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University of New Mexico
UNM Digital Repository
Faculty and Staff Publications
2013
Unsolved Problems in Special and General Relativity
Florentin Smarandache University of New Mexico, smarand@unm.edu
Mathematics
Follow this and additional works at: https://digitalrepository.unm.edu/math_fsp Part of the Mathematics Commons
Recommended Citation Smarandache, Florentin. "Unsolved Problems in Special and General Relativity." (2013). https://digitalrepository.unm.edu/math_fsp/64
This Book is brought to you for free and open access by the Mathematics at UNM Digital Repository. It has been accepted for inclusion in Faculty and Staff Publications by an authorized administrator of UNM Digital Repository. For more information, please contact amywinter@unm.edu.
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: info@edupublisher.com
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: victorchristianto@gmail.com. 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.
In the next paper, he also found a new gravitational formula: F = − mc2 R , established the expansion theory of the universe, and obtained the expansion acceleration: ge = u4 C 2 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
12 New Gravitational Formula: F
=
mc2 −
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 dihua36@gmail.com
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:
( ) ε
=
24π 3
a2 T 2c2 1− e2
,
(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 ×106 [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
365318
Mercury makes
= 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:
φ
=
π
 1 +
3
4 α (α1
+α2
)
.
(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
=
1 r1
and
α 2
=
1 r2
signify the reciprocal values of
the orbit’s maximum and minimum distances r1 and r2 from the sun.
α
=
2kW c2
≈ 2.9535 ×103 [m]
is
a
constant
with
the
gravitational
constant
k = 6.673 ×10 −11 [m 3 kg −1 s −2 ] and the sun’s gravitational mass W ≈ 1.9891×1030 [kg].
Mercury’s r1 ≈ 6.9818 ×1010 [m] and r2 ≈ 4.6002 ×1010 [m]. So, its
α1 ≈ 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:
ε
=
2(φ
−π)
=
3
2 πα(α1
+α2 ) ≈
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 (α1 + α 2 )]∫
α1
dx ,
− (x − α1 )(x − α 2 )(1 − αx)
(3)
4
or approximately, upon expansion of (1 − αx)−1 2 ,
∫α2
φ = [1 + α (α1 + α 2 )]
α1
1
+
α 2
x dx 
.
− (x − α1 )(x − α 2 )
(4)
“The
integration”
Einstein
writes,
“yields
φ
 = π 1 +
3
4 α (α1
+ α 2 ) .”
This
is
a
fatal
error! Actually, a correct integration should be as follows:
∫
1 +
α 2
x dx 
=∫
dx
+α ∫
xdx
− (x − α1 )(x − α 2 ) − (x − α1 )(x − α 2 ) 2 − (x − α1 )(x − α 2 )
=∫
dx
 + α −
− (x − α1 )(x − α 2 ) 2 
−
(x
− α1 )(x
−α2
)
+
α1
+α2 2
∫
dx
 
− (x − α1 )(x − α 2 ) 
=
 1
+
α 4
(α1
+
α
2
)
∫
dx
α
−
− (x − α1 )(x − α 2 ) 2
− (x − α1 )(x − α 2 )
=
 1
+
α 4
(α1
+
α
2
)
×
arcsin
2x
− (α1 + α 2
α2 −α1
)
−
α 2
− (x − α1 )(x − α 2 ) .
Therefore,
α2
∫
α1
1 +
α 2
x dx 
− (x − α1 )(x − α 2 )
=
 1 +
α 4
(α1
+α2
)
 arcsin 
α α
2 2
− α1 − α1
−
arcsin α1 α2
−α2 − α1
  
=
 1
+
α 4
(α1
+
α
2
)[arcsin1
−
arcsin(−
1)]
=
 1
+
α 4
(α1
+
α
2
)
⋅
2
arcsin1
=
π
 1
+
α 4
(α1
+
α
2
)
,
not
Einstein’s π
 1 +
3
4 α (α1
+
α2
)
!
Finally, the correct integration yields:
α2
φ = [1 + α (α1 + α 2 )]∫
α1
−
1 +
α 2
x
dx 
(x − α1 )(x − α 2
)
=
[1 + α (α1
+α2
)]π
 1 +
α 4
(α1
+α2
)
=
π
 1
+
5 4
α
(α1
+
α2
)
+
1 4
α
2
(α1
+
α2
)2
 
.
5
and
ε
=
2(φ
−π)=
π
2 α (α1
+ α 2 )[5 + α (α1
+ α 2 )] ≈ 8.3651×10−7 [rad]
per
mercury-
year
or
8.3651×10 −7 × 415.28 ≈ 3.4738 ×10 −4 [rad] ≈ 71.5 ’’ per 100 earth-years.
It is far different from 43 ’’ ofthe astronomical observation.
Einstein’s explanation contains one more operational error. Although
[1+ α(α1 + α2 )] ≈ 1
since
Mercury’s
( ) α (α1 + α 2 ) = 2.9535 ×103 1.432309 ×10−11 + 2.173847 ×10−11 ≈ 1.0651×10−7 << 1 ,
the [α (α1 + α 2 )] is not negligible. Because, the very fine quantity of Mercury’s perihelion
motion ε = 2(φ − π ) originates exactly from the very small difference between φ and π , so
that
the
approximation
of
α2
φ=∫
1 +
α 2
x dx 
α1 − (x − α1 )(x − α 2 )
instead of
α2
φ = [1 + α (α1 + α 2 )]∫
α1
1 +
α 2
x dx 
− (x − α1 )(x − α 2 )
is misleading. Actually, without his arbitrary
approximation, Einstein’s wrong integration would have led to:
α2
φ = [1 + α (α1 + α 2 )]∫
α1
−
1
+
α 2
x dx 
(x − α1 )(x − α 2
)
=
[1 + α (α1
+α2
)]π
 1 +
3
4 α (α1
+α2
)
=
π
 1 +
7 4
α (α1
+
α2
)+
3 4
α
2
(α1
+
α2
)2
 
and
ε
=
2(φ
−π)=
π 2
α (α1
+ α 2 )[7
+ 3α (α1
+ α 2 )] ≈ 11.711×10−7 [rad]
per
mercury-
year,
or
11.711×10−7 × 415.28 ≈ 4.8633 ×10−4 [rad] ≈ 100.1” per 100 earth-years.
The result would be even worse!
3 Einstein’s Formula (1) is Questionable
According to Einstein’s formula (1), ε ≠ 0 even if e = 0 . However, if a planet moves along a circular orbit ( e = 0 ) without eccentricity, then its orbit has neither perihelion nor aphelion. How can it have perihelion motion ε ≠ 0 ?
Mercury’s orbit is not a strict ellipse. That’s why it has perihelion motion. Nevertheless,
6
Einstein makes an approximation by use of the relationships among an elliptic orbit’s parameters:
( ) r1 = a(1+ e) ,
r2 = a(1− e) ,
11 1
1
2
α1 + α 2 = r1 + r2 = a(1 + e) + a(1 − e) = a 1 − e2
.
( ) Thus, his equation (2) becomes
φ
=
π
 1
+
3 2
a
α 1−
e2
 
and he approximately obtains:
ε
=
2(φ
−π)=
3π
α
a(1 −
)e2 .
(5)
Since elliptic orbit’s period is T =
2π kW
a3 2,
so
α
=
2kW c2
8π 2a 3 = T 2c2
which leads (5)
to his formula (1):
( ) ε
=
24π 3
a2 T 2c2 1− e2
with irrational appearance of the eccentricity e in it.
For every round of its orbit ( 360o = 1296000 ”),Mercury’s perihelion motion is just
about 1”. To deal with such a fine quantity, it does not allow Einstein to do so many arbitrary approximations.
4 Conclusion and More Einstein’s general theory of relativity cannot explain Mercury’s perihelion motion. He
obtained “for the planet Mercury, a perihelion advance of 43” per century” by an incorrect
integral calculus and many arbitrary approximations. His formula (1) is a poorly patched wrong result, tailored specially for Mercury. That is why his formula (1) fails to explain the perihelion motions for Earth and Mars. Einstein was unfair to blame “the small eccentricities of the orbits of these planets” for his failure. To sum up, Einstein’s general theory of relativity is dubious.
Moreover, based solely on the principle of relativity without any postulate (such as Einstein’s constant speed of light and Lorentz-Fitzgerald’s length-contraction), this author has developed a new relativistic mechanics [2] . The new relativistic mechanics can precisely explain all the three astronomical phenomena (the sunlight’s red shift, the perihelion motion of Mercury and the angular deflection of light by the sun’s gravitation) within mechanical framework. In short, gravitation is force by nature. Geometrized gravitation with fourdimensional space-time warped by matter is not true.
Reference [1] A. Einstein, The Collected Papers of Albert Einstein, Princeton University, 6:112-116. [2] Di Hua, Challenging Einstein’s Theory of Relativity, China Astronautics Publishing Co.,
7
Ltd, November 2011
Special Relativity Arising from a Misunderstanding of Experimental Results on the Constant Speed of Light
Li Zifeng
(Yanshan University, Qinhuangdao, Hebei, 066004, China)
Abstract: All experiments show that the speed of light relative to its source measured in vacuum is constant. Einstein interpreted this fact such that any ray of light moves in the “stationary” system with a fixed velocity c, whether the ray is emitted by a stationary or by a moving body, and established Special Relativity accordingly. This 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. Keywords: Special Relativity, light speed, Einstein, Lorentz transformation
1 Introduction Special Relativity was established by Einstein nearly a century ago1 and has become
nowadays a compulsory course in many universities2. However, the rationality of its derivation process and its conclusions are still under suspicion3-28.
This paper briefly reviews the basic hypotheses and the main viewpoints of space-time in Special Relativity. The derivations and the mistakes involved in the Lorentz transformation and Einstein’s original paper are analyzed. The transformation between two coordinate systems moving uniformly relatively to another will be revised. It will be 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. 2 Summary of Special Relativity2
2.1 Basic hypotheses in Special Relativity (1) Principle of relativity: For describing any law of motion, all inertial coordinate systems
moving uniformly relatively to another are equal. (2) Principle of the constant speed of light: The speed of light measured in vacuum in all
inertial coordinate systems moving uniformly relatively to another is the same. 2.2 Lorentz transformation
Two coordinate systems K and K ′ (OXYZ and O′X ′Y ′Z ′ ), with their respective axes parallel to another, move uniformly relatively to another with a speed v of K ′ relative to K along X-axis. The time count starts when O and O′ coincide with each other, as shown in Fig. 1.
8
Y
Y′
y
y'
P
vt
O
O′
X X′
z
z'
x′
x
Z
Z'
____________________________________________________
Figure 1. Coordinate system 1
Let (x, y, z, t) be an event appearing in K at time t, the same event appears in K ′ as ( x′, y′, z′,t' ) at time t ′ . Time-space coordinates ( x, y, z, t ) and ( x′, y′, z′, t′ ) that describe the
same event satisfy the Lorentz transformation
x' =
x − vt
, y'= y, z'= z,t'=
t
−
vx c2
. (1)
1
−
 
v c
 
2
1
−
 
v c
 
2
x=
x'+vt' , y = y', z = z', t =
t
'+
vx' c2
. (2)
1
−
 
v c
 
2
1
−
 
v c
 
2
where, c is the speed of light. The derivation of the Lorentz transformation is as follows.
For point O, x = 0 is observed in K all the time; but x′ = −vt ′ is observed in K ′ at time t ′ ,
viz. x'+vt' = 0 . Therefore it could be seen that x and x'+vt' become zero at the same time for
the point O. Then, suppose that there is a direct ratio k between x and x'+vt' all the time, i.e.,
x = k(x'+vt' ) .
(3)
Or, for point O′ ,
x' = k' (x − vt) .
(4)
The principle of relativity requires that K is equal to K ′ . The two equations above have to
be of the same form, such that k is equal to k ′
k = k'.
(5)
Thus
x' = k(x − vt) .
(6)
To establish the transformation, the constant k must be determined. According to the
principle of the constant speed of light, if a light signal goes along OX when O and O′ are at
the same point ( t = t' = 0 ), at any time t ( t' in K ′ ), the positions of this signal at these two coordinate systems are as follows respectively
x = ct, x' = ct' .
(7)
Substituting equation (7) into the product of equation (3) and equation (6), we have
9
k = c = 1 . (8)
c2 − v2
1
−
 
v c
 
2
Substituting equation (8) into (3) and (4), we have
x' =
x − vt
,t'=
t
−
vx c2
.
(9)
1
−
 
v c
 
2
1
−
 
v c
 
2
x=
x'+vt'
,t =
t
'+
vx' c2
.
(10)
1
−
 
v c
 
2
1
−
 
v c
 
2
2.3 Key points of Special Relativity Based on the Lorentz transformation, Special Relativity concluded that: (1) Simultaneity effect: If two events appear at two points in a coordinate system at rest
synchronously, the times that these two events appear in another coordinate system moving uniformly are not same.
(2) Length contraction effect: In a coordinate system with a relative speed, the length of an object measured along the speed direction of the system is shorter than that measured in another coordinate system in which the object is at rest.
(3) Time dilation effect: For an event, the time measured in a coordinate system with relative speed to the place is longer than that measured in another coordinate system in which the place is at rest. 2.4 Dynamics of Special Relativity
(1) The mass of an object measured in a moving coordinate system is larger than that measured in the coordinate system in which the object is at rest.
(2) The energy of an object equals its mass multiplied by the square of the speed of light.
3 Some Mistakes in Special Relativity
3.1 Wrong comprehending of experimental results on the constant speed of light Until now, all experiments show that the speed of light relative to its source measured in
vacuum is constant. This can be explained as follows. (1) For light signals in vacuum radiated from sources that are fixed in any inertial
coordinate systems, measured speeds of these light signals relative to their sources (or coordinate systems) respectively are equal.
(2) For light signals in vacuum radiated from a definite source, light speeds relative to its source measured in coordinate systems moving uniformly relatively to another are equal.
The above fact described by Ref. 2, and Section 2.1 of this paper, is changed to “the speed of light measured in vacuum in all inertial coordinate systems moving uniformly relatively to another is the same”, named as “principle of the constant speed of light”. It does not point out that the speed of the light is relative to its source. In the derivation of the Lorentz transformation, the above fact is formulated such that for light in vacuum radiated from a definite source, light speeds relative to any coordinate systems are equal. In Einstein’s words, any ray of light moves in the “stationary” system of coordinates with the determined velocity
10
c, whether the ray is emitted by a stationary or by a moving body. This is also named “the principle of the constant speed of light”. This is wrong, because it neglects relative motions between coordinate systems, as listed in Table 1.
Table 1. Experimental result of light speed and the principle of the constant speed of light
True fact Incomplete
Wrong
statement explanation
The speed of The speed of Any ray of light
light relative to light
moves in the
its
source measured in “stationary”
measured in vacuum in all system
of
vacuum in all inertial
coordinates
Statement
inertial coordinate
coordinate with
the
systems
determined
systems moving moving
velocity
c,
uniformly
uniformly whether the ray
relatively to relatively to be emitted by a
another
is another is the stationary or by
constant.
same.
a moving body.
The principle The principle of
of
the the constant
Name
No
constant
speed of light
speed of light by Einstein.
by ref 2.
Not pointing Neglecting
out that the relative motions
Mistakes
No
speed is light between
relative to its coordinate
source.
systems.
Equations (1) through (6) describe an object’s motion in a fixed system, its motion in another moving system and the possible transformation between these two systems. Here, k must be determined using equation (7). In equation (7), x = ct describes a photon emitted from a source fixed at the origin of the fixed system. Equation x' = ct ' describes another photon emitted from a source fixed at the origin of the moving system. There is a relative motion between these two sources. So, there is a relative motion between these two photons from two different sources. Equations (1) through (6) describe one object in two systems. On
the other hand, Equations (7) x = ct, x' = ct' describe two different objects (photons)
moving in two systems independently. It is problematic to substitute Eq. (7) into equation (6). Actually, to obtain k , x = ct, x' = ct'−vt' must be used instead of those in Eq. (7).
3.2 The coordinate in the direction of motion of the Lorentz transformation20 is 0=0
With reference to the equations in Section 2.2, in expression x' = x − vt ,
1
−
 
v c
 
2
11
， because x − vt ≡ 0 , we have x' ≡ 0 . Similarly in expression x =
x'+vt' , x'+vt' ≡ 0
1
−
 
