detail were finished in about two years. Without the devoted and active help of Kramers this would hardly have been possible. In the papers mentioned, statistical thermodynamical considerations play an important role. But also in connection with my own problems, which Bohr followed in his kind and helpful way, I learned much from his deep understanding of this subject. I was then strongly impressed by Gibbs' canonical ensemble, which in so direct a way gives the formal solution of all kinds of temperature equilibrium problems. But from Bohr I was to learn that this method also marks essential progress from Boltzmann's ideas as to the very definition of the concept of temperature. As Bohr pointed out, this could be read out of Gibbs' book. But, as he said, when this book was spoken of: "When a person has mastered a subject thoroughly, he will then write so that hardly anyone can understand him". Something of this characterizes Bohr's own writings, which have to be read and re-read with the utmost attention in order to be understood. This was at first rather surprising to his young pupils, who so often witnessed his astonishing gift for explaining orally both his own ideas and those of others. On the whole there was a great contrast, or shall we say complementarity, between the way he expressed himself officially, whether in writing or orally, and privately with only a few listeners. While in the first case he

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took the greatset care to get the most accurately shaded formulation of the matter-which demanded a similar accuracy from the reader-and also the greatest care not to offend those he criticized, in the latter case he would express himself with drastic imagery and strong expressions of admiration as well as criticism. It was mainly through Kramers that in the summer of 1918 I learned about Bohr's characteristic way of working. Thus, while Kramers was busy with his doctor's thesis-a beautiful and penetrating application of the correspondence principle to the problem of the intensity of spectral lines-he spent much of his time telling me about both Bohr's and his own work. But the next summer I had the occasion to see for myself how Bohr worked, since I had to be Kramer's substitute, while (upon taking his degree in Leiden in the spring 191 9) he remained with his family in Holland first for a holiday and then because of illness. Bohr was present at the doctor's disputation and here he met Lorentz and made the acquaintance of Ehrenfest, which was the beginning of a friendship that lasted until Ehrenfest's death. Bohr also gave a lecture at Leiden, in which he summarized the results of the last years' work. He intended to publish this lecture, which was given in English, and, as always with Bohr, this meant reworking it from its very foundation. The place where we worked was a hired room not far from the country house where Bohr and his family stayed during this and some of the following summers before they moved into their own house at Tisvilde Hegn. With some writing paper and a pencil in front of me I was placed at a table around which Bohr wandered, alternately dictating in English and explaining in Danish, while I tried to get the English text on to paper. Sometimes there were long interruptions either for pondering over what was to follow, or because Bohr had thought about something outside the theme which he had to tell me about. Thus, once, in connection with some criticism of Einstein's general relativity theory presented to him by Helge Holst, he worked out a detailed discussion of the so-called clock paradox such as it would occur on a straight-line journey out into space and back again. Often, also, work was interrupted by short running trips or cycling to the shore together with the family for bathing. The aim of the dictation was a presentation of the essence of the quantum theory of atoms and molecules, a continuation of the attempts

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in this direction which he had published in a series of papers in the Philosophical Magazine in the years 1913-15. While he had been highly successful in this respect for the simplest atomic system, consisting of a nucleus and a single electron-the result being the momentous paper in the Reports of the Royal Danish Academy (Part I and 11)-it became clear gradually that his original electron-ring models of atoms and molecules with more than one electron do not present a correct basis for the application of correspondence considerations. The more complicated spectra also exhibited the multiplet structure and the anomalous Zeeman effect, whose explanation by the electron spin did not appear until several years later. However, Bohr's general interpretation of the spectral laws discovered by Rydberg remained the solid foundation. This general interpretation was developed further, especially through Bohr's correspondence treatment of the motion of a particle in a central field of force. Thus, according to Bohr's interpretation of Rydberg's laws, such a field of force would be a fair approximation for the action of the rest of the atom on the outermost electron in states leading to the emission of the lines in a general series spectrum. These results, which were to form part of the content of the third of the big papers, were not yet published but were mentioned in the Leiden lecture and together with other still unfinished work they were to be presented in the planned article. Among the unfinished items was an investigation, begun together with Kramers, of the helium atom with its two electrons. This investigation, the subject of much effort, belonged to those attempts-like the electron rings-for which the time was not yet ripe. This was especially so with respect to the explanation of the strange appearance of two quite separated helium spectra, a fact that led many physicists so consider helium as a mixture of two elements, parahelium arid orthohelium. Bohr, however, saw that this could not be reconciled with the interpretation of the atomic number, at which he had arrived already in 1912. All these unsolved problems doubtless contributed towards delaying the completion of the paper; in spite of a multitude of beautiflll unpublished or partially published results supporting Bohr's general view on atomic problems. To these belonged the interpretation of the investigations of Wood and Strutt on the resonance radiation, and those of Franck and

A portrait from the 192o's.

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Trying to ride a motorcycle belonging to one of the younger coll aborators.

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Hertz on electron collisions, which gave such striking confirmation of the assumption that every spectral line belongs to a separate transition process. However, the Leiden lecture was never published, and its contents were included in a later paper written in connection with a lecture in Berlin the following spring. During the following years I made several sojourns in Copenhagen, where Kramers was still Bohr's nearest collaborator. During this time both the permanent and the temporary circle around Bohr grew considerably. In the summer of I 9 I 9, Hevesy, his old friend from the years in Manchester, came to Denmark, where he remained from the following year, and he performed a series of important investigations, which were followed with great interest by Bohr. In the autumn of the same year Siegbahn, who had started his important work on the X-ray spectra of the elements with a group of young collaborators had arranged a small conference in Lund, where Bohr and Sommerfeld lectured. In rebuttal to those who say that Bohr was a bad lecturer-which he often was, putting too much into his lecture and articulating indistinctly due to phase difference between thought and speech-I use to refer to this lecture, where content, form and presentation made a captivating unity, the like of which I have hardly ever heard. Later that autumn Sommerfdd came to Copenhagen, and this led to a new exchange of ideas and, in spite of differing opinions with regard to atomic questions and a great difference in age, to very friendly relations between him and Bohr. Around New Year 1920 Bohr went with me and some of my Swedish friends on a skiing tour to Dalame, where he impressed everybody by his practical ability. This occasioned the following amusing compliment (in Swedish) by one of the company: "The only criterion that the professor is a professor is that the professor always forgets his gloves". In the evening, in the little cottage where we lived, he told us much about his general views and, among other things, why he took so critical a stand towards every kind of so-called parapsychological phenomena, emphasizing wireless telegraphy (as radio was then called) as one of the strongest arguments against telepathy. During his visit to Berlin in the spring of I 920 Bohr met Einstein, Planck and several other German physicists for the first time; among them was Franck, with whom he contracted a warm friendship. Franck

