Unsolved Problems in Special and General Relativity 9781599732206, 1599732203

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Unsolved Problems in Special and General

Relativity Chief Editor: Florentin Smarandache Vice Chief Editors:

Fu Yuhua & Zhao Fengjuan Education Publishing - ISBN: 9781599732206

Florentin Smarandache editor-in chief Fu Yuhua Zhao Fengjuan associate editors

Unsolved Problems in Special and General Relativity 21 collected papers

Educational Publishing & Journal of Matter Regularity (Beijing)

2013

i

Unsolved Problems in Special and General Relativity 21 collected papers

Florentin Smarandache editor-in-chief Fu Yuhua Zhao Fengjuan associate editors

2013

ii

This book can be ordered on paper or electronic formats from: Education Publishing 1313 Chesapeake Avenue Columbus, Ohio 43212 USA Tel. (614) 485-0721 E-mail: [email protected]

Copyright 2013 by EducationPublishing & Journal of Matter Regularity (Beijing), Editors and the Authors for their

papers Front and back covers by the Editor-in-Chief & V. Christianto Peer-reviewers: Eng. Victor Christianto, Indonesia, URL: http://www.sciprint.org, email: [email protected]. Prof. Marinela Preoteasa, Str. Mânastirii, Nr 7, Bloc 1C, Scara A, Et. 3, Ap. 13, Slatina, Jud. Olt, Cod postal: 230038, Romania. Prof. Valeri Kroumov, Dept. of Electrical and Electronic Engineering, Okayama University of Science, 1-1 Ridai-cho, Kita-ku, Okayama 700-0005, Japan.

ISBN: 9781599732206 Printed in the United States of America

iii

Preface This book includes 21 papers written by 23 authors and co-authors. All papers included herein are produced by scholars from People’s Republic of China, except two papers written by Prof. L. Sapogin, V. A. Dzhanibekov, Yu. A. Ryabov from Russia, and by Prof. Florentin Smarandache from USA. The editors hope that all these papers will contribute to the advance of scholarly research on several aspects of Special and General Relativity. This book is suitable for students and scholars interested in studies on physics. The first paper is written by Hua Di. He writes that Einstein’s general theory of relativity cannot explain the perihelion motion of Mercury. Einstein’s explanation, based on wrong integral calculus and arbitrary approximations, is a complete failure. The following paper is written by Li Zifeng. His paper reviews basic hypotheses and viewpoints of space-time relationship in Special Relativity; analyzes derivation processes and the mistakes in the Lorentz transformation and Einstein’s original paper. The transformation between two coordinate systems moving uniformly relatively to another is established. It is shown that Special Relativity based upon the Lorentz transformation is not correct, and that the relative speed between two objects can be faster than the speed of light. The next paper is written by Li Wen-Xiu. His paper presents problems with the special theory of relativity (STR), including: (1) The principle of relativity as interpreted by Einstein conflicts with the uniqueness of the universe. (2) The light principle conflicts with the notion that natural phenomena depend only upon mutual interaction and the involved relative motion. The principle contains a tacit assumption that leads to self-contradiction. The next paper by Shi Yong-Cheng says that Einstein’s book “The Meaning of Relativity” contains of a supper mistake which leads to the famous twin “paradox”. The following paper by Xu Jianmin proposes the assumptions of radiation and redshift, establishes the quantum gravitational field equations and motion equations, and presents that particles move along the path with the minimum entropy production. The paper also applies the equivalence principle of acceleration and the gravitational field into the electromagnetic field, which makes the electromagnetic field equation to have the same form with gravitational field equation. The next paper is written by Dong Jingfeng. By the analysis of twin paradox, it is pointed out that the constriction of space-time is the only effect of measurement and all paradoxes do not exist actually. The essence of special relativity is a number method for ways to provide math and physical idea. The following paper is written by Duan Zhongxiao. Through comparing the two Lorentz transformations located at different regions, the author finds that for two inertial systems running the relative uniform speed translational motion, if two clocks are synchronous in one system, they are also synchronous looked from another system; this means that the relative character of simultaneity is not the ultimate source of temporal and spatial transformation. Thus we know that it is wrong to introduce the one-way spreading light signals along with all directions in space into transformation. Fu Yuhua writes the next paper. He says that special theory of relativity and general theory of relativity have three basic shortcomings. First, the special and general theory of relativity respectively have two basic principles, altogether have four basic principles in the iv

interior of relativity, these obviously do not conform to the truth uniqueness. Second, for the two basic principles of special theory of relativity and the two basic principles of general theory of relativity, no one is generally correct. Third, establishes the physical theory from the mathematics principle instead of the physical principle. Based on these, the applicable scopes of special and general theory of relativity are presented. Guo Kaizhe and Guo Chongwu write the following paper. They write that there are magnetic field forces between positive charge and negative charge in an electric dipole which is moving in a laboratory reference frame. Whereas, examining the electric dipole in a reference frame which is at rest relative to the electric dipole, we find no magnetic field force exists between the two charges. The next paper is written by Guo Ying-Huan and Guo Zhen-Hua. They write that by carefully comparing the results given by the general theory of relativity and the actual astronomical observation, the contradiction between them is found to be difficult to overcome. Furthermore, there is no sign so far of the existence of “the waves” predicted by the general theory of relativity. Hu Chang-Wei writes the next paper. According to him, in the absolute space-time theory, the ether is a compressible superfluid, a change in the ether density causes a change in the actual space-time standard, and thus, the phenomena occur. The relativity made up the shortcoming of absolute space-time theory in quantity, while the physical basis of relativity can be described and its limitations can be showed on the basis of absolute space-time theory. Jiang Chun-Xuan writes the following paper. Using two methods he deduces the new gravitational formula. Gravity is the tachyonic centripetal force. 2 In the next paper, he also found a new gravitational formula: F = − mc , established R 4 the expansion theory of the universe, and obtained the expansion acceleration: g e = u 2 . C R

Liu Taixiang writes the following paper. On the basis of the system relativity, the author firstly proves the absoluteness of movement, and then deduces the conclusion that time derives from movement, then subsequently obtains such properties of time as one dimension, irreversibility, infiniteness, non-uniformity and relativity, etc. by illustrating the relationship between time and space and the concept of universe state, and ultimately deduces a steady cosmological model and a prospect of the total universe. Tu Runsheng writes the next paper. He writes that in a limited number of experiments that support Theory of Relativity, there also exist some points that are not supportive of the theory. Therefore, Theory of Relativity does not solve the problem of experimental verification. The following paper is written by Wu Fengming. According to the “paradox of singularity theorem” proof of concept of time, the mathematical logic and the prerequisite conditions, based on successive analytical, logical argumentation about time singularity theorem proving the beginning and the end of the conclusions cannot be established. Yang Shijia writes that he has studied Einstein's original “on the Electrodynamics of Moving Body” for many years, found its own 30 unsolved problems at least, Einstein's theory of relativity is a mistake from beginning to end.

v

Chao Shenglin writes in the next paper that if ones think of the possibility of the existence of the superluminal-speeds (the speeds faster than that of light) and re-describe the special theory of relativity following Einstein's way, it could be supposed that the physical spacetime is a Finsler space-time. In the following paper, Fu Yuhua writes that although the explanation of general relativity for the advance of planetary perihelion is reasonably consistent with the observed data, because its orbit is not closed, whether or not it is consistent with the law of conservation of energy has not been verified. For this reason a new explanation is presented: The advance of planetary perihelion is the combined result of two motions. The first elliptical motion creates the perihelion, and the second vortex motion creates the advance of perihelion. Sapogin, Dzhanibekov, and Ryabov discuss the problems of new unitary quantum view of the world in its applications to the different aspects of the reality. In the last paper, Florentin Smarandache revisits several paradoxes, inconsistencies, contradictions, and anomalies in the Special and General Theories of Relativity. Also, he reproposes new types of Relativities and two physical experiments. Florentin Smarandache

vi

Unsolved Problems in Special and General Relativity Contents Preface …………………………………………………………………………..…………..iv 1 Einstein’s Explanation of Perihelion Motion of Mercury Hua Di ………………………………………………………………………………...……...3 2Special Relativity Arising from a Misunderstanding of Experimental Results on the Constant Speed of Light Li Zifeng …………………………………………………………………………...…………8 3 Problems with the Special theory of Relativity Li Wen-Xiu …………………………………………………………………………………..21 4 Criticism to Einstein’s Physics Thinking in His Book “The Meaning of Relativity” Shi Yong-Cheng ……………………………………………………………………………...33 5 Using Space-time Quantization to Solve the Problems Unsolved by General Relativity Xu Jianmin ……………………………………………………………….……..……………41 6 New Exploration for the Enigma of Paradox in Special Relativity Dong Jingfeng ………………………………………………………………………………..59 7 Unsolved Problems in Special Relativity and Methods to Solve Them Duan Zhongxiao ……………………………………………………………………………...66 8 Shortcomings and Applicable Scopes of Special and General Theory of Relativity Fu Yuhua ……………………………………………………………………………………..81 9 Reconsideration on Validity of the Principle of Relativity in Relativistic Electromagnetism Guo Kaizhe, Guo Chongwu ……………………………………………………………...…104 10 Is The General Theory of Relativity a Scientific Theory? Guo Ying-Huan, Guo Zhen-Hua …………………………………………………………....108 11 The Theory of Relativity and Compressibility Ether Hu Chang-Wei ……………………………………………………………………………....113

mc 2 12 New Gravitational Formula: F = − R Jiang Chun-Xuan …………………………………………………………...……………...125 13 The Expansion Theory of the Universe Without Dark Energy Jiang Chun-Xuan …………………………………………………………………..............131 14 An Unsettled Issue of Time in Relativity Theory and New Comprehension on Time Liu Taixiang ……………………………………………………………..……………...…141 15 Theory of Relativity Does Not Solve the Problem of Experimental Verification 1

Tu Runsheng ……………………………………….......…………………………………...154 16 Analysis of “Singular Point Theorems”—Further Understanding of Relativistic Time View Wu Fengming ……………………………………………………………………………….173 17 The Own Unresolved Issues of Einstein's Original Work: On the Electrodynamics of Moving Body Yang Shijia …………………………………………………………………………………181 18 The Theory of Relativity and Cosmology on the Finsler Space-time Cao Shenglin ……………………………………………………………………………….191 19 New Explanation of Advance of Planetary Perihelion and Solar System’s Vortex Motion Fu Yuhua …………………………………………………………………………………..249 20 Relativistic Problems in the Unitary View Quantum View of The World Leo G. Sapogin, V.A. Dzhanibekov, and Yu. A. Ryabov …………………………..……..253 21 Questioning the Special and General Relativity Florentin Smarandache ……………………………………………………..……………..288

2

Einstein’s Explanation of Perihelion Motion of Mercury Hua Di Academician, Russian Academy of Cosmonautics Research Fellow (ret.), Stanford University [email protected] Abstract: Einstein’s general theory of relativity cannot explain the perihelion motion of Mercury. His explanation, based on wrong integral calculus and arbitrary approximations, is a complete failure. Keywords: Einstein, general theory of relativity, perihelion motion of Mercury Einstein applied his general theory of relativity to explain three astronomical phenomena: The sunlight’s red shift (1911), the perihelion motion of Mercury (1915) and the angular deflection of light by the sun’s gravitation (1916). Among the three, the explanation of perihelion motion of Mercury was his dearest. In a letter to a friend he wrote: “Last month was one of the most exciting, intense and, of course, harvest periods in my life. …… An equation yields correct data of the perihelion motion of Mercury and you can imagine how glad I was! For a few days I was beside myself with excitement, unable to do anything, immersed in an enchanted dream-like stupor.” 1 Einstein’s Explanation from His General Theory of Relativity In his 1915 paper “Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity” [1] Einstein provided the following formula for calculating perihelion motion of planets:

a2 ε = 24π 2 2 , T c 1 − e2 3

(

)

(1)

where ε is the perihelion advance in the sense of orbital motion after a complete orbit, T the orbital period, a the orbit’s semi major axis, e the orbit’s eccentricity and c the velocity of light. For Mercury: T ≈ 87.969 [earth day]

≈ 7.6 × 10 6 [s], a ≈ 5.791 × 1010 [m] and

e ≈ 0.205631 . With these data, his formula (1) yields Mercury’s perihelion motion

ε ≈ 5.013 × 10 −7 [radian] per mercury-year. For every 100 earth-year (365318 earth-day) 3

Mercury makes

365318 = 415.28 orbital rounds. Therefore, its perihelion motion per 100 87.969

earth-years is:

5.013 × 10 −7 × 415.28 ≈ 2.08 × 10 −4 [rad] ≈ 43 ’’ Matching the astronomical observation. Einstein declared his success: “I find an important confirmation of this most fundamental theory of relativity, showing that it explains qualitatively and quantitatively the secular rotation of the orbit of Mercury.” According to Einstein’s 1915 paper, his formula (1) comes from an equation:

3





φ = π 1 + α (α 1 + α 2 ) .  4 

(2)

φ is the angle described by the radius-vector between perihelion and aphelion. Therefore, the perihelion advance is ε = 2(φ − π ) . α 1 = the

orbit’s

maximum

and

α=

2kW ≈ 2.9535 × 10 3 [m] 2 c

1 1 and α 2 = signify the reciprocal values of r1 r2

minimum is

a

distances

constant

and

r1

with

the

r2

from

gravitational

the

sun.

constant

k = 6.673 × 10 −11 [m 3 kg −1 s −2 ] and the sun’s gravitational mass W ≈ 1.9891 × 10 30 [kg]. Mercury’s

r1 ≈ 6.9818 × 1010 [m]

and

r2 ≈ 4.6002 × 1010 [m].

So,

its

α 1 ≈ 1.432309 × 10 −11 [ m −1 ] and α 2 ≈ 2.173847 × 10 −11 [ m −1 ]. Placing these data directly into Einstein’s equation (2), without needlessly resorting to his formula (1) which will be questioned in §3, it can be obtained:

3 2

ε = 2(φ − π ) = πα (α 1 + α 2 ) ≈ 5.019 × 10 −7 [rad] per mercury-year or

5.019 × 10 −7 × 415.28 ≈ 2.084 × 10 −4 [rad] ≈ 43 ’’ per 100 earth-years.