v c
 
2
results in x ≡ 0 . Also in Section 2.2, there is a statement “For point O, x = 0 is observed in K all the time; but x′ = −vt ′ observed in K ′ at time t ′ , viz. x'+vt' = 0 . Therefore it could be viewed that x and x'+vt' become zero at the same time for the point O. Then, suppose that there is a direct ratio k between x and x'+vt' all the time, i.e., x = k(x'+vt' ) ”. Because x'+vt' = 0 always holds,
x = 0 holds all the time. “Or, for point O′ , x' = k' (x − vt) ”.Because x + vt = 0 is valid all the time, x′ = 0 always
holds. So, the coordinate in the direction of motion of the Lorentz transformation is 0=0.
3.3 Wrong derivation of equations
3.3.1Description of an event replacing description of another event Equations (3) through (6) describe the point O in two coordinate systems. Equation (7)
describes the positions of two photons radiated from sources fixed in these two coordinate systems at their origins respectively, not the positions of one photon. By substitution of equation (7) into equations (3) through (6), the description of an event replaces the description of another event. A substitution mistake occurs.
Y
Y′
y
y'
P
vt
O ct A O′ ct' A' X X′
z
z'
x′
x
Z
Z'
____________________________________________________
Figure 2. Coordinate system 2
Based on equation (7), in OXYZ as shown in Fig. 2, a photon starts form point O at time t=0, and arrives at point A at time t; in O′X ′Y ′Z ′ , another photon starts form point O' at time t' =0, and arrives at point A' at time t' . It is obvious that these are two events of two different photons. It would be clearer if these two origins do not lie at the same point, with an original displacement S at time t=0, as shown in Fig. 3.
Let’s follow the derivation process of the Lorentz transformation. Two coordinate systems K and K ′ (OXYZ and O′X ′Y ′Z ′ ), with their corresponding axes parallel to each other respectively, move uniformly relatively to the other, the speed of K ′ is v relative to K along the X-axis. The time count starts when O′ is S from O in the +X direction.
12
Y
Y′
y
y'
P
vt+S
O ct A O′ ct' A' X X ′
z
z '
x′
x
Z
Z'
____________________________________________________
Figure 3. Coordinate system 3
For point O, x = 0 is observed in K all the time; but x′ = −vt′ − S is observed in K ′ at
time t ′ , viz. x'+vt'+S = 0 . Thus it can be seen that x and x'+vt'+S become zero at the same
time for this point. Then, suppose that there is a direct ratio between x and x'+vt'+S for all
the time, and let k be the proportional factor such that
x = k(x'+vt'+S) .
(11)
Similarly for point O′ , we have
x'= k'(x − vt − S) .
(12)
From the principle of relativity, K is equal to K ′ . The two equations above must be of the
same form. Therefore, k must be equal to k ′
k = k'.
(13)
We further have
x'= k(x − vt − S) .
(14)
To finish the transformation, the constant k must be given. Absurdity 1.Based upon the principle of the constant speed of light, if a light signal goes
along OX when O and O′ at the same point ( t = t' = 0 ), at any time t ( t' in K ′ ), the positions
at these two coordinate systems are
x = ct, x' = ct'
(15)
respectively. It is obvious that these are two events of two sources.
Substitution of equation (15) into the product of equation (11) and equation (14) yields
xx' = k 2 (x'+vt'+S)(x − vt c2tt' = k 2 (ct'+vt'+S)(ct −
− S) vt −
S
).
(16)
k is indeterministic. Absurdity2.From the principle of the constant speed of light, if a light signal goes along
OX when O and O′ coincide with each other ( t = t' = 0 ), at any time t ( t' in K ′ ), the positions
at these two coordinate systems are as follows, respectively
x = ct, x' = ct'−S .
(17)
It is obvious that these are two events of two sources.
Substitution of equation (17) into the product of equation (11) and equation (14) gives
xx' = k 2 (x'+vt'+S)(x c2t(t'−S) = k 2 (ct'+vt
− vt − S) '+S)(ct −
vt
−
S
).
(18)
k is also indeterministic. 3.3.2 Direct transformation is not equal to indirect transformation
13
Suppose there are three coordinate systems K , K ′ and K" (OXYZ, O′X ′Y ′Z ′
and O" X "Y"Z" ), whose respective axes are parallels to one another, move uniformly
relatively to another, speed of K ′ is v relative to K along X-axis, speed of K" is u relative to
K ′ along the X-axis. The time count starts when O, O′ and O" are located at the same point.
The direct transformation from K to K" is
x"= x − (v + u)t .
(19)
1
−
 
v
+ c
u
 
2
Y
Y′
Y"
y
y'
P
y"
vt
ut
O
O′
X
O" X ′
z
z'
x′
z" X"
x
x"
Z
Z'
Z"
____________________________________________________
Figure 4. Coordinate system 4
The indirect transformation from K to K" via K ′ is
uv
x"= x'−ut' = x(1 + c2 ) − (u + v)t . (20)
1
−
 
u c
 
2
1
−
 
u c
 
2
1
−
 
v c
 
2
It is obvious that equation (19) is not equivalent to equation (20).
3.4 The relative speed between two objects can neither reach nor exceed the light speed The process of the above derivations does not make the assumption that the relative speed
between two objects is smaller than the light speed, but the result is that the relative speed between two objects can neither reach nor exceed the light speed. The Lorentz transformation is self-contradictory. Now, astronomy observations find that many planets move apart faster than the light speed.
3.5 There is an antinomy between the length contraction effect and the principle of relativity
The length contraction effect indicates that if a sphere is fixed in a coordinate system, this sphere observed in another coordinate system moving uniformly relatively to the system will become an ellipsoid. A direct extension to this claim is that if the relative speed equals the light speed, the sphere will become a circle, changing from 3-dimensions to 2-dimensions. Therefore, there is an antinomy between the length contraction effect and the principle of relativity.
4 Mistakes in Einstein’s “On the Electrodynamics of Moving Bodies”
14
4.1 Excerpt from Einstein’s paper1
The following reflections are based on the principle of relativity and on the principle of the
constancy of the velocity of light. These two principles we define as follows:
(1) The laws by which the states of physical systems undergo change are not affected,
whether these changes of state be referred to the one or the other of two systems of co-
ordinates in uniform translational motion.
(2) Any ray of light moves in the “stationary” system of coordinates with the determined
velocity c, whether the ray be emitted by a stationary or by a moving body. Hence
velocity = light path . time interval
We imagine further that at the two ends A and B of the rod, clocks are placed which
synchronize with the clocks of the stationary system, that is to say that their indications
correspond at any instant to the “time of the stationary system” at the places where they
happen to be. These clocks are therefore “synchronous in the stationary system”.
We imagine further that with each clock there is a moving observer, and that these
observers apply to both clocks the criterion established for the synchronization of two clocks.
Let a ray of light depart from A at the time tA , let it be reflected at B at the time tB , and
reach A again at the time tA′ .
Taking into consideration the principle of the constancy of the velocity of light we find that
tB
− tA
=
rAB c−v
and
t A′
− tB
=
rAB c+v
,
(21)
where rAB denotes the length of the moving rod—measured in the stationary system.
Observers moving with the moving rod would thus find that the two clocks were not
synchronous, while observers in the stationary system would declare the clocks to be
synchronous.
Let us in “stationary” space take two systems of co-ordinates, i.e. two systems, each of three rigid material lines, perpendicular to one another, and issuing from a point. Let the axes of X of the two systems coincide, and their axes of Y and Z respectively be parallel. Let each system be provided with a rigid measuring-rod and a number of clocks, and let the two measuring-rods, and likewise all the clocks of the two systems, be in all respects alike.
Now to the origin of one of the two systems (k) let a constant velocity v be imparted in the direction of the increasing x of the other stationary system (K), and let this velocity be communicated to the axes of the co-ordinates, the relevant measuring-rod, and the clocks. To any time of the stationary system K there then will correspond a definite position of the axes of the moving system, and from reasons of symmetry we are entitled to assume that the motion of k may be such that the axes of the moving system are at the time t (this “t” always denotes a time of the stationary system) parallel to the axes of the stationary system.
We now imagine space to be measured from the stationary system K by means of the stationary measuring-rod, and also from the moving system k by means of the measuring-rod moving with it; and that we thus obtain the co-ordinates x, y, z, andξ,η,ζ, respectively. Further, let the time t of the stationary system be determined for all points thereof at which there are
clocks by means of light signals in the manner indicated before; similarly let the timeτ of the
moving system be determined for all points of the moving system at which there are clocks at rest relatively to that system by applying the method, given before, of light signals between the points at which the latter clocks are located.
15
To any system of values x, y, z, t, which completely defines the place and time of an event in the stationary system, there belongs a system of values ξ,η,ζ,τ, determining that event relatively to the system k, and our task is now to find the system of equations connecting
these quantities. In the first place it is clear that the equations must be linear on account of the properties of
homogeneity which we attribute to space and time. If we place x' = x − vt , it is clear that a point at rest in the system k must have a system of
values x', y, z , independent of time. We first define τ as a function of x', y, z , and t. To do
this we have to express in equations thatτ is nothing else than the summary of the data of clocks at rest in system k, which have been synchronized according to the rule given before.
From the origin of system k let a ray be emitted at the time τ 0 along the X-axis to x′ , and
at the time τ 1 be reflected thence to the origin of the coordinate, arriving there at the time τ 2 ;
we then must have
1 2
(τ
0
+τ2
)
=
τ1
.
(22)
by inserting the arguments of the function τ and applying the principle of the constancy of
the velocity of light in the stationary system:
1 2
 τ
(0,0,0,
t)
+
τ
(0,0,0,
t
+
x′ c−v
+
c
x′ +v
 )
.
(23)
= τ (x′,0,0,t + x′ ) c−v
Hence, if x' be chosen infinitesimally small,
1 ( 1 + 1 ) ∂τ = ∂τ + 1 ∂τ . (24) 2 c − v c + v ∂t ∂x′ c − v ∂t
or
∂τ +
∂x′
c2
v − v2
∂τ ∂t
= 0.
(25)
With the help of this result we easily determine the quantities ξ,η,ζ, by expressing in equations that light (as required by the principle of the constancy of the velocity of light, in combination with the principle of relativity) is also propagated with velocity c when measured in the moving system.
We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity.
4.2 Mistakes (1) Equation (21) is derived from the assumption that “Any ray of light moves in the stationary system of co-ordinates with the determined velocity c, whether it is emitted by a stationary or by a moving body”. In fact, the light seen by us is emitted by the body observed by us, no matter whether this body is moving or not, and the light speed is c relative to the body. So, Eq. (21) is just a hypothetical phenomenon that does not exist in the world. The fact is that observers moving with the moving rod and observers in the stationary system will find
16
that the two clocks are synchronous. For further theories of moving objects observation, see ref. 26.
(2) It is evident that if equation (21) is true (equation (21) is false in fact), then equation (22) will be false. But the author continued to substitute equation (21) into equation (22). As a consequence, equation (23) is incorrect.
(3) There is a mistake from equation (23) to equation (24). From equation (23), there is
1 2 ∂(t +
∂τ
x′ +
x′
)
(
∂t ∂x′
+
c
1 −
v
+
c
1 +
v
)
c−v c+v
. (26)
+
1 2
∂τ ∂t
∂t ∂x'
=
∂τ ∂x′
+
∂(t
∂τ +c
x′ −v
)
(
∂t ∂x′
+
1) c−v
Because x' = x − vt ,
∂τ
∂τ
∂(t +
x′ c−v
+
x′ ) c+v
≠
∂t
and
∂(t
∂τ
+
c
x′ −v
)
≠
∂τ ∂t
,
then
1 ( 1 + 1 ) ∂τ ≠ ∂τ + 1 ∂τ . (27) 2 c − v c + v ∂t ∂x′ c − v ∂t
(4) For a definite ray, it is first defined that the ray moves with velocity c relative to the
stationary system; then, it is also defined that the ray moves with velocity c relative to the
moving system. This is an evident mistake.
(5) In equations (21), (23) and (24), the velocity between bodies and photons c + v exceeds
the light velocity c. This conflicts with the main claim of Special Relativity.
(6) “If we place x' = x − vt , it is clear that a point at rest in the system k must have a system
of values x', y, z , independent of time”. Here, first, let x' = x − vt , then let x′ be independent
of t . This is a conflict.
(7) First assuming x' = x − vt , and then the result is ξ =
x − vt . ξ = x' . This is also a
1
−
 
v c
 
2
conflict.
Einstein’s paper “On the Electrodynamics of Moving Bodies” is full of mistakes and conflicts.
5 Correct Transformation26 5.1 Re-establishment of transformations
To finish the transformation, the constant k must be determined. Based upon the experimental result of the constant speed of light, if a light signal goes along OX when O
17
and O′ are at the same point ( t = t' = 0 ), at any time t ( t' in K ′ ), the positions at these two
coordinate systems are as follows respectively
x = ct, x' = ct'−vt' .
(28)
Substitution of equation (28) into the product of equation (3) and equation (6) yields
k =1.
(29)
Substitution of equation (29) into (3) and (4) yields
x= x' =
x'+vt' x − vt
 