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was also one of the first scientific guests of the new institute at Blegdamsvej in the winter of I 9 2 I. Towards the end of the summer of I920 the circle around Bohr had a further semi-permanent addition through the arrival of Rosseland. His somewhat sharp but fundamentally benevolent personality and his great scientific gifts-both of them highly estimated by Bohr-led to pleasant companionship and fruitful collaboration. He was later to become one of the pioneers of the introduction of the new atomic theory into astronomy. A great event for all of us that same autumn was a visit by Rutherford, of whom Bohr had told us so much; he lectured about his remarkable new nuclear experiments, the first artificial transformation of atomic nuclei, made in I9I9. At this time, Bohr's work with the correspondence interpretation of spectra and the closely connected elucidation of the electron structure of atoms had started in earnest. It happened here, as so often with Bohr's work, that he found a way to circumvent the unsolved problems, which seemingly stopped further advance, by means of a combination of general theoretical points of view and well chosen 'empirical facts, thus obtaining reliable results of fundamental importance. Thereby, less successful attempts by other physicists were often a source of inspiration to him. While the helium problem had stopped him for the time being, he was now to receive help from the line-spectrum of the next element, lithium. Although a closer understanding of the helium spectrum was stiil lacking, the high ionization energy of helium made it clear that in the ground state both electrons were in states corresponding to the ground state of the hydrogen atom (I-quantum state). It was therefore natural to assume that the same would hold for the binding of the third electron in the ground state of the lithium atom. However, this does not at all fit in with the low ionization energy of lithium, to which the metallic properties of this element are due. The assumption, that the electron here stops at the next lowest state ( 2-quantum state) immediately fitted in with the lithium spectrum. By means of a study of the spectra of the elements following lithium Bohr could now show that up to neon the additional electrons are still bound in 2-quantum states, such that 8 of the IO electrons of this element must be assumed to be in 2-quantum states and 2 in I-quantum

GLIMPSES OF NIELS BOHR AS SCIENTIST AND THINKER

states. Just as the 2-quantum states first appear after helium, the first inactive gas, he could further show that the first 3-quantum electron appears in sodium, an alkali metal like lithium, which follows neon, the second inactive gas. Here was the beginning of the understanding of the peculiar periodic change of the properties of the elements, when ordered according to increasing atomic number, i.e. nuclear charge. The group structure of atoms revealed through this work of Bohr's-first group: two I-quantum electrons; second group: eight 2-quantum electrons etc.-also gave the background for the discovery of an important law of nature, the exclusion principle formulated by Pauli, which was to become one of the main pillars of elementary particle physics. The closer elaboration of Bohr's ideas concerning electron binding, where X-ray spectra also came to play an essential role, led to the interesting discovery of a new element, and gave a good illustration of the conviction Bohr felt, when he had thought something through thoroughly, and also of his willingness to change his opinion when facts made it necessary. When his considerations had reached the interpretation of the rare-earth metals, he believed, for good reasons, that the next element, no. 72, which had not yet been discovered, would belong to the same group as zirconium and have similar chemical properties to that element. At about the same time, however, two French scientists, Dauvillier and Urbain, believed that they had proved that the element 72 was another rare-earth metal, to which they gave the name celtium. Their reason for this was an X-ray analysis of a preparation containing a mixture of rare-earth metals. Shortly afterwards Rutherford had mentioned this apparent discovery of a new element in an article in Nature. When Bohr came to know of it, his first reaction was to consider it as a fact, implying that his reasons for assuming the rare-earth group to end with no. 7 I were inadequate. But after renewed consideration of the matter he became more and more convinced that either there must be some fundamental error in his way of reasoning, or the statement of the French scientists must be wrong. Therefore, in the autumn of I922 he proposed to Coster (who had just come to Copenhagen), and to Hevesy that they find out whether an X-ray analysis of material containing zirconium would not reveal the presence of element no. 72. They succeeded almost beyond expectation and they were soon able to 6*

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isolate the new element- which they named hafnium-in such large amounts that its atomic weight could be determined. A little earlier, in June 1922, Bohr gave a series of lectures in Gi:ittingen about his views and results. A large part of those scientists who were working on atomic problems came to these lectures, which were later called "Bohrfestspiele" by the German physicists. Gi:ittingen had long been one of the main centres for mathematics and physics, and contained at that time a brilliant group of scientists in these fields. Among the older mathematicians were Felix Klein, Hilbert, Landau and Runge, with whom Bohr had friendly connections through his brother Harald, the same being the case with Courant, who was about his own age. Among the physicists in Gi:ittingen were both Franck and Born; and young Pauli, whose outstanding article about relativity theory had recently appeared in the Enzyklopiidie der mathematischen Wissenschaften, was now Born's assistant, while Hund had just become Franck's assistant. Both of them-and also young Heisenberg, who had arrived from Munich together with Sommerfeld, who was his teacher and Pauli's-were soon to become members of Bohr's circle in Copenhagen. Ehrenfest, who had spent a memorable visit there half a year earlier, had now arrived from Leiden. I must abstain from mentioning all the distinguished physicists, old and young, who were present at Bohr's lectures, where I had accompanied him as his assistant; to do so would make an almost homeric ship's catalogue. Bohr, who had earlier met with considerable criticism and lack of understanding, had at this time become one to whom all listened with reverence, so that the discussions about the lectures were rather concerned with whether Bohr had meant this or that, than the matter itself. In the autumn Pauli came to Copenhagen; with him also irreverence came into its own, supported by Bohr's self-criticism and sense of humour. In December the same year Bohr received the Nobel prize in Stockholm. At the obligatory lecture, for which he had chosen to talk about the constitution of atoms, he discovered that he had forgotten his notes and slides at the hotel, so he had to begin without them, while they were fetched. This, however, was rather an advantage, because it forced him to improvise, such as he did in private conversations. During these years I spent a great part of my time in Copenhagen. However, from the autumn of 1922 until the early spring of 1926 I was seldom

GLIMPSES OF NIELS BOHR AS SCIENTIST AND THINKER

there, being mostly in Sweden and the U.S.A., but during the following five years I was permanently in Copenhagen. During my absence I was, however, able to follow the main features of the developments there by short visits and letters, not least through Kramers, who as university lecturer was now still more firmly attached to the Institute at Blegdamsvej. As already mentioned, Pauli came to Copenhagen in the autumn of I922 for a longer stay, and Heisenberg's more permanent stay began two years later. Apart from continued refinement of Bohr's correspondence argument, the difficult points of the theory became increasingly the subject of eager discussions. In the first place these discussions turned about the impossibility of finding a place for the anomalous Zeeman effect and the multiplet structure of spectral lines within the frame work so far considered. But also in other ways this framework proved to be too narrow and even inconsistent. This was, for instance, the case with Bohr's assumption that the stationary states could be mechanically described, although such a description was excluded for the transition processes. He had by no means regarded this assumption as obvious, but so far it had contributed essentially to the development of his program. At the same time the quantum paradox, as it appeared in the radiation problem, became more and more urgent. During the decade I913-23, Bohr had undoubtedly been the leading scientist with respect to the whole complex of problems comprised by the new atomic theory which was erected on the quantum postulate (in spite of important contributions from other physicists). The time now approached when the main progress was to come from scientists of a younger generation, but with Bohr still as a giver of ideas and increasingly as the philosophical integrator of the knowledge obtained. Thus, in close connection with earlier ideas of Bohr, Kramers succeeded in 1924 in formulating a quantum theory for the dispersion of light through its interaction with atomic systems. At the same time this was a most beautiful application of the correspondence argument and pointed ahead towards a rigorous quantum mechanics. This work arose in connection with the already mentioned attempt of Bohr to solve the quantum paradox by giving up the rigorous validity of the energy principle; Kramers' work retained its value after this attempt had proved to be mistaken. About the same time, in connection with the study made by a number of physicists of the multiplet structure of spectral lines and the anomalous