2 Einstein’s Fatal Error in Integral Calculus Einstein obtained his equation (2) from an integration deduced approximately from his general theory of relativity: α2

φ = [1 + α (α 1 + α 2 )] ∫

α1

dx − ( x − α 1 )( x − α 2 )(1 − αx ) 4

,

(3)

or approximately, upon expansion of (1 − αx )

α2

φ = [1 + α (α 1 + α 2 )] ∫

α1

−1 2

 α  1 + x dx 2   . − (x − α 1 )( x − α 2 )

,

(4)

 

“The integration” Einstein writes, “yields φ = π 1 +

3  α (α 1 + α 2 ) .” This is a fatal 4 

error! Actually, a correct integration should be as follows:

∫ =∫

 α  1 + x dx α dx 2   =∫ + − ( x − α 1 )( x − α 2 ) − ( x − α 1 )( x − α 2 ) 2 dx

− (x − α 1 )( x − α 2 )

+

α

− − ( x − α 1 )( x − α 2 ) + 2 

∫

xdx − ( x − α 1 )( x − α 2 )

α1 + α 2 2

∫

  − ( x − α 1 )( x − α 2 )  dx

dx α  α  − − ( x − α 1 )( x − α 2 ) = 1 + (α 1 + α 2 ) ∫  4  − ( x − α 1 )( x − α 2 ) 2

2 x − (α 1 + α 2 ) α   α − − ( x − α 1 )( x − α 2 ) . = 1 + (α 1 + α 2 ) × arcsin 2 α 2 − α1   4 α2

Therefore,

∫

α1

 α  1 + x dx α − α1 α −α2  2   α   = 1 + (α 1 + α 2 ) arcsin 2 − arcsin 1 α 2 − α1 α 2 − α 1  − ( x − α 1 )( x − α 2 )  4 

 α  = 1 + (α 1 + α 2 )[arcsin1 − arcsin(− 1)]  4   α   α  = 1 + (α 1 + α 2 ) ⋅ 2 arcsin1 = π 1 + (α 1 + α 2 ) ,  4   4   

not Einstein’s π 1 +

3  α (α 1 + α 2 ) ! 4 

Finally, the correct integration yields: α2

φ = [1 + α (α 1 + α 2 )] ∫

α1

 α  1 + x dx 2   α   = [1 + α (α 1 + α 2 )]π 1 + (α 1 + α 2 ) − (x − α 1 )( x − α 2 )  4 

1  5 2 = π 1 + α (α 1 + α 2 ) + α 2 (α 1 + α 2 )  . 4  4  5

ε = 2(φ − π ) =

and

π 2

α (α 1 + α 2 )[5 + α (α 1 + α 2 )] ≈ 8.3651 × 10 −7 [rad] per mercury-

year

8.3651 × 10 −7 × 415 .28 ≈ 3.4738 × 10 −4 [rad] ≈ 71.5 ’’ per 100 earth-years.

or

It is far different from 43 ’’ ofthe astronomical observation. Einstein’s

explanation

contains

one

[1 + α (α1 + α 2 )] ≈ 1

more

operational

since

error.

Although Mercury’s

α (α 1 + α 2 ) = 2.9535 × 10 3 (1.432309 × 10 −11 + 2.173847 × 10 −11 ) ≈ 1.0651 × 10 −7 0 ，direction of g is opposite to that of

（3）is

ω = ω 0 exp( − gt / c )

（4）

Since the speed of gravitational field is light velocity, the formula above could be written as:

ω = ω0 exp( − gr / c 2 )

（5）

Meanwhile, the following formula could also be figured out based on c = λν .

k = k0 exp(−gr / c 2 ) Take the logarithm on both sides of equation (5),

g = − ln(

（6）

ω c2 ) ω0 r

This is the equation of static gravitational field. The equation shows that, all the fields between same high frequency and same low frequency are equal, and they have nothing to do with the matters of field source. Under the circumstance of weak gravitational field, the frequency change could be taken as continuous process, and equation

F =−

h dω c dt

（7）

（1） could be written as:

Given V is force potential.

F = −∇V (r ) r1 h V (r ) = − ∫ f .dr + V0 r0 c t1

= −h ∫ f .dt + V0 t0

（8）

= −h ∫ dω + V0 ω1

ω0

V (r ) − V0 = −h (ω1 − ω 0 ) The formula above indicates that the force field generated by quantum redshift is conservative force field. Frequency difference constitutes potential difference. When considering k → ∇ ,

f = f0 exp(Gm / c 2 r) = ∇ 2ϕ Poisson's equation is substituted into above equation.

f0 exp(Gm / c 2 r) = 4π Gρ

（9）

4Comparison of quantum gravity space-time and general relativity space-time If

ω 0 is taken as the quantum frequency measured by the clock moving along with the

，

observer and

λ0 is

，

the space measured by a ruler moving along with observer then the 44

frequency and wavelength of next neighbouring quantum are ω and λ calculated by the following two equations:

，and

they are

（ ） λ = λ exp(GM / c r) （10）

ω = ω 0 exp(−GM / c 2 r) 5a 2

0

Here, the space-time is quantized. In a strong gravitational field, it is neither possible to continuously read values in space-time coordinates, nor to get zero, since the frequency and wavelength could not be zero. In the equations, exp(GM / c 2 r) is the quantum space-time metric, which is used to measure the space-time. In quantum gravity, coordinate no longer has direct metric meaning. Space-time coordinate is determined by metric, and meanwhile the space-time also affects metric. Therefore, in a strong gravitational field, there is no globally unified space-time. Under the condition of

，

，

GM / c 2 r 1 or β1 1. c

(3.6)

and

t=

t '+ βc x'

β 2 −1

,x =

x'+vt '

β 2 −1

In the same way, the transformation (2.4) could also be resolved into two parts at the light cone:

t=

β1t '+ 1c x'

β 12 − 1

,x =

β 1 x'+ ct ' β 12 − 1

, y = y' , z = z '; β1 =

v1 > 1. c

(3.7)

, y = y' , z = z '; β1 =

v1 < 1. c

(3.8)

and

t=

β1t '+ 1c x' 1 − β 12

,x =

β 1 x'+ ct ' 1 − β 12

It is very interesting that transformations (3.5) and (3.7) have two major features: Firstly, they keep the same sign between the ds2 and the ds’2;i.e.:

dsv2 = dsv′ 2 .

(3.9)

Secondly, their inverse transformations are of the form

t' =

t − βc x 1− β

2

, x' =

and 207

x − vt 1− β 2

, y' = y, z ' = z; β < 1.

(3.10)

t' =

β 1t − 1c x 2

β1 − 1

, x' =

β 1 x − ct

, y ' = y , z ' = z ; β 1 > 1.

β12 − 1

(3.11)

These transformations keep the same sign between x,t and x’,t’. So, they will be called the time-like transformations and (3.5) will be called the time-like representation of the time-like transformation (TRTT), and (3-7) the space-like representation of time-like transformation (SRTT). In the same manner, transformations (3.6) and (3.8) have two common major features, too. Firstly, they will change the sign between ds2 and ds’2,i.e.:

− dsv2 = dsv′ 2 .

(3.12)

Secondly, their inverse transformations are of the form

− t' =

t − βc x 2

,− x ' =

x − vt

,− x ' =

β 1 x − ct

β =1

, y ' = y, z ' = z; β > 1.

(3.13)

, y ' = y , z ' = z ; β 1 < 1.

(3.14)

β 2 −1

and

− t' =

β 1t − 1c x 1− β

2 1

1 − β 12

These transformations will change the sign between x,t and x’,t’. They will be called the space-like transformations and (3.6) will be called the space-like representation of space-like transformation (SRST); and (3.8) the time-like representation of space-like transformation (TRST). Now, we have had four types of form of the space-time transformation under ds2: Type I. TRTT, (3.5), it is just the Lorentz transformation; Type II. SRTT, (3.7), it is the space-like representation of the Lorentz transformation with the dual velocity v1=c2/v, it is larger than the velocity of light; Type III. SRST, (3.6), it is just the superluminal Lorentz transformation (see Recami, 1986 and Sen Gupta, 1973); Type IV. TRST, (3.8), it is the time-like representation of the superluminal Lorentz transformation with the dual velocity v1=c2/v, but it is less than the velocity of light.

3.3.The Catastrophe of Physical Quantities on the Finsler Metric ds4 Firstly, we shall consider the question of the catastrophe of the measurement of length and time increment. According to the nature of catastrophe of space-time, the expression for

～

the length of a moving scale ∆x’ measured by a fixed observer (2.6) (2.9) could be resolved into two parts:

208

∆x' = ∆x 1 − β 2 , β < 1.

(3.15)

− ∆x' = ∆x β 2 − 1, β > 1.

(3.16)

− ∆x' = c∆t 1 − β12 , β 1 < 1.

(3.17)

∆x' = c∆t β 12 − 1, β 1 > 1.

(3.18)

The expression for the time increment ∆τ of the clock at rest with respect to the moving system could be resolved into two parts at the light cone:

∆τ = ∆t 1 − β 2 , β < 1;

(3.19)

− ∆τ = ∆t β 2 − 1, β > 1.

(3.20)

− ∆τ =

∆x 1 − β 12 , β 1 < 1; c

(3.21)

∆τ =

∆x β 12 − 1, β1 > 1; c

(3.22)

It is very interesting that the ∆x’ (or ∆x) will exchange with ∆t (or ∆τ) in the expressions (3.17),(3.18),(3.21), and (3.22). If we let (see the formula (3.20))

f ( E , P ) = E 4 + c 4 P 4 − 2c 2 E 2 P 2

(3.23)

as the catastrophe theory, we could find a catastrophe set (3.24)

E = ±P

and we could have four types of the representation for the momentum, the energy, and the mass of a moving particle with the rest mass m: Type I. TRTT

p T (v ) =

mv 1− β 2

, E T (v ) =

mc 2 1− β 2

, M T (v ) =

m 1− β 2

; β < 1.

(3.25)

Type II. SRTT

p S {v1} =

mv1

β12 − 1

, E S (v1 ) =

mc 2

β12 − 1 209

, M S (v1 ) =

m

β 12 − 1

; β 1 > 1. (3.26)

Type III. SRST

p S {v} =

− mv

β 2 −1

− mc 2

, E S (v ) =

β 2 −1

−m

, M S (v ) =

β 2 −1

; β > 1.

(3.27)

Type IV. TRST

p S {v1} =

− mv1 1 − β 12

, E S (v1 ) =

− mc 2

−m

, M S (v1 ) =

1 − β 12

1 − β 12

; β 1 < 1. (3.28)

The transformations between type I (or type II) and type III (or type IV) have the forms

p T (v ) =

mv 1− β 2

mc 2

E T (v ) = M T (v ) =

=

2

1− β

(3.29)

= cp T (v1 ).

(3.30)

=

2

= β 1 M T (v1 ).

(3.31)

=

β 12 − 1 mv1c 2 1

β −1 β 1m

m 1− β

1 T E (v1 ). c

mc =

2 1

β −1

and

− mv

p S (v ) =

β −1 − mc 2

E (v ) = S

M S (v ) =

=

2

2

β −1 −m 2

β −1

=

=

1 S E (v1 ). c

(3.32)

= cp S (v1 ).

(3.33)

= β 1 M S (v1 ).

(3.34)

M (c) = m.

(3.35)

− mc

1− β

=

2 1

− mv1c 1− β

2 1

− β1m 1− β

2 1

With these forms above, we could get that when β=β1=1,

cP(c) = E (c) = mc 2

and

Note that although all through Einstein's relativistic physics there occur indications that mass and energy are equivalent according to the formula

E = mc 2 . But it is only an Einstein's hypothesis. It is very interesting that from type I and type IV we could get

E 2 − c 2 p 2 = m2c 4 ,

v c)

(3.36)

v>c

and

v1 > c

(i.e., v < c)

(3.37)

and from type II and type III

E 2 − c 2 p 2 = −m 2 c 4 ,

Here, we have forgotten the indices for the types in Equations (3.35) to (3.37). If we let the 210

H2(E,P)=E2

－c P , then we could get 2 2

f ( H , mc) = H 4 − (mc 2 ) 4 . It is a type II of the double-cusp catastrophe, we could also get (3.36) and (3.37) from it.

3.4.The Catastrophe a Charged Particle in an Electromagnetic Field on The Finsler Space-timeds4 The Hamilton-Jacobi equation for a particle in an electromagnetic field in the Finsler space-time, formula (2.25) is a type II of the double-cusp catastrophe. We could get that

e ∂S c 2 (∇S − A) 2 − ( + cΦ) 2 + m 2 c 4 = 0 , ∂t c

(3.39)

for type I and type IV of the space-time transformation.

e ∂S c 2 (∇S − A) 2 − ( + cΦ) 2 − m 2 c 4 = 0 , c ∂t

(3.40)

for type II and type III of the space-time transformation. Now, we consider the catastrophe change of the equation of a charge in an electromagnetic field. By equation (2.26), we could get

d mv e = eEe + v × H e , 2 dt 1 − β c

v c.

(3.42)

and

−

mv

e = eEe + v × H e , c β 2 −1

If we integrate (3.41) and (3.42), then

mc 2 1− β 2

mc 2 −

1 − β 02

= eU ,

v0 < c

(3.43)

= eU ,

v0 > c .

(3.44)

and

mc 2 2 0

β −1

mc 2 −

2

β −1

So, the velocity v has

  eU v = c 1−  + 1 / 1 − β 02    mc and 211

−2

< c,

iff

v0 < c,

(3.45)

  eU − 1 / β 02 − 1  v = c 1+    mc

−2

> c,

v0 > c .

iff

(3.46)

The expressions (3.45) and (3.46) mean that if v0c. The velocity of light will be a bilateral limit: I.e., it is both of the maximum for the subluminal-speeds and the minimum for the superluminal-speeds. If we let

f ( H e , Ee ) = H e4 + Ee4 − 2H e2 Ee2 ,

(3.47)

we will get that the catastrophe set is (3.48)

H e = ± Ee

and we could obtain the space-time transformation equations for the electromagnetic field components: (by (2.31) and (2.32)) Type I. TRTT

   H x′ = H x ,  H y + βE z  ,  H ′y = 1− β 2    H ′ = H z − βE y ,  z 1− β 2 

E ′x = E x , E ′y = E ′z =

E y − βH z 1− β 2 E z + βH y 1− β 2

,

(3.49)

.