.
(30)
t = t' 
This is the classic Galilean transformation. There is no light speed in it.
5.2 Equation (28) accords with experimental result of the constant speed of light
As shown in Fig. 2, if a photon emitted from a source fixed at O of OXYZ system moves
from O at time t = 0 , arrives at A at time t, then its relative speed to O (or source) in OXYZ
OA is
=
x = ct = c ;
and
its relative
speed
to
O′
in O′X ′Y ′Z ′ is
O ′A = x' (A) = ct'−vt' = c − v ;
t tt
t'
t'
t'
and the measured speed of this photon relative to its source in O′X ′Y ′Z ′ is
OA t'
=
x'( A) − x'(O) t'
=
(ct'−vt'
)− t'
(−vt'
)
=
c
.
For
a
specific
photon,
its
relative
speeds
to
different systems are varied; its relative speeds to its source measured in different systems are
the same.
5.3 Deductions Special Relativity based upon the Lorentz transformation is not correct. As the key
components of Special Relativity, the simultaneity effect, length contraction effect, time dilation effect, mass increasing effect and the question of rest energy are all groundless. The relative speed between two objects can exceed the light speed.
6. Conclusions (1) Special Relativity is derived from a misunderstanding of experimental results involving
the constant speed of light. (2) Special Relativity based upon the Lorentz transformation is not correct. (3) Descriptions of a definite event in all inertial coordinate systems moving uniformly
relatively to another are equal. (4) The relative speed between two objects can exceed the light speed. (5) Einstein’s paper “On the Electrodynamics of Moving Bodies” is full of mistakes and
conflicts.
Acknowledgments The author gratefully acknowledges Dr. Thomas Smid for discussions. Li Zifeng is a professor of Yanshan University, China, Technical Editor of SPE Drilling & Completion. Before joining Yanshan University, he was a professor of Daqing Petroleum Institute and then a professor of China University of Geosciences. He has published 100 papers and 4 books on drill string, casing, rod pumping mechanics & well bore stability. He
18
holds a BS degree in drilling engineering and an MS degree in machinery engineering from
Daqing Petroleum Institute and a Ph.D. degree in petroleum development engineering from
China University of Petroleum.
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Problems with the Special theory of Relativity Li Wen-Xiu Department of Earth and Space Sciences University of Science and Technology of China wxl@ustc.edu.cn
Abstract: This 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. (3) The Lorentz transformation(LT) is based, not upon the so-called light principle, but rather upon a general time-space dependence, and lacks a proof of necessity and uniqueness. (4) The LT contradicts its premises, holding for no observer. (5) The Lorentz contraction is shown untenable in practice. (6) The prediction of time dilation is only a special case of a general result that is self-contradictory.
Keywords: Special Relativity, principle of relativity, light principle, Lorentz transformation, Lorentz contraction, time dilation.
1 Introduction There is no doubt that the physical Universe is the only object of study of physics. The
basic view of the world, underlying all physical theories and justified by history of physics, is the doctrine that the world is made up of objects whose existence is independent of human consciousness. The objectivity, reality, and uniqueness of the universe are therefore the initial premises of natural sciences. Based on this view, the phenomena of nature, which ultimately depend only upon interaction between matter and relative motion thereof, can simultaneously and equally be described by means of any single coordinate system; i.e., nothing in the Universe can be changed by the employment of a coordinate system.
Consider, for example, a stone dropped, but not thrown, to the embankment by Einstein standing at a window of a railway carriage, which is traveling uniformly with respect to the embankment. With respect to the embankment, the railway carriage, or any other body in the Universe, the stone traverses an absolutely definite, independent trajectory. Clearly, the phrase ‘the motion of the stone’ has no definite meaning without the reference body being specified. Given a single specified coordinate system, all motions of all bodies in the Universe with respect to this frame, and with respect to one another, can be described simultaneously by means of this frame. Whatever coordinate system is employed, the trajectory traced by Einstein’s stone with respect to the ground is a parabola, while that with respect to the carriage is a straight line.
It is incorrect to consider a coordinate system as able to describe only motions of bodies
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with respect to itself. It is even more fallacious to regard a coordinate transformation as a reference-body switch of relative motions[1]. When the coordinate system rigidly attached to the ground is employed, the carriage is still there, and the motion of the stone with respect to it cannot be destroyed or altered by the employment of that frame. Everybody knows how to figure out the trajectory of this motion by using this system, just as well as by using the system rigidly attached to the carriage. It is only because the stone is in an absolutely definite, independent motion with respect to every other body in the Universe that we can simultaneously compare them and find them different from each other, whereby we obtain the knowledge that motion is relative.
It is therefore not right to interpret the relativity of motion only as: ’viewed from the embankment’ the stone is in a parabola motion, while ‘viewed from the carriage’ it is in a straight line motion. The phrase ‘viewed from the embankment’ is ambiguous. It is unlucky for physics that such phraseology has come into use in published articles. Although it means here ‘with respect to the embankment’, one often fails to know what it means; say, “viewed from the coordinate system S’”, in S the laws of electrodynamics are in the form of Maxwell’s equation, whereas in S’, they are not. This kind of phraseology also makes the coordinate system now subject, then object, depending on one’s requirement.
One should also know that not only “viewed from the embankment” the stone is in straight line motion with respect to the carriage, but also “viewed from anywhere”, the stone is in straight line motion relative to the carriage too, as well as in parabolic motion relative to the embankment. The two relative motions are really both absolute, here meaning that either of them has already contained within it the consequence of all physical effects exerted upon it, and cannot still be anything different depending on viewpoint.
In accord with the special theory of relativity (STR), ‘relativity’ means that one and the same thing is different according to different definitions (the phrase ‘when viewed from different inertial observers’ is here equivalent to ‘according to different definitions’[3]). The relativity of lengths, masses, and times, all refer to one and the same body or one and the same pair of clocks, as clearly stated by Miller [2]:
“There were no such notions as the true time or the true length of an object; rather these
were relative concepts: For example, the length of the rod was either or rAB, depending
upon the rod’s motion relative to an inertial observer”. Surely, Miller is correct only ‘when viewed from STR’. According to STR, there were also no such notions as the true length contraction or the true time dilation; rather these were relative effects: for example, the length of the rod was contracted by either the factor α or the factor β, depending upon the rod’s speed relative to an inertial observer. All the experiments that have been claimed to confirm STR turn out to confirm at most these untrue effects. Even the two postulates set forth by Einstein are untrue ‘when viewed in any coordinate system whatsoever’[3].
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When we delve into how Miller obtained such conclusions, we find all these conclusions self-contradictory. When we, as observers not standing on Olympus, measure the length of the
rod to be , we are unable simultaneously to know and believe that other observers in motion
relative to us should regard it as shorter than . How can we come to such a conclusion? All
we can do is use our standards of length and time to measure all bodies and all time intervals, and we must thereby find that during two events every object in the Universe, moving or not with respect to us, must age the amount equal to the interval of the two events, independent of the reading of the clock traveling with it. It is not allowed by STR for us, on the one hand, to measure the interval of the two events with our own standard of time, and, on the other hand, to measure the aging of the object with the readings of the clock which is traveling with the object and which, according to STR, we do not think keeps the correct time, in order that we can agree that the object, if moving relatively to us, ages less than the interval of the two events.
It is perhaps necessary to point out here that Einstein’s defining the reading of a clock as time is no less absurd than defining the reading of a speedometer as speed, the reading of a log as distance, the reading of a counter as number, the reading of a potentiometer as electric potential. A clock is nothing but a measuring instrument. If no quantity precedes, no measuring instrument is necessary, without mentioning the fact that no one can design an instrument for measuring the unknown quantity, still less can one know the measuring precision and the stability of the instrument. Therefore time and the unit of time must both be well defined before any clock or watch comes into use.
1. The Principle of Relativity The so-called principle of relativity, which, as quoted by Rindler [4], reads in Einstein’s
own words as: “All inertial frames are totally equivalent for the performance of all physical experiments”, and which is said to be evolved from the ‘fact’ that in a ship “all motions and all mechanics happen in the same way whether the ship is at rest or is moving uniformly”.[4] This cannot be regarded as an important law of nature, since, considering the fact that there is only one Universe while there are an infinite number of inertial coordinate systems, there is no case such that in every inertial coordinate system there is an identical physical system at rest and under otherwise exactly the same conditions.
In fact, the ship is never moving uniformly with respect to Earth. When the ship is said to move uniformly, it is actually at rest in the coordinate system of which the origin is located at the center of Earth, and which is rotating with respect to the Earth around the axis through its origin and perpendicular to the alleged velocity of the ship, with the angular velocity ω=v/R, where v is the alleged speed of the ship, R the radius of the Earth. Especially when v is large enough, all motions and all mechanics will not happen in the same way as when the ship is at
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rest. Besides, granted that the ship is moving uniformly, it is not the ship, but rather a uniformly moving flatcar, that can be regarded as an inertial coordinate system. One cannot see what is seen in the ship when he is on the flatcar. The reason is very simple: there is only one atmosphere that cannot be in the same state of motion relative to the Earth as relative to the flatcar.
It is to be emphasized that the Einsteinian relativity is essentially different from the Galilean relativity, which says that all inertial coordinate systems are totally equivalent for the description of the Universe.
2 The Light Principle It is well known that the LT is set up on the two postulates put forward by Einstein [5] in
1905. The so-called principle of the constancy of light speed reads, in Einstein’s own words, “Any ray of light moves in the ‘stationary’ system of coordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body”.
What is concerned with and meaningful is only the speed of light relative to its receiver, which is obviously independent of reference frames, and of which the principle should completely be stated, namely, the light emitting body and the light receiver should both be involved in the principle, since both of them are generally in motion in the ‘stationary’ system of coordinates. However, the light principle does not refer to light receiver at all, violating completely the mutuality of motion between emitting body and receiver. This, together with the tacit assumption mentioned below, make the speed of light with respect to the light receiver from the outset observer dependent [3]. This is the root of why simultaneity is relative.
Even in accordance with Einstein’s understanding of this principle, as shown first in defining time and then in deriving the LT, the principle should strictly and completely be stated as follows: The speed of light with respect to every inertial coordinate system, only when measured by stationary observers of that system according to their own stationary clocks synchronized by using light signals in accordance with the synchronization definition that is made based upon this now being stated principle which postulates that the speed of …(repeating exactly the same statement endlessly).
This endless statement is the root of the circular demonstration present in STR, making STR from the outset untenable. The reason for the statement being endless lies in the fact that the principle, in itself through the definition of velocity, already contains time, which is in turn to be re-defined based upon this principle; i.e., that the principle is not qualified to be a principle, unless time is previously otherwise defined [6].
Einstein’s argumentation of the relativity of simultaneity involves a tacit assumption which reads: when an observer A at rest in an inertial coordinate system receives a ray of light at time t, the observer B who is in motion relative to A, and happens to be adjacent to A, can also receive this ray of light. It is based upon this tacit assumption that Einstein uses c-v and
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c+v in demonstrating the relativity of time, although his usage is still illegal in terms of STR [7]. This assumption has been shown untenable [1,8], and now we shall further show that it may lead to absurd conclusions.
Suppose the coordinate system K’ is in uniform motion relative to the coordinate system K in the x-direction with speed v, with the axes of x of the two system coinciding. Now let a ray of light be emitted at time t=t’=0 when the origins of the two systems coincide, from the instant common origin, in the direction of the instant common y-axes. According to the light principle, in either coordinate system the ray of light is propagated only along the yaxis; i.e., only the observers at rest on y-axis can receive the ray of light. However, since the y’-axis is moving relatively to the y-axis, when an observer at rest on y’-axis receives the ray of light, there must be some observer who is at rest in system K but not on the y-axis runs into him and, according to the tacit assumption, receives the ray of light too. This leads to the absurd conclusion that, in system K, not only the observers located on the y-axis, but all observers located above the x-axis, can receive the ray of light since v can take any value
from to , and vice versa in system K’.
3 Derivation of the LT In physics, in fact, the only bases underlying all physical equations is the unquestionable
fact that a thing is always identical with itself. In other words, both sides of every equation always stand for one and the same quantity. This has already been, and will forever be, the unique basis for us to establish physical equations, the coordinate transformation equations being no exception.
Suppose there are two bodies, A and B, if we want to express the position of A with respect to B, we need, first of all, to establish a Cartesian coordinate system, K, rigidly attached to B and with B at the origin, then measure the three coordinates, x, y, and z of A to obtain the position of A relative to B,
(1) Now for some reason we need to express this very relative position in terms of a coordinate system, K’, which is in uniform motion with velocity v with respect to B. Let the position of A with respect to K’ at time t be
(2)
Since the position of B with respect to K’ is
(3)
The position of A with respect to B is therefore
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(4)
It is the fact that Eqs. (1) and (4) are one and the same position of A with respect to B that gives the Galilean transformation (GT) equations
,
,
(5)
With the proof of the uniqueness and necessity of these equations absolutely unnecessary. Moreover, we have no choice but to accept all features of these equations. In other words, not before, but only after these equations have been so soundly obtained can we know and believe all their properties to be true.
By contrast, the derivation of the LT is completely groundless. Einstein and others, such as Bergmann [9] and Rindler [10], made no proof of the uniqueness and necessity of the LT equations either before or after the derivation of the LT. Moreover, their derivations are full of fictitious assumptions, such as the linear dependence of t’, not only on t, but also on x, y, and z, and the properties of homogeneity of space and time (in fact, these assumptions are not only petitio principii, but also in conflict with the conclusions resulting from the LT based on them. For example, ‘viewed from either of the two coordinate systems in uniform relative motion’ clocks in the other system placed along the y- or z-axis are synchronized with each other, whereas those placed along the x-axis are not; namely, time is not homogeneous and for a similar reason neither is space).
The LT is said to be derived from Einstein’s two formal postulates that are mathematically expressed as
,
(6)
It is explicit that t and t’ are both arbitrary constants, not independent variables in the same sense as x, y, and z, namely that only when they are both given are the two equations both spherical equations; nevertheless, they are treated, in deriving the LT, as independent variables, on completely equal footing with x, y, and z, since Einstein substitutes x, y, z, t, contained in Eq. (6) for the spacial coordinates x, y, z, and the time t of an arbitrary event. Clearly, this treatment not only makes space and time interrelated, as definitely shown by the LT, but also makes Eq. (6) no more or less than the time-space dependence, which is obviously absurd.
Without any proof of the uniqueness of the LT, Rindler alleged, after his derivation of the LT, “if there is a transformation satisfying the requirements of SR, then it must be (the LT)”. Rindler’s allegation has been shown outright untenable by Xu Shaozhi and Xu Xiangqun [7].
What is even more seriously shown by Xu Shaozhi and Xu Xiangqun is that the LT is actually not based upon Einstein’s two postulates as expressed by Eq.(6) but upon the
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following equation
(7)
With t and t’ being independent variables on completely equal footing with x, y, and z, which is now absolutely in conflict with the light principle, being really an interrelation of time and space. This fact not only implies that the LT is not based on Eq. (6), much less on Einstein’s two postulates, but reveals how space and time have already been from the outset interrelated as well. 4 Premises of the LT
Besides what is exposed above, the other premises of the LT are obviously as follows: First, each coordinate system is equipped with a rigid measuring rod and a number of clocks, each measuring rod and all clocks being ‘in all respects alike’. Second, the clocks fixed at different points of each system are synchronized with each other.
On reflection, we find that we do not know to whom we are saying these premises; i.e., for whom these premises hold good. According to the STR, even we ourselves do not accept them as valid, if we are not really on Olympus. An observer at rest in S would find the clocks in S’ not synchronized to one another, the two measuring-rods and the clocks in S and S’ in no respects alike, and vice versa. Therefore, no observer in either system can derive the LT, much less can they accept it as correct. Although the observers in either system do not accept the LT, it is very strange that when we use the LT (granted that we are entitled to use it) to get from the space-time coordinates of an event relative to S to the new space-time coordinates of that event relative to S’ for the observers in S’, the observers in S’ have to regard the new space-time coordinates not only as true but also as measured by themselves. We know of no other place in physics where there exists such a peremptory logic. Observers are no more or less than puppets when viewed from Einstein. We wish we were not observers.
5 Lorentz Contraction The following experiment indicates the impossibility of the Lorentz contraction. Turn a railway carriage upside down so that its front and rear wheels can turn freely. Join
the two wheels with a rigid rod by means of two eccentric axles fixed respectively on the edges of the two wheels. Practice tells us that only when the length of the rod is equal to the distance between the two central axles of the two wheels can the two wheels still turn freely. We now suppose the rod is equal to the distance, and these wheels are turned swiftly; the rod is thus in motion with respect to the carriage, suffering the Lorentz contraction ‘when viewed in the coordinate system attached rigidly to the carriage’. Since the two central axles are rigidly fixed on the carriage, the distance between them does not suffer such an effect. The rod is therefore shorter than the distance between the two central axles, whence it follows that these wheels cannot be turned. This conclusion is obviously out of accord with the fact that these wheels are turning.
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It is to be noted that, in accordance with STR, Lorentz contraction means that the length of a rod, under any conditions whatsoever, at any instant, is simultaneously different ‘viewed from different inertial observers’, not that the rod has different lengths at different times or in different situations. The length of a rod is always the consequence of all known and unknown effects acted on it by all objects present in the Universe. Even granted that there is an ether, the notion that, in the ether, when a rod is moving with speed v parallel to its length, its length is shorter compared to its resting length, has nothing to do with the Lorentz contraction. 6 Time Dilation
Immediately after his discussion of length contraction, Einstein made another prediction. He argued as follows:
“We imagine one of the clocks which are qualified to make the time t when at rest
relatively to the stationary system (the system S in this paper), and the time (t’ in this
paper) when at rest relatively to the moving system (S’ in this paper), to be located at the
origin of the coordinates of (S’), and so adjusted that it marks the time . What is the
rate of this clock, when viewed from the stationary system?”
“Between the quantities and , which refer to the position of the clock, we have,
evidently,
and
Therefore,
Whence it follows that the time marked by the clock (viewed in the stationary system) is
slow by
seconds per second, or neglecting magnitudes of fourth and
higher order, by
”.
The late Herbert Dingle made a reasonable objection to Einstein’s conclusion. He made a parallel passage, leading to the opposite conclusion [11, 12, 13]:
Which shows that the moving clock is fast by
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seconds per second, being in
conflict with Einstein’s conclusion. In order to show Einstein’s conclusion being untenable, we should first ascertain what
he meant by the phrase ‘viewed in the stationary system’. In STR, this kind of phraseology appears in every conclusion, and has different meanings in different conclusions, really being an elixir playing the role of confusing reader’s mind. Here it may be in the place of the phrase ‘compared to the stationary clock’.
It is common sense that whenever one compares two things, there always exist two exactly equivalent statements of the result. Take, for example, the comparison of the two clocks, A and B. If one finds the clock A to be m seconds per second slower than B, one will claim that the clock B is m seconds per second faster than A. In other words, ‘compared to B the clock A runs slow’ is exactly equivalent to ‘compared to A the clock B runs fast’. Besides,
the relation
is nothing but the equation
connecting the interval , ‘viewed from the moving system’, of the two events occurring
respectively at
and , and the interval t, ‘viewed from the stationary system’, of the
same two events. Why is it ‘viewed in the stationary system’ but not ‘viewed in the moving system’ that is to be added to the relation? Is science language games?
Therefore, Einstein’s conclusion is exactly equivalent to the assertion that the stationary clock is fast by the same amount compared to the moving clock which, as shown by Dingle, should be faster than the stationary clock. This is what is shown by Dingle to be the inconsistency of the theory.
For refutation of Dingle’s objection, Max Born [14] and McCrea [15] made an argument to the effect that Einstein’s conclusion results from the comparison of the proper time interval of the moving clock to the stationary non-proper time interval, whereas Dingle’s results from the comparison of the stationary proper time interval to the moving non-proper
time interval. The two conclusions therefore ‘refer to different physical situations’; and
have not the same meaning in the two expressions. Dingle’s conclusion is therefore not in conflict with Einstein’s conclusion.
What a strange explanation. We now fail to know how many different meanings the
time t (or ) has. This is the first time we have heard that physical situation can alter the
nature of time. And we also fail to know why, neither Max Born nor McCrea explains whether there is any relation between a proper time interval and its corresponding non-proper time interval of the same coordinate system. As known, since clocks are all synchronized, there must be a certain relation between the two intervals. As long as such relation exists, whatsoever it may be, Dingle’s objection must hold good.
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The following demonstration may be necessary for further refuting Max Born’s
argument and similar ones. Between the two times and , there is a general relation that can
be drawn from the LT, and of which both Einstein’s and Dingle’s conclusionsare merely
special cases. Let us assume that at the time
, a mass point M that is moving with
constant speed in the x-direction, passes through the origin of S, which coincides at that
moment with the origin of S’, and at S-time arrives at
. According to Einstein’s logic
exactly, between the quantities and , which refer to the position of M, we have evidently,
and
. Therefore,
, where is the
Lorentz factor, whence it follows that the time marked by the clock of S’ (viewed in the
stationary system S) is slow by
seconds per second when
, fast by
seconds per second when
.
Clearly, this result reduces to Einstein’s conclusion when
, and to Dingle’s
when
. Nothing shows that the two conclusions refer to different physical situations in
which and have not the same meaning. This general result is now the comparison of the two non-proper time intervals between the same two events. What in this theory can make now one, and then the other, the greater one?
Max Born’s argument means that, in the stationary system, although all clocks fixed at
different places are synchronized with each other, the non-proper time interval has no
relation to any proper time interval of the clock at rest at
, namely, this clock has no
reading corresponding to , or in other words, that one cannot use any proper time interval of
the clock at
to calculate the position of the moving clock, namely, if we let stand for
the proper time interval of the clock at
, whatever may be,
. If really so, we
would fail to understand as to what Einstein meant by “the property of homogeneity which we refer to time”, and the theory would completely be meaningless, because it makes us unable to determine even the position and velocity of the moon relative to the earth, since it is impossible for us to place clocks at different points on the orbit of the moon. If not, however,
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no matter what the relation between and may be, Dingle’s objection is valid.
In fact, the equality of to has been used by all authors, including Einstein
himself (Einstein clearly knows that a theory which even fails to give the relation between
and cannot be regarded as a good theory). The strong evidence is that in the quoted paper Einstein simultaneously uses both proper time interval and non-proper time interval to
express the same velocity of light , namely,
, using the proper time
interval,
, using the non-proper time interval. This completely means that
the two time-intervals have the same meaning. We are surprised that those physicists claiming to be of integrity should be regardless of these facts when they explain away Dingle’s objection.
7 Concluding Remarks Every problem presented above is fatal to STR. This determines that STR must suffer
acute refutation. We know that the STR is per se an observer-dependent theory. But this does not mean that we should start from this viewpoint to disprove this viewpoint, and are considered to be wrong when we demonstrate and assert something really independent of observers. First to ascertain why it is observer-dependent, and then point out where and how it goes wrong by demonstrating how and why it is really independent of observers, is a valid way to disprove this theory.
It is surprising that, although some authors confess that STR is inconsistent, they hold the doctrine that Einstein was so fortunate that he frequently came to the right conclusions by using false reasoning, and claim that all relativistic paradoxes of length contraction of rods, etc., have been resolved through absolute space and time physics, derived from the Galilei covariant Maxwell equations. Clearly, according to the above analysis, these authors’ claim shows only that their ‘theory’ is no better than STR.
References [1] Wen-xiu Li, “Is Galilean Relativity Really Incompatible With Maxwell’s Equations?”,
Physics Essays 7, 255-260(1994). [2] A. I. Miller, Albert Einstein’s Special Theory of Relativity, p. 205(Addison-Wesley,
Boston, 1981). [3] Wen-Xiu Li, “On the Relativity of Length and Times”, Apeiron 2, 16-19(1995). [4] W. Rindler,Essential Relativity, 2nd ed., pp. 7, 4 (Springer-Verlag, New York, 1977). [5] A. Einstein, “On the Electrodynamics of Moving Bodies”, in H. A. Lorentz et al, The
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Principle of Relativity, p.41(Dover, New York, 1952). [6] Wen-Xiu Li, “Logical Inconsistencies in Special Relativity theory”, Galilean
Electrodynamics 10, 49-50 & 56(1999). [7] Xu Shaozhi and Xu Xiangqun, “A Reexamination of the Lorentz Transformation”,
Galilean Electrodynamics 3, 5-8(1992). [8] Wen-Xiu Li, “On the Galilean Relativity of the Laws of Electrodynamics”, Physics Essays
7, 403-409(1994). [9] P. G. Bergmann, Introduction to the Theory of Relativity, p. 33(Prentice-Hall, Englewood
Cliffs, N. J., 1942). [10] Ref. 4, p. 33. [11] H. Dingle, “Special Theory of Relativity”, Nature 195, 985-986(1962). [12] H. Dingle, “Special Theory of Relativity”, Nature 197, 1248-1249(1963). [13] H. Dingle, “Special Theory of Relativity”, Nature 216, 119-122(1967). [14] M. Born, “Special Theory of Relativity”, Nature 197, 1287-1288(1963). [15] W. H. McCrea, “Why the Special Theory of Relativity is Correct”, Nature 216, 122124(1967).
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Criticism To Einstein’s Physics Thinking in His Book “The Meaning of Relativity” Shi Yong-Cheng
， (ShaoxingUniversity, Shaoxing 312000, P. R. China. E-mail:shiycgood@126.com)
Abstract: It is discovered that Einstein’s book “The Meaning of Relativity” contains of a supper mistake which leads to the famous twin “paradox”. It is proven that the principle of constancy of the velocity of light in a vacuum is the result obtained by artificially set of measuring instruments and then the Galilean transformation and Lorenz transformation are unified based on the verification of their equivalency crossing 300 years history of physical
－ space-time with one step smashing the shackles of Einstein theory of relativity limitation of
the velocity of macro object movement and eliminating the fairytale of Shrink-foot clock slow
Keywords:Lorentz transformation, Ideal clock, Geographic time-difference
1 Criticism to Einstein physics thinking in STR
The Galilean transformation
 x′ = x −Vτ , y′ = y, z′ = z,
(1)
 τ ′ = τ ,
(2)
was put forward by physicist in the 16th century and it can make the equation of Newton
mechanics second law has covariance, but it can’t made that electromagnetic field equation
has covariance, therefore Einstein attempted to change general understanding for time in
Newton mechanics and then to build new transformation while he first employed the principle
of the constancy of the velocity of light in a vacuum, to complete the definition of time by means of his scheme of adjustment of the clocks at rest relatively to an inertial system K [1].
After these clocks are regulated according to the Einstein scheme in K, all these clocks have a
same rate and have not geographic time difference and then if the time t recorded by the clock situated at rest at the origin O of the system K to be denoted by τ, the time t recorded by arbitrary clock situated at rest at a point where x≠0 in the system K is same with τ, therefore
we have
t =τ.
(2′)
In his book[1] Einstein said that space and time data have a physically real, and a mere fictitious, significance; in particular this holds for all the relation in which coordinates and time enter .There is, therefore, sense in asking whether those equations are true or not, as well as in asking what the true equations of transformation are by which we pass from one inertial system K to another, K', moving relatively to it. We point out that Einstein’s problem and
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thinking above are no any sense and are wrong. Since space and time data relate both of different observers and different measurement instruments, therefore these data has not any physically real significance and then the so-called true equations of transformation cannot be uniquely settled. It was proven that equations of transformation settled by means of the principle of the constancy of the velocity of light in a vacuum is not uniquely true equations, the equations of Galilean transformation are also true equations of transformation, they are equivalent each other’s [4]. In order to obtain new equations of transformation to replace the Galilean transformation, Einstein started from linear transformation of the type (see [1], p-32, (24) )
x′ µ
=
a µ
+
b µα
x α
,
( A)
where x'µ to be the space-time coordinates of an event in another inertial system K', moving relative to K, applying the principle of special relativity and the principle of the constancy of the velocity of light , he obtained the Lorenz transformation[1] p-34
  