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Zeeman effect, Pauli arrived at another important result, namely that the electron possesses in addition to its ordinary three kinematical degrees of freedom, a fourth degree of freedom corresponding to a quantum number, which can take on just two numerical values. This was the starting point for his exclusion principle, in which Bohr's fundamental considerations about the electron groups of atoms found their final clarification. The fourth degree of freedom was soon to obtain interesting interpretation in the notion of spin put forward by Goudsmit and Uhlenbeck-and somewhat earlier by Kronig (who, however, did not publish his considerations) -which led to an explanation of the main features of the anomalous Zeeman effect and the multiplet structure. Heisenberg, who had been in Copenhagen most of the time from the autumn of I924, when on vacation on Heligoland in the summer of I925, got an idea concerning the rigorous formulation of the quantum-theoretical laws, in line with the correspondence argument, which was to become of the utmost importance for the subsequent development of quantum theory and its applications. Thus, starting from Kramers' theory of the dispersion of light, to whose further development Heisenberg himself had contributed during his stay in Copenhagen, he found an adequate way of transcribing mechanics in the sense of quantum theory by means of those quantities which describe the transitions from one stationary state to another, as well as the dispersion of light by an atom. His way performing this was by means of a rule, which he formulated, for the combination of such quantities, the immediate background of which was the fundamental relation determining the frequencies of the light emitted in a transition process in terms of the energy difference of the states in question. This idea of Heisenberg was soon made into a formally complete quantum theory by Born, Jordan and Heisenberg himself and almost simultaneously by Dirac, who got his first inspiration from a visit by Heisenberg to Cambridge. A beautiful contribution was given as early as the autumn of I925 by Pauli, who was now in Hamburg; he solved the problem of the hydrogen atom by means of an algebraic method based on the new mechanics. This included both the case of the free atom, as well as the presence of electric and magnetic fields, where the earlier difficulties were now removed. But as Pauli remarked, the quantum mechanics of Heisenberg still lacked that side of a mechanical description, dealing with

GLIMPSES OF NIELS BOHR AS SCIENTIST AND THINKER

the motion of a particle in space and time. Moreover, the theory did not yet fulfil the claim of relativity theory. In both respects essential progress was soon to follow. It may be easily imagined that the work of Heisenberg, which was closely in line with what Bohr aimed at in correspondence considerations-but which at that time he still regarded as a distant goal-would make the deepest impression on him and the whole Copenhagen group. I remember my own astonishment, when Kramers in the autumn of 1925 sent me a postcard, saying that there was now a new formulation of quantum theory without explicit quantum conditions but, in their place, a mysterious algebraic relation with non-commuting quantities. Only in the following term-from March 1926- did I come into personal contact with the commotion created by this new advance, which was now further increased by Schrodinger's wave-mechanical papers, based on an earlier idea of de Broglie. The same spring Heisenberg and Pauli returned to Copenhagen, and there were eager discussions about the deeper meaning of the new theoretical ideas, and especially about the relation between Schrodinger's wave equation and Heisenberg's algebraic quantum mechanics. Immediately after his arrival Pauli showed us a remarkable mathematical connection between the two formalisms, through which the mystery of the fact, that their results coincided in all cases treated, was removed. A paper by Schrodinger which appeared shortly afterwards showed that he had also found this connection. During the summer there were further important contributions to the theory, among which Born's treatment of collision problems may be mentioned. Here the statistical character of quantum theory was related to the wave function which Schrodinger had regarded as a field quantity in analogy with classical wave optics. At this time, Bohr and the Institute lost the invaluable collaborator and member Kramers, who now returned to his native country as professor in Utrecht. His successor as lecturer was Heisenberg, who like his predecessor, gave his lectures in Danish, which he already spoke fluently. These are two good instances of Bohr's contribution to the propagation of the Danish language. In the autumn the discussions continued with more and more participants. Dirac had now arrived in Copenhagen and, although he did not

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take much part in these debates, he indirectly influenced them strongly through his important work, which made it increasingly clear that quantum mechanics is one connected theory. A generalization similar to Dirac's was developed about the same time by Jordan in Gottingen; he also later came to Copenhagen. The discussion culminated when Schrodinger arrived for a short visit and told us about his attempts at developing quantum mechanics into a literal wave theory similar to that which had replaced the corpuscular theory of light at the beginning of the I 9th century. At the end, however, he declared himself convinced by Bohr's and Heisenberg's arguments to the contrary (see p. 103) a conviction which, strangely enough, he later repented. Still, however, the physical content of the mathematical formalism of quantum mechanics was far from clear, the old quantum paradox regarding the relation of waves and particles being no longer confined to light, but according to the ideas of de Broglie and Schrodinger (which in the meantime had obtained direct experimental verification) was extended also to material particles. In the spring of I927 Bohr received the impetus for his definitive clarification of this side of quantum theory through a very important paper by Heisenberg, in which the so-called indeterminacy principle was formulated. According to this principle a reciprocal relation exists between the optimal precision with which two quantities such as a component of momentum and the corresponding coordinate (or energy and time) can be simultaneously defined. Heisenberg had also tried to demonstrate the physical meaning of these relations by means of ideal experiments. While Bohr was deeply impressed by the general formulation of such relations, on second thoughts he could not help feeling critical about Heisenberg's discussion of the ideal experiments. However, both the results and the failures in Heisenberg's work became a source of inspiration to him, and from then on he worked almost day and night on these questions. The problem was also in perfect harmony with Bohr's natural bent, where his powerful grasp and fine feeling for the limits of visualizability and his philosophical-critical sense were added to his thoroughgoing knowledge of the properties of wave motion derived from his early study of Rayleigh's works. Still, he was now up against difficulties, which were comparable with those he met in his early work.

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As usual, he started writing very soon, i. e. dictating, and at the same time new ideas and new doubts would come to him, so that what was written one day was rejected the next. In this way was spent what remained of the spring and the whole summer, when the work was done at Bohr's summer resort at Tisvilde. Foremost was the problem of the definition of an optimal measurement of a position coordinate or a momentum component of an electron. For the first kind of measurement Heisenberg had proposed to use what he called a y-ray microscope, in which the electron was supposed to be illuminated by y-rays and the scattered radiation was to be observed by some focussing procedure. The use of y-rays instead of ordinary light was for the purpose of making the accuracy so high that the error became small compared with the dimensions of the atom. Heisenberg had now noted that the Compton effect in the scattering of light would produce a change of the momentum of the electron, its value after the measurement being different from that what it was before. He regarded this as the feature corresponding to the lack of definition of the momentum, which, according to the indeterminacy principle, was associated with accurate definition of the position. However, Bohr showed that the lack of definition of the momentum is not directly related to its being changed by the Compton effect but is connected with the necessary uncertainty in the knowledge of the Compton effect in an arrangement that can be used for an accurate measurement of position. He carried through a detailed investigation for both kinds of measurement, and was thereby able to show that there is a complete agreement between the possibilities of optimal observation and those following from Heisenberg's relations. What has been sketched here is only one example from the abundance of considerations concerning the relation between possible observations and definitions according to quantum theory, which was clarified in Bohr's work. In it the wave concept proved to be the natural tool, the problem being the relation between the space-time description and the momentum-energy conservation in atomic processes. In this way Bohr obtained a simplified derivation of the indeterminacy relations which Heisenberg had discovered by means of developments based on the algebraic form of quantum mechanics. Although by the end of the summer Bohr had essentially been able to solve the problems he had set his mind to, no manuscript had resulted from all the dictating. This was a disappointment since he had promised .to