Type II. SRTT

   H x′ = H x ,  β1 H y + E z  ,  H ′y = β 12 − 1   H ′ = β1 H z − E y ,  z β 12 − 1  Type III. SRST

212

E ′x = E x , E ′y = E ′z =

β1 E y − H z β 12 − 1 β1 E z + H y β 12 − 1

, .

(3.50)

   H x′ = H x ,  H y + βE z  , − H ′y = β 2 −1    − H ′ = H z − βE y , z  β 2 −1 

E ′x = E x , − E ′y = − E ′z =

E y − βH z

β 2 −1 E z + βH y β 2 −1

,

(3.51)

.

Type IV. TRST

   H x′ = H x ,  β1 H y + E z  , − H ′y = 2 β − 1  1  − H ′ = β 1 H z − E y , z  1 − β 12 

E x′ = E x , − E ′y = − E z′ =

β1 E y − H z 1 − β 12

β1 E z + H y 1 − β 12

,

(3.52)

.

3.5 The Interchange of the Forces Between the Attraction and the Rejection Usually, because of the equivalence of energy and mass in the relativity theory, ones believe that an object has due to its motion will add to its mass. In other words, it will make it harder to increase its speed. This effect is only really significant for objects moving at speeds close to the speed of light. So, only light, or other waves that have no intrinsic mass, can move at the speed of light. The mass is the measure of the gravitational and inertial properties of matter. Once thought to be conceivably different, gravitational mass and inertial mass have recently been shown to be the same to one part in 1011. Inertial mass is defined through Newton's second law, F=ma, in which m is mass of body. F is the force action upon it, and a is the acceleration of the body induced by the force. If two bodies are acted upon by the same force (as in the idealized case of connection with a massless spring), their instantaneous accelerations will be in inverse ratio to their masses. Now, we need discuss the problem of defining mass m in terms of the force and acceleration. This, however, implies that force has already been independently defined, which is by no means the case.

3.5.1. Electromagnetic Mass and Electromagnetic Force It is well known that the mass of the electron is about 2000 times smaller than that of the hydrogen atom. Hence the idea occurs that the electron has, perhaps, no “ordinary” mass at all, but is nothing other than an “atom of electricity”, and that its mass is entirely 213

electromagnetic in origin. Then, the theory found strong support in refined observations of cathode rays and of the β-rays of radioactive substances, which are also ejected electrons. If magnetic action on these rays allows us to determine the ratio of the charge to the mass,

and also their velocity v, and that at first a definite value for

e , mel

e was obtained, which was mel

independent of v if vm1 and E20>m2, the equality (11.1) can be satisfied only if M>m1+m2, i.e. a body can disintegrate spontaneously into parts the sum of whose masses is less than the mass of the body. On the other hand, if

M0 and for all y M*x, and for any admissible y , i

i

f(x,y) > 0.

(5.10)

Besides this,

 ∂ 2 F 2 (x , y det i j  ∂x ∂x

)  ≠ 0. 

(5.11)

Under these conditions, the triple (M,M*x,F(x,y)) is called an N-dimensional Finsler space, and F(x,y) is called a Finslerian metric function. The value of the metric function F(x,y) is treated in Finsler geometry as the length of the tangent vector yiattached to the point xi. if a Finsler space allows a coordinate system xi such that F does not depend on these xi, the Finsler space and the metric function are called Minkowskian. It will be noted that, in mathematical works devoted to the Finsler geometry, additional conditions are usually imposed on the metric function F which ensure the positive definiteness of the quadratic form Z

i

Z j ∂ 2 F 2 ( x , y ) / ∂x i ∂x

j

at any point xi and for any

non-zero vector yi ∈ Mx. However, it is clear already in the Riemannian formulation of general relativity theory that the metric structure of space-time cannot be positively definite, for the

－

space-time metric tensor must be of the indefinite signature ( +++). This reason alone makes one expect that it is indefinite metrics that may be of interest in a Finslerian extension of general relativity. Accordingly, we refrain deliberately from imposing the condition of positive definiteness, thereby admitting that the Finsler space under study can be indefinite. As regards the homogeneity condition (5.9) it should be pointed out that the necessity of postulation (5.9) follows from the invariant notions inherent in any centroaffine space, the tangent space Mx being an example of such a space. Indeed, the ratio of the lengths of any two collinear vectors yi1 and yi2 = kyi1 of the centroaffine space may be invariantly defined to be

y 11 y 13 = =L= k , y 21 y 22 which does not involve any metric function. Therefore, (5.9) is nothing but the requirement of consistence of the Finslerian definition of length with the centroaffine definition. The 223

Finslerian metric function is required in order to compare the lengths of non-collinear vectors. If a fundamental function F(x,y) is defined for all line-elements in the region R(R ⊂ M), it would be natural to regard F as defining a distance in M, for instance the 'length' of the curve

C between the points P1 and P2 could well be defined by the integral t2

 dx i  dt . I = ∫  x i , dt  t1 

(5.12)

More precisely, if A(xi) and B(xi+ dxi) $ are two neighboring points of R, the distance ds between them is defined by

ds = F ( x j , dx j ),

(5.13)

Since F is homogeneous of first degree in the dxi, this would lead to the required integral. In this manner a metric is imposed on our M. If, in particular, the function F is of the form

F (x i , x j ) =

g ij ( x k )dx i dx j ,

(5.14)

where the gij(xk) are coefficients independent of the yi, the metric defined by F is the metric of a Riemannian space. In this paper we will assume that

F (x i , y i ) = [(eijkl g ijkl (x h )dx i dx j dx k dx l ]1/4, eijkl = ±1, i , j , k , l = 0,1,2,3. (5.15) An even function form for the dx is i

F ( x i , x j ) = 4 e ij g iijj ( x k )dx i dx i dx j dx j ,

(5.16)

where

+ 1, i = j ,   e ij = + δ , i ≠ j , i , and , j ≠ 0, 0 ≤ δ ≤ 1,  − b , i ≠ j , i , or , j = 0, 0 ≤ b ≤ 1.  In particular, a degenerate form is

F ( x i ) = 4 [e ij g ij ( x k )dx i dx j ] 2 ,

δ = 1,

(5.17)

where ds2 =gijdxidxj is usual Riemannian metric in the general relativity. It is natural to assume that all distances are positive; hence, we stipulate condition (5.10). On the other hand, the homogeneity condition (5.9) plays an important constructive role in Finsler geometry, many Finslerian relations being based on identities ensuing from (5.9). To derive these identities, let us consider any function Z(x,y) which is differentiable and positively homogeneous of degree r with respect to yi; that is, Z(x,ky) = krZ(x,y) for any k> 0, where the degree r may be any real number. On differentiation the latter equality with respect 224

to k and puttionk=1, we find that

Z ( x , ky ) = k r Z ( x , y ) implies y

i

∂Z ( x , y ) = rZ ( x , y ) . (5.18) ∂y i

The assertion (5.18) is known in the literature as the Euler theorem on homogeneous functions. The application of (5.18) to F2 yields

F 2 ( x , y ) = g ij ( x , y ) y i y j ,

(5.19)

where

g ij ( x , y ) =

1 ∂2 F 2 (x , y ) 2 ∂y i ∂y j

(5.20)

is called the Finslerian metric tensor, it is a quadratic form. It is very interesting that the condition (5.11) is just requisite of the Morse lemma.

5.2.2. The Catastrophe Change on the Finsler Space-timeF(x,y) Because the Finsler space-time under our study can be indefinite, it must have to make

 ∂2F 2 det  i  ∂y ∂y

j

  = 0 

(5.21)

on some non-zero subset of the space-time manifold M. So, with the Thom theorem (splitting lemma), we could get

f ( x , y ) = F NM ( x , y ′1 ,L, y ′ k ) + M if the matrix ( ∂ 2 F 2 / ∂y i ∂y

j

n −k

( x , y ′ k +1 ,L, y ′ n ),

(5.22)

) has k zero eigenvalues and s negative eigenvalues. Then the

Thom theorem (classification theorem) tells that

FNM ( x , y ′) = Cat ( x , k ), Cat ( x , k ) = CG ( k ) + Pert( x , k ),

(5.23)

where Cat(x,k), the catastrophe function, is a function of k canonical state variables y1,…,yk and n canonical control parameters x1,…,xn. The catastrophe function Cat(x,k) has a further decomposition (another splitting) into two parts CG(k) and Pert(x,k). The catastrophe germ,

CG(x), depends on only the k state variables. All of its mixed second partial derivatives vanish at the critical point. The perturbation, Pert(x,k), depends on the k state variables and on the n canonical control parameters. It is clear that if equation (5.21) is satisfied then as (5.20) it will be held that det(gij)=0, with the theory of the quadratic form we get 225

(5.24)

ds 2 = g ij dx i dx

j

= 0,

(5.25)

it is known that (5.25) is just the light cone in the general relativity. On the other hand, det(gij) > 0 and det(gij) < 0,

(5.26)

with the theory of the quadratic form we get

ds2=gijdxidxj>0 and ds2= gijdxidxj 0

 Det ≠ 0  ( materialstates )   Det = 0 (sin guiarities) 

thetimelikestate, ds < 0 thespacelikestate; ds 2 = 0 thelightlikestate dx i = 0 i = 0,1,2,3; theorigin. 2

(5.28)

From (5.21) and (5.28), it means that the light cone is still a catastrophe set on the curve space-time manifold M, and both the time-like state and the space-like state are possible states of moving particles as had been already pointed out in the flat space-time but, here the catastrophe function has Pert(x), it is only CG(k) in the flat space-time. So, we expect that the catastrophe nature will be shown on the horizon of the fields of the general relativity.

5.3. The Catastrophe Nature in the Schwarzschild Field 5.3.1. The Geodesic Equations and Its Integrations of the Schwarzschild Field By way of example, we will discuss the spherically symmetric and static metric which obeys the Einstein field equation

ds 2 = − µdt 2 + µ −1dr 2 + r 2 (d θ 2 + sin 2 θd φ 2 ),

－

(5.29)

－

where µ= 1 rs/r =1 2m/r (rs = 2m is called the Schwarzschild radius or gravitational radius). In this equation and thereafter in this paper, the geometric unit, c= G=1, has been adopted. It is well known that the geodesic equations followed from (5.29) have three first integrations:

r2

µ

226

dθ =h, ds

dr =k, ds

(5.30)

(5.31)

2

2

1  dr   h  1   +   − = −E . µ  ds   r  µ

(5.32)

If we use t to replace s, we get

dθ 1  r = B 2 1 − s dt r r  2

 , 

h , k

B =

(5.33)

2

E 1  dr   B  1  +  − = − 2 = A, 3  k µ  dt   r  µ

(5.34)

We see that the constant A could be taken as different values: A< 0

for subluminal-speeds (the time-like state),

A= 0

for light speed (the light like state),

A> 0

for superluminal-speeds (the space-like state).

In order to show clearly the catastrophe nature of the Schwarzschild field, we will consider a motion along radial direction. In equation (5.34) let B=0, we will get

v =

dr = ±µ dt

Aµ +1 .

(5.35)

The velocity v is the coordinate velocity obtained by a distant observer. In the general relativity, generally, a particle can move only with the velocity 01; a −1

r − rs  r  2 , t − t 0 = ( rs + 4) − rrs  + 3  + rs ln 3 r + rs  rs 

a = 1.

(5.40)

It shows that the particle will stop at an infinite distance for a=1.

t − t0 = + rs ln

(1 − a ) r 2 + arrs a −1

+

( 2 − 3a ) rs

ars   ln  (1 − a ) r 2 + arrs + r 1 − a +  2 1− a  2 (1 − a ) 3 

rs (2 − a )r + ars − 2 (1 − a ) r 2 + arrs , r − rs

[

]

0 < a < 1. (5.41)

It shows that the particle with continuously move with a velocity v = 1 − a < 1 at infinite distance for 0 100rs the interaction varies according to the inverse-square law approximately, but it is repulsive, and at r≤100rs the inverse-square law is violated. Integrating Equation (5.35) yields

t − t0 =

( A + 1) r 2 − Arr s A +1

+

(3 A + 2) rs

Ar s   ln  ( A + 1) r 2 − Arrs + A + 1r − + A 2 1 +   2 ( A + 1) 3

2

rs ln

( A + 2) rrs − Ar s − 2 rs ( A + 1) r 2 − Arr s r − rs

= F ( A , r , rs ),

A > 0. (5.42)

These results show that the motion of a particle is indeed very different when A has different values. In particular, from (5.42), we get the rvs. t diagram given in Figures 5.3 and 5.4. In Figure 5.3, we compare the r-t curves for particles with same gravitational mass (rs= 1 ly) but different A’s. From this comparison we find that particle with higher beginning velocity has higher limit velocity at infinity, longer delayed time before expansion and higher acceleration, and vice versa. Taking A=143, i.e., vmax=12, but using different value of the gravitation mass at center, 229

rs=10－4,5,10 ly, we get diagram of Fig.5.4. It shows that if particles move out from place just outside the Schwarzschild radius then the expansion will be slower for higher central mass. For example, if rs= 10-4 ly, then a particle moves to r = 100 ly from initial place near the rs takes about 8.33 years. But,if rs= 5 ly, then it should take 45 years. From equations (5.33) and (5.34) we could get several very interesting results when A>0 for the non-radial motions in the Schwarzschild fields: 1. From (5.33) we see that in the rate of revolution θ& = frac dθdt as a function of r, when

r=rm=1.5×rs.

(5.43)

it will get a maximum. So, if the maximum had been found by the observations and from it determined rm, then rs=rm/1.5. 2. From (5.33) and (5.34) we get

dθ = B r ( A + 1)r 3 − Ar s r 2 − B 2 r + B 2 rs . dr

[

(5.44)

]

It is clear that formula (5.44) is a hyperbola when A>>1. And the solution of (5.44) may then be determined by elliptic integral

θ −θ0 =

 r − r4 r − r1 r2 − r3 r1 − r4 2B sn −1  2 , ( r1 − r3 )( r2 − r4 )  r1 − r4 r − r2 r1 − r3 r2 − r4

= θ ( A , rs , B , r ),

( r1 > r2

 =  

(5.45)

> r3 > r4 ).