x1′ =
x1 −ν l , 1−ν 2
( 29 )
 
l′ = l −ν x1 , 1−ν 2
 
x2′ = x2 ,
 x3′ = x3,
where γ= 1/δ, δ = √(1-ν2), ν = v/c, and l (= ct), l'(= ct') to be light-time. This transformation make that the Maxwell electromagnetic equations have covariance.
Eliminating x1 in the second equation of (29) by means of the first equation of (29), we obtain following geographic time difference formula of clocks in moving inertial system K'
l′ = δ l −ν x1′,
(B)
which indicates :(10) all clocks situated at rest at the space points where x1'≠0 have same rate and different geographic time difference -νx1' with the standard clock situated at rest at origin O', (20) the rates of all clocks situated at rest at the space points of the inertial frame of reference K' are δ (= √(1-ν2)) time of the rate of the clocks situated at rest at the space points
of the inertial frame of reference K where all clocks have been synchronized according
Einstein’s scheme of adjustment of the clocks at rest relatively to an inertial system .
Replace x1, x2, x3, l by x, y, z, ct, these equations can be written in the form
 x′ = β (x − vt), y′ = y, z′ = z,
(1*)
 
t′ = β (t − vx c2 ),
(2*)
where β=1/δ. Since equations (A) has not any information which shows what measuringsticks and what clocks to be applied in the system K', the Lorentz transformation only
34
guarantees that the principle of the constancy of the velocity of light holds, but it cannotguarantees that the space-time coordinates of an event in system K' calculated by means of Lorentz transformation do not conflict with his scheme of adjustment of the clocks in another inertial system. Therefore it is fantasy that Einstein and his followers considered that the coordinates (x', y', z', t') in K' are found in the same way as the coordinates in K by means of standard clocks at rest in K' [2] (p36).
What measuring-sticks and what clocks should be applied for the system K’? whole deducing process of Lorentz transformation indicates that they should not be decided by Einstein and his followers, but they must be determined by Lorentz transformation. The famous twin “paradox” in STR shows that the Einstein scheme of adjustment of the clocks cannot be applied in the system K'. It is proven that the famous twin “paradox” in STR will not existed after the clocks to be regulated according to the geographic time difference formula (B)[4].
2Simultaneity and pig brain When they consider the concept of simultaneously, they take same criterion for
simultaneity in K and K' and then obtained a mistake conclusion that the concept of simultaneity has lost its absolute meaning[2](P34) since their criterion for simultaneity cannot holds in K'. Their famous example on the simultaneity of two events occurring at different points just verifies that Einstein scheme of adjustment of the clocks is unlawful in K'. Since different clocks situated at rest at different places in K' have different geographic time difference expressed by the formula (B) [3]( , chpt.4)[4] they are simultaneous with the standard clock situated at rest at the origin O' after their geographic time difference to be reduced. Therefore the simultaneity between two event in different space points in system K still has its exact meaning for the men as observers in K' since the signals of light can carry TV information relating the registered exact time of local clocks when the event happening and observers can transform local time to standard time. A pig reading in a flying aircraft cannot understanding it is simultaneous events that a Peking dog and a Washington dog died at a same Greenwich Mean Time when the TV signal coming from Washington early arrives at the aircraft than the TV signal coming from Peking while its owner will understanding that the two dogs are simultaneously died from registered time of the Washington local clock and registered time of the Peking local clock whose images are showed respectively in the two TV signals.
3 Twin “paradox” and Einstein’s super mistake In order to expose the truthful face of Einstein’s mythology on moving clocks, let us to examine the paragraph in page 36 of his book[1]as follows:“A clock at rest at the origin x1=0 of K, whose beasts are characterized by l = n , will, when observed from K', have beats characterized by
35
n
l′ =
,
(C)
1−ν 2
This follows from the second of equation (29) and shows that the clock goes slower than if it were at rest relatively to K'”. It is obvious here Einstein compared the clock (which is now denoted by (C) situated at rest at origin O of K with the clock (which is now denoted by C'.) situated at rest at a fixed point A' of the x1'.-axis. When l=n, the clock C just meeting the clock C'. Therefore we can obtain the coordinate of the clock C' on x1-axis as follows
x1′ = −ν l′ = −
νn . 1−ν 2
Replace n by l in Eq. (C), we obtain
l = 1−ν 2 l′,
(C *)
Consider that the clock C' at rest at the origin x1'=0, we can obtain from the first and second equations of (B)
l′ = 1−ν 2l,
(C **)
Einstein and his followers considered that (C*), (C**) are equivalent to following formulas
respectively
∆l = 1−ν 2 ∆l′,
( D *)
∆l′ = 1−ν 2 ∆l,
(D **)
and then present the mythology of moving clocks based upon (D*) and (D**) which leads to
the famous twin “paradox”. However we will prove that the formula (D*) is not equivalent to
(C*) and it does not hold.
Since l,l′ are instantaneously registered time, it is Einstein’s supper mistake that their
comparison has been considered as the criterion for the comparison of rates of clocks . We must consider their started time respectively to compare their time difference respectively. When the origin O coinciding with origin O', for all clocks situated at rest at different space points in K, we have l = 0 since these clocks are regulated according to the Einstein scheme. Therefore we have
∆l = l − 0 = n.
For clock C' when the origin O coinciding with origin O', its registered time can be obtained from (B) by putting t =0 and x1'= -νl' as follows
 l′ = −ν−
νn
 =
ν 2n
.
 1−ν 2  1−ν 2
36
Fig 1. At t' = t =0, the clock C which is situated at rest at the origin O coinciding with the origin O'
while the clock C' which is situated at rest at the point A' specified by coordinate x'=x'1=-νl'
on the x'-axis records the geographic time difference l'=-ν2n/√(1-ν2).
Therefore we obtain
∆l′ =
n
ν 2n −
= 1−ν 2 n.
(E*)
1−ν 2 1−ν 2
Then we have
∆l′ = 1−ν 2 ∆l,
(E)
which is same with (D**) and leads to an opposite consequence to Einstein as follows: “The clock goes faster than if it were at rest relatively to K'”. The formula (E) comes from (C*) and (C**) respectively that shows that (E) and its physics deduction are independent of observers. The local clocks situated at rest at different space points in K' go slower than the local clocks situated at rest at different space points in K where Einstein scheme has been performed. This result holds for all observers and then there is no a little of relativity.
4Equivalence between Galilean transformation and Lorentz transformation From the pointing out of Galilean transformation to confirmation of Lorenz transformation by Einstein and then the establishment of special theory of relativity by Einstein, it stepped over about 300 years; therefore, the modern physics theory building was established in the 20th century. However, the book “A Brief History of Time” (Stephen Hawking) became popular all around world and Einstein theory of relativity of hundred years’ history was considered as supreme civilization. The verification of the equivalency between Galilean transformation and Lorenz transformation---marking the end of Einstein theory of relativity: utilizing the following SGTD formula (Shi geographic time difference formula)
t = τ + λx,
(3) t′ = τ ′ − λ x′,
(4)
37
where
( ) （ ） λ = 1− 1− v2 c2 / v = ( 1+V 2 c2 −1) /V , 5
V = dx dτ ,
(6)
v = dx dt,
(7)
v = V 1+V 2 c2 ,
(8)
utilizing extremely simple elementary mathematical operation, it can make strict derivation
each other between Galilean transformation (1) and(2)and Lorenz transformation (1*) and(2*)
(see relating paper 4 and 5), so it denies the traditional fallacy that Galilean transformation is
the low speed similarity of Lorenz transformation while the same correctness of these two
transformations is definitely proven. The velocity v, V in (6), (7) relate the different
definitions of velocity. Using clock without geographic time difference to measure time, the
velocity definition is (6), so we call it proper velocity. The macro object proper velocity and
light proper velocity obey the Galilean addition theorem for velocities, vacuum light speed is
changeable and Newtonian mechanics is beyond limitation of Lorenz transformation---
velocity is no limit. The velocity in (7) is coordinate velocity and macro object movement
coordinate velocity and coordinate light speed obey the Einstein velocities addition formula:
the vacuum coordinate light speed is not changeable, the coordinate velocity of any macro
object can’t surpass light speed in vacuum. In the application science filed of mechanics and
electrodynamics relating with large scale time and space area, it can use these two
transformations, however, Lorenz transformation relates with artificial setup of different
location with geographic time difference and it is not suitable to apply, therefore it does not
have the actual value and for space navigation, it is useless at all.
Considering the geographic time difference(3),(4) hided in time coordinate in Lorenz
transformation, the calculation made by the transformation shows: the moving clock and
static clock work at the same rate and moving rule and static ruler have the same length which completely denies the fallacy of Einstein[4].
5Lorenz transformation in absolute Space-time Because the time variable t in Maxwell field equation is measured by synchronous clock
without time difference, butLorenz transformation deduced by Einstein from symmetry determines that the time variables before and after transformation all have non-zero time difference, so the Lorenz transformation deduced by Einstein can’t be used for the Maxwell electromagnetic field equation, however, we prove that Lorenz transformation still holds giving up symmetry (see relating paper 4). In this article, we consider two inertial reference frames K, K´ which is moving along positive direction of x- axis relative K. In K all clocks are synchronized with zero geographic time differences. In K´ we take shorter unit measurement rule which has δ* time of the length of the unit measurement rule used in K, her δ* to be thecoefficient of Shrink-foot
38
δ ∗ = 1 − v2 C 2 ,.C ∈ (v, ∞ ) ,
.
(9)
here C is a constant and it can be arbitrarily chosen in the real interval (v,∞), and take slowly δ time synchronized clocks than the clocks in K while non-zero geographic time differences
to be set for these clock according to following Shi formulas
t′
=
δ
∗t
−
vx′ C2
.
Therefore the Galilean transformation can then be expressed in the form
  