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give a lecture at a congress in commemoration of the centenary of Volta's death, which was to take place in Como in September. Under strong pressure from his brother Harald, who in such cases was a faithful helper, he finally succeeded in producing a very short manuscript for a letter to Nature, which was to be sent from the Institute the morning after he and Mrs. Bohr were to have gone south by the night train from Copenhagen. When I came to the Institute next morning it appeared, however, that they had not taken the night train but had only just left-Bohr had forgotten that he had put their passports on the desk in his office-and he had taken the manuscript with him. The sequel, however, was lucky. In Como he met Pauli, who became extremely interested in all the new ideas and, after the congress, during a stay at Lake Como together with Bohr, helped him by means of a suitable mixture of criticism and sympathetic understanding to write a much fuller manuscript-now in German-apparently almost ready for print, so that it could be sent to Naturwissenschaften soon after his return to Copenhagen, and about the same time-in English translation-to Nature. But soon it became clear that this, still, was only the beginning. During the whole of the autumn of 1927 and the winter of 1928 there was an almost uninterrupted correcting of proofs, to which most members of the Institute contributed; at one time a proof was replaced by a new manuscript, because the numerous corrections made it almost illegible. The last proof was finished about Easter time 1928. In order to give an idea of the main results of this great work of Bohr's I should just mention the emphasis he laid on the indispensability, also in quantum theory, of the fundamental concepts of classical physics-such as space and time coordinates and momentum and energy. Thus, as he pointed out, unambiguos conclusions from observations require that the experiments themselves be describable by means of classical physics, i. e. that effects connected with Planck's quantum of action may be neglected, as far as the measuring arrangements are concerned. The existence of a finite quantum of action then means that only in special cases can different experimental arrangements be reconcilable- i. e. in the sense that conclusions drawn from a measurement with one kind of arrangement can be used together with those drawn from a second measurement with another arrangement. Thus, an accurate determination of the position of a particle

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9I

will, as we have seen, more or less wipe out the former knowledge of its momentum. Bohr denoted by the word complementarity this relationship, which is intimately connected with the statistical character of the quantum-theoretical description of nature, calling such concepts as space coordinates and momentum components complementary to one another. Hence, in quantum theory the situation is such that certain concepts, indispensable for a complete description, are in a sense contradictory to each other, the word complementarity expressing this peculiar kind of contrariety, where one member of such a pair of concepts is the complement of the other member but also sets a limit to its simultaneous use. About a month after the Como congress there was a Solvay conference in Brussels, the theme of which was "electrons and photons". I remember how eagerly Bohr was looking forward to this opportunity of meeting Einstein again and telling him about his way of looking at the quantum problems, which he believed Einstein would not only grasp at once but also consider as a satisfactory solution of the old quantum paradox, since he himself built so largely on Einstein's earlier ideas. What happened was, however, very similar to what occurred to Einstein some ten years earlier with Mach regarding relativity theory, but with the great difference that Einstein entered into Bohr's ideas with the deepest interest. As Bohr himself has described so beautifully, Einstein put forward one after another ingeniously devised ideal experiments----at first in Brussels, then in Ehrenfest's home in Leiden, and also on later occasions-by means of which each time he meant to demonstrate the incompleteness of Bohr's view. Bohr came home from the journey rather disappointed but at the same time happy about the opportunity he had had of delivering a detailed defence of his view against so profound an opponent. And it amused him to tell how he was able to refute each of Einstein's examples and, especially, that Einstein each time had admitted the fallacy of his reasoning, however maintaining his conviction that the statistical mode of description used in quantum theory is essentially incomplete. While Bohr was busy elaborating the viewpoint of complementarity, new progress was steadily forthcoming regarding the quantum-theoretical formalism and its application to various physical problems which had hitherto resisted theoretical explanation-such as Dirac's treatment of the

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radiation problem and especially his theory of the electron; Pauli's, Jordan's and Heisenberg's development of the foundation of quantum field theory; the deep treatment of the quantum theory of systems of identical particles by Heisenberg, Dirac, Hund, Jordan, Wigner and others, just to mention those which appear to me to have been of the greatest importance. But since Bohr's reaction to these advances mainly falls within the period ' treated by Rosenfeld, I shall not touch on it here. Instead, I shall sketch his later work on the general problem of complementarity at the end of the twenties. The new insight Bohr had acquired regarding the foundation of physics-the characteristic feature of which is that in quantum theory, in contrast to classical physics, the influence exerted by an observation on the object to be observed must never be forgotten*)-led him back to the epistemological considerations of his early years, to his old idea that thinking about one's thinking represents a singularity of the consciousness. This had a form closely analogous to the physical situation, namely: "For describing our mental activity we require on one hand an objectively given content to be placed in opposition to a perceiving subject, while on the other hand, as is already implied in such an assertion, no sharp separation between object and subject can be maintained, since the perceiving subject also belongs to our mental content." This quotation is taken from Bohr's article in the Naturwissenschaften written in connection with Planck's jubilee in Ig29, where, after a survey of his general view of the quantum theory, he took the opportunity to hint at how the idea of complementarity forms the natural background for the discussion of essential philosophical and psychological problems. Among other things he pointed in this connection to the instructive analogy between the wave-particle paradox of quantum theory and the apparent contrast between the continuous progression of associative thinking and the conservation of the unity of personality, the interference of observation in the atomic case corresponding to the change brought about by self-analysis in the colouring of our sensations. But Bohr would also point to psychological experience in daily life in *) As it will appear from the following chapter, Bohr later changed his terminology at this point. To avoid misunderstandings he preferred not to talk of an observat10n as influencing the object of investigation but rather to use the word "phenomenon" to describe observations gained under specified conditions including an account of the whole experimental arrangement.

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connection with the difficulty of distinguishing between subject and object, in order to facilitate understanding of the new situation in physics, where his view appeared too radical or mysterious even to many physicists. In this connection he chose as a particularly simple example the use of a stick when trying to find one's way in a dark room. Here the dividing line between subject and object is placed at its end, when the stick is grasped firmly, while, when it is loosely held, the stick appears as an object. I shall conclude these glimpses of Niels Bohr as scientist and thinker by some of his own words at the end of the article just mentioned, namely: "Above all, my purpose has been to give expression to our enthusiasm for the prospects which have been opened up for the whole of science by Planck's discovery. In addition, it has been my desire to emphasize as strongly as possible how profoundly the new knowledge has shaken the foundation underlying the building up of concepts, on which not only the classical description of physics rests, but also all our ordinary mode of thinking. It is above all to this emancipation that we owe the wonderful progress in our insight into the phenomena of nature which has been made during the last generation, a progress far exceeding all the hopes which one ventured to cherish just a few years ago. Perhaps the most distinguishing characteristic of the present position of physics is that almost all the ideas which have ever proved to be fruitful in the investigation of nature have found their right place in a common harmony without thereby having diminished their fruitfulness."

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radiation problem and especially his theory of the electron; Pauli's, Jordan's and Heisenberg's development of the foundation of quantum field theory; the deep treatment of the quantum theory of systems of identical particles by Heisenberg, Dirac, Hund, Jordan, Wigner and others, just to mention those which appear to me to have been of the greatest importance. But since Bohr's reaction to these advances mainly falls within the period ' treated by Rosenfeld, I shall not touch on it here. Instead, I shall sketch his later work on the general problem of complementarity at the end of the twenties. The new insight Bohr had acquired regarding the foundation of physics-the characteristic feature of which is that in quantum theory, in contrast to classical physics, the influence exerted by an observation on the object to be observed must never be forgotten*)-led him back to the epistemological considerations of his early years, to his old idea that thinking about one's thinking represents a singularity of the consciousness. This had a form closely analogous to the physical situation, namely: "For describing our mental activity we require on one hand an objectively given content to be placed in opposition to a perceiving subject, while on the other hand, as is already implied in such an assertion, no sharp separation between object and subject can be maintained, since the perceiving subject also belongs to our mental content." This quotation is taken from Bohr's article in the Naturwissenschaften written in connection with Planck's jubilee in I929, where, after a survey of his general view of the quantum theory, he took the opportunity to hint at how the idea of complementarity forms the natural background for the discussion of essential philosophical and psychological problems. Among other things he pointed in this connection to the instructive analogy between the wave-particle paradox of quantum theory and the apparent contrast between the continuous progression of associative thinking and the conservation of the unity of personality, the interference of observation in the atomic case corresponding to the change brought about by self-analysis in the colouring of our sensations. But Bohr would also point to psychological experience in daily life in *) As it will appear from the following chapter, Bohr later changed his termir.10logy at this point. To avoid misunderstandings he preferred not to talk of an observation as influencing the object of investigation but rather to use the word "phenomenon" to describe observa tions gained under specified conditions including an account of the

whole experimental arrangement.