§6. The Superluminal Expansion of the Extragalactic Radio Sources 6.1. The Observation of the Superluminal Phenomena 6.1.1. Radio Sources With Superluminal Velocities Brightness distributions in some extragalactic radio sources have been seen to vary so rapidly transverse velocity of expansion is greater than the velocity of light (assuming a cosmological origin for the redshift). The term superluminal was used to describe this phenomenon. The observations have all been obtained with very-long-baseline interferometry (VLBI) systems using two to five radio telescopes, spaced over thousands of kilometers, to form multi-element interferometers. According to the standard model of cosmology, the angular size θ of an object with redshift

z can be converted into a linear separation R,

R =

θ 2 0

H 0 q (1 + z ) 2

[q z + (q

230

0

0

− 1) 1 + 2q 0 z − 1 ,

(

)]

(6.1)

where H0=80 kms

－1Mpc－1 is Habble constant; q0 is the deceleration parameter being taken

to be 0.05 in following. The derivations of θ or/and R with respect to t will give the expansion rate

dθ dθ = (1 + z ) dt dt 0

or v =

dR dR . = (1 + z ) dt dt 0

(6.2)

So far, over 65 objects are identified to be superluminal expansive (2 objects in the Galaxy). The observational data are given in Table 1. Source 0016+731 0106+013 0108+388 0133+207 0153+744

0212+735 0234+258 0235+164

Table 1. The Data of Superluminal Radio Sources Βapp Name Redshift z Component Q,S5 1.781 8.3 Q,4C01.02 2.107 C2 8.2 G,OC314 0.669 1.60 1.30 1.80 2.20 0.424

0742+318 0833+654

Q,2C31.30

0.462 1.112

B C0 D

－2.2

231

Note

0835+580

1.534

0836+710

2.170

0850+581 0851+202

Q,4C58.17 B,OJ287

1.322 0.306

0906+430

Q,3C216

0.670

0923+392

Q,4C39.25

0.699

1039+811 1040+123 1101+384

Q,S5 Q,3C345 B,MKN421

1.26 1.029 0.031

1137+660 1150+812 1156+295 1222+216 1226+023

Q,3C263 Q,S5 Q,4C29.45 Q,4C21.35 Q,3C373

0.652 1.25 0.729 0.435 0.158

Q,3C279

0.538

B,B2

0.996

1253

－055

1308+326

1334

－127

B C D SW1 SW2 A B A B A2 C1 C2 C2 B C2 C3 C4 C5 C7 C7a C8 C9 ? C3 K1 K2 K3

0.541

1458+718

Q,3C309.1

0.905

1618+177 1641+399

Q,3C334 Q,3C345

0.555 0.595

B

1642+690 1721+343

Q,4C69.21 Q,4C34.47

0.751 0.2055

1749+701 1803+784 1807+698

B,S5 B,S5 3C371

0.77 0.684 0.05

C2 C3 C4 C5 B C

232

－4.4

10.40 4.53 5.79 3.90 c ),

for

sup erlu min al − speed , i .e .,v > c (or v 1 < c ).

(7.22)

It was just analyzed by Dirac for the anti-particle. So, we guess that a particle with the superluminal-speed v>c could be regarded as its anti-particle with the dual velocity v1=c2/vmgh. So, there are no changes in the system, but the energy has appeared.”

Prospects Let us remember the problem about the maintenance of long-term flights to the outer space with electricity. The Prof. Uchastkin’s analogy describes precisely a theoretical approach for solving this problem. Of course, there is a great deal to do though, to understand what phenomenon will play the role of those “quantum potatoes” and how to construct an instrument that would be able to support a minimal energy to “bring them to the fourth floor”. How can a spaceship be supplied with energy during many months of flight? Near the Earth, photovoltaic cells are used but the more the distance to the Sun is increasing, the more needless they are; using of a nuclear energy source is problematical for different causes. Today we can neither improve this situation considerably nor do we have even any theoretical conditions which could let us approach it. On the base of such a situation there are common ideas of the construction of matter and its properties. Now then, a new conception of physics is being proposed. Like many others as well. If we stay by the space technology, it’s over constructing of engines based on new principles of energy production, maintaining of real-time telecommunication on the distances in outer space, free of limits which are proper to the diffusion of electromagnetic waves… It follows from the foregoing that UUQT opens up a perspective of a solution for the communication problem on extremely wide distances in outer space for it excludes the limits of information exchange between Earth and spaceship. The theory also predicts the approaches to creating of

272

the new energy sources and of the new types of engines that would be almost ideal for creating of spaceships of the future. Conventional jet propulsions transform the conducted energy in the kinetic energy of the beam of a working body flowing from the engine, and the reaction force of this beam – the pulling force – accelerate the spaceship. Therefore space flights to extremely wide distances will require huge stocks of working body. A classical progression curve reflects the velocity increasing of a thrown-off mass of the working body. Though there is a possibility for creating of a very weak constant pulling – but! – without throwing off of mass. Let us use the method of analogy again. Regard a classical trick problem in physics for universities’ admission tests: there is a boat in motionless water and a man with a sandbag in this boat. Can he move the boat by performing any manipulations with the sandbag, for an endless time? Correct answer: throw the sandbag from the front part of the boat to its back, then carry it back slowly, throw it again and so on. As the viscous friction force by Stocks is proportional to the velocity, the boat will perform swinging motions, over which some linear movement will be applied. Based on this idea, marsch buggies were constructed in Germany – there is heavy mass moving in there, in one direction quickly and back slowly. Many decades ago, the same effect (Dean’s engine) was wide-ragingly discussed in the USSR in popular science magazines and on TV. There is a similar phenomenon in the classical electrodynamics as well as in the quantum electrodynamics and it’s related to the Lorentz radiative friction force. The appearance of Lorentz’ force becomes evident by considering the interaction of the charge and the field caused by it.For a motionless charge the force of such an interaction – or “self-action” – is equal to zero, otherwise the free charge would experience a self-acceleration. The charge begins to move, but the electromagnetic field, as its spread’s velocity is finite, can’t reschedule immediately. The accelerated charge practically flies onto its own field; with other words, this effect can be described as appearance of energy flow which is directed upstream to the flow and slowing it down. It generates “electromagnetic viscosity” which value is related to the acceleration. How can this phenomenon be used? If there is a charge cloud in flat capacitor, it is possible to make it swing between sheets with different values of acceleration forwards and backwards by applying a sawing motion to the sheets. Because of 273

different forces of radiation friction in the alternate and opposite direction, pulling force appears along the lines of electric field. The radiation of such accelerated charges is always perpendicular to their movement and can be screened, but the most important thing on it is the fact that it doesn’t change its impulse in relation to the direction of the capacitor’s field.It may be paradoxical, but it seems that we get a pulling force by spending energy for this process without throwing-off of any mass in the direction, which is opposite to the motion’s one. The authors even published in the US-magazine “Journal of New Energy” vol.5, #1, 2000 an article, containing an exact analytical solution of this problem: the pulling of some micrograms appears in a flat capacitor, containing a cloud of

electrons in which the distance between the

sheets is many meters long, by applying of sawing potential of millions of volts.Of course, it is an insignificant result in relation to such a huge (hypothetical) instrument employment, and the using of electron cloud in a flat capacitor has practically no prospects. But if stabile charged particles exist which mass is at least one-millionth of electron mass, then this idea becomes very interesting from the technical point of view. Do such stabile charged leptons exist at all and how is it possible to generate them in a sufficiently large number? Today nobody can give an answer... To generate pulling it is still possible to throw off the mass/ matter, “getting” it in a specially created potential hole, accelerating in it in the same time. UUQT allows such solution generally that is evident from the “Maternity home” solution. Let us consider the results. UUQT will in future let us solve several basic problems of the worldwide energy supply and all problems in outer space: immediate information changing, the problem of energy supply and constructing of new engine types. It is absolutely precipitant to make technical plans for those solutions, but the foregoing should be considered not as a wanton imagination, but as a possible future programmer of fundamental research to transpose our civilization to new physical principles. Evaluation of UQT ideas resulted in instinctively absolutely clear picture of quantum events in terms of figures and movements. And philosophical principal of Complementarity can be now hidden with well-deserved honors.In spite of mathematical complexity Unitary Quantum Theory will stop ordinary Quantum Mechanics paradox and consequently frank words of Richard Feynman: “I can easily say that nobody understands quantum mechanics” will become the property of history. Moreover, by solving the QUT equations it became possible to obtain with the high precision an electron charge, as for scalar telegraph UQT equation it gave with appropriate precision mass spectrums of all elementary particles (Sapogin at all, 274

2008a, 2008b, 2010). The same spectrum was followed from the solution of the Schrödinger and Klein-Gordon integro-differential equations. The risk of computed mass spectrum being random is less than

. Of course such results cannot be

obtained without sacrifice. What would we offered in sacrifice if replaced an Ordinary Quantum Mechanics by the Unitary Unified Quantum Field Theory Field (UUQFT)? 1. There are no in UUQFT strict principles of superposition. It is violated if wave packets are colliding. 2. There are no strict close systems in UUQFT and the Conservation Laws works for very big energies only. Note that the Conservation Laws forbid beginnings of the Universe. 3. The classical relativistic relation between energy and impulses is valid in UUQFT only after averaging of observed phenomena and Relativistic Invariance itself is not "the sacred cow". 4. The Space in UUQFT is non homogenous and non isotropic. 5. The particles and their interaction are not local. 6. The existing Standard Model Quantum Theory of Elementary Particles requires much alteration. 7. Thevelocityconceptasquotientfromdivisionof the traversed path tosome time interval is not quite appropriate in UQT. If a wave packet (particle) is spreading along the Megagalaxy and then appearing somewhere else, what should we do with the rate, if nothing moves between the points of disappearance and arrival, does it mean that particle has just simply disappeared and then appeared in a new place? There was observed resembling crushing defeat of physics 50 years ago as "weak interaction" burst, so to say, into physics. As soon UQT is nonlinear it automatically combines all four interactions that can pass from one into another at different distances. Below we analyze the most important fields of science from UUQFT general physics positions. Lorentz transformations. It’s quite complicated. The special relativity – is in fact Lorentz transformations (1904) derived by V.Vogt (1887) in the century before last. These transformations followed from the properties of Maxwell equations which are also proposed in the nineteenth century (1873). One of these equations connecting electrostatic field divergence and electric charge (Gauss' law of flux), in fact is just another mathematical notation of Coulomb's law for point charges. But today anybody knows that Coulomb’s law is valid for fixed point charges only. If charges are frequently moving Coulomb’s law is not performed. Besides anybody knows that lasers beams are scattered in vacuum one over another, which is absolutely impossible in Maxwell equations. That means that Maxwell equations are approximate - and for the moving point charges experimental results essentially differs from the estimated ones in the case charges areas are overlapping. Few people think about the shocking nonsense of presenting in any course of physics 275

of point charge electric field in the form of a certain “sun” with field lines symmetrically coming from the point. But electric field – is a vector, and what for is it directed? The total sum of such vectors is null, isn’t it? There are no attempts to talk about, but such idealization is not correct. We should note that Sir Isaak Newton did not used term of a point charge at all, but it’s ridiculous to think that such simple idea had not come to him! As for Einstein, he considered “electron is a stranger in electrodynamics”. Maxwell equations are not ultimate truth and so we should forget, disavow the common statement about relativist invariance requirement being obligatory “permission” for any future theory. To reassure severe critics we should note that UQT is relativistically invariant, it allows to obtain correct correlation between an energy and impulse, mass increases with a rate, as for relativistic invariance just follow of the fact that the envelope of moving packet is quiet in any (including non-inertial) reference systems. To be honest we should note that subwaves the particles consist of are relativistically abnormal, at the same time envelope wave function following from their movement confirms terms of Lorentz transformations. The success of Maxwell equations in description of the prior-quantum view of world was very impressing. Its correlation of the classical mechanics in forms of requirement to correspond Lorentz transformations was perfectly confirmed by the experiments that all these had resulted in unreasoned statement of Maxwell equations being an ultimate truth… Other reasons for this were later very carefully investigated by a disciple of one of the authors (L.S.), Professor Yu.L.Ratis. (S.Korolev Samara State Aero-Space University), who has formulated the modern spinor quantum electrodynamics from the UQT point of view: 1. Maxwell equations contain constant c, which is interpreted as phase velocity of a plane electromagnetic wave in the vacuum. 2. Michelson and Morley have never measured the dependence of the velocity of a plane electromagnetic wave in the vacuum on the reference system velocity as soon plane waves were mathematical abstraction and it was impossible to analyze their properties in the laboratory experiment in principle. 3. Electromagnetic waves cannot exist in vacuum by definition. A spatial domain where an electromagnetic wave is spreading – is no longer a vacuum. Once electromagnetic field arises in some spatial region at the same moment such domain acquires new characteristic – it became a material media. And such media possesses special material attributes including power and impulse. 4. Since electromagnetic wave while coming through the abstract vacuum (the mathematical vacuum) transforms it in a material media (physical vacuum) it will interact with this media. 5. The result of the electromagnetic wave and physical vacuum interaction are compact wave packets, called photons. 6. The group velocity of the wave packet (photon) spreading in the media with the normal dispersion is always less its phase velocity. All abovementioned allows making unambiguous conclusion: the main difficulties of 276

the modern relativistic quantum theory of the field arise from deeply fallacious presuppositions in its base. The reason for this tragic global error was a tripe substitution of ideas – velocity of electromagnetic wave packets ‘c’ being transformed in numerous experiments physics have construed as constant ‘c’ appearing in Maxwell equations and Lorentz transformations. Such blind admiration of Maxwell and Einstein geniuses (authors in no case do not doubt in the genius of these persons) had led XX century physics up a blind alley. The way out was in the necessity of revision of the entire fundamental postulates underlying the modern physics. Exactly that was done by UUQFT.(Sapogin, 2010, 2011) Some time ago CERN has conducted repeated experiments of the neutrino velocity measurement that appeared to be higher than velocity of the light. For UUQFT they were like a balm into the wounds. The administration of CERN renounced after sometimes these results considering them as the consequence of experimental errors. As far as the authors know, not all participants of this experiment agree to such renouncing. Besides, many astronomers detect superluminal velocities during observations of stars and galaxies.In fact the movements in excess of the light velocity were discovered earlier by numerous groups of researches. Nearly everybody disbelieved it. And now the neutrino movements exceeding the velocity of the light were disclosed in CERN. The importance of these experiments for UUQFT is settled in the article (Sapogin,2011) where at the page 69 it is written that “this should be considered as direct experimental proof of UUQFT principle”. Note, this question is terribly complicate and probably is to be leaved to next generations. From one side, the time in UQT exists, so to say, in our head only. From other side, the Lorenz Transformations describe correctly some experimental facts, for example, the mass growing with velocity. Otherwise, all atomic accelerators would be out of order. Thereafter, it is a big mistake to consider all Special Relativity Theory as erroneous. There are also other ideas. For example, at «New Relativistic Paradoxes and Open Questions», by Florentin Smarandache, shows several paradoxes, inconsistencies, contradictions, and anomalies in the Theory of Relativity. According to the author, not all physical laws are the same in all inertial reference frames, and he gives several counter-examples. He also supports superluminal speeds, and he considers that the speed of light in vacuum is variable depending on the moving reference frame. The author explains that the red shift and blue shift are not entirely due to the Doppler Effect, but also to the medium composition (i.e. its physical elements, fields, density, heterogeneity, properties, etc.). Professor Smarandache considers that the space is not curved and the light near massive cosmic bodies bends not because of the gravity only as the General Theory of Relativity asserts (Gravitational Lensing), but because of the Medium Lensing. In order to make the distinction between “clock” and “time”, he suggests a first experiment with a different clock type for the GPS clocks, for proving that the resulted dilation and contraction factors are different from those obtained with the cesium atomic clock; and a second experiment with different medium compositions 277