x′ = 1 (x − vt), δ∗
 
t
′
=
δ
∗t
−
vx′ C2
,
y′ = y,
z′ = z,
which is the Shi’s Galilean transformation which guarantees that the Maxwell equations to be co-variant with respect to the transformation in the absolute space-time.Shi’s Galilean transformation has the same mathematical formulas with the Lorentz transformation, but they are different transformation since there are different installations of clocks and rules respectively in two inertial systems for the Shi’s Galilean transformation, and then iteliminating the fairytale of Shrink-foot clock slow. Shi’s Galilean transformation is independent of the Einstein’s suppositions on the physical symmetry and the principle of constancy of the velocity of light in vacuum. Shi’s Galilean transformation continues to have the fundamental hypotheses of the Newton mechanics:
(1). Time is absolute, (2). Length is absolute. The transformation result of Lorenz transformation on Maxwell field equation keeps the same physics effect with Galilean transformation besides their different mathematical formats. For the most typical physical deduction “the moving clock works slower” of Einstein theory of relativity, we change a letter for it in the result “the moving clock adjusts slower” as the end of Einstein theory of relativity. It has been proven that Shi’s Galilean transformation with its inverse transformation has same artificial installation of measurement instruments.[6] The curtain of a physical farce spanning the two centuries will fall down soon.
References [1] Einstein, The Meaning of Relativity, Princeton University Press.1955. [2]C.Moller,The Theory of Relativity,Clarendon Press.Oxford,1972 [3]Bergmann.P.G.(1942).Introduction to the theory of relativity, Prentice Hall,New York [4] Yong-Cheng shi , Einstein’s Mistakes in Special Theory of Relativity and their corrections,
39
Matter Regularity, Vol.11 Sum No.43, p6-p29 , 2011 USA. www.qiji.cn/eprint/abs/3579.html. www.qiji.cn/eprint/abs/3580.html.(2007) www.wbabin.net/science/yongcheng.pdf [5] Using one letter to correct Einstein theory of relativity, Shi Yongcheng. .Beijing theory of relativity association the 5th annual meeting paper album.4 VOL, 2009, p136-144 [6] Shi Yongcheng,The remark about “Using one letter to overrun the Einstein theory of relativity”, 2010-3-19, Matter Regularity, p87ol.10 No38, 2010-4-30. [7] Shi Yong-Cheng, Shi’s Galilean transformation, 2010-5. gsjournal.net www.wbabin.net/science/yongcheng5.pdf [8] Shi Yong-Cheng, The Demise of Eintein’s STR—Verification of the equivalency between the Galilean and Lorenz transformations, www.wbabin.net/science/yongcheng7.pdf
40
Using Space-time Quantization to Solve the Problems Unsolved by General Relativity
Xu Jianmin (Lawyer of Beijing Unitalen Law Office,jianminshu213@yahoo.com.cn)
Abstract: Based on the law of thermodynamics, the paper 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. Under the quantization of space-time, the unification of electromagnetic field and gravitational field is achieved. An attempt is also made to propose a scheme to unify all fields, namely, all fields are quantum metric fields. The reason for different strengths of fields is their different fine structure constants. The problems of singularity in gravitational field and the infinity in quantum electrodynamics are solved, and all equations return to classical theories under extreme conditions.
Keywords: quantum field, redshift, minimum entropy production, general relativity
1Introduction As is well known, the following problems of general relativity have not been solved:
firstly, the equivalence principle resulted from the direct proportion between inertia mass and gravitational mass and the Mach principle notably established based on the assumption of instantaneousaction-at-a-distance could not be the first principles. They should be rooted on a higher level of principles. What is the final principle then? Secondly, the problem of singularity. Since the establishment of general relativity, some solutions have occurred singularities which make the metric difficult to be defined. Although some physicists believe that both collapsed star and evolution of the universe would inevitably lead to singularities, the equation of general relativity fails on the singularities with zero time existence, zero volume, infinite density and infinite gravity. Thirdly, problem of unified field. After the establishment of general relativity, Einstein attempted to unify gravitational field and electromagnetic field based on the general relativity, but failed. The problem here is whether the geometrization of space-time could be taken as the foundation of the total field. If not, what is the foundation of the unification? Fourthly, the problem of quantization of space-time. If all fields are defined on the framework of space-time, then the quantization of field is actually the quantization of space-time, but it is the problem which has not been solved by the general relativity. Obviously, problems above are fundamental and significant problems of physics. It is impossible to solve the problems just in this paper. The paper only attempts to draw the outline of the issue. The basic idea of the paper is to build the general relativity on a higher level of principle, and based on this, to realize the quantization of fields and the unification of gravitational field and electromagnetic field. Meanwhile, new theory is consistent with the general relativity in the following aspects: Space-time is completely dynamic; physical equations should be covariant to any transformation of coordinates. To all
41
observers, no matter whether it is uniform motion, accelerated movement or rotation, laws of nature appear the same. The metric determines the space-time, and space-time affects the metric. This is the so called background independence.
2General assumptions established based on law of thermodynamics Any physical theory needs one or several basic assumptions, and these assumptions may
come from the observation of objective world or from logical reasoning. Early in the beginning of the 20th century, Poincare pointed out that, if a scientific law is taken as the observation result in the eyes of a mathematician, and is taken as a theorem of mathematics in the eyes of observers, then the law could be taken as the consolidated and long lasting foundation of the overall physics. He regarded the first and second law of thermodynamics are these types of laws. Apparently, the law of conservation of energy is the foundation of present physics, while the second law of thermodynamics is in an embarrassing position. There is a serious contradiction between the law and the most of the physics. On the one hand, almost all of our empirical processes are irreversible, and they should be interpreted by the second law of thermodynamics; on the other hand, the second law of thermodynamics almost has no reason to exist in all physics, including classical mechanics, quantum mechanics, quantum electrodynamics and the theory of relativity. Some physicists like Boltzmann hold that classical mechanics is the foundation of all physics, and the second law of thermodynamics is just the logic conclusion of classical mechanics. So he attempted to use mechanics to interpret entropy in order to solve the contradiction between classical mechanics and the second law of thermodynamics, but failed. Along with the development of physics, there has been an increasing awareness that taking mechanics as the foundation of physics is not reliable. People think if the mechanics could not be used to interpret the entropy, then whether it is possible to use entropy to interpret thermodynamics? The logical consequences of the thinking above must be consistent with the ideal of Poincare, namely, the law of thermodynamics is the only foundation of the overall physics. The paper attempts to establish such a new physical theory, which accords with the viewpoint that entropy is irreversible and could return to the currently applied and recognized kinetic theory under the extreme conditions.
According to the statistical interpretation of Boltzmann on entropy, the nature of entropy is that, in an isolated system, any biogenetic process always makes energy irreversibly tend to a balance state, or each change of entropy is to make the physical system transfer towards a balance state or towards a state with larger probability. This kind of balancing process should include both the balancing of energy density and balancing of energy magnitude. Therefore, we propose the following assumptions according to the concept of entropy:
）1 Hypothesis of radiation and redshift. In an system consisting of material objects and
empty space, since the energy density of material object is larger than that of empty space, the energy radiation from material objects to empty space is a spontaneous process; the redshift of quantum in an isolated system is spontaneous, and the quantum could not automatically occur blue shift;
2) Equivalence between acceleration and the gravitational field. Field generates particle acceleration, and acceleration generates inertial field. The principle could also be expressed like this: if a process tending to balance (redshift) is damaged by acceleration, then an inertial field for the recovery of balance (blue shift) must be generated; if the former process is a positive process, then the latter is a reversed process of recovery. Positive comes from negative, vice versa. Inertia originates from entropy.
42
3) Principle of minimum entropy production: particles moving along with the path with the minimum entropy production
3 Quantum gravitational field equation
In an isolated system, the energy density of material objects is larger than that of space,
and the radiation of energy from material objects to space is a natural process. By taking the
earth as an example, given earth radiates quantum hω with certain frequency, and its
momentum is as follows:
p0
=
hω 0 c
， ＝ In the formula, h is simplified Planck constant ω0 is the frequency of quantum when t 0,
and c is light velocity. According to hypothesis, the quantum should continue to carry out red
shift towards empty space, and the change of quantum momentum is:
h
h
∆p = − c (ω − ω0 ) = − c ∆ω = −( p − p0 )
“-”stands for quantum redshift. The change of momentum could be expressed as:
∆p h ∆ω =−
∆t c ∆t
Namely, the impulsive force generated by quantum redshift, (Note that, in order to provide
convenience, vectors used in the paper are one dimensional)
F = − h ∆ω c ∆t
（1）
Since the direction of impulse force is same with the momentum increase, the negative sign
shows that the direction of the force generated by quantum redshift points to field source. This
kind of radiation is isotropic spherical radiation, and the force of this radiation to the earth
surface is symmetrical.
Given
f
=
∆ω ∆t
Then
h F=− f
（2）
c
As a new function, f could be called frequency fluctuation rate. According to the equivalence
theory of mass and energy, energy quantum has mass, and the force generated by the quantum
should be equivalent to the universal gravitation of Isaac Newton, namely,
h −
c
f
=
hω c2
g
f = −gk
（3）
k = 2π
In the formula,
λ is wave vector. Negative sign means that the direction of f
decrease is opposite to the field direction, namely, it is an attractive force. As a scalar
， product the formula above could also be written as f = −gkcosθ . In the formula, θ is the
43
included angle between g and k; when θ = π / 2 , f = 0 , which means that no energy change
； ， ， occurs on the equipotential line when θ = π f > 0 direction of g is opposite to that of
，k namely, there is repulsive force.
（ ） Obviously, the solution of formula 3 is
ω = ω0exp( − gt / c )
（4）
Since the speed of gravitational field is light velocity, the formula above could be written as:
（ ） ω = ω0exp( −gr / c2 ) 5
Meanwhile, the following formula could also be figured out based on c = λν .
k = k0 exp(−gr / c2 )
Take the logarithm on both sides of equation (5),
g = − ln( ω ) c2 ω0 r
（6）
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 1 could be written as:
（ ） F
=
−
h c
dω dt
7
Given V is force potential.
F = −∇V (r)
∫ V (r)
=
−
r1 r0
h c
f
.dr
+ V0
∫ =
−h
t1 t0
f
.dt
+ V0
（8）
∫ = −h ω1 dω + V0 ω0
V (r) − V0 = −h(ω1 − ω0 )
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
/
c2r)
=
2
∇ϕ
Poisson's equation is substituted into above equation.
（ ） f0 exp(Gm / c2r) = 4πGρ 9
4Comparison of quantum gravity space-time and general relativity space-time
If ω0 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 areω and λ and they are
calculated by the following two equations:
（ ） ω = ω0 exp(−GM / c2r) 5a （ ） λ = λ0 exp(GM / c2r) 10
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 / c2r)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 / c2r << 1 namely, in a weak gravitational field Taylor
expansions of above two equations are made as follows:
（ ） ω = ω0(1− GM / c2r +......) 11 （ ） λ = λ0 (1+ GM / c2r +......) 12
Obviously, 1+ GM / c2r is Schwarzschild metric. So, the time interval is ∆t = 1 / ∆ω , and space interval is ∆r = ∆λ . Choosing a proper coordinate for equation (12), we can get the
following equation.
∆r = 4πGρr3 / 9c2 In the equation, ρ is the mass density within the sphere. This is the Einstein's Law of space
mean curvature, namely, Einstein field equation. The frequency and wavelength of quantum are related to the distribution of matters. Therefore, space-time is not absolute, but changes along with different locations. In strong gravitational field, the space-time variables are discrete, namely, quantized. In the equation (5), when
r → R = Gm / c2 The frequency of the quantum shows a nonlinear variation. But when r → 0
ω →0，
It indicates that the asymptotic freedom occurs inside the particles. Since the wavelength of the quantum from particle radiation cannot be smaller than the particles themselves, and the wavelength of the particles cannot equal to zero, which means that space-time has a limit, and
thus there can be no singularity problems. When r → ∞ , ω = ω0
it is an inertial system with no field. But since the wavelength of quantum can neither be zero nor infinity, the formula above will never occur, and there must exist at zero-point energy. From the following formula,
∆ω = ω0GM / c2r
it can be seen that changes of local phase generate the gravitational field, or, in other words, the introduction of gravitational field is a must to keep local phase unchanged. Therefore, quantum gravity field complies with the principles and specifications.
5 Equation of Motion
45
Since
f
=
dω dt
g = − c ω0
exp(
−
gt c
)
Substitute the formula above into equation (7) to obtain
F
=
hg c2
ω0
e
−
gt c
Considering
the
mass
of
energy
m
quantum
=
hω0 c2
,
and
hence
（ ） gt
a
=
−
g0e
c
13
a is the acceleration of particles, and this is the equation of motion. The acceleration of
an object has nothing to do with its mass.
For object motion, the equation should be used in three levels.
Firstly, for extremely strong gravitational field, the object acceleration changes
exponentially.
Secondly,
for
strong
gravitational
field
with
particle
oscillation,
namely
when
gt c
<< 1
,
conduct Taylor expansion to the left side of the equation above.
（ ） a
=
g0
−
g0 × v c
+ ......
14
In the formula, v = g0t . The first item on the right side of the equation is the inertial
field paralleled with g0 , which can be written as g//; the second item on the right side
g ＝－ g
⊥
c is the inertial field vertical to a , which is named transverse field for short, and
can also be called gravitomagnetic field. These two fields can be referred to as dynamic
gravitational field, and they are the sources of gravitational waves. The resultant force on an
accelerating object in gravitational field with particle oscillation is:
ｇ （ ） F = m( g0 + v ×
)
⊥
15
Obviously, it is equivalent to the Lorentz force.
Thirdly, in the case that acceleration is very small or the gravitational field is very weak, the
second item on the right side of the above equation can be ignored, and then go back to
Newton's equation.
6 Wave Equation
Particle oscillation results in gravitational waves and the wave equations are:
k
×
g//
=
ω
g ⊥
k
×
g ⊥
=
µ0ε0ωg//
Among them, ω and k are the frequency and wave vector of the field point energy level
respectively. In a weak gravitational field,
∇
×
g//
=
ω
g ⊥
∇×
g ⊥
=
µ0ε 0ω g//
46
Single particle acceleration won't produce gravitational waves, and only particles oscillating back and forth would produce gravitational waves. When single particle
accelerates, the inertial field g // and the gravitational field g0 are in opposite directions, and
they can almost offset in a weak field, so that it's as if inside a lift free falling in the earth's
， gravitational field. However when particles oscillate back and forth, g // and g⊥ could form
and outspread gravitational waves through mutual excitation. Accelerating particles may
interact with the gravitational waves. This effect can be detected at the time of solar eclipse.
When solar eclipse occurs, the moon is suddenly attracted by the solar gravitational field to
accelerate, and then reverberated back due to the earth's gravity attraction, generating
oscillation (acceleration). At this time, the acceleration of the moon approximately equals to
the solar gravitational field for the moon orbiting the sun. According to formula (15), if
ignoring the transverse field, the inertial field generated by the moon equals to its acceleration
generated by the sun. The additional acting force imposed on moving bodies on the earth such
as
torsional
pendulum
by
this
inertial
field
F
is
≈
mg太
.
In
the
formula,
m
is
the
mass
of
the
torsional pendulum, and g太 is the gravitational acceleration of the sun. According to
estimation,
the
force
F
is
≈
GM 太
r2
m
≈
5.89 ×10-3 m
.
Since
they
are
moving
gravitational
field, they only affect accelerating objects. Only moving bodies (accelerating) produce
gravitational waves, and therefore gravitational waves can only be detected by moving
bodies. Experimental physicists are expected to inspect the conclusions drawn above.
7Entropy of Open System
Any reversible process accords with this equation
∫ fdt = 0
（16）
The work produced by quantum redshift
dw
=
Fdr
=
−
h c
fdr
=
−hfdt
∫ ∫ ∫ W
=
2 Fdr = −h t2
1
t1
fdt = − h ω2 dω = −h(ω 2 − ω1 ) ω1
Thus equivalent work produced by quantum redshift only relates to the quantum at the
beginning and the end states, but has nothing to do with the path of the quantum. According to
the law of conservation of energy, the work generated from quantum redshift transformation
into field and their energy dissipations are equivalent. Therefore, it is in a reversible state
∫2
ω2 − ω1 = R 1 fdt = 0
∆ω = 0 f = 0
R in the formula represents the integral along the reversible process. However, in a static gravitational field, due to the quantum redshift, there must be
∫2 fdt < 0
Hence 1
ω2 < ω1 ∆ω < 0 f < 0
47
It is an irreversible process. To combine both reversible and irreversible circumstances
∆ω ≤ 0 f ≤ 0
That is to say, in a static gravitational field, frequency variation rate never increase.
Moreover, in a gravitational field, due to
gt
ω
−
=e c
ω0
（17）
ω
ω 0 is the probability of quantum redshift, and take logarithms on both sides of the equation
above, obtaining
ln( ω ) = − gt
ω0
c
S = k ln( ω )
Therefore, entropy is
ω0 (18)
S = −k gt
or
c
Among them, k is the Boltzmann constant. The equation above is the relationship between
field and entropy.
Since f ≤ 0 under the natural state, the entropy increase process is the decrease process of
frequency variation rate f .
∆S
= S2
− S1
=
k
(
g1r1 c2
−
g 2 r2 c2
)
=
k
V1
− V2 c2
>0
V here is gravitational potential. The increase of entropy means the capability to produce
work declines.
Then we discuss the entropy change in the gravitational field with accelerating particle
system.
From the concept of entropy, quantum redshift is the natural direction of energy transfer,
and could proceed spontaneously. Blue shift is the unnatural direction, and it cannot proceed
without external influence. Acceleration is the unnatural direction, and cannot proceed
without external force. Here we popularize Prigogine’s Entropy Change Theory. Prigogine
（ ） thought the entropy change of system dS is equal to the sum of entropy flow
（ ） （ ） deS and entropy production diS within the system. Namely,
（ ） dS = deS + diS(diS ≥ 0) 19
in an isolated system, deS = 0 , so dS = diS ≥ 0 .
In a system with acceleration, inertial field makes the original red-shifted quantum have a blue shift again, like negative entropy flow entering the system from the outside.
des < 0
However, since acceleration must be with a gravitomagnetic field vertical to it, and this field makes no contribution to the quantum's blue-shift of the original field. This could also be proven by the aspect of field to do work. An object accelerating at the radial direction
48
certainly generate a gravitomagnetic field vertical to the radial direction.
mg ⊥
=
mg0
1 2
ar c3
×
vr
（20）
The displacement at radial direction is
vrdt = dr
Both sides of equation (20) multiply by vr dt , and the right side is 0, which means the
Coriolis field doesn’t do any work on the mass point, and the blue-shift of inertial field is not
able to restore the red-shifted quantum into original state, namely, there is always
（ ） deS + diS ≥ 0 21
So the second law of thermodynamics is effective generally.
8 Particles always move along the path with minimum entropy production In classical mechanics, the movements of particles comply with the principle of least
action. According to the principle, the difference between mean kinetic energy and mean potential energy of the path where particles go from one point to another point should be as small as possible. Particles choose a shortest path after considering all the paths in the process of movement. This seems contradictory with human intellect. Nobody could explain the reason of the existence of such principle contradictory with human intellect even today. The red-shift field theory could explain this. The acceleration of particle breaks the original process (positive process) approaching to balance. So there must be a reversed process (reverse process), and this reversed process will certainly approximate to the positive process as far as possible. The difference of these two processes should be the least.
For a complete process of acceleration, the energy change is: under the circumstance of weak gravitational field, doing Taylor expansion on formula (5) and ignoring small amounts above second order, we can get
ω1 = ω0 (1− gr / c2 )
This is the change of red-shift of positive field. The change of blue-shift of inertial field generated by particles' acceleration— reverse field is
ω2 = ω1(1+ gr / c2 )
So the total change of energy is
ω2 = ω0{1− (gr / c2 )2}
Apparently, the difference between kinetic energy and potential energy is a second order small
amount. The principle of least action is to ignore this second order small amount, namely,
δ ∫ ∆ω = 0
We know is the clock-measuring frequency difference fixed on the movement reference system. It’s the reciprocal value of time difference, so the formula above could also be expressed as the longest original time.
This is the principle of least action of reversible kinetics. The second law of thermodynamics shows that every acceleration movement has a largest inertia correspondingly, the difference between original field and inertial field is always the least, and nature is always tending to balance. This is the essence of principle of least action.
However, for irreversible kinetics, the system’s tending to balance is still an irresistible force.
Nevertheless, when the boundary conditions prevent the system from going to a balance, the
system chooses the second best, going toward the state of minimum entropy production,
49
namely, approaching to the balanced state as far as possible. Particles move along the path
with minimum entropy production.
S
=
−k
gr c2
Entropy
production
rate
Θ=
dsi dt
=
k c2
dr dt
Gm r2
Entropy production could be expressed as the product of flow and force.
Without proving, we believe that the entropy production rate is constantly
positive. Θ > 0
When the system deviates from steady state, it transits to steady state
dΘ < 0 dt (deviating from steady state)
dΘ = 0 dt (steady state).
Entropy doesn’t change with the passage of time, dS = 0 , namely, des = −dis < 0 .
The energy flow or material flow coming from the environment (acceleration of particles)
determines a negative entropy flow, but it’s counteracted by the entropy in the system, and the
system transmits entropy to the outside. A stationary state with nonequilibrium state is
formed.
9 The same principle and different metric field
If all the fields are defined on space-time, and the measurement of space-time is
accomplished by metric, then all the fields are metric fields. If the frequency and wavelength of quantum is space-time itself, then unified field is the theory of using metric to measure the changes of different frequencies and wavelengths.
The equivalence principle aforementioned is given by entropy theorem directly, which is
different from the Einstein's equivalence principle of general relativity. Firstly, the
equivalence principle is not restricted to gravitational field, and the new equivalence principle is effective at all fields. Secondly, there is no need of auxiliary of Mach principle, and inertial field is directly from acceleration, rather than from remote matters. We make this conclusion before: all the fields between same high frequency and same low frequency are equal, having no relation with the material of field source. If this field includes both gravitational field and electromagnetic field, then we need to popularize the equivalence principle of acceleration
and gravitational field. This popularization is very simple, namely, equivalence of acceleration and electromagnetic field, if
ω = ω0 exp(−at / c)
Acceleration of electrons a = qE / m
e and m are respectively the charge and mass of electron, E is electric field strength.
Then we get
ω = ω0 exp(−qEt / mc)
（24）
Similarly, for electromagnetic field,
f
=
dω dt
=
qE mc ω0
exp(−
qEt ) mc
50
So
F
=
qE m
hω c2
exp(− qEt ) mc
We get
a = qE exp(− qEt )
m
mc
（25）
When at << c , ignoring small amounts above second order, then
a
=
qE m
−
qE c
qEt m
+
......
Namely, F = q( E0 + v × B)
In the formula, v = qEt m
Above equations of gravitational field and electromagnetic field are not only unified in
forms, but also have the same generation mechanism, both being the products of quantum
frequency variation. For purpose of convenience, we express both fields by the formula of
gravitational field, only changing
g to
eE m when involving electromagnetic field.
10 Export of fine structure constant
From equation （22), we can get
ω = ω0 exp(−e2 / 4πε0mc2r)（27）
In a weak field, when system is deviated from the steady state, the law of minimum
entropy production requires the system to tend to a steady stationary state.
s=
k ln ω ω0
= −k
e2 4πε0mc2r
（28）
s is a determined amount which does not change along with the time. In addition, it
should have a maximum value, so in the equation of (26), r should be the minimum value.
Based on quantization of space-time, it is not allowed to freely take values on the space-time
coordinates, and r should be the wavelength of a certain quantum. Since entropy requires that
particle is not allowed to radiate the quantum with higher static energy than itself. For