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connection with the difficulty of distinguishing between subject and object, in order to facilitate understanding of the new situation in physics, where his view appeared too radical or mysterious even to many physicists. In this connection he chose as a particularly simple example the use of a stick when trying to find one's way in a dark room. Here the dividing line between subject and object is placed at its end, when the stick is grasped firmly, while, when it is loosely held, the stick appears as an object. I shall conclude these glimpses of Niels Bohr as scientist and thinker by some of his own words at the end of the article just mentioned, namely: "Above all, my purpose has been to give expression to our enthusiasm for the prospects which have been opened up for the whole of science by Planck's discovery. In addition, it has been my desire to emphasize as strongly as possible how profoundly the new knowledge has shaken the foundation underlying the building up of concepts, on which not only the classical description of physics rests, but also all our ordinary mode of thinking. It is above all to this emancipation that we owe the wonderful progress in our insight into the phenomena of nature which has been made during the last generation, a progress far exceeding all the hopes which one ventured to cherish just a few years ago. Perhaps the most distinguishing characteristic of the present position of physics is that almost all the ideas which have ever proved to be fruitful in the investigation of nature have found their right place in a common harmony without thereby having diminished their fruitfulness."

Q.UANTUM THEORY AND ITS INTERPRETATION

Quantum Theory and Its Interpretation by Werner Heisenberg

I met Niels Bohr for the first time in Gottingen in the summer of 1922, when Bohr, at the invitation of the faculty of exact sciences, held a series of lectures which we later liked to call the "Bohr Festival". Sommerfeld, ' my teacher in Munich, had taken me along to Gottingen, although I was at that time only a 20-year-old student in my fourth semester. Sommerfeld was warmly interested in his students, and he had noticed how strongly Bohr and his atomic theory interested me. The first impression of Bohr still remains quite clearly in my memory. Full of youthful excitement, but a little self-conscious and shy, his head a little to one side, the Danish physicist stood on the platform in the auditorium, the strong Gottingen summer light streaming in through the open windows. He spoke softly and with some hesitation, but behind every carefully chosen word one could discern a long chain of thought, which eventually faded somewhere in the background into a philosophical viewpoint which fascinated me. At the end of the second or third lecture Bohr spoke of a calculation, which his collaborator, Kramers from Holland, had carried out on the so-called "quadratic" Stark-effect in the hydrogen atom, and Bohr concluded with the remark that in spite of all the internal difficulties of atomic theory at that time, one should assume that Kramers' results were correct and would be verified by experiment. I knew Kramers' work rather well as I had reviewed it in Sommerfeld's seminar in Munich, and ' therefore I dared to dissent during the discussion afterwards. I did not believe that Kramers' results were perfectly correct, for the quadratic Stark-effect could be thought of as a limiting case of the scattering of light with very large wave-length. But since one knew in advance that a calculation of scattering on a hydrogen atom by the methods of classical physics must lead to a wrong result-the characteristic resonance effect would occur with the electron's orbital frequency-Kramers' calculation could hardly be expected to give a correct result. Bohr answered that one

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should here ta~e into account the reaction of the radiation on the atom but he was obviously worried by this objection. When the discussion wa~ over, Bohr came to me and suggested that we should go for a walk together on the Hainberg outside Gottingen. Of course, I was very willing. That discussion, which took us back and forth over Hainberg's wooded heights, was the first thorough discussion I can remember on the fundamental physical and philosophical problems of modem atomic theory, and it has certainly had a decisive influence on my later career. For the first time I understood that Bohr's view of his theory was much more sceptical than that of many other physicists-e. g. Sommerfeld-at that time, and that his insight into the structure of the theory was not a result of a mathematic~! analysis of the basic assumptions, but rather of an intense occupation with the actual phenomena, such that it was possible for him to sense the relationship intuitively rather than derive them formally. Thus I understood: knowledge of nature was primarily obtained in this ~ay, and onl~ as the next step can one succeed in fixing one's knowledge m mathematical form and subjecting it to complete rational analysis. Bohr was primarily a philosopher, not a physicist, but he understood that natural philosophy in our day and age carries weight only if its every detail can be subjected to the inexorable test of experiment. ~ohr invited me to come to Copenhagen for a few weeks the following spnng, and perhaps later, possibly on a scholarship, to work there for a longer period. Thus an infinitely instructive period began for me of close and friendly collaboration with Niels Bohr. Fortunately for me, this time coincided with the period when the difficulties in quantum theory became more and more embarassing, its internal contradictions seemed to become worse and worse, and to force us into a crisis which by an almost dramatic series of surprising discoveries in the course of a few years led to a solution of the fundamental problems. If I remember correctly, the visit to Copenhagen took place during the Easter holidays in I 923 -i:-). The first few days I was deeply depressed by the superiority of the young physicists from all over the world who surrounded Bohr. Most of them could speak several foreign languages, while I could not express myself reasonably in even one; they knew of the world . ~) It can be conduded from the correspondence that Heisenberg's Easter holiday visit to Copenhagen actually occurred in 1924 (Editor's note).

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outside, of many vanous people's culture and literature, they played various musical instruments extremely well, and above all, they understood much more of modern atomic physics than I. That I should be able to find a place in such a circle seemed quite hopeless. Nevertheless, I soon became friends with several of its members. I remember with particular pleasure my first discussions with Kramers from Holland, Urey from U. S. k, and Rosseland from Norway. They all seemed to know Bohr well and to respect him highly, and they were full of optimism with regard to the development of Bohr's theory. The richest yield of these weeks was, of course, the discussions with Bohr himself. As the administration of the Institute even then rested heavily on Bohr, he proposed that we should take a few days' walking tour in North Zealand, so that we could discuss together all the physical questions without fear of interruptions. Bohr was also obviously glad that in this way he could show me some of the places in Denmark which meant particularly much to him. Hamlet's castle Kronborg at the northern end of the Sound between Denmark and Sweden, the elaborate renaissance palace Frederiksborg in the lake near Hillerod, the great forest which stretches northwards to Esrum lake and the small fishing villages on the Kattegat from Gilleleje to Tisvildeleje. On the course of this tour Bohr told me much about the history of the country and its palaces, and of events from the earliest times with connections to the Icelandic Sagas, which he knew so well. In a few days I learned more about Scandinavia than I had done in all my school days. I learned too to appreciate the happy and peaceful country, which in our century had been spared major catastrophies; and in return I had to tell Bohr of the war, revolution, hunger and need that had occurred in my own country during my schooldays. Our talks embraced much more than physics and natural science, and I was glad that Bohr also enjoyed all sorts of youthful pastimes. On the beach we often tried to see who could throw a stone furthest out, or whether we could hit a floating log. Bohr told that he and Kramers had once found a mine left over from the war, and they had tried to see who of them could hit the detonator. After several vain attempts, they realized that they would never be able to enjoy the victory if they had hit it, for the explosion of the mine would have killed them both. After that they found another target. Bohr's tendency to philosophical generalization was

..,

Q.UANTUM THEORY AND ITS INTERPRETATION

O ne of tlce ;em·ly m eet ings at the Institute w ith fo rm e r :nem bers of th e lnstitu.te . Sitting in th e fi rs t row, from the left: K le in, Bo hr, H eisenbe rg, fau li , G a mow, La nda u , K 1a m e1s.