for proving that different degrees of red shifts/blu shifts would result. To regret, the authors today have no decisive position to these complicate questions. Standard model As soon relativistic invariance underlies every of the numerous quantum theories of the field, it leaves a devilish imprint at everything. Nevertheless relativistic ratio between energy and impulse although being absolutely correct in fact are not obligatory follow from relativistic invariance only and can result from another mathematical reasons that will be discovered in future. Nowadays Standard Model (SM) combines the most elegant mathematical miracles of researches which hands were tied with relativistic strait-jacket and it not so bad describes these experimental data. Amazing that it was possible to think it out at all. Nowadays to confirm SM one should find a Higgs boson and for this purpose the governments of some countries assigned essential sums for the construction of Large Hadron Collider (LHC). For entire SM the interaction with Higgs field is extremely important, as soon without such a field other particles just will not have mass at all, and that till lead into the theory destruction. To start with we should note that the Higgs field is material and can be identified with media (aether) as it was in former centuries. But SM authors as well as modern physics have carefully forgotten about it. We would not like to raise here once again the old discussion about it. It’s a quite complicated problem and let us leaves it to the next generation. But another problem of SM has never mentioned before: in the interaction with Higgs field any particle obtains mass. As for Higgs boson itself, it is totally falling out of this universal for every particle mechanism of mass generation! And that is not a mere trifle, such “mismatching” being fundamental fraught with certain consequences for SM. After Higgs boson discovery nothing valuable for the world will happen except an immense banquet. Of course boson will justify the waste of tens billions of Euros… But even now some opinions in CERN are expressed that probably boson nondisclosure will reveal a series of new breath-taking prospects… and where were these voices before construction, we wonder? But that’s not the point! If this elusive particle were the only weakness of SM! To our regret today this theory cannot compute correctly the masses of elementary particles including the mass of Higgs boson. More worse, that SM contains from 20 to 60 adjusting – arbitrary! - parameters (there are different versions of SM). SM does not have theoretically proved algorithm for spectrum mass computation – and no ideas how to do it! All these bear strong resemblance to the situation with Ptolemaic model of Solar system before appearance of Kepler’s laws and Newton’s mechanics. This earthcentered model of the planets movement in Solar system at the moment of appearance had required introduction of 40 epicycles, specially selected for the coordination of theoretical forecasts and observations. Its description of planets positions was quite good; but later to increase the forecasts accuracy it had required another 40 additional epicycles… Good mathematicians know that epicycles are in fact analogues of 278

Fourier coefficients in moment decomposition in accordance with Kepler’s laws; so by adding epicycles the accuracy of the Ptolemaic model can be increased too. However that does not mean that the Ptolemaic model is adequately describing the reality. Quite the contrary… The Unitary Quantum Theory allowed computing the mass spectrum of elementary particles without any adjusting parameters. By the way computed spectrum (Sapogin at all, 2008ab, 2010) has particle with mass 131.51711 GeV (L=2, m=2). Once desired it can be called Higgs boson, it lies within declared by the CERN+Tevatron mass interval 125-140 GeV expected to contain Higgs boson. CERN promises to obtain more precise mass value by December 2012. Note the following remarkable fact: the standard theory allowed to detect spectra by using always the quantum equations with outer potential and as corollaries to geometric relations between de Broglie wave’s length and characteristic dimension of potential function. The quantum equation of our theory do not contain the outer potential and describe a particle in empty free space; the mass quantization arises owing to the delicate balance of dispersion and non-linearity which provides the stability of some wave packets number. It is the first case when spectra are detected by using the quantum equations without outer potential. Nuclear physics. Nuclear physics as a part of quantum theory is very luckless. Thus the potential of the strong interactions is so complicated that no one even very bulky and intricate mathematical expression is able to describe with more or less veracity the experiments of two nucleons interaction. This interaction depends in very complicated manner from all parameters of the nucleons movement and their orientation towards vectors of velocity, acceleration, spin, magnetic movement, etc. Scarcely one can find a parameter which practice interaction does not depend on. From UQT point of view the strong interactions appear in the result of nucleons represented by the wave packets overlapping. Today the way of mathematical notation of the overlapping wave packets interaction is absolutely vague as soon nonlinear interaction in any space-time point of the waves is different due to different amplitudes. It’s a really complicated problem as soon there is only one nonlinear mathematical problem existing for each space-time point and even with the intuitive clearance of situation we do not expects its soon solution. The complete understanding of the nuclear structure hardly can be expected in the soonest time without exact expression for the potential of the strong interaction. In general it should be noted that quantum world looks more clear and simple in UQT than in the general quantum mechanics, but we cannot repeat it while speaking about the mathematics used. The appearance of the exact analytical solution of the scalar problem of elementary particles mass spectrum can be considered as Fate gift (or God’s help) for UQT. By the way the standard Schrödingerquantum mechanics has the same gift – the exact analytical decision of the Hydrogen atom. The nuclear process in terms of small energies should be reviewed. Today the strict nuclear physics does not assume nuclear reactions at small energies that contradict experimental data. Here we should also note our skepticism towards the idea of 279

nuclear fusion in Tokamaks, we consider this way as hopeless. To justify these experiments we have to mention that the decision was made in the absentia of other ideas and under the great pressure of the future power problems. But the use of the reactions of classical cold fusion for the power output is also difficult due to the complexity of colliding nuclei phasing. This phenomenon is well described by the equation with oscillating charge, while the cold nuclear fusion had been predicted in UQT 6 years before its real discovery (Sapogin, 1983). Solid-state physics. The band theory of solid is based at the point on the solution of the task of an electron movement in the field of two or more charges. But this problem does not have analytical solution jet, in practice a speculative quality solution is used only. The results are that electrons in the solid have quite specific allowed power bands. This field of the science is very successful and hardly will be revised. Any solution of the equations with the oscillating charge for the electron moving in the field of few nuclei also result in appearance of allowed and forbidden bands (Sapogin at all, 2003, 2005,2008a,2011a). Somewhat apart is classical tunneling effect. In UQT the probability of tunneling effect appearance depends on the phase of the wave function (in contrast to the ordinary quantum theory, where at the squaring of the wave function module it dependence on the wave phase totally disappears). It could be interesting to prove such dependence by the experiments. It can be easily done if creating a new transistor on the basis of absolutely new principle of the electron current control (Sapogin at all, 2011b). We are not going to analyze the modern theory of superconductivity, but we are sure that the equation with oscillating charge will deepen on both understanding of superconductivity as well as mysterious properties of quantum liquids. Astrophysics and Cosmology. The authors regret not being in sympathized with the ideas of the Universe origin from one singular point. The most amazing in this theory is a detailed computation of events occurred in the first fractions of the second just after the Big Bang. Today when the fundamental physics is making only first shy steps towards the real understanding of the quantum processes we still do not have clear model of the particles, or understanding of a spin appearance, a charge and magnetic moments. According to UQT the processes of the multiple particle production at collision is a common result of the waves packets of big amplitudes diffraction in periodic structures one another, as for the multiple outgoing in different directions particles they correspond to the general diffraction maximums. But we do not assume the responsibility of the mechanism of the multiple particles production for the Universe appearance. To our opinion the complete understanding of the quantum world will arise only after solving of 32 nonlinear integro-differential equations of UQT (Sapogin at all,1984,2003,2005,2008a). To their regret the authors like castrates in a harem can only look at these equations. And many cosmologists would like to use theories assuming existence Universe localities where the energy is coming into being and also other localities where the energy annihilates. For example, British astronomer Fred Hoyle has developed the 280

theory of Universe where it takes the place the continuous creation of matter. He wrote:“… Different atoms constituting the matter do not exist at some given moment of time and then after instant they exist already. I must admit this idea may look as strange… But all our ideas about creation are strange. According to previous theories the whole quantity of matter in Universe was coming into being just as whole and all process of creation looks as super-gigantic instant explosion. As for me, such idea seems much stranger, than idea of continuous creation…” F.Hoyle, La nature de l’Universe, 1952. The official astronomical science does not accept the ideas of F.Hoyle and of some other astronomers (H.Bondi, T.Gold, and P.Jordan) about continuous creation of matter in Universe because the Conservation Laws are considered as infallible. But from the viewpoint of our UQT these ideas are quite not strange. Our real ‘world’ continuum consists of an enormous quantity of particles moving with different velocities. Partial waves of the postulated vanishing particles create real vacuum fluctuations that change in a very random way. Certain particles randomly appear in such a system, owing to the harmonic component energy of other vanished particles. The number of such “dependant particles” changes, though; they suddenly appear and vanish forever, as the probability of their reappearance is negligibly small, and so we do expect that all particles are indebted to each other for their existence. Yet, if some particles are disappearing within an object, other particles are arising at the same moment in that object due to the contribution of those vanishing particles’ harmonic components –and vice versa. The simultaneous presence of all of the particles within one discrete macroscopic object is unreal. Some constituent particles vanish within the object while others appear. In general, a mass object is extant overall, but is not instantaneously substantive and merely a ‘false’ image. It is clear that the number of particles according to such a theory is inconstant and all their ongoing processes are random, and their probability analysis will remain always on the agenda of future research. In accordance with UQT there are another solutions for the quantum harmonic oscillator besides stationary, where the given tiny incipient fluctuation is growing, gaining power and finally becoming a particle. It is so called "Mathernity Home” solution. There are also other solutions where substance (power) is disappearing. Such solutions have been called “Crematorium”. May be Metagalaxy is simply entangled in searching the balance, isn’t it? All this allows expecting that space continuum in the centers of Galaxies produces different particles, electrons, protons, neutrons, which are the sources of light atoms. Later thanks to the gravitation light atoms are transformed into gas nebulas where under gravity compression the stars are lighting. It’s quite possible that the current theory of Stars evolution is correct in general while describing (via Supernova) the production of other atoms apart Hydrogen and Carbon the planets consist of. We do not think nuclear process at small energies (which are possible in UQT, but impossible in standard quantum theory) will essentially modify evolutionary view of the Galaxies development. It is interesting that the state with the minimum quantum values L=0,m=0 belongs to 281

the very heavy neutral scalar particle (WIMP) with our name Dzhan and mass about 69.6 TeV, which in principle should purely interact with the others (Sapogin at all, 2005, 2008ab, 2010). With the growth of the quantum numbers the mass of the particle is diminishing. So there should be a lot of Dzhan-particles due to the small quantum numbers. And probably their existence is responsible for the dark matter in general, in accordance with some evaluations Metagalaxy consist of up to 80-90% of the dark matter. Gravitational theory. No doubt that Gravitational theory should follow from 32 nonlinear integrodifferential equations of UQT and the authors are expecting that it can be done in future (Sapogin at all, 1984, 2005, 2008a). Nevertheless we will make now some conservative assertions. The current data regarding the Universe expansion can be interpreted as the change of the gravitational potential sign (gravity is replacing by repulsion) at great distances for the great masses. Probably the difference between absolute the values of electric charge of a proton and a electron, say in 15 – 20 signs, is responsible for his phenomena, but for us this idea is extremely unsympathetic. On the other hand there is an impression that the variation of the gravity potential is momentary and acts at the same time in all spatial domains (long-range action). Thus any attempts to propose lateness correction of the changes of gravitational potential in the planetary motion equation require the said changes to be occurred with velocities which are many times higher than the velocity of light. Apart there is the question of existence and velocities of the gravity waves, where is no clarity at all. It could be clarified between 16 and 22 of July 1994 when comet Shoemaker-Levy had collided with Jupiter, but humanity missed such possibility. At the moment of the comet huge cores collision with the Jupiter ball of gas its surface should started radial oscillations and created gravity waves, if they exist at all. It’s astonishing but astronomers all over the world in every observatory were able to observe this phenomenon nearly in real time conditions (the light was coming from Jupiter to the Earth about an hour), as for the gravity specialists they had overslept such a chance to study gravity waves velocity at all as far as the authors are informed. At the same time according to the processed information (Hlistunov at all, 2011) from Russian Command-andMeasuring Complex for the monitoring and control of the space objects at the entire moment of collision geodesic satellites “Topex-Poceidon” and “GEO_IK” began swaying at their orbits. Normally the orbit of a geodesic satellite lies inside the tube with about 1 km diameter and the orbit can be control with the high accuracy – not more than one meter precision for the position data and centimeters per second for velocity. During the collision the sensors registered 5-8 times increase of the trajectory tube diameter. In the same article Hlistunov at all on the basis of correlation analysis of the position data measurements and information obtained from earthquake-detection station it was shown that the waves of gravitational potential variation were the trigger for earthquakes. To the authors’ regret they do not have the similar information from NASA. Chemical catalysis. The process of chemical catalysis and the catalysts are the great mystery of the 282

modern science. The number of chemical catalysis theories equals the number of chemical catalytic processes. Specialist of chemical catalysis used to think that this or that reaction is not being processed only if a special catalyst has not been found. Even Michael Faraday studied these problems. He seems to say platinum black being the universal catalyst. Only this (while platinum practically does not react with anything) immediately suggests an idea that chemical processes are not enabled at all and we should look for the physical universal mechanism of reactions. The UQT has such a process. The details are listed in the articles (Sapogin at all, 2003, 2005, 2008a, 2011c). The universal mechanism of heterogeneous catalysis for example in Ammonia synthesis consists of the following: Nitrogen molecular falls into a cavity (hole) of the catalyst few tens of Angstrom unit size. At some initial terms molecular starts oscillating with an energy augmentation implementing thus solution “Maternity home” like in a normal potential well. If the augmented energy excesses the binding energy of molecular Nitrogen then atomic Nitrogen at the exit from the cavity will be caught by protons (Hydrogen), form Ammonia and then quit the game and free cavity for the new deeds. We are sure that in such a way water can be decomposed for Oxygen and Hydrogen. At normal conditions the mixture of Oxygen and Hydrogen is stable. In other words two stable substances (water and gas mixture) are simply divided by a high energy barrier, that can be overcome (tunneling effect analogue) by using the exact catalyst and the UQT ideas. For today a lot of experiments of water decompositions are known, the energy evolved in the process of hydrogen combustion is ten times higher than necessary for decomposition. It makes possible to design an engine running from water. Conclusion It seems that if UQT were correctly describing the world properties the radical transformation of the civilization would be possible. In conclusion we should express our astonishment that UQT is incomprehensible for any thinking person, it’s a mystery to us. We are concluding by reminding of the prophetical words of the famous US sciencefiction author Arthur Clarke: “Something that is theoretically possible will be achieved practically independent of technical difficulties. It’s enough to desire it.” (back translation)- Profiles of the Future, 1963. We would like to add the amazing phrase of A. de Saint-Exupéry: “The truth is not something that could be proved, but something that makes all things easy and clear” (back translation). Acknowledgements: The authors thank for discussions to professors F. Smarandache, V.A.Boichenko, A.S.Bogomolv, V.V.Graboshnikov,Yu.P.Savin, V.I.Uchastkin. REFERENCES: Jammer M. (1961). Concepts of mass in classical and modern physics. Harvard University Press. 283