electromagnetic field, the minimum wavelength emitted from electron should not be smaller
than the Compton wavelength of the electron. The quantum wavelength of electron radiation
is most likely to be the Compton wavelength of the electron. r = D e then the exponential part
of equation（25）becomes a constant, and it is called fine structure constant. This constant
indicates the strength of this field. Then
ω = ω0e−α
In the formula, α is fine structure constant. For electromagnetic field
e2
1
α = 4πε0ch ≈ 137.040
g2 For strong nuclear fieldα = 4πε0ch
51
In the formula, g is strong nuclear
For the deduction of the fine structure constant of strong nuclear field, we must turn the
frequency of the quantum into the particle with mass. We assume π meson is the energy level
in atomic nucleus, and the redshift of the proton could only occur by reaching π with one
step. Namely,
π
=
p exp(−
g2 4πε 0 m0 c 2 r0
)
In the formula, m0 and r0 are the mass and wavelength of proton respectively, the fine
structure constant of neutron is
，（ ） αn
=
ln
π p
=
−(g2
/
4πε0c2r0
)
=
−1.91
29
Meanwhile, when proton has redshift to π meson, recoil must occur, so as to have an inertial
field in which particle blue shift occurs. So
π = ( p − π ) exp( g 2 / 4πε 0c 2r)
Fine structure constant of proton is:
（ ） α p
= ln
π p−π
= 1.79
30
Since the directions of transverse fields (magnetic field) generated by red shift and blue
shift are opposite, so the field strength is finally represented on the difference of the two
transverse fields, namely 0.12. The hadronic charge is calculated through formula (27), namely, g = 2.59 ×10 −18 ,
which is 1.616 ×101 times of electron charge.
The ratio between the strength of strong nuclear field and that of electromagnetic field is
／ ＝ 0.12 0.0073 1.643×101.
For gravitational field,
GM α = c2R
R is radius of object. For example, the fine structure constants of sun and earth are
（ ） αgSun
=
GMSun c 2r 0
=
2. 11 × 10−6
31
（ ） E GMarth
α gEarth =
c 2r 0
= 6. 95 × 10−10
32
For weak gravitational field, we could globally define the space-time, namely, the r of above two equations could directly use the distance between sun and earth.
Under Planck length of L = Gh / c3 , fine structure constant is Gh / c3r2
Here, R is wavelength, and space-time must be locally defined.
11 Physical significance of fine structure constant and the physical problems solved
52
We can see that, fine structure constant not only can measure the strength of fields, but it
is also the probability of mechanical quantity in the field to the inherent mechanical quantity;
meanwhile, it is taken as the metric to measure variation of space-time and phase.
h
， F = − f
It can be seen from
c force is in direct proportion to the frequency
fluctuation rate, and the frequency fluctuation rate is in direct proportion to frequency. Therefore, the larger the fluctuation rate of frequency is, the larger the energy level spacing of the equipotential surface, the more remarkable of its non-continuity and the stronger the force will be. Along with the quantum redshift, the frequency decrease, frequency fluctuation rate decreases, and the energy level spacing also decreases. Consequently, the far field energy level will show continuity, and the force will become weaker. It can be seen from equation
， ， ω = 0
(25), when r → ∞ ω = ω0 , no field exists. When r is close to zero, ω0
namely,
when the wavelength of particles is extremely small, the frequency will maintain unchanged, which is also called asymptotic freedom. From the angle of the quantization of space-time, it is not possible for above two cases to exist, because the wavelength of the quantum could neither be infinite, nor be zero. As a result, the above two cases could only approximately exist. From above analysis, we can work out the relation schema between the total field intensity and the particle wavelength.
E
λ
λl λ p λe λg
， Here, λl λp，λe，andλg stands for Planck wavelength and wavelengths of proton,
electron as well as graviton respectively. There are different fine structure constants on these
points. Since the particle mass is discrete, the fine structure constant is also discrete. Each fine
structure constant could only measure the strength of the section it represented, so the above
figure is only the rough description.
By using fine structure constant, we can solve the energy level and field problems inside the
hydrogen atom. Energy level or fields come from the quantum redshift caused by the energy
quantum radiated from nucleus. Therefore
1 λ1
=
1 De
(1 −
q2
/
4πε0mec2r)
When inertial field (blue shift) is generated by electron acceleration (transition), the change of
wave number of quantum is as the following:
1 = 1 (1+ q2 / 4πε0mec2r) λ2 λ1
53
The average total energy change of a redshift and a blue shift is
（ ） 1
λ
=
1 D
e
{1 −
1 2
(q2
/
4πε0 mec 2 r )2 }
33
Time-space is quantized, so when r = nD e, (here n could be either integer or fraction, when
n = 1, 2, 3......)
1 λ
=
1 D
e
{1 −
1 2
(a2
/ n2 )}
In the formula, a is fine structure constant. This is the energy level of hydrogen atom.
The anomalous magnetic moment of particles could be calculated by using fine structure
constant.
， Given r is the wavelength of the electron, namely, r = h then electron magnetic moment mc
could be calculated by equation (25).
（ ） us
=
−u0exp(−
a 2π
)
34
In the formula, a is fine structure constant, and u0 is electronic inherent magnetic moment.
， Since a << 1 the above equation could be written as: 2π
us = −u0 exp{1−α / 2π +1 / 2(α / 2π )2 −...........}
Since electron acceleration generates an inertial field, namely, positive electron, and a
magnetic field. Inertial field restores the original field through blue shift, and generates a
magnetic field again at the same time. It is an alternating process between positive and
negative fields, so the above equation must be further corrected. We still make analogy of
vacuum polarization of quantum electrodynamics and electron self-energy process:
So called vacuum polarization means the red shift of atomic nucleus after radiating a photon.
， ω1
=
ω0
exp( −
a 2π
)
It accelerates electron and the acceleration generates an inertial field, namely positive
electron, which further makes photon blue shift, and is equivalent to an absorption of the
photons. Namely,
ω2
=
ω1(1+
a 2π
)
=
ω
0−ω0(
a 2π
)2
∆ω
= ω0
− ω2
=
ω0
(
a 2π
)2
Or the probability is ∆ω = ( a )2 ω0 2π
The so called electron self-energy means electron is accelerated to emit virtual photon,
generating a positive electron and a magnetic field. The virtual photon is blue shifted by
positive electron, namely being absorbed, and its probability increases ( a )2 times. If the 2π
two processes above are continuous, then the probability is ( a )4 . 2π
54
Since a field must have a reversed field, or a blue shift must be with a red shift, the
remaining ∆ω after the offset of both is accumulated, namely, path summing (quantum
electrodynamics is path integral) is the track of particle. By using above methods, the mutual effect between light and matter and the mutual effect between electron and electron will not occur infinity, so it is not necessary to carry out renormalization. Reason for infinity occurred in quantum electrodynamics is that electron emission and assimilation of virtual photons must involve the change of electron mass and electric charge, while the red shift and blue shift only involves field. In other words, the electron acceleration has nothing to do with the mass and charge of electron. It is the equivalence principle of electromagnetic field. Anomalous magnetic moment of protons and neutrons: we have got the fine structure
（ ） （ constants of protons and neutrons respectively from equations of 27 and 28). Since
protons have electric charge and natural magnetic moments, proton magnetic moment
is un = un0 (1+1.79). In the formula, 1.79µn0 is anomalous magnetic moment. Neutron has
， neither charge nor natural magnetic moments, and its magnetic moment is un = −1.91uN all
of which are anomalous magnetic moments. By the same token, the fine structure constant of gravitational field could be used to
calculate the curve of light movement and precession of perihelion of Mercury in gravitational field. Bending of the light and the precession of perihelion of Mercury are the results of the effect of gravitomagnetic field.
Given ω0 is the frequency of incident photons, the frequency of photons after the effect
of gravitational field is,
ω = ω0exp(-GM/c2r) = ω0 ( 1 − GM / c2r )
G is the gravitational constant, M is the mass of stars, and r is the radius of stars. The average
value of energy deviation in every degree of freedom is
∆ω / ω0 = GM / c2r
For the reason that the movements of photons have four degrees of freedom, among which no
one is superior to the others, namely, they are statistically independent, so the deflected angle
of photons is
∆ω 4GM ω0 = c2r
It must be pointed that when calculating the above red-shift, if not ignoring the small
amount,
the
final
result
should
have
a
modification
of
(
GM c2r
)2
.
∆p gr p = c2 is the probability of Mercury’s deviating from the normal track, so the deflected
2πGM
， radian in one degree of freedom of each circle around the sun is c2r . However among
the three degrees of freedom, no one is superior than the others, namely, they are statistically
3× 2πGM independent, so there must be c2r .To precisely calculate the procession of Mercury’s
55
perihelion, small amount like
(
GM c2r
)
2
should
be
included.
GM c2 r
is actually the irreversible
part, so the procession is irreversible, namely, the part of entropy production, which is also the
reason why procession is continuously cumulative.
12 Discussion about range of force and polarity
The repulsion problem of gravitational field: a positive field must be with a negative
field. If the positive field is a field along with time, then the reversed field will be against
time. We use Einstein elevator to explain this question.
When the lift goes free fall in the gravitational field of earth, acceleration would generate
an inertial field with a reversed direction against the gravitational field. Given this inertial
field is ginertia , ignoring horizontal field g0 ≈ −ginertia , we get ω = ω0 exp[−(g0 − ginertia )t / c]
（35）
ω = ω0 f = 0 g = 0
Namely, the red-shift quantum forming gravitational field in the lift is blue-shifted by the inertial field with reversed direction. There is neither energy change under the first order approximation nor field in the lift. The objects in the lift have no acceleration and they are under zero gravity condition.
Now assuming when the lift is in the free fall in gravitational field, a force with the same direction and acceleration on the lift is exerted. According to the equivalence principle of acceleration and field, this new field will surely generate an inertial field superposed with the
original inertial field. Then we get ginertia > g0, from ω = ω0 exp[−(g0 − ginertia )t / c]
f >0
Namely, the quantum in the lift is blue-shifted, which means that the energy of system increases, and leads to a repulsion force. If the lift is completely closed, the person in the lift would feel there is a repulsion force between him and the floor of lift and he is making accelerated movement toward the top of lift.
Why gravitational field is rarely seen? This is actually a problem of probability. Redshift has a larger probability than blue-shift. Because red-shift is a natural process in which energy is tending to a balance without external force, while the realization of blue-shift needs external force. Under natural state (not bound state), two electrons with the same nature are impossible to have repulsion force. One electron accelerating to the other one under external force would surely generate blue shift, generate repulsion force. So the blue-shift can’t take place under natural state, and blue-shift is the cause of repulsion force.
If the mass (gravitational mass) which accelerates objects is positive mass, then the mass of accelerated objects (inertial mass) is negative mass. This negative mass is against time, just as the positive charge is an electric charge against time. Charge could only be distinguished between positive and negative in an electromagnetic field. It’s meaningless to talk about the polarity of electron without field. Similarly, gravitational mass and inertial mass could only be distinguished in a field. The direction of gravitomagnetic fields (or called spin) generated by gravitational mass are different from the one generated by the inertial mass.
The quantization of space-time would certainly lead to the quantization of the range of
force. From f = −gk we can see there is a frequency variation in every wave vector interval,
56
namely, a recoil force. So the range of force is in direct proportion to the wavelength. The
smaller the wavelength is, the shorter the range of force will be. The wavelength of
interacting particle of strong and weak nuclear force is small, so it’s a short-range force.
Along with the red-shift of quantum, the wavelength increases, and its change is not apparent
until it presents an approximate continuity, recoil force of single quantum getting close and
range of force increasing, which is the reason why gravity or electricity are long-range forces.
13. Discussion about dark energy and dark matter
According to the cosmologic observation, the mass determined by aster orbital velocity is
seriously inconsistent with the galaxy mass observed by direct counting and the former is ten
times higher than the latter, which make people think there is a kind of dark matter. The mass
determined by star orbital velocity is calculated on the basis of Newton’s laws of motion. We
know that Newton’s laws of motion is supposed to be modified. Spectrum redshift
（ ） z
=
∆ω ω0
=
gr c2
36
According to Hubble’s law:
（ ） z = H 0r = r 37 cR
H 0 is Hubble constant, and R is universe radius. Comparing the two formulas above we can
get:
r gr R = c2
g = c 2 ≈ 1.5 ×10−10 (m / s 2 ) R
This is the acceleration of cosmic expansion generated by gravitomagnetic field, which is not included in the Newtonian mechanics. So the Newtonian mechanics must be modified as follows:
（ ） ar
g = g//e−c2 38
gr Under weak gravitational field or when c 2 << 1 , the Taylor expansion of above equation
keeps the second order approximation
（ ） g
=
g//
−
g//
ar c2
39
The second item on the right is vertical field
g ⊥
=
GM r
a ⊥
c2
Vertical field is perpendicular to the direction of propagation r and changes along with 1/r. It
depends on the acceleration of aster in a simple and direct form. Without acceleration, there is
no such vertical field. Obviously, with the increase of spatial distance, the longitudinal field
g// changing with 1 / r2 disappears, and only vertical field is left.
It is just because Newton law of gravitation cannot explain the expansion acceleration of
the universe; then people assume that there exists dark matter in addition to visible matter.
When Newtonian mechanics is corrected, and gravitational field is taken as the result of
57
quantum redshift, the hypothesis of existence of dark matter becomes needless. Actually, vertical field is the result of quantum redshift, and the redshift is an immediate
inference of the second law of thermodynamics. In other words, redshift is the initial causation of generation of gravitational force. The so-called cosmic expansion is based on the theory of Doppler redshift. It indicates that the astral accelerated motion is the cause, and the redshift is the result. In the absence of external force, objects accelerate automatically. This is a process of entropy reduction, and it doesn’t accord with the second law of thermodynamics. Therefore, we believe that it seems a little far-fetched to infer the existence of Doppler motion from quantum redshift, then arrive at the cosmic expansion, and consequently reach a conclusion of the existence assumption of dark energy. Reference Poincare, translated by Ye Yunli, Science and Hypothesis, Commercial Press, 1997, P92. About the author: Xu Jianmin, male, born in February, 1960, native Beijing, a lawyer of Beijing Unitalen Law Office Mailing address: Ya Yuan, Western Hill, Baijiatuan, Wenquan Town, Haidian District, Beijing, Tel. 13366005271
58
New Exploration for the Enigma of Paradox in Special Relativity Dong Jingfeng (Scientific and Technology Bureau in Rushi County, Henan Province, 472200, China)
Abstract : By the analysis of twin paradox, it is pointed out that the constriction of spacetime is the only effect of measurement and all paradox do not exist actually. The essence of special relativity is a number method forways to provide math and physical idea. Experiments to verify special relativity have verified general relativity. Keywords: Twin paradox, Time Standard, Measurement effect
Since the establishing special relativity by Einstein in 1905, a century has passed. So many experiments show that the theory is correct in very high precision. Special relativity has been used widely and become one of the most important foundations of modern physics. But meanwhile, so many paradoxes appears in the theory just as twin paradox, submarine paradox, slide paradox soft rope paradox, right-angle level paradox, the paradox of strict length limit, the paradox of seeing form of moving body and stress constriction of length and so on. Theses paradox caused furious argument and much diverge. The understanding for space-time constriction is very different: it is untrue, it is unphysical and true, it is apparent, mathematical, it is seeing effect, it is decided by measurement, it is a relative result of simultaneity and so on. Many beginners are puzzled by the space-time concepts of relativity and the relativity of simultaneity. It is necessary for us to make clear the essence of special relativity to eliminate theses paradox.
1 New explore for twin paradox 1.1 Definition of twin paradox
According to special relativity, suppose that new born twin A carried a digital clock A and was at rest at the original point of the airship reference system representing by the coordinate oxyz (time coordinate is t ). His brother B carried a digital clock B and was at rest at the original point of the earth reference system representing by the coordinate OXYZ (time coordinate is T ). Suppose that both reference systems are superposition each other at
time T1 = t1 =0, and the airship moved along + X axis in speed u . When A is 20 years old, the
airship returns along the same way. When airship arrived original place, according to Einstein’s theory and without considering the change of speed from + u to −u , A found that the recorded time of B clock was less and B is young than A . But B found that the recorded
59
time of A clock was less and A is younger than B . This is so-called twin paradox. The real situation would be that A clock was less and A is younger than B . This conclusion is recognized now (see document [1], page 60 ).
1.2 Analyzing on viewpoint of special relativity. By consider the fact that the speed of airship changed from + u to −u , the adherent of
Einstein insists that both A and B are inertial systems in the process. They use the method deducting the effect of simultaneity to eliminate twin paradox. . This is called as the method of special relativity only to use the idea of special relativity (see document [1], page 60).
In fact, all so-called analyze, calculation and conclusion of special relativity on twin paradox are incorrect. The reasons are follows.
The so-called twin paradox is calculated by using formula ∆T = γ ⋅ ∆t . But the
formula is effect only under the ∆x = 0 condition, ∆t ≠ 0 and ∆X = γ ⋅ u∆t ≠ 0 . When A
returned to the earth, we have ∆X = 0 , so that the condition ∆X = γ ⋅ u∆t ≠ 0 cannot be
satisfied. The calculation is wrong.
～ As shown in Document [2], 77 78, many scholars try to explain twin paradox
recurring to space-time diagram now. But they forget the basic and key conclusion which can be considered correct, that is there are different time standard on different reference frame. Because when airship swerved to return to the earth, its speeds and directions were different before and after swerved. So the time’s reading of A clock are different before and after swerved. Because of neglecting the difference of speed, the adherent of Einstein calculate the new time standard in the swerved airship (according to special relativity, airship should be considered as two different inertial reference system with different speed before and after airship swerved.), so the result is certainly wrong.
There are some scholars who try to explain twin paradox by the atomic clock traveling around the earth, the disk circumrotates and the µ meson fly to explain twin paradox (see
～ Document [1]61 88pages). This is also wrong. So called twin paradox is calculated by time
expansion formula ∆T = γ ⋅ ∆t . But the formula ∆T = γ ⋅ ∆t is deduced based on the
concept of inertial reference frame, so it is only suitable to inertial system. But the experiments just as atomic clock traveling around the earth are not on inertial system, so these experiments cannot verified twin paradox.
For this problem, some scholars consider that the orbit can be divided into infinite limited sect and each sect can be considered as inertial system, though the process of airship traveling around the earth is not inertial. Then by the integral of time quantum, we can still
60
～ ～ obtain twin paradox (see Document [2], page 73 78, Document [1], page 61 88). This idea
is also wrong, for the result of integral only represent the time sum of each sect of inertial processes. It does not represent the change of time standard caused by the change of speed from an inertial system into another inertial system. So the result of integral is incorrect, (the mistake is the same with ).Some scholars consider that the relativity of time originates from the differences of time’s direction. The time observed in the static reference frame is the time’s projection of moving reference frame down to the static reference frame. So the person who travels by airship would be older for his time forms a curve. Meanwhile, the person who is at rest on the earth would be younger, for his time is linear. But this opinion is untrue. In fact, in light of Person A, his time is a linear, but in light of B, his time is curved.
The detail calculation above to use special relativity to explain the so-called twin paradox
《 》 。 referees to the professor Shi Jiaoming’s work The Enigma and Beauty of Dynamics [3]
2 The essence of special relativity The most important distinguish between special relativity and classical mechanics is the
definition of simultaneity. The essential difference between special relativity and classical mechanics is the definition of simultaneity. Though the simultaneity is implicated in classical mechanics, but there exists no sign which can propagate in infinite speed in practices, and we can only use light signal to adjust clocks in reality. In other word, the contraction of moving ruler and the slowing of moving clock are caused by our measurement using light as toll. If we do not use light as toll, or do no any measurement, there would have no effect happen. For a simple example, a man who is in an airship which moves in a high speed spend two minute to drink a cup of water by his measurement But the person on the ground thinks that the man on airship take longer time to drink water, because the person can only use light’s single (which need time to propagate) to transform information for no infinite time setting signal. However, the time the man on airship takes to drink water does not change. In this way, twin paradox is easy to solve. No one of two twins becomes older actually though they think another’s time becoming slow by measurement. If we do not think so, as an ideal experiment, we let the earth splitting into two parts, each one carry one of twins apart away in a high speed, then let them meet again. Which one is younger? No one can answer this problem if we do not consider problem as above. Based on this nature of special relativity, we can conclude that when an observer observes an object, owing to the difference of observational conditions (the motion state of observer’s reference frame), he can reach completely different results (the constrictions of time and length). This result explains a principle of philosophy, i.e., condition decides law and observation.
By this character of special relativity, we prefer to consider it as a philosophic principle in the name of physics, that is, for an observer, the result of measurement is completely
61
different under different condition (i.e., the moving state of reference frame which observer located). It indicates a philosophic principle: condition decides law and measure results.
So the paradoxes of special relativity do not exist. Taken the submarine paradox as an example, we first suppose that a submarine submerged keeps balance without raising or sinking in sea water. Then suppose that the submarine moves in a speed nearing light’s speed. Because the length would contract in the direction of motion, according to observers who are at rest on the surface of sea, the density of submarine would become great so that the submarine would sink. But according to the sailors who are in submarine, the sea water moves back off, and the density of sea water becomes great with greater buoyancy, so that submarine would be floated up. According to special relativity, two viewpoints are alright. What would be for submarine, sinking or floating? By our viewpoint, it is easy to decide. The contraction of sea water is only a measurement effect caused by observers in different reference frames. But there are constrictions or both submarine and sea water. The paradox of submarine does not exist actually.
So we can say that the essence of special relativity is only a method of mathematics. It exposures the connection of space and time and provides mathematic method and physical idea for general relativity.
3 Why does special relativity not represent practical space? Because of the common existence of gravitation, there are always accelerations among
any reference frames. We have no real inertial reference systems. The Lorentz transformation holds only for inertial reference systems which move in uniform speed. The experiment verification of special relativity should be carried out in the inertial reference systems which move in uniform speed, but this condition cannot be satisfied in practice.
The observation of modern astronomy shows that, men rotates with the earth, the earth rotates with the sun, the sun rotates with the Milky and Way galaxy rotates around its center. So there is no real inertial reference frame in the universe. The scale is bigger and material is thinner, the gravity is weaker and the reference frame is more nearly inertial reference frame. Even though the earth is considered as reference frame approximately, the experiments carried out on it cannot avoid the influence of acceleration. It is an unverifiable problem whether or not physical processes are the same in different inertial reference frames. Because there are the relative motions of experimental instrument and observers between two reference frames, if we want to verify the predication of special relativity, we should move the instrument and matter from one reference to another through accelerating or decelerating it. In this way, the non-inertial motions are involved.Because there are the motion processes of acceleration and deceleration, the physical effect cannot be explained by special relativity.