N iels Boh r talki ng w ith h is cl osest coll a bora tors, Wer_ner H eisen berg _a n d W olfgan g P a u li in the Institute's lun ch room. Bo th of them played a n important par t m d eveloping q ua n tum

p hysics .

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often stimulated by very simple games. Once, when on a lonely road I threw a stone at a distant telegraph post, and contrary to all expectations the stone hit, he said, "to aim at such a distant object and hit it, is of course impossible. But if one has the impudence to throw in that direction without aiming, and in addition to imagine something so absurd as that one might hit it, yes, then perhaps it can happen. The idea that something perhaps could happen can be stronger than practice and will." Of course, discussions of the difficulties of atomic physics took a major place in our talks. I first saw them in all their clarity as a result of Bohr's analysis, and perhaps our discussions strengthened the scepticism with which Bohr already regarded the stage which atomic physics had then reached. We were still far from a solution, and even such important discoveries as the Compton effect, which became known in that year, only sharpened the difficulties and contradictions. When we returned to Copenhagen after our walking tour, I felt that through Bohr I knew much more of the spirit of atomic theory of the future, then I had before. It was as .though the dense fog which surrounded us had somehow or other lifted a little, as though one could even then glimpse the contours of the mountains which we would later have to conquer to obtain a view over the relations between atomic phenomena. In the summer term of 1923 I worked in Munich on my doctoral thesis, the subject of which came from a completely different field of physics, namely hydrodynamics. I followed the development of atomic physics so to say at a distance. That autumn I obtained a post as Born's assistant at the University of Gottingen, and from then on took part in discussions with the people there on the problems of atomic theory. I was first able to revisit the Institute on Blegdamsvej in the winter term of I 924-25, supported by a Rockefeller scholarship obtained on Bohr's recommendation. From the beginning a close scientific collaboration developed between Bohr, his nearest collaborator, Kramers, and myself, and the discussions between two or three of us at a time soon became a fixed point on the programme, and were for me the most important part of the day-more important than seminars and lectures. The central point in our discussions at that time was dispersion theory; i. e. the theory of the scattering of light on atoms. Kramers had just published a very important paper on this subject. Kramers' considerations

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should be extended to include the so called Raman-effect (scattering accompanied by a change of colour of the light). Here it was obviously a question of guessing the correct mathematical formulae on the basis of analogies, for one could not derive them; at that time one had no basis for such calculations. It was very instructive for me to see how Bohr continued to try to advance through the physical interpretation of the formulae and thus to reach a decision, while it was much more natural for me to use a formal mathematical view which in some sense was an aesthetic judgment. Fortunately, both methods led to the same result in the long run, and I tried to convince Bohr that this had to be so if the theory was to be simple and clear. But I noticed that mathematical clarity had in itself no virtue for Bohr. He feared that the formal mathematical structure would obscure the physical core of the problem, and in any case, he was convinced that a complete physical explanation should absolutely precede the mathematical formulation. I was perhaps, already at that point, more prepared than Bohr to leave the models and take the step over to mathematical abstraction. At any rate, I found in the formulae, which were the result of my collaboration with Kramers, a mathematics which in a certain sense worked automatically independently of all physical models. This mathematical scheme had for me a magical attraction, and I was fascinated by the thought that perhaps here could be seen the first threads of an enormous net of deep-set relations. I was just as happy about the result of a discussion with Bohr and Kramers on the question of the polarization of fluorescent light. Bohr had written a draft to a short note on this question in connection with some experiments at Franck's institute, while, disregarding all pictures and models, I used my more formal viewpoint on Bohr's problem and reached quantitative results that went somewhat further than Bohr's work. I succeeded in convincing Bohr and Kramers of the correctness of my formulae, but when I again returned to Bohr's office after lunch, Bohr and Kramers had agreed that my formulae were wrong and tried to explain their viewpoint to me. This developed into a long and heated discussion, during which, as I recall, the necessity for detachment from the intuitive models was for the first time stated emphatically and declared to be the guiding principle in all future work. Bohr's way of thinking, which in history is perhaps most clearly represented by such figures as Faraday

QUANTUM THEORY AND ITS INTERPRETATION

and Gibbs, enabled him to expose the core of the problem with inimitable clarity, but he hesitated to take the step into mathematical abstraction, though he did not speak against it. We finally concluded that the formulae were correct, and I felt that we had come a good bit closer to the atomic theory of the future. Bohr took just as active a part in the work of many of the Institute people, and, as he was always extremely thorough, this activity often took so much time that it came into conflict with his own work and the administration of the Institute. Bohr thus often felt hard pressed, and then it was even more difficult for him to formulate his own thoughts in writing. When he did it he usually dictated the first draft to me, and I admired the care with which every word was weighed and altered again and again. Bohr's hospitable week-end cottage in Tisvilde also played an important role in our scientific life at that time. I often spent a few days there with his family. We walked together through the wood to the beach, enjoyed the view from the wooded, sandy heights over the clear blue Kattegat, where old-fashioned sailing ships still carried their cargoes, and we often swam quite far out to sea. On one occasion Bohr had come very far out, and when I tried to swim out to him, I discovered to my horror that a current was sweeping us further and further from land. Nor could Bohr succeed in reaching the beach although we now strained every muscle to come in towards land, and it was obvious that he was tired. I experienced some anxious minutes, as we were quite alone, and I did not know what to do. Fortunately we managed to reach a little sand bank in spite of the current, and eventually came up onto it. Bohr rested there for some time. The distance from the sandbank to the beach was still considerable, but, after resting, we could, by swimming as fast as possible, make way landwards without difficulty and finally reached the beach. Bohr and his family had also a little horse and carriage, and, as the children regarded me as a friend, I was sometimes given the particular honour of being allowed to drive around the woods with one of them. Guests came often from Copenhagen or abroad to Tisvilde, and their own thoughts or accounts of new experiments brought new life into the scientific discussions of the problems of atomic theory, which worried us all. I lectured again in Gottingen in the summer of Ig25. In addition, during a short sick leave on Heligoland in June, I wrote the first draft 7•

t''I

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of the quantum mechanics, which for me represented in a certain sense the quintessence of our discussions in Copenhagen-a mathematical formulation of Bohr's correspondence principle. I hoped that, by means of a mathematical method which for me was still new and very strange, I had found a way to the remarkable relations, which had already been glimpsed from time to time during discussions with Bohr and Kramers. After visiting Holland and England in the following summer holiday, I again came to Copenhagen for some weeks to discuss the new situation with Bohr. He was extremely interested, and at any rate no longer had any objections to completely abandon the earlier models. To what extent it would be possible to use these mathematical methods to build a complete theory was, however, still uncertain at that time. From these weeks I remember with particular pleasure a short stay in Bohr's week-end cottage, to which the three mathematicians Harald Bohr, Hardy from Cambridge and Besikovitch from Russia also had come. The discussion soon turned to the new developments in atomic theory and the three mathematicians discussed in a way which I found very stimulating, what mathematical relation could be hidden in my methods. My knowledge of mathematics was unfortunately much too limited to allow me to follow them in detail. But the discussion left me with a strong feeling that parts of an extensive net of important relations had here been revealed. Later that afternoon we played boccia; we split ourselves into two teams, and, as Harald Bohr and Hardy were passionate sportsmen, both sides struggled bitterly. Only Besikovitch, who was obviously completely inexperienced, had unfortunately little success. The game ended oddly. Niels Bohr's team were some points behind, but had the final throw, which was Besikovitch's. Realizing the hopelessness of the situation he threw the ball backwards over his shoulder into the garden. To his surprise the ball struck precisely the right spot and won the game for him to general acclamation. I remembered Bohr's remark on the road to Gilleleje without however speculating too deeply about it. On the way back to Copenhagen in the train Hardy gave me a mathematical problem "for practice". It was the theory of a Chinese game which had just been worked out exactly. I tried my very best to solve the problem, until Harald suddenly said reproachingly to Hardy, "You shouldn't use a young man's mathematical force on that sort of nonsense". At that point I had found part