Sapogin L.G. (1973). «United Field and Quantum Mechanics», System Researches (Physical Researches) Acad. Science USSR, Vladivostok, 2, pp. 54-84, (Russian). Sapogin L.G. (1979). «On Unitary Quantum Mechanics». NuovoCimento, vol. 53A, No 2, p.251. Sapogin L.G. (1980). “A Unitary Quantum Field Theory”. Annales de la Fondation Louis de Broglie, vol.5, No 4, p.285-300. Sapogin L.G. (1982a). A Statistical Theory of Measurements in Unitary Quantum Mechanics. NuovoCimento, vol.70B, No.1, p.80. Sapogin L.G. (1982b). A Statistical Theory of the Detector in Unitary Quantum Mechanics. NuovoCimento, vol.71B, No.3 , p.246. Sapogin L.G. (1983), Journal «Technics for a young», No.1, page 41. (Russian). SapoginL.G. ,Boichenko V.A., (1984). “On the Equation of the Unitary Quantum Theory”. Annales de la Fondation Louis de Broglie, vol. 9, No.3, p.221. Sapogin L.G., Boichenko V.A. (1988). “On the Solution of One Non-linear Equation”. NuovoCimento, vol.102B, No 4, p.433. Sapogin L.G., Boichenko V.A. (1991). “On the Charge and Mass of Particles in Unitary Quantum Theory”. NuovoCimento, vol.104A, No 10, p.1483. Sapogin, L.G.,I.V.Kulikov (1995) “Cold Nuclear Fusion in the Unitary Quantum Theory», Chinese Journal of Nuclear Physics, vol.17, No 4, p.360-370,. Sapogin, L.G. (1996) “Cold Nuclear Fusion and Energy Generation Processes in Terms of the Schroedinger Equation”. Chinese Journal of Nuclear Physics vol.19,#2, p.115-120, 1996 Sapogin L.G., RyabovYu.A., Utchastkin V.I. (2003). Unitary Quantum Theory and a New Energy Sources. Ed. MADI, Moscow, (Russian). Sapogin L.G., RyabovYu.A, Boichenko V.A. (2005). Unitary Quantum Theory and a New Sources of Energy, Archer Enterprises, Geneva, NY, USA. Sapogin L.G., Ryabov Yu. A., Boichenko V. A. (2008a). Unitary Quantum Theory and a New Sources of Energy, Ed. Science-Press, Moscow, (Russian, transl. from English). Sapogin L.G., Ryabov Yu. A. (2008b). «On the mass spectrum of elementary particles in Unitary Quantum Theory», The Old and New Concepts of Physics, Vol. 5, No 3 www.uni.lodz.pl/concepts Sapogin L.G., Dzhanibekov V.A.(2008c), Journal «Technics for a young», No.9,11, February (Russian). Sapogin L.G., Ryabov Yu. A. (2010). «New Theoretical Results about the Mass Spectrum of Elementary Particles». Applied Physics Research, vol. 2, No 1, p.8698, May. www.ccsenet.org/apr Sapogin L.G.(2010),”About Unitary Quantum Field Theory” Applied Physics Research, vol. 2, No 2, p.114-140, November. www.ccsenet.org/apr Sapogin L.G., Ryabov Yu. A. (2011a). "Approximation Equations with oscillating charge in Unitary Quantum Theory and its applications to the analysis of some quantum problems." International Journal of Applied Science and Technology,Vol.1, No 5, September. www.ijastnet.com 284

Sapogin L.G., Dzhanibekov V.A., Sapogin V.G. (2011b).” A new approach to control electroncurrent in Unitary Quantum Theory”. International Journal of Applied Science and Technology,Vol.1,No.6, November.www.ijastnet.com Sapogin L.G., Ryabov Yu. A. (2011c).”Unitary Quantum Theory and Catalytic Process Theory.” International Journal of Pure and Applied Sciences and Technolodgy 3(2),pp.93-120 www.ijopaasat.in Sapogin L.G.(2011),”An Unitary Unified Quantum Field Theory” Global Journal of Science Frontier Research,vol.11, Issue 4,Version 1.0, July. Sapogin L.G. (2012), Journal «Technics for a young», No.2, page 2-11, February (Russian). Sapogin L.G., Ryabov Yu. A.,Dzhanibekov V.A. (2012a),"Problems in the Unitary Quantum View of the World" International Journal of Applied Science and Technology,Vol.2, No .5, May. www.ijastnet.com Sapogin L.G.,Dzhanibekov V.A. (2012b),"Object Lessons of the Unitary Quantum Theory " Journal of Modern Physics and Applied ,Vol., No .1 page 1-22, http://scik.org Smarandach Florentin (2012) “New Relativistic Paradoxes and Open Questions”, Somipress. Wang L.J. etc. (2000). “Gain-assisted superluminal light propagation”, Nature, 406, p.277-279. W.Hlistunov,Poduvalcev V.V.,Mogilyuk J.G. (2011) ”Science and Education”-pub. electronic scientific and technical periodic #11,November.

Figures

Figure 1. Experiments with individual photons on semitransparent mirror

285

Figure 2. Behaviour of wave packet in linear dispersion medium (i.e., rather like a series of stroboscopic photographs).

Figure 3.

Figure 4.

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Figure 5. Experiments of L.Wang - superluminal light propagation.

Figure 6.

Figure 7. Work for transferring the charge depends on the mode of transferring and on the path. 287

Questioning the Special and General Relativity Florentin Smarandache University of New Mexico 705 Gurley Ave., Gallup, NM 87301, USA [email protected]

Abstract. In this paper one revisits several paradoxes, inconsistencies, contradictions, and anomalies in the Special and General Theories of Relativity. Also, one reproposes new types of Relativities and two physical experiments 1. Introduction. We have published two books [1, 2] questioning the special and general theories of relativity. a) In the first book we presented our 1972 hypothesis that there is no speed barrier in the universe and one can construct arbitrary speeds -thus refuting the speed of light postulate. While Einstein considered a relative space and relative time but the ultimate speedof light, we do the opposite: we consider an absolute time and absolute space but no ultimate speed, and we call it the Absolute Theory of Relativity (ATR). The ATR has no time dilation, no length contraction, no relativity of simultaneity, and no relativistic paradoxes. We then parameterize Einstein’s thought experiment with atomic clocks, supposing that we know neither if the space and time are relative or absolute, nor if thespeed of light is ultimate speed or not. We obtain a Parameterized Special Theory ofRelativity (PSTR). Our PSTR generalizes not only Einstein’s Special Theory of Relativity,but also our ATR, and introduces three more possible Relativities to be studied in the future. Afterwards, we extend our research considering not only constant velocities butconstant accelerations too. Eventually we proposed a NoninertialMultirelativity for the same thought experiment, i.e. considering non-constant accelerations and arbitrary 3D-curves. b) In the second book we considered that not all physical laws are the same in all inertial reference frames, and we gave several counter-examples. We also supported superluminal speeds, and we considered that the speed of light in vacuum is variable depending on the moving reference frame. Space and time are absolute (universal), and separated from each other. Lorentz contraction and Minkovski’s metric are unrealistic. We explained that the redshift and blueshift are not entirely due to the Doppler Effect, but rather to the Medium Gradient and Refraction Index (which are 288

determined by the medium composition: i.e. its physical elements, fields, density, heterogeneity, properties, etc.). We considered that the space is not curved and the light near massive cosmic bodies bends not because of the gravity only as the General Theory of Relativity asserts (Gravitational Lensing), but because of the Medium Lensing. In order to make the distinction between “clock” and “time”, we suggested a first experiment with a different clock type for the GPS clocks, for proving that the resulted dilation and contraction factors are different from those obtained with the cesium atomic clock; and a second experiment with different medium compositions for proving that different degrees of redshifts/blushifts and different degrees of medium lensing would result. In the next sections we revisit several relativistic inconsistencies and we propose new research directions.

2. Multirelativity with Nonconstant Acceleration and 3D-Curves. In a 3D-Euclidean space for location and in an1D-oriented Euclidean space for time we consider a reference frame F1 with respect to which a particle P0 travels with a nonconstant acceleration a0 on a 3D curve C0 in an elapsed time ∆t0. Then we suppose the reference frame F1 is moving with nonconstant acceleration a1on a 3D curve C1 with respect to another reference frame F2. Similarly, the reference frame F2 is moving with a nonconstant acceleration a2 on a 3D curve C2 with respect to another reference frame F3. And so on: the reference frame Fn-1 is moving with a nonconstant acceleration an-1 on a 3D curve Cn-1 with respect to another reference frame Fn (where n>2). We call this a NoninertialMultirelativity, i.e. the most general case. 2.1. Research Problems on

Multirelativity. a)

How would the particle’s trajectory curve C0 be seen by an observer in the reference frame Fn ?

b)

What would be the particle’s speed (acceleration) as measured by the observer from the reference frame Fn ?

c)

What would be the elapsed time of the particle as seen by the observer in the reference frame Fn ? What are the transformation equations

d) from a reference frame to another? e)

Similar questions for rotating reference systems.

Particular cases would be helpful in starting such research, for example studying particles or reference frames travelling on linear curves, or on special curves, with constant speeds or constant accelerations, in reference frames that 289

have one, two, or three parallel coordinate axes. Then later trying to generalize the results.

2.2.

Example in Multirelativityof Nonlinear 3D-Trajectories of Particle and Reference Frames.

Since each constant speed v can be considered a constant zero-acceleration with initial velocity v, we treat the general case (i.e. the constant acceleration). Let’s consider in the reference frame F1 a particle P0traveling on a curve C0 from A to B:

B

B’

C0 A Fig. 1 with a constant acceleration a0 and initial velocity v0. Let’s take into consideration the earth’s gravity g too that influences the trajectory. F1 (which has the Cartesian system X1Y1Z1) is moving with a constant acceleration a1 with initial velocity v1 in the positive direction of the X1-axis (the OY1- and OZ1-axes are parallel respectively with OY2 and OZ2) with respect to the frame F2 (whose Cartesian system is X2Y2Z2). The arclength of AB is noted by d. →

From an observer in F2 the trajectory AB of the particle P0 in F1 is seen as a 2D- or →

3D-curve AB ' . The curve AB’ is described in F2 by a function

f (a0 , v0, a1, v1, g, C0, A, B,θ ) = ( x2(t), y2(t), z2(t))

(1)

i.e. ∆t

2

2

2

ArcLength(AB') = ∫ [ x2 '(t)] +[ y2 '(t)] +[ z2 '(t)] dt ≡ L(∆t ', ∆t) 0

(2)

where x2’(t), y2’(t), z2’(t) are respectively the derivatives of x2(t), y2(t), z2(t) with respect to t, and L(∆t’,∆t) is a notation to mean that the arclengthL, from A to B’, depends on ∆tand also on d, but d depends on ∆t’. The distance traveled by the reference frame F1 in ∆t elapsed time is 290

s1 = v1 (∆t ) +

1 2 a1 (∆t ) 2

(3) Supposing that particle’s traveling is seen as a constant acceleration by the observer in F2, then we have:

L ( ∆t ' , ∆t ) = x v0 (∆t ) +

1 2 x a0 (∆t ) (4) 2

where x v0 = the initial particle’s velocity as seen by the observer in F2, and x a0 = the particle’s constant acceleration as seen by the observer in F2. We know that in F1: AB = d = v 0 (∆t ') +

1 2 a 0 (∆t ') . 2

(5)

Depending on the suppositions regarding he connections between ∆t’ and ∆t (in an absolute time reference frame they are equal), or on the supposition about the acceleration of the particle

x a0 and x v0 we get particular cases in formula (1).

The reader can repeat this thought experiment for the case when the accelerations a0and a1 are not constant, and the reference frame F1 is moving with respect to the reference frame F2 on an arbitrary 3D-curve.

3. Length Contraction is Independent of Time The length contraction is, according to the Theory of Relativity, along the direction of the motion. And if the length is perpendicular on the direction of motion there is no contraction (according to the same theory). My question is this: it looks that the length contraction is independent of time (according to the Theory of Relativity)!... i.e. if a rocket flies one second, or the rocket flies one year the rocket's along-the-motion length contraction is the same, since the contraction factor

(6) depends on the rocket's speed (v) and on the light speed in vacuum (c) only. I find this as unfair, incomplete. It is logical that flying more and more should increase the length contraction. What about the cosmic bodies that continuously travel, do they contract only once or are they continuously contracting? 291

4. Elasticity of Relativistic Rigid Bodies? In the classical Twin Paradox, according to the Special Theory of Relativity, when the traveling twin blasts off from the Earth to a relative velocity v =

with

respect to the Earth, his measuring stick and other physical objects in the direction of relative motion shrink to half their lengths. How is that possible in the real physical world to have let’s say a rigid rocket shrinking to half and then later elongated back to normal (as an elastic material)? It is more science fiction… What is the explanation for the traveler's measuring stick and other physical objects, in effect, return to the same length to their original length in the Stay-At-Home, but there is no record of their having shrunk? Where this quantity of Joules of energy come from in order to shrink and then tacitly elongate back the stick? If it's a rigid (not elastic) object, how can it shrink and then elongate back to normal? It might get broken in this situation. This is like a science game…

5. Relativistic Masses vs. Absolute Masses Similarly, the relativistic masses are considered as increasing when traveling at a relativistic speed. But if the object is rigid, doesn’t it break? And, by the way, not all masses are variable, there exist absolute masses in the universe.