So speaking strictly, “the space-time in which special relativity holds is the space-time without material [4]”. As we know that space-time is the most foundational form of material’s existence. The space-time without material is only theoretical abstraction, or does not exist
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actually. From this angle, special relativity is only a method of mathematics. It points out that the action of a universal constant c (light’s speed) in the law of nature. The relativity of simultaneity is disclosed. The closed relation between time and space is uncovered by means of the four dimensions space-time and the Lorentz transformation. The invariability of four dimensions element ds2 provides mathematical method and physical idea for t general relativity. It should be pointed out that the mathematical method here indicates the calculation in “four dimensions”, not mathematical tools. It is obvious that what used in special relativity are Euripides geometry and algebra equation, but in general relativity, what used are nonEuripides geometry and tensor analysis. The effects of special relativity are not dynamic ones, having nothing to do with the physical process of material and interaction force. It is only kinematical ones relative to correlation between objects, just as the multi-values of velocities [5].
4 The essence of experiments of special relativity is to verify the conclusion of general relativity
The space-time theory of special relativity does not relative to acceleration. It only considers the measurement relation of space-time between two references which are in inertial motion states. At first, we suppose that they are at rest each other and define the same unit time and length. Otherwise we cannot define the same unit time and length when two reference frames are at relative motion states. It is necessary for us to accelerate one of them if we want introduce relative velocity between two reference frames which are at rest each other at beginning. After acceleration stops and two frames reach the state of relative motion, the structure of space-time of accelerated frame would change[6]. This process of acceleration can be explained by general relativity (the principle of equivalence), i.e., the frame can be considered to place into gravity field. All experimental condition in the earth does not satisfies the demand of inertial reference frame, why all experiments coincide with the predication of special relativity? The practical space-time is that of general relativity. The transformation of special relativity which is only ideal and linear one does not involve gravitation and acceleration. The ideal situation can only be approached but not be reached. Just known this localization of special relativity, Einstein developed general relativity. So speaking strictly, special relativity is an only mathematics to disclosure the retraction of material moving state on space-time as well as the closed connection between time and space. It provides a firm foundation of mathematics and physics for general relativity. By means of the equation of gravitational field, the space-time metric, and the energy and momentum of material motion are connected by general relativity. In this way, the law of object accelerated motion in gravitational field is obtained. General relativity is just the extension of special relativity.
In general relativity, the effects of rule becoming short and clock becoming slow is determined by the potential of gravity or the material distribution and motion. The measurement results of space-time have nothing to do with the choice of coordinate system.
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What decides space-time is only the moving state of material. The does not depends on the difference of observations. So the effects of general relativity are absolute, which do not change with measurement method. The absoluteness is the real reason that special relativity acknowledge that the effects of clock being slow and mass increasing is measurement effects and the result verified by experiment is real effects and the objects moving in high speed have physical changes. In general relativity, the effects of “clock becoming slow and ruler becoming short” are the real result of dynamic, not measurement effect [7]. That is to say, the real reason to cause the changes of mass, length, time is acceleration or gravity fields.
5Conclusion As we known that the effects of “ruler becoming short and clock becoming slow” in
special relativity are caused by the change of observation condition. They have nothing to do with practical forms of observed objects. In other word, the practical forms do not changed under different conditions of observation. The “reality” of special relativity stays in the level of information, not in the ontological level. So many persons who discuss special relativity confuse the reality of the two levels. They consider the original explain of Einstein about “ruler becoming short and clock becoming slow”as a evidence to deny the reality of special relativity, or demote it as “explaining relativity using traditional idea”. In fact, most explanation about twin paradox, submarine paradox and so no are wrong. As long as considering “ruler becoming short and clock becoming slow” as measurement effects, all paradox would not appear.
Therefore, we cannot use special relativity to explain the experiments of atomic clock travel around the earth, µ meson decay and mass increase, for these physical phenomena represent the real change of objects which move in high speed. They are different from the observation effect of special relativity. We should use general relativity to explain them. The author thinks that there is a faultage between special relativity and general relativity. The theory existing in this faultage can explain these experiments simply and clearly without introducing any logical paradox. So the author hope that scholars are interesting in this problem and do further research. The influence of frame’s recti lineal and uniform motion on space-time structure is different from that of acceleration motion. Special relativity is only suitable for the reference frame which is in uniform motion. As soon as it oversteps this extent, special relativity would lose effect. Different from special relativity, general relativity is suitable to non-inertial motion to explain the physical events when reference frame does acceleration motion or in gravity fields. There is no any logical contraction and paradox to use general relativity to explain these experiments. The author hopes other scholar who are interesting in these problems to do further research.
References [1] Zhang Yuanzhong, Experimental foundation of Special Relativity, Beijing, Science
64
Publishing Company, 1979.9. [2] Liu Liao, Zhang Yunzhong , Special Relativity, Shijiazhuang, Hebei Publishing Education
Company, 1987.9. [3] Shi Jiaoming, Enigma and Beauty of Dynamics, [M], Hebei Science and Technology
Publishing Company, 2007.8 [4] Zhang Jialu, Relativity Physics, Thermodynamics and Statistical Physics, [M] Chinese
Science and technology Publishing Company. 1990 [5] Mei Xiaochun ,The Absolution of Velocity Caused by Acceleration Process and Absolute Theory of Space-time with Variable Scalar of Space-time [J],( Wait for publication of)
． [6] Xue Xiaochou, The philosophy Problems of Modern Physics [J] Journal of Xinxiang
Normal University ( Version of Social Scince), No.1, 1983 [7] Zhang Zhengjiu, Modern Relativity and Black hole Physics, Wuhan, Huazhong Normal
University Publishing Company 1986.8. [8] Cheng Jianguo, Dong Jingfeng, Understanding and Treatment Relativity Correctly,
Advance Science, [J] No.3, 008. About the author: The author is the Director of Scientific and Technology Bureau in Rushi County, Henan Province, the commissioner of Special Committee of Chinese Physical History, the visiting researcher of Institute of Innovative Physics in Fuzhou. The major area of the author’s research is relativity, particle physics, atomic physics. As the master of partial committee, the author has attended 15 domestic and international meetings of physics, and has published more than 40 papers inScientific Inquiry, Matter Regularity, Advance Science, Science, High Technology and Industrialization, Achievement of Science and Technology, Journal Of Shandong Normal University, Learned Foreland. Tel: 15516323715, E-mail: dongjingfeng@sohu.com
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Unsolved Problems in Special Relativity and Methods to Solve Them Duan Zhongxiao (Member of Beijing Relativity Theory Research Federation, Room 3-1-1, Building Jia-8, No.77, Dongmao Rd., Shenhe District, Shenyang, Liaoning, 110161, China) (E-mail: pingsan11111@126.com)
Abstract: The special relativity is based on the principle of constant speed of light and the assumption that the inertial systems are all “Equality (Equal Right)”. However, 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. Based on this the further analysis proposes that, all the above mentioned problems can be solved only in the way that theoretically introducing the vacuum matter, vacuum energy, as well as the two-way spreading vacuum matter waves along with any directions in space. According to an important characteristic of the Lorentz transformation, namely the continuous transformations will be equivalent to one certain transformation, the author deeply considers the “Equality” of inertial systems and concludes that, the principle of relativity and the “Equality” of inertial systems are two entirely different things, the principle of relativity is correct, but the “Equality” is wrong. Based on the above discussions, the author also finds many problems and errors in the special relativity (for details see the text of this paper). On this basis, the author already established “The Matter Space-time Theory of Relativity” (“Matter Theory” for short). “Matter Theory” is based on the matter space only. The two principles and other assumptions are no longer needed. “Matter Theory” overcomes almost all the problems and errors in special relativity, explains all the contents that can be explained by special relativity, and presents many new predictions, such as the conclusions of “Matter Theory” show that not only the moving clock will slow down, but also all the inertial systems running the relative uniform speed translational motion will have the characteristics of multi-level of space-time. Besides this paper, other results can be found in reference [1]. Keywords: Matter space, vacuum matter wave, principle of relativity, application condition of the principle of relativity, inertia reference system
1 Vacuum’s matter space essence and basic characteristics 1.1 Using Lorentz transformation to discuss vacuum’s matter space essence
66
Looking at the single Lorentz transformation alone, vacuum’s matter space essence and its action cannot be reflected in the transformation. Because as long as theoretically introducing the light signal and based on the hypothesis of “Equality”, then the Lorentz transformation can be established. However, when we compare the two Lorentz transformations in different regions, the matter space and its action in the transformation are obvious.
Supposing that the space is uniform and isotropic, thus the transformation rule is not restricted by time, region and direction. In this aspect the actual performance is as follows: The experiment to test the validity of theory is not restricted by time, region and direction also. For different times, different regions and different directions, doing the same experiments, if the theory is correct and the experimental procedure is perfect also, thus the results must be the same.
This objective fact can be described more strictly theoretically. The Lorentz transformation is based on the Cartesian rectangular coordinate system, this coordinates system is formed by the origin of coordinates and three frame straight lines. However a very simple fact is, the origin is chosen arbitrarily, and not restricted by the spatial location. Therefore, the frames are also chosen arbitrarily, and not restricted by the spatial location. Starting from this fact to discuss the problem, we find that the matter space is existed really, and the action of matter space in transformation is irreplaceable. Supposing that there are two inertial systems ΣA and ΣB running the relative uniform
speed translational motion, and the speed of ΣB relative to ΣA is v . Choosing anyone straight line in ΣA and taking this line as the x coordinate axis in the
three coordinate systems to be established below. From this line arbitrarily choosing different
three points oA , oA1 , and oA2 , and taking these three points as three origins. Thus in ΣA we
have established three Cartesian rectangular coordinate systems,
（ ） （ ） （ ） ΣA xA , yA , zA , tA , ΣA1 xA1 , yA1 , zA1 , tA1 , and ΣA2 xA2 , yA2 , zA2 , tA2 .
namely
Similarly, choosing anyone straight line in ΣB and taking this line as the x coordinate
axis in the three coordinate systems to be established below. From this line arbitrarily
choosing different three points oB , oB1 , and oB2 , and taking these three points as three
origins. Thus in ΣA we have established three Cartesian rectangular coordinate systems,
（ ） （ ） （ ） namely ΣB xB , yB , zB , tB , ΣB1 xB1 , yB1 , zB1 , tB1 , and ΣB2 xB2 , yB2 , zB2 , tB2 .
In order to simplify the discussion, further provisions are as follows:
1) The x coordinate axis in the coordinate system ΣB is also the x axis in ΣA, and they
have the same direction;
2) The movement of ΣB is relative to ΣA along the positive directionof the common x
axis (in order to prove that the transformation rule is not restricted by the direction, we should
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also discuss the case that ΣB is relative to ΣA along the negative direction of the common x
axis, but the process and result are the same to the case of positive direction, therefore we will not discuss it);
3) In ΣA and ΣB, for all the cases, the coordinates y and z are all equal to zero;
4) Supposing that as tA = tB = 0 for the time in ΣA and time in ΣB, oA is superposed on
oB , oA1 is superposed on oB1 , and oA2 is superposed on oB2 (this moment,
tA = tA1 = tA2 = 0 and tB = tB1 = tB2 = 0 ).
Therefore at the time tA1 in ΣA1, the Lorentz transformation between ΣA1 and ΣB1 is as
follows:
xB1 = γ (xA1 − vtA1)
(1.1-1)
tB1
=
γ
(t A1
−
vxA1 c2
)
(1.1-2)
At the time tA2 in ΣA2, the Lorentz transformation between ΣA2 and ΣB2 is as follows:
xB2 = γ (xA2 − vtA2 )
(1.1-3)
tB2
=
γ (tA2
−
vxA2 c2
)
(1.1-4)
Supposing that at the time tA in ΣA, the time in ΣA1 is tA1 , and the time in ΣA2 is tA2 .
Because for the same inertial system, the clocks are synchronous, therefore we have:
tA = tA1 = tA2 .
For the reason that the light signal is also assumed arbitrarily, it is not restricted by the time and region. Therefore, when we assume that one light signal is radiated from the origin
oA , we can also assume that at this time other two light signals are radiated from oA1 and
oA2 respectively, and at the time tA in ΣA we have: xA = xA1 = xA2 = ctA = ctA1 = ctA2 .
Substituting xA1 = xA2 , tA1 = tA2 into Eq. (1.1-3) and Eq. (1.1-4), we can get
xB2 = γ (xA1 − vtA1)
(1.1-5)
tB2
=
γ (tA1
−
vxA1 c2
)
(1.1-6)
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To compare Eq. (1.1-1) with Eq. (1.1-5), and compare Eq. (1.1-2) with Eq. (1.1-6), we can get
xB1 = xB2 , tB1 = tB2 (1.1-7)
Substituting Eq. (1.1-7) into Eq. (1.1-3), Eq. (1.1-4), we can get
xB1 = γ (xA2 − vtA2 )
(1.1-8)
tB1
=
γ
(t A2
−
vxA2 c2
)
(1.1-9)
For the reason that xB1 and xB2 are located at the different regions of ΣB, therefore the
clocks used to measure tB1 and tB2 are also located at different regions. For the same inertial
system the clocks are synchronous, therefore the two clocks are synchronous in ΣB. To compare Eq. (1.1-2) with Eq. (1.1-6), we know that, observing from ΣA, the clock used to
measure tB1 and the one to measure tB2 are also synchronous, then we can get the following
conclusions: 1) For two inertial systems running the relative uniform speed translational motion, if the
clocks are synchronous in one system, observing from another system they are still synchronous.
2) The relative character of simultaneity is not the ultimate source of the rule of temporal and spatial transformation. Namely, the relative character of simultaneity serves no useful purpose to the rule of temporal and spatial transformation.
3) It is wrong to introduce the one-way spreading light signals along with all directions into transformation equation, and the relative character of simultaneity is nothing but the apparent phenomenon appeared by introducing the one-way spreading light signal into the equation.
4) Although the rates of the clocks in two systems running the relative uniform speed translational motion may be different, the ratio of the rates of the clocks in two systems is absolute. Therefore, the temporal and spatial transformation will not be reversible.
5) All the temporal and spatial transformations are not originated from the relative motion of physical system.
6) Although the principle of relativity is correct, while the assumption that the inertial systems are all “Equality (Equal Right)” is wrong.
We would like to emphasize several points in the above discussion, because they decide the main features of the transformation rules.
1) The tA (including tA1 , tA2 ) in ΣA, the tB (including tB1 , tB2 ) in ΣB, represent arbitrary
times in ΣA, ΣB. This indicates that the temporal and spatial transformation rules and their
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actions are not restricted by time, they are existed eternally, and affect the rules of physical state changes in the physical system.
2) In ΣA the origins of coordinates of ΣA1, ΣA2 are arbitrary non-superposed space points in ΣA; in ΣB the origins of coordinates of ΣB1, ΣB2 are arbitrary non-superposed space points in ΣB. Therefore the consistencies of above transformation rules (such as the consistencies of Eq. (1.1-1), Eq. (1.1-2) and Eq. (1.1-5), Eq. (1.1-6)) show that the transformation rules are not restricted by the spatial locations (namely the coordinate’s locations).
The more in-depth discussion on this content will present the more definite conclusions as follows.
The temporal and spatial transformations between two systems running the relative uniform speed translational motion exactly are the transformations between arbitrary space points in one system and arbitrary space points in another system.
Our discussions are carried out in the uniform isotropic space, therefore
xA1 , xA2 , xB1 , xB2 and (xA1 − vtA1) , ( xA2 − vtA2 ) can be interpreted as the set of points,
and based on this we can get the above conclusions by means of brief discussion. 3) In the above discussion we assume that the movement of ΣB is running along with the
positive direction of the common x axis. If we assume that the movement of ΣB is running along with the negative direction of the common x axis, or changing the direction of x axis
and the direction of signal propagation, we can get the same results as above conclusions. This means that the transformation rules are not restricted by direction. In the above discussion, for the transformation equation, we deny the action of light
signals (one-way spreading along with all directions in space), but we do not deny the status
and action of c in the transformation equation. This requires us to give c a new physical
content.
In the transformation, if the action of c is irreplaceable, then from the basic
characteristics of the transformation roles we can get:
1) The action of c must not be restricted by time, and not restricted by spatial position and direction; namely the actions of c are existed at anywhere and anytime, and effected on the transformation rules eternally. This action of c fully explains its characteristics of matter space. That means that c is the energy wave of matter space, and we name this wave the
vacuum matter wave. 2) In order to ensure the transformation rules do not appear the problems of the relative
character of simultaneity, and ensure the transformation rules are not restricted by directions, the spreading of vacuum matter wave along with all directions in space must be two-way.
3) In order to ensure the relativistic effects of transformation rules (such as the rule of moving clock slows down), the vacuum matter wave’s propagation velocity must be limited.
4) In order to ensure the transformation rules are always identical, and not restricted by time and space (namely all the transformations between any space point in one system and
70
any space point in another system are identical), the spreading rates of vacuum matter waves must be always identical at anywhere and anytime, and in the inertial systems running the relative uniform speed translational motion, the vacuum matter waves’ propagation velocities must be invariable (measured by each system’s clock and measuring ruler).
1.2 Theoretical foundation of vacuum matter, vacuum energy and vacuum matter wave Based on the above discussions we can get the basic characteristics of matter space: 1) In vacuum the mass points with energy are uniformly distributed. The mass point’s
energy is spreading outward in the form of spherical wave. Therefore, each mass point not only is spreading energy outward, but also receiving energy. This determines that the wave is two-way spreading along with any direction in space. These matter, energy and energy wave are named vacuum matter, vacuum energy and vacuum matter wave by us.
2) The vacuum matter waves are existed at anywhere and anytime; and spreading with the limited invariable rate at anywhere and anytime. The spreading rate of vacuum matter
wave is indicated as cm .
3) The spreading rates of vacuum matter waves in the inertial systems running the
relative uniform speed translational motion are all equal to cm (measured by each system’s
clock and measuring ruler).
It should be noted that “The Matter Space-time Theory of Relativity” [1] (“Matter Theory” for short) is based on the matter space and vacuum matter wave, the two principles and other assumptions are no longer needed.
2 Discussion on the application conditions of the principle of relativity The author affirms the principle of relativity, but also proves that the application of
principle of relativity is conditional, while in the past this is not clear for many people. One of the important reasons created the unsolved problems in special relativity is unclear for the application conditions of the principle of relativity.
Although in the past many people do not know the application conditions of the principle of relativity, but the correct theory and the correct parts of theory can be established with the prerequisite to conform the application conditions of the principle of relativity. The correct experiments testing theory are all in progress with the prerequisite to conform the application conditions of the principle of relativity.
The principle of relativity tells us that, in all inertial systems running the relative uniform speed translational motion, the laws of physics are identical in the mathematical form. But both the establishment of laws of physics and the experiments testing theory must contain two
71
contents: 1) The observer and the inertial system at which the observer is located; 2) The observation object (or experiment object).
The principle of relativity does not tell us that, whether or not all the physical objects running the uniform speed translational motion relative to a certain inertial system will obey the laws of physics established in this inertial system (for all the inertial systems the laws are identical in the mathematical form).It also does not tell us that, in all the inertial systems running the uniform speed translational motion relative to a certain physical object, whether or not all the observing results about this physical object will obey the laws of physics established in each inertial system (for all the inertial systems the laws are identical in the mathematical form).
The following discussions will show that, for specific physical object, there are two types of different inertial systems. The first one can make the correct observation and description about the physical state changing rule of this physical object, while the second cannot. In order to distinguish these two types of inertial systems, the first one is called the inertial reference system of this physical system (in the past, the inertial system and the inertial reference system are not distinguished).
After the deep discussion on the transformation between the two inertial systems running the relative uniform speed translational motion, we can get:
1) In all the inertial systems running the relative uniform speed translational motion, the laws of physics with identical mathematical form are all established between the physical system and its inertial reference system;
2) For the two inertial systems ΣA and ΣB, running the relative uniform speed translational motion, if ΣA is the inertial reference system of ΣB, definitely ΣB is not the inertial reference system of ΣA.
These two sections are the application conditions of the principle of relativity. The application conditions of the principle of relativity are not the theoretical foundation, but they are the prerequisite for establishing the theory, before the establishment of theory, we must stress that the theory should be consistent with the application conditions of the principle of relativity, otherwise the theory will not be valuable. We will make the concrete argument below.
（ 、 ） （ 、 ） Supposing that there are three inertial systems, ΣA xA tA , ΣB xB tB and
（ 、 ） ΣC xc tc , mutually running the relative uniform speed translational motion. Further
assuming that the speed of ΣB relative to ΣA is v1 , the speed of ΣC relative to ΣA is v2 , and
＞ v2 v1 , the speed of ΣC relative to ΣB is w . For the sake of convenient, we make the
following provisions:
1) Supposing that the three x axes of ΣA, ΣB and ΣC are superposed.
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2) ΣB and ΣC are moving along with the positive direction of the x axis of ΣA.
From the Lorentz transformation we can get: The transformation equations between ΣA and ΣB are as follows
（ ） （ ） xB = γ (xA − v1tA)
2-1
tB
= γ (tA
−
v1xA c2
)
2-2
The inverse transformation equations are as follows
（ ） （ ） xA = γ (xB + v1tB )
2-3
tA
=
γ
(tB
+
v1xB c2
)
2-4
The transformation equations between ΣA and ΣC are as follows
（ ） （ ） xc = γ ′(xA − v2tA)
2-5
tc
=
γ
′(tA
−
v2 xA c2
)
2-6
The inverse transformation equations are as follows
（ ） （ ） xA = γ ′(xc + v2tc )
2-7
tA
=
γ
′(tc
+
v2 xc c2
)
2-8
The transformation equations between ΣB and ΣC are as follows
（ ） （ ） xc = γ ′′(xB − wtB )
2-9
tc
=
γ
′′(tB
−
wxB c2
)
2-10
The inverse transformation equations are as follows
（ ） （ ） xB = γ ′′(xc + wtc )
2-11
tB
=
γ
′′(tc
+
wxc c2
)
2-12
Supposing that Eq. (2-1), (2-2), (2-5), (2-6), (2-9), (2-10) are all correct. Substituting Eq. (2-1) and Eq. (2-2) into Eq. (2-9), we can get
（ xc
=
γ ′′ γ
(xA
− v1tA)
−
wγ
(tA
−
v1xA c2
 )
=
γ ′′γ
(xA
−
w + v1
1+
wv1 c2
 t A ) 1 +
wv1 c2
 