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of the theory and presented it to Hardy. He only answered dryly, "Well, your new atomic theory may at least work for the hydrogen atom". During the winter term of I 925-26 I had to honour my teaching duties in Gottingen. In addition I worked with Born and Jordan on the mathematical formulation of quantum mechanics. Born and Jordan had achieved a decisive advance in the mathematical analysis of the new mechanics, and, independently of them, Dirac in Cambridge had attacked these problems and had reached practically the same results as Born and Jordan. During the whole of that winter term we were thus busy opening up the newly discovered mathematical terrain and making it accessible. In the meantime Kramers had accepted a professorship in Holland, and Bohr offered me the lectureship in theoretical physics at the University of Copenhagen which Kramers had occupied. I was therefore again able to take a full part in the scientific work in Copenhagen from Easter I926, and, just as earlier, my daily discussions with Bohr constituted the most important part of my scientific life. Atomic theory was now being worked on in many centres. The thoughts which de Broglie had advanced in I 924 on the dualism between particle and wave picture had been taken up by Schrodinger and developed into the so-called wave mechanics. At this time (Easter I 926) Schrodinger's first results were just published, but we soon heard that Schrodinger had probably succeeded in showing the mathematical equivalence of his wave mechanics and the newly developed quantum mechanics. This advance was now the focus of our discussions in Copenhagen. Bohr considered Schrodinger's investigations to be very important for two reasons. For the. first it strengthened our trust in the correctness of the mathematical formalism, which could now be called, with equal justice, quantum mechanics or wave mechanics. Secondly, the question arose as to whether one should seek a physical interpretation of the formalism along quite other lines than those hitherto considered by the Copenhagen group. Bohr realized at once that it was here we would find the solution to those fundamental problems with which he had struggled incessantly since I 9 I 3, and in the light of the newly won knowledge he concentrated all his thought on a critical test of those arguments which had led him to ideas such as stationary states and quantum transitions. From now on the interpretation of quantum mechanics was the most important subject of our discussion. I myself was not

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really willing to concede Schrodinger's theory a part in the interpretation of quantum theory. I considered it rather as an extremely useful tool for solving the mathematical problems of quantum mechanics, but not more. Bohr, on the other hand seemed inclined to place the wave-particle dualism among the basic assumptions of the theory. It was in accord with this attitude that I was mainly busy with the practical application of quantum mechanics to the spectrum of the helium at~m. Foster's beautiful measurements of the Stark-effect in the helium spectrum played an important role in this work. Foster had come to Copenhagen for a short stay from Canada to compare his results with those of the new theory. Most of the discussions took place in Mrs. Maar's week-end cottage which lay high on a hillside in Aalsgaarde near Elsinore. On the garden benches between the rosebeds, from where we had so of ten looked across the Sound to the mountains on the Swedish coast, we spread out the enlargements of Foster's spectral photographs and the measured line positions were compared with the results of the theory. The agreement was perfect, and we were happy to see how many of the most complicated and apparently unconnected details resulted more or less automatically from the formulae of quantum mechanics. Bohr too was glad to note how the Stark-effect once again, just as ten years earlier with the hydrogen atom, proved one of the most beautiful confirmations that one was on the right road to an understanding of the atom. Bohr and I also often discussed the theory of the normal helium spectrum which I had attacked making free use of both the Schrodinger and Gottingen methods. To our great satisfaction the existence of the two spectra of orthohelium and parahelium could now bederived from general principles, and the connection of this result with the "Pauli principle" paved the way to a final understanding of the periodic system of the elements. In June I travelled with the still halffinished work to Norway, stayed a week in Lillehammer by Mjosa Lake to complete the manuscript, and then hiked alone with the manuscript in my rucksack from the valley called Gudbrandsdal through the Jotunheim mountains to Sognefjord, from where I returned to Copenhagen by ship and rail. Bohr was satisfied with the paper which could then be sent to the printers. In July I visited my parents in Munich and on this occasion I heard

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Io3

a lecture given by Schrodinger for the physicists in Munich about his work on wave mechanics. It was thus that I first became acquainted with the interpretation Schrodinger wanted to give his mathematical formalism of wave mechanics, and I was very disturbed about the confusion with which I believed this would burden atomic theory. Unfortunately, nothing came of my attempt during the discussion to put things in order. My argument that one could not even understand Planck's radiation law on the basis of Schrodinger's interpretation convinced no one. vVilhelm Wien, who held the chair of experimental physics at the University of Munich answered rather sharply that one must really put an end to quantum jumps and the whole atomic mysticism, and the difficulties I had mentioned would certainly soon be solved by Schrodinger. I no longer remember whether or not I wrote to Bohr of this encounter in Munich. Be that as it may, Bohr shortly afterwards invited Schrodinger to Copenhagen and asked him not only to lecture on his wave mechanics, but also to stay in Copenhagen so long that there would be adequate time to discuss the interpretation of quantum theory. As far as I remember these discussions took place in Copenhagen around September Ig26 and in particular they left me with a very strong impression of Bohr's personality. For though Bohr was an unusually considerate and obliging person, he was able in such a discussion, which concerned epistemological problems which he considered to be of vital importance, to insist fanatically and with almost terrifying relentlessness on complete clarity in all arguments. He would not give up, even after hours of struggling, before Schrodinger had admitted that this interpretation was insufficient, and could not even explain Planck's law. Every attempt from Schrodinger's side to get round this bitter result was slowly refuted point by point in infinitely laborious discussions. It was perhaps from over-exertion that after a few days Schrodinger became ill and had to lie abed as a guest in Bohr's home. Even here it was hard to get Bohr away from Schrodinger's bed and the phrase, "But, Schrodinger, you must at least admit that ... " could be heard again and again. Once Schrodinger burst out almost desperately, "If one has to go on with these damned quantum jumps, then I'm sorry that I ever started to work on atomic theory". To which Bohr answered, "But the rest of us are so grateful that you did, for you have thus brought atomic physics

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a decisive step forward." Schrodinger finally left Copenhagen rather discouraged, while we at Bohr's Institute felt that at least Schrodinger's interpretation of quantum theory, an interpretation rather too hastily arrived at using the classical wave-theories as models, was now disposed of, but that we still lacked some important ideas before we could really reach a full understanding of quantum mechanics. From now on the discussions between Bohr and his co-workers in Copenhagen became more and more concentrated on the central problem in quantum theory: how the mathematical formalism was to be applied to each individual problem, and thus how the frequently discussed paradoxes, such as e.g. the apparent contradiction between the wave and particle models, could be cleared up. Ever new imaginary experiments were thought up, each displaying the paradoxes in a more clear-cut way than its predecessors, and we tried to guess what answer nature would probably give to each experiment. In the course of these efforts Bohr and I went off in somewhat different directions. Two years earlier Bohr, with Kramers and Slater, had published a paper in which he had tried to take the dualism between the particle- and wave-models as his starting point for the interpretation of quantum theory. The waves should be interpreted as a probability field, even though this forces one to renounce energy conservation for individual processes. In the meantime Bothe and Geiger had demonstrated the validity of energy conservation for these individual processes. Nevertheless, Bohr felt correctly that the apparent dualism was so central a phenomenon that he thought it should be the natural starting point for any interpretation. I myself put my trust in the newly developed mathematical formalism. In as much as the interpretation of certain quantities was already determined by the fundamental assumptions of quantum mechanics, I believed that a simple consequent development of these assumptions would result in the obvious general interpretation and that one should not increase one's debt to illustrative models. Thanks to this difference of views these difficult problems were illuminated and investigated from all sides, though the paradoxes were not so easy to eliminate. At that time I lived in the attic of the Institute on Blegdamsvej, and Bohr often came up to my room late at night to talk with me of the difficulties in quantum theory which tortured both of us. On the one