6. Miraculous Return to the Original Length! A rocket has length L at rest, afterwards in flying the length shrinks to L·C(v), then suddenly stops. According to the Special Theory of Relativity the rocket’s length L·C(v) tacitly returns to its original length! [As the rocket was made of… plasticizer!]

7. Miraculous Return to the Original Mass! Similarly, assume the rigid rocket’s mass at rest is M; after flying this mass increases to M/C(v). Then, when the rockets stops, according to the Special Theory of Relativity the mass tacitly… returns to its original value (as it was elastic… rocket!).

8. Symmetry and Asymmetry! In some examples, the Special Theory of Relativity considers a symmetric time dilation of two inertial reference frames. But in other examples, such as in the GPS position system where the satellite 292

clocks are slowed because of the satellite velocity, it considers an asymmetric time dilation of two inertial reference frames. As in the cause of the Twin Paradox, the time dilation was simply… abandoned! Again an auto-contradiction.

9. Physical and Non-Physical Time Dilation! The proponents of the Special Theory of Relativity contradict themselves when for some examples they say there is a physicaltime dilation (e.g. for particle accelerators, GPS, VBLI, NASA), and for other examples there is a non-physical time dilation (for interpreting the Twin Paradox). This is a self-contradiction. In the Absolute Theory of Relativity [2] one considers an absolute space, absolute time, absolute observer, and superluminal speeds are allowed. Superluminal phenomena do not involve traveling in time, neither objects traveling at c to having infinite masses, nor objects at superluminal speeds to having imaginary masses. The speed of light in vacuum is not "c" in all reference frames, but varies. It depends on the speed of its frame of reference and on the observer’s frame of reference. Simultaneity does exist and it is objective in nature. ATR has no time dilation, no length contraction, no relativitistic simultaneities, and all STR paradoxes disappear in ATR.

10. Density Increasing? According to the Special Theory of Relativity the mass of a moving object increases with the speed of the object, but what really increases: the object density, the object volume, or both? Because: Mass = Volume × Density

(7)

and since the object length decreases (in the direction of movement), then should we understand that the object volume also decreases? a) What is the Mass-Increasing Factor equal to? Einstein himself disliked the concept of relativistic mass given by the formula:

M (v ) =

m v2 1− 2 c

(8)

wherem = rest mass, 293

andM = relativistic mass of the object moving at speed v. b) What is the Volume-Increasing Factor equal to? c) What is the Density-Increasing Factor equal to?

11. The Mass Paradox The increasing in a moving frame of reference gives birth to another paradox. If there are n ≥ 2 simultaneous observers, each one moving with a different speed v1, v2, …, and respectively vn with respect to the body, then the mass of the body has simultaneously n different values, M(v1), M(v2), …, M(vn) respectively in the previous formula, which is impossible and ridiculous in practice, alike in the paradoxism movement. 12. Another Superluminal Thought Experiment Suppose we have two particles A and B that fly in the opposite direction from the fixed point O, with the speeds v1 and respectively v2 with respect to an observer that stays in the point O, as in the below figure: A

O

B Fig. 2

Let’s consider that v1 + v2 ≥ c. A) But, an observer that travels with particle A (therefore he is at rest with particle A) measures the speed of particle B as being v =v1 + v2 ≥ c. Similarly for an observer that travels with particle B: he measures the speed of particle A as also being superluminal: v =v1 + v2 ≥ c. B) If we suppose v1 = c and v2> 0, then for the observer that travels with particle A his speed with respect to observer in O is c. But, in the same time, for the observer that travels with particle A his speed with respect to particle B should be greater that c, otherwise it would result that particle B was stationary with respect to observer in O. It results that c + v2> c for non-null v2, contrarily to the Special Theory of Relativity. C) Let’s recall several of Einstein’s relativistic formulas: a) Time Dilation Formula is:

∆t (v) =

∆t ' v2 1− 2 c

(9)

where∆t = non-proper time, and∆t’ = proper time. 294

b) Length Contraction Formula is:

v2 L(v) = L '. 1 − 2 c

(10)

whereL = non-proper length, andL’ = proper length.

v, is:

c) Relativistic Momentum Formula of an object of mass m, moving with speed

mv

p (v ) =

v2 1− 2 c

.

(11)

d) Energy Formula of an object at rest, with rest mass m, is E0 = mc2. (12) e) The Total Energy Formula of an object of mass m, moving at speed v, is:

E (v ) =

mc 2 v2 1− 2 c

.

(13)

f) Kinetic Energy Formula of an object of mass m, moving at speed v, is:

    1 E (v) = mc 2  − 1 2  . v  1− 2  c  

(14)

Let’s consider instead of particles two objects A and B flying in opposite directions as above. C1) Firstly, when a clock goes at speed c with respect to any observer frame, the Special Theory of Relativity breakdown (because time dilates to infinity, length contracts to zero, relativistic momentum is infinity, the total energy and the kinetic energy are also infinite)! One actually gets the indeterminacy 1/0. Similarly in Lorentz Relativity for a clock going at speed c with respect to the Preferred Frame. C2) Not talking about superluminal speeds for which, according to the Special Theory of Relativity, the non-proper time, non-proper length, relativistic momentum, total energy and kinetic energy becomes… imaginary! D)

We

have

hypothesized

[2]

that

superluminal particles do exist and they do not necessitate infinite energy for 295

traveling since the above Einstein’s 2.13.C a)-f) relativistic formulas are valid in an imaginary space, not in the real one.

13. Another Dilemma about Length Contraction The distance between Earth and Alpha Centauri (which is the closest star to our solar system) is 4.3 light-years, as measured by an observer on our planet. A particle travels from Alpha Centauri to Earth at speed v = c (for example a photon) relative to the observer on Earth. According to Einstein’s Special Theory of Relativity: .

(15) (16)

whereL’ = proper length (which is the distance between two points measured by an observer at rest with respect to them); L = non-proper length (distance between two points measured by an observer that is not at rest with respect to them); v = constant speed of the moving reference frame; c = speed of light in vacuum. Therefore the contracted length: ,

(17)

which is a contradictory result since the distance between Alpha Centauri and Earth is much far from zero, and even from the reference frame of the moving photon it takes to the photon 4.3 light-years to get to Earth. 14. The Paradox of Simultaneity: Who is the Killer? We change Einstein’s thought experiment on simultaneity in the following way. Let’s consider a train moving as below from left to right: A

M

B

A’

M’ B’ Fig. 3. The Paradox of Simultaneity And a passenger Marcello in the middle point M of AB. A and B are the end and respectively the beginning of the train. Assume that in the train at the joints A and B there are Alex and respectively Barbara carrying each of them a gun of same caliber and bullet speed. Simultaneously, according to an observer Ot who stays at the midpoint M in the train, Alex and Barbara fatally shoot Marcello in the heart. Therefore according to observer in the train Ot, both Alex and Barbara are guilty of first degree murder, since both their bullets penetrate Marcello’s heart in the same 296

time. Therefore Alex and Barbara are both killers. Let’s consider another observer Oe on the embankment, who sits at the midpoint M’ which coincides with M. Similarly on the embankment the points A’ and B’ coincide respectively with A and B. According to the observer on the embankment, Oe, upon Einstein’s Special Theory of Relativity because the train moves from left to right, Barbara’s bullet penetrates Marcello’s heart and kills him before Alex. Therefore Barbara is a killer. But Alex is not a killer, since his bullet arrives later than Barbara’s, therefore Alex’s bullet penetrates a dead body (not a living body). According to the observer on embankment, Oe, it’s Barbara who fired the gun before Alex did. Contradiction. 14.1. The Dilemma of Simultaneity Let’s consider two entangled particles A and B flying in the opposite directions. Let’s assume they are so far away that light needs much time to travel from A to B. If A is in state s, it instantaneously causes B to be in state s too. We disagree with Theory of Relativity’s statement that there are no influences that travel faster than light. According to the Special Theory of Relativity we have: A) For an observer O1,traveling with particle A at time t, the event “A is in state s” occurs before the event “B is in state s”. B) For another observer O2,traveling with particle B at time t, the event “A is in state s” occurs after the event “B is in state s”. C) But these two observers are in contradiction with a quantum observer O3, which sits in the point M, where the particles started to fly from. O3, measuring particle A to be in state s at time t, will automatically know that particle B is in state s as well. Therefore, for the quantum experimenter O3 the particles A and B are simultaneously in the state s.

A

14.2.

M

B Fig. 4 Relativity of Simultaneity is Just an Appearance

In general let’s consider two simultaneous events in a reference frame at rest with respect to the events. In a moving reference frame, the same events don’t look simultaneous, but this is only an appearance, a subjective impression. In our Absolute Theory of Relativity we have no relativity of simultaneity. 15. Minowski’sSpacetime in Heterogeneous Medium In general, let’s consider two simultaneous events in a reference frame at rest with respect to the events. In a moving reference frame the same events don’t look simultaneous, but this is only an appearance. 297

Let’s consider the locations L1(x1, y1, z1) and L2(x2, y2, z2) and times t1 < t2. The spacetime distance between the events E1 = {I bread} at (x1, y1, z1 ,t1), and E2 = {I bread} at (x2, y2, z2, t2) gives the answer:

(18) Let’s say that d(E1, E2) = 0, then d(E1, E2) means that light has travelled in vacuum from location L1 to location L2 in the period of time t2 - t1. L2 L1 Fig. 5 But we see no connection between the fact that “I bread” and the fact that “light travels in vacuum on a distance equals to |L1L2|”! Let’s change this thought experiment and suppose that both locations L1(x1, y1, z1) and L2(x2, y2, z2) are under water, somewhere in the Pacific Ocean. Now light in the water has a smaller speed (cw) than in vacuum, i.e. cw< c. Therefore within the same interval of time t2 - t1, light travels in the water a lesser distance than L1L2. Thus d(E1, E2) has a different representation now L1L: L2 L1 L Fig.6 And, if instead of water we consider another liquid, then d(E1, E2) would give another new result. Therefore, if we straightforwardly extend Minkowski’sspacetime for an aquatic only medium, i.e. all locations Li(xi, yi, zi) are under water, but we still refer to the light speed but in the water (cw) then the coordinates of underwater events Ew would be Ew(xi, yi, zi ,cw, ti) and Minkowski underwater distance would be:

(19) But if the underwater medium is completely dark it might be better to consider the speed of sound as aquatic animals used in order to communicate (similarly as submarines use sonar). Let’s denote by sw the underwater speed of sound. Then the underwater events Ews(xi, yi, zi ,sw.ti) with respect to the speed of sound would have the Minkowski underwater distance:

(20) Similarly for any medium M where all locations Li(xi, yi, zi) are settled in, and for speed of any waves W that can travel from a location to another location in this 298

medium. 15.1.

Spacetime Diagram Didn’t Take into Account the Medium Composition

The problem becomes more complex when one has a heterogeneous medium and the waves travel with a speed v1 in a part and another speed v2 in another part, and so on [we mean the speed of light in liquids, in plastic, in glass, in quartz, in non-vacuum space in general]… 15.2. The Spacetime-Interval does not Distinguish Between Events’

Nature. If an event E1 occurs at location L1(x1, y1, z1) and time t1, and another event E2 occurs at the location L2(x2, y2, z2) and time t2, with t1 2 parts, will the planet gravitational field be also split among these n parts? Is the gravitational field conserved or transformed? If transformed, would it be into energy? 22. What Happens to the Curved Space around a Massive Object that has been

Destroyed? A) According to the General Theory of Relativity the space is curved around a massive object. Then, after the planet explodes (due to internal forces) or destroyed (because of external forces) does the space around it still remain curved or does it straighten back to flat? How would the disappearance of a planet impact the other planets? Will its orbit be occupied by another cosmic object that might be forming from residues that fall into this orbit? B) If space is curved around a star and forms tracks that planets travel following these tracks as rail-roads, why not other (small, or medium, or massive) objects are falling into these tracks and traveling around the star on the same orbits?

23. What Happens to the Planets that Orbit a Star that has Died? 302

If a star explodes or is destroyed or dies, what happens to the planets that orbit it? Will they continue to orbit by inertia the point where the star used to be? For how long time? 24. Is Time an Entity without Beginning and Ending? Is there a beginning and ending of time? Or is the time an entity without ending or beginning? We dough the Big Bang Theory that asserts a creatio ex nihilo of the Universe… If it was a point in the Big Bang that exploded, where did this point come from? What was before that point? 25. Creating Gravity Massive cosmic bodies create gravity. Is there a bound for such cosmic bodies (depending on mass, volume, density, and may be position) starting from which cosmic bodies create gravity, while below that bound they don’t create gravity? 26. Not All Physical Laws are the Same in All Inertial Reference Frames A. Different Inertial Values for a Moving Object. The laws of physics are not the same in all directions for a moving object according to the Special Theory of Relativity, since lengths which are oblique to the direction motion are contracted with the oblique-factor OC(v,θ), while the lengths along the motion direction are contracted with a different factor C(v), but lengths that are perpendicular to the direction motion are not contracted at all; which require different inertia values for the moving object. B. There are universal constants that are not quite “constant” throughout the universe. C. Would it be possible to get physical systems where the energy conservation law doesn’t hold? D. Would it be possible to get physical systems where the Earth’s physical laws are invalid? Maybe our laws are only local, but non-local laws may apply in other galaxies. We believe on other planets, or in other solar systems, galaxies the laws of physics are not the same. The Laws of Physics are influenced by the medium composition, velocity, etc. of the frame of reference.

27. Back in Time? If the time runs faster at the top of a gravitational field than at the bottom of a gravitational field, then sending a signal from top down could be like a message sent 303

back in time, which is unrealistic! 28. Wormholes do not Exist in a Real World The Wormholes were predicted by the Theory of Relativity [through Hermann Weyl in 1921 and John Archibald Wheeler in 1957], but the Wormholes permit time travel (that is unrealistic) and violate the causality. The Wormholes can be valid in an imaginary space only. 29. Newton’s Physics or Einstein’s Metaphysics? Is it any threshold of the speeds, let’s say speeds 0

we apply

Einstein’s Special Relativity? The proponents of Special Relativity say that Einstein’s Velocity Addition Formula

v1 + v 2 =

v1 + v 2 v1 ⋅ v 2 1+ 2 c

(29) prevails for any speeds. But this formula fails for superluminal speeds. 30. Neither 2c is a Speed Limit We do not agree with the Lorentz Relativity and the Lorentz Ether Relativity that support superluminal speeds up to a limit of 2c, although the absolute velocities are added using normal arithmetic in these two Relativities. We think there can constructed speeds that overpass2c as well. 31. Subjective Dilation-Time For two observers, in two moving referential frames, each one sees a time dilation for the other (time-dilation symmetry). But this is clearly a subjective time dilation, not an objective time dilation. These symmetric time dilations cannot be simultaneously done in practice; it is absurd. 32. Subjective Local Time vs. Objective Global Time The proponents of the Theory of Relativity assert that the so-called black hole is so powerful, that even the time itself is brought to a stop. But this looks very much as science fiction, since the objective time goes on anyway. 33. Relative vs. Absolute Space and Time Einstein says that there is no absolute space or absolute time. But we argue that we can mathematically consider an absolute space and absolute time, in order to eliminate all paradoxes and anomalies from Theory of Relativity. Relative Space and Time are referring to Subjective Theory of Relativities, while Absolute Space and Time are referring to Objective Theory of Relativity {see the 304

Absolute Theory of Relativity [2]}. The observers are relative, subjective indeed, but mathematically there can be considered an Absolute Observer. {There are things which are absolute.} 34. Contraction of the Universe? If the Universe is expanding (therefore moving), according to the Special Theory of Relativity it should be contracting along the moving direction. Continuously moving bringing continuously contracting?… therefore until getting back to a point (as the supposed original Big Bang)? 35. The Michelson-Morley Null Experiment was not quite Null While the establishment interpreted the result of Michelson-Morley Experiment as null, many other researchers considered it as not quite null. The supposed Michelson-Morley Null Experiment instigated the physical theorists to invent Relativity Theories with abnormal/non-practical length contraction, time dilation, mass increase, etc.

36. Variable Speed of Light in Vacuum The speed of light in vacuum is not invariant as seen by different frame of reference observers. It depends on the light source and its frame of reference. Its addition with other speeds follows the classical law of velocity addition. 37. Instantaneous Acceleration? In all paradoxes involving movement it is supposed that something goes at a constant uniform speed. One assumes a so-called "instantaneous acceleration": it is considered the ideal case when jumping from zero velocity directly to velocity v, and similarly jumping back from v to zero velocity when stopping. Therefore, many Thought Experiments are just approximations, no matter how large is the segment of constant speed with respect to the acceleration segment, because one cannot get to the constant speed without starting from zero speed. 38. Where the Extra-Mass Comes from? Relativistic Mass increases with speed according to the Theory of Relativity. But an elementary question arises: where the extra-mass comes from? Also, how the extra-mass was produced? Where did the extra-energy come from? Assuming that the initial mass has a charge, then does the increased mass have the same charge? 39. Space is Not Curved For a 1D(one-dimensional)-curve one can see its curvature in a 2D-space. For a 2D-surface one can see its curvature in a 3D-space. But how to see the curvature of a 3D-body, since there is no 4D-space in the real world? {We do not talk about the spacetime which has dimension four, since the spacetime is unreal.} Some physicists assume the possibility of hidden dimension(s), but such things have 305

not yet been found. Since there is no 4D-space in the real world (time is not taken into consideration since it is an independent entity), the 3D-space cannot be curved. 40. Black Hole is an Imaginary Cosmic Body Since the Black Hole purely aroused from the mathematical solution by Schwarzschild (and Hilbert) to the Einstein’s Field Equations, and because Einstein’s Field Equations do not describe the real universe, the Black Hole is so far just an imaginary cosmic body (or the notion of “black hole” has to be redefined). While the Black Body, for example, is a theoretical ideal (not entirely realized in practice, but only approximated…), which has not at all the power of reflecting light, the relativists consider the Black Hole as a physical object (!) 41. Fact or Mathematical Artifact? Interestingly, even the Black Hole’s center, which is a point of infinite density and zero volume (which looks fantastic!), is considered a real physical entity, although clearly it is a mathematical artifact. 42. What is the Maximum Discovered Density in the Universe? Since no experiment has ever shown a density being infinite for a physical object in the universe, our question is what would be the maximum discovered density in the universe? Would it be possible to create any given density? 43. Maximum Strongest Fields? a) What is the strongest gravitational field in the universe? What would be the maximum gravitational field to be produced in the laboratory? b) Similarly, what is the strongest electric field in the universe? What would be the maximum electric field to be produced in the laboratory? c) Similarly, what is the strongest magnetic field in the universe? What would be the maximum magnetic field to be produced in the laboratory? 44. How to Compute the Mass of a Singularity Point? Let’s consider the Black Hole’s singularity that occurs for r = 0 in 1/2

 2Gm  g 00 =  1 − 2  c r  

(30)

where

m = mass of the spherically cosmic body; G = gravitational constant of the body; r = distance from the cosmic body to the clock; c = speed of light in vacuum; and represents, according to the relativists, an infinitely dense point-mass that is at the center of the Black Hole. 306

It is not clear how to compute the mass of this singularity, since Mass = Volume × Density = = 0 × ∞ = 0, ∞, or another value? (31) Another singularity occurs for

r=

2Gm c2

(32)

in

g11 =

−1 1/2

 2Gm  1 − 2  c r  

(33)

And it is considered by relativists as Schwarzschild radius of a Black Hole, or the radius of the event horizon. 45. Mute Body What about a cosmic body whose escape speed would be greater than the speed of sound (instead of the speed of light)? Therefore, no sound would come out from that body, so it would be labeled as “mute body”! 46. Travel in Time is Science Fiction Relativists also support the travel to the past and travel to the future. But these are not possible in reality (see the traveling time paradoxes, where travelers change the past or the future). Because, for example, if somebody has changed the past, we don’t know which one was the real past, the original one or the changed one? It is not possible to have two or pasts! Relativists conclude that it is possible to travel in the future in the real world, because when we board an aircraft, for example, we are moving with respect to those who remain behind, therefore our time will pass slowly compared to those who remain behind. But this is an illusion since according to the absolute observer time is the same in moving or staying reference frame. Maybe the biological or subjective time changes, but not the objective time. 47. Time Coming to a Halt? According to the relativists, when 1/2

 2Gm  1 − 2  = 0 cr  

(34)

the time would come to a halt, because Schwarzschild’s solution to Einstein’s Field Equations for a spherically symmetric body shows that the rate of the clock is reduced by the factor 1/2

 2Gm  1 − 2  . cr  

(35) 307

But in the real world this is fantasy! 48. No Wormholes Therefore, Einstein-Rosen Bridge, as a solution to Einstein’s Field Equations, which allegedly connects different regions of the universe and just could be used as a time machine, is just fictitious. 49. Escape Velocity The escape velocity from an alleged Black Hole is c = 2Gm / r .

(36)

But in the future technology, it would be able to accelerate a photon inside of a Black Home’s event horizon to have it travels at a speed greater than c. Also the superluminal particles would escape. Thus the Black Hole would not be black any longer. 50. What about more Cosmic Bodies? Schwarzschild considered only one cosmic spherical body when solving Einstein’s Field Equations. But, what about more cosmic bodies (or more Black Holes)? 51. No Universe Expansion since Earth is not the Center of the Universe Hubble’s Law (1929) says that all galaxies are moving away from Earth at a velocity which is directly proportional to their distances from Earth. It presumes that, due only to the velocity at which the galaxies are moving away from the Earth, one has the redshift. Yet, it looks that Hubble’s Law is not followed by the quasars, which have big redshifts, emit large amounts of energy and lie behind our Milky Galaxy. According to Hubble’s Law, the universe is expanding, and the velocity of a receding galaxy with respect to our Earth is v = H0·D (37) whereH0 = Hubble’s Constant, and Ho is between 50-100 (typically 70) km/sec per megaparsec (3.26 million light-years); andD = distance from the galaxy to the Earth. But, if the galaxies recede with respect to the Earth at a velocity proportional to their distances from Earth, it involves that our Earth is, or is becoming, the center of the universe.

308

Fig. 9. Diagram of Allegedly Expansion Universe In the above diagram, the Earth stays in the expansion center, and G1, G2, …, Gn, … are galaxies, while G1’, G2’, …, Gn’, … are respectively their expansion positions after a certain t1. The diagram is continuously extended in all directions, according to Hubble’s Law, and after times t2, t3,… the corresponding new positions of the galaxies would respectively be G1’’, G2’’, …, Gn’’, … at time t2, then G1’’’, G2’’’, …, Gn’’’, … at time t3, etc. the galaxies getting further and further from the Earth, i.e. pushing the Earth closer and closer to the center of all galaxies. Even if Earth was not the center of the universe at the alleged Big Bang, after such permanent expansion of the universe with respect to the Earth, it would result that the Earth is in process of becoming the center of the universe… But the experiments do not show that. 52. Photon’s Wavelength Stretching and Shrinking? The photon is considered of having a dual form: wave and particle. If the photon is a wave, it has been asserted that the photon’s wavelength is stretched inside the intergalactic space, because of the expansion of the universe. But what happens with the photon’s wavelength when the photon enters a galactic space (which is not expanding), and afterwards it exists the galactic space and enters an intergalactic space (which is expanding), and so on? But, when the wavelength increases the wave frequency decreases (redshift); therefore the wave’s momentum and energy are diminished in the expansion of the universe. It seems to be an antithesis between the quantum mechanics (Copenhagen style) and the universe expansion. 309

If the photon is a particle, similarly because of the so-called expansion of the universe, does its pathlength increases inside the intergalactic space (which is expanding) and decreases inside the galactic space (which is not expanding)? Thus, what happens with its pathlength when the photon passes from an intergalactic space to a galactic space, then again to intergalactic space, and so on?

53. White Holes? From Einstein’s Field Equations one can also deduce the so-called White Holes, which are opposite to the Black Holes, and their property is that things are spewing out from the While Holes. But then if all matter is spewing out, as in antigravity, then the White Hole would contain no matter at all. Will it then remain only as a pure antigravity field? Very strange cosmic object…

54. Scientific Perversity If data obtained from any experiment or application matches the Theory of Relativity, then that type of data is considered covered by and supporting the Theory of Relativity. But, if such data does not match the Theory of Relativity predictions, then it is considered as not covered by the Theory of Relativity, and therefore (!) not contradicting the Theory of Relativity. All pretended tests of General Relativity can be solved without using the General Relativity. That’s why it became a break in the developing of science since every experiment and theory has not to be in conflict with Einstein’s Theory of Relativity, which became a fictitious theory producing confusions, ambiguities and self-contradictions. Unfortunately the optical illusions were taken for realities… An untrue hypothesis that “the speed of light is constant in vacuum in all reference frames (no matter with what uniformly moving speeds!) in all directions” generates a theory whose consequences are weird, non-common sense, even anti-logical and unrealistic. From invalid postulates one gets ridiculous conclusions like in comic stories. The physicists dream too much and suddenly they invent fantasy theories and require us to take them for granted. Theories that produce fantastic consequences are fantastic themselves. Einstein’s Relativity is more a science game than reality. Lorentz Transformation is just a distortion factor of the reality. The Gravitational Waves have not been discovered. Einstein’s Field Equations and Pseudotensor are valid in an imaginary space only. There is no proof that Einstein’s Field Equations do not violate the common law of conservation of energy and momentum. Other times, in order to bridge the gap between the Theory of Relativity and experimentally found data, all kind of strange things and ideas are invented. Instead of fitting the theory to better describe the reality, the reality is distorted in 310

order to fit into the theory!

References: 1. Smarandache, Florentin, Absolute Theory of Relativity & Parameterized Special Theory of Relativity &NoninertialMultirelativity, 92 p., 1982, Somipress, Fès, Morocco. 2. Smarandache, Florentin, New Relativistic Paradoxes and Open Questions, 126 p., 1983, Somipress, Fès, Morocco. 3. Bell, J. S., On the Einstein-Podolsky-Rosen Paradox,Physics 1, pp. 195-200, 1964. 4. Bohm, D., The Paradox of Einstein, Rosen, and Podolsky,Quantum Th., pp. 611-623, 1951. 5. Einstein, A.; Podolsky, B.; and Rosen, N., Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Phys. Rev. 47, pp. 777-780, 1935. 6. Smarandache, F., There is No Speed Barrier in the Universe, mss., Liceul Pedagogic Rm. Valcea, Physics Prof. Elena Albu,1972. 7. Rindler, W., Length Contraction Paradox, Am. J. Phys., 29(6), 1961. 8. Einstein, A., ZurEletrodynamikbewegterKörper, Annalen der Physik, Vol. 17, pp. 891-921, 1905. 9. A. Einstein, On the Electrodynamics of Moving Bodies, Annalen der Physik, 17, 891-921, 1905.

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Unsolved Problems in Special and General Relativity This book includes 21 papers written by 23 authors and co-authors. All papers included herein are produced by scholars from People’s Republic of China, except two papers written by Prof. L. Sapogin, V.A. Dzhanibekov, Yu. A. Ryabov from Russia, and by Prof. Florentin Smarandache from USA. The editors hope that the papers included here will contribute to advance scholarly research on some aspects of Special and General Relativity. This book is suitable for students and scholars interested in studies on physics. Contributors: Hua Di Li Zifeng Li Wen-Xiu

Hu Chang-Wei Jiang Chun-Xuan Liu Taixiang

Shi Yong-Cheng Xu Jianmin

Tu Runsheng Wu Fengming

Dong Jingfeng Duan Zhongxiao Fu Yuhua Guo Kaizhe

Yang Shijia Cao Shenglin Leo G. Sapogin

Guo Chongwu Guo Ying-Huan Guo Zhen-Hua

V.A. Dzhanibekov Yu. A. Ryabov Florentin Smarandache