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I

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hand, we felt that the solution was just around the corner, in so far as we possessed a mathematical description which was obviously f;ee of contradictions, while on the other hand we did not know how this mathematics should be used to describe even the most simple experimental situations such as e. g. the track of an electron in a cloud chamber. In quantum mechanics one had started out on the assumption that such electron tracks just do not exist, and, from the viewpoint of wave mechanics, it was difficult to understand how a localized wave phenomenon, something like a wave packet, did not disperse again after a short time. At this time Dirac and Jordan developed the transformation theory to which Born and Jordan in earlier investigations had already laid the foundation, and the completion of this mathematical formalism again confirmed us in our belief that there was no more to change in the formal structure of quantum mechanics, and that the remaining problem was to express the connection between the mathematics and experiment in a way free of contradictions. But how this was to be done remained unclear. Our evening discussions quite often lasted till after midnight, and we occasionally parted somewhat discontented, for the difference in the directions in which we sought the solution seemed often to make the problem more difficult. Still, deeply disquieted after one of these discussions I went for a walk in the Frelledpark, which lies behind the Institute, to breathe the fresh air and calm down before going to bed. On this walk under the stars, the obvious idea occurred to me that one should postulate that nature allowed only experimental situations to occur which could be described within the framework of the formalism of quantum mechanics. This would apparently imply, as one could see from the mathematical formalism, that one could not simultaneously know the position and velocity of a particle. There was no immediate possibility of discussing this idea in detail with Bohr, because just at this time (end of February, 1927) he had left for a skiing holiday in Norway. Bohr was probably also glad to be able to devote himself to a few weeks' completely undisturbed thinking about the interpretation of quantum theory. Left alone in Copenhagen I too was able to give my thoughts freer play, and I decided to make the above uncertainty the central point in the interpretation. Remembering a discussion I had had long before with a

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fellow student in Gottingen, I got the idea of investigating the possibility of determining the position of a particle with the aid of a gamma-ray microscope, and in this way soon arrived at an interpretation which I believed to be coherent and free of contradictions. I then wrote a long letter to Pauli, more or less the draft of a paper, and Pauli's answer was decidedly positive and encouraging. When Bohr returned from Norway, I was already able to present him with the first version of a paper along with the letter from Pauli. At first Bohr was rather dissatisfied. He pointed out to me that certain statements in this first version were still incorrectly founded, and as he always insisted on relentless clarity in every detail, these points offended him deeply. Further, he had probably already grown familiar, while he was in Norway, with the concept of complementarity which would make it possible to take the dualism between the wave and particle picture as a suitable starting point for an interpretation. This concept of complementarity fitted well the fundamental philosophical attitude which he had always had, and in which the limitations of our means of expressing ourselves entered as a central philosophical problem. He therefore took objection to the fact that I had not started from the dualism between particles and waves. After several weeks of discussion, which were not devoid of stress, we soon concluded, not least thanks to Oskar Klein's participation, that we really meant the same, and that the uncertainty relations were just a special case of the more general complementarity principle. Thus, I sent my improved paper to the printer and Bohr prepared a detailed publication on complementarity. How closely the idea of complementarity was in accord with Bohr's older philosophical ideas became apparent through an episode, which, if I remember correctly, took place on a sailing trip from Copenhagen to Svendborg on the island Fyn. At that time Bohr and a colleague and friend owned a sailing boat, the captain of which was the brilliant and extremely charming chemist Bjerrum. The distinguished surgeon Chievitz kept spirits high even in stormy weather, and the other friends contributed each in his way to this happy and untroubled existence. Bohr was full of the new interpretation of quantum theory, and as the boat took us full sail southwards in sunshine, there was plenty of time to tell of this scientific event and to reflect philosophically on the nature of atomic

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theory. Bohr began by talking of the difficulties of language, of the limitations of all our means of expressing ourselves, which one had to take into account from the very beginning if one wants to practice science, and he explained how satisfying it was that this limitation had already been expressed in the foundation of atomic theory in a mathematically lucid way. Finally, one of the friends remarked drily, "But, Niels, this is not really new, you said exactly the same ten years ago". The Solvay Conference in Brussels in the autumn of 1927 closed this marvellous period in the history of atomic theory. Planck, Einstein, Lorentz, Bohr, de Broglie, Born and Schrodinger, and from the younger generation Kramers, Pauli, and Dirac, were gathered here and the discussions were soon focussed to a duel between Einstein and Bohr on the question as to what extent atomic theory in its present form could be considered to be the final solution of the difficulties which had been discussed for several decades. We generally met already at breakfast in the hotel, and Einstein began to describe an ideal experiment in which he thought the inner contradictions of the Copenhagen interpretation were particularly clearly visible. Einstein, Bohr and I walked together from the hotel to the congress building, and I listened to the lively discussion between these two people whose philosophical attitudes were so different, and from time to time I added a remark on the structure of the mathematical formalism. During the meeting and particularly in the pauses we younger people, mostly Pauli and I, tried to analyse Einstein's experiment, and at lunch time the discussions continued between Bohr and the others from Copenhagen. Bohr had usually finished the complete analysis of the ideal experiment late in the afternoon and showed it to Einstein at the supper table. Einstein had no good objection to this analysis, but in his heart he was not convinced. Bohr's friend Ehrenfest, who was also a close friend of Einstein, said to him, "I'm ashamed of you, Einstein. You put yourself here just in the same position as your opponents in their futile attempts to refute your relativity theory". These discussions continued even at the next Solvay meeting in 1930, and it was probably on this occasion that Einstein at breakfast proposed the famous experiment (discussed in Bohr's article on the occasion of Einstein's 7oth birthday ). in which the colour of a light quantum is to be determined by weighing the source before and after the quantum's

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emission. As this problem involved gravity, one had to include the theory of gravity, in other words, general relativity theory in the analysis .. It was a particular triumph for Bohr that he was able to show that evenmg, by using just Einstein's own formulae fr~m general ~elativity, that ~ven. i~ this experiment the uncertainty relations are vahd, and that Emstem s objections were unfounded. With this the Copenhagen interpretation of quantum theory seemed from now on to stand on solid ground. Late in the autumn of 1927 I had to leave Copenhagen as I had accepted a professorship at the University of Leipzig. I returned to Copenhagen, however, almost every year for a few weeks to talk over with Bohr the problems which occupied us both; but the period of close collaboration, that had been full to the brim with exciting scientific advance, and where I learned so infinitely much from Bohr, was unfortunately over.

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Recollections from the Years 1929-1931 I

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by Hendrik B. G. Casimir

In the spring of 1929, I went with Ehrenfest to a meeting at Bohr's Institute. For me, then a young student, it was a great experience. I had never before attended such a conference and I had not travelled much. I remember the journey in great detail: the train through Germany and Ehrenf est's witty comments on many things, the little hotel at Hamburg where we spent the night, the good old Gedser-W arnemiinde ferry-it had been a severe winter and ice was still drifting around-the first impressions of a new town and a new language. But among all these reminiscences one remark of Ehrenfest's stands out. Somewhere between Hamburg and \Varnemiinde he said: "Jetzt wirst du Niels Bohr kennen lernen und im Leben eines jungen Physikers ist das