2-
）13
Because γ ′′ =
1 ;γ =
w2 1− c2
， 1 so Eq. (2-13) can be written as
1
−
v12 c2
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( )( ( ) ) ( ) （ xc
=
  
xA
−
1
w + v1 + wv1 /
c
2
1− w2 / c2
t
A
 
1+
1 − v12
wv1 / c2
/
c2
  
xA
−
w + v1 1 + wv1 /
c2
tA
  
=
1−
(
w
+
v1
2
)
1 + wv1 / c2 2 c2
2-
）14 Supposing
（ ） u
=
w + v1
1
+
wv1 c2
2-15
（ ） （ ） Substituting Eq. 2-15 into Eq. 2-14 , we can get
（ ） xc =
( xA − utA )
1− u2 / c2
2-16
Because the continuous transformations will be equivalent to one certain transformation, comparing Eq. (2-16) with Eq. (2-5), we can get
（ ） v2
=
u
=
w + v1 1+ wv1 /
c2
2-17
Supposing that the inverse transformation equations between ΣB and ΣC are correct,
（ ） （ ） （ ） substituting Eq. 2-5 and Eq. 2-6 into Eq. 2-11 , it gives
xB
=
γ ′′ γ ′(xA
−
v2tA )
+
wγ ′(tA
−
v2 xA c2
 )
( ) （ ） =
γ
′′γ
′( xA
+
1
w − v2 − wv2 /
c2 tA)
1− wv2
/
c2
2-18
1
1
Substituting γ ′′ =
;γ′ =
（ ） into Eq. 2-18 , it gives
1− w2 / c2
1 − v22 / c2
( )( ) ( ) （ ） xB
  
xA
+
w − v2 1− wv2 /
c2
tA

 
1
−
wv2 c2
 
=
=
1 − w2 / c2 1 − v22 / c2
  
xA
+
1
w − v2 − wv2 /
c2
tA
  
1−
(
w
−
v2
2
)
1 − wv2 / c2 2 c2
2-19
Supposing
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（ ） u′
=
w − v2 1− wv2 /
c2
2-20
（ ） （ ） Substituting Eq. 2-20 into Eq. 2-19 , it gives
（ ） xB =
( xA + u′tA )
1− u′2 / c2
2-21
Because the continuous transformations will be equivalent to one certain transformation, comparing Eq. (2-21) with Eq. (2-1), we can get
（ ） v1
=
−u′
=
− w − v2 1− wv2 /
c2
2-22
（ ） （ ） Substituting Eq. 2-17 into Eq. 2-22 , it gives
（ ） v1
=
−
1
−
w
−
1
w + v1 + wv1 /
c
2
 w
w + v1 1 + wv1 /
c2
  
/
c2
2-23
In order to guarantee Eq. (2-23) is correct, only in the case that w = 0 , however, from the initial assuming we know that w ≠ 0 , so Eq. (2-23) is not correct. Eq. (2-23) is not correct
means that either Eq. (2-17) is not correct, or Eq. (2-22) is not correct, and both may be not
correct. Eq. (2-17) is derived by comparing Eq. (2-16) with Eq. (2-5), while Eq. (2-5) is from
the first set of transformation equation, we already assume that the first set of transformation
equation should be correct, so Eq. (2-5) is correct. Eq. (2-16) is derived by both of Eq. (2-14)
and Eq. (2-15), both of Eq. (2-14) and Eq. (2-15) are derived by three of Eq. (2-1), Eq. (2-2),
and Eq. (2-9). Eq. (2-1), Eq. (2-2) and Eq. (2-9) are from the first set of transformation
equation. We already assume that the first set of transformation equation should be correct, so
Eq. (2-1), Eq. (2-2) and Eq. (2-9) are correct, therefore Eq. (2-16) is correct. This means that
Eq. (2-17) is correct.
From the above discussion we know that, Eq. (2-23) is not correct only means that Eq.
(2-22) is not correct. While Eq.(2-22) is derived by comparing Eq.(2-21) with Eq.(2-1),
however, from the initial assuming we know that Eq.(2-1) is correct, so Eq.(2-22) is not
correct only means that Eq.(2-21) is not correct, Eq.(2-21) is derived by both of Eq.(2-20) and
Eq.(2-19), both of Eq.(2-20) and Eq.(2-19) are derived by three of Eq.(2-5), Eq.(2-6) and
Eq.(2-11), we already assume that both of Eq.(2-5) and Eq.(2-6) are correct, so Eq.(2-21) is
not correct only means that Eq.(2-11) is not correct.
From the results of above discussion we can get the conclusions as follows.
In the case that supposing that the first set of Lorentz transformation equations Eqs. (2-
1), (2-2), (2-5), (2-6), (2-9), (2-10) are all correct, then the inverse transformation equations
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Eq. (2-11) and Eq. (2-12) between ΣB and ΣC will not be correct. While ΣB and ΣC are two arbitrary inertial systems running the relative uniform speed translational motion, so the above results show that, between the two inertial systems running the relative uniform speed translational motion, if one set of Lorentz transformation equations are correct, then another set of transformation equations will not be correct. This conclusion has proven that for two arbitrary inertial systems running the relative uniform speed translational motion, they cannot be “Equality (Equal Right)”.This conclusion is derived in the case that supposing that the first set of Lorentz transformation equations Eqs. (2-1), (2-2), (2-5), (2-6), (2-9), (2-10) are all correct, if they are really correct, then the above conclusion must be correct. However the purpose of our discussion is to prove that for two arbitrary inertial systems running the relative uniform speed translational motion, they cannot be “Equality (Equal Right)”. If that is really true, then the Lorentz transformations cannot be mutually inverse. This means that in the Lorentz transformation equations, only one set of transformation equation are correct. But before the new theory is established, for the two sets of transformation equation (including the inverse transformation equation), we don't know which one is correct. Therefore, we would also like to assume that another set of Lorentz transformation (inverse transformation) are correct, and use this set of transformation to discuss the problem of inertial systems’ “Equality (Equal Right)”. If this discussion gives the same result as given in the previous conclusion, it will be proven that regardless of which set of transformation equation are correct, the conclusions are the same, namely: In the two sets of Lorentz transformation equations, if one set are correct, the another set must not be correct. So, for two arbitrary inertial systems running the relative uniform speed translational motion, they cannot be “Equality (Equal Right)”.
Supposing that the inverse transformation equations Eqs. (2-3), (2-4), (2-7), (2-8), (211), (2-12) are correct, substituting Eq. (2-11) and Eq. (2-12) into Eq. (2-3), it gives
xA = γ γ ′′(xc + wtc ) + v1γ ′′(tc + wxc / c2 )
Because γ =
1
；γ ′′ =
1
，so it can be written as follows
1 − v12 / c2
1− w2 / c2
( )( ( ) ) xA
=
( xc
+
1
+
w+ wv1
v1 /
c2
1 − v12 / c2
tc ) 1+ wv1 / 1− w2 / c2
c2
=
（ ） xc
+
w + v1 1+ wv1 /
c2
tc
2-24
( ) 1−
(
w
+
v1
2
)
1 + wv1 / c2 2 c2
Supposing
（ ） u
=
1
w + v1 + wv1 /
c2
2-25
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Substituting Eq. (2-25) into Eq. (2-24), it gives
( ) （ ） xA =
( xc + utc )
1− u2 / c2
2-26
（ ） （ ） Comparing Eq. 2-26 with Eq. 2-7 , we can get
（ ） v2
=
u
=
w + v1 1+ wv1 /
c2
2-27
（ ） （ ） （ ） Substituting Eq. 2-9 and Eq. 2-10 into Eq. 2-7 , it gives
xA = γ ′ γ ′′(xB − wtB ) + v2γ ′′(tB − wxB / c2 )
( ) =
( xB
− w − v2 1− wv2 /
c2
tB )
1− wv2
/
c2
=
( )( ) 1− v22 / c2 1− w2 / c2
（ ） xB
−
w − v2 1− wv2 /
c2
tB
2-28
( ) 1−
(
w
−
v2
2
)
1 − wv2 / c2 2 c2
Supposing
（ ） u′
=
w − v1 1− wv2 /
c2
2-29
（ ） （ ） Substituting Eq. 2-29 into Eq. 2-28 , we can get
( ) （ ） xA =
( xB − u′tB )
1− u′2 / c2
2-30
（ ） （ ） Comparing Eq. 2-30 with Eq. 2-3 , it gives
（ ） v1
=
−u′
=
− w − v2 1− wv2 /
c2
2-31
（ ） （ ） Substituting Eq. 2-27 into Eq. 2-31 , we can get
（ ） v1
=
−
1
w
−
1
w + v1 + wv1 /
c2
w
  
1
w + v1 + wv1 /
c
2
−
c2
  
2-32
In order to guarantee Eq. (2-32) is correct, only in the case that w = 0 , however, from
the initial assuming we know that w ≠ 0 , so Eq. (2-32) is not correct. Eq. (2-32) is derived
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（ ） （ ） by Eq. 2-31 and Eq. 2-27 , Eq. (2-32) is not correct means that either Eq. (2-31) is not
correct, or Eq. (2-27) is not correct, and both may be not correct. Eq.(2-27) is derived by comparing Eq.(2-26) with Eq.(2-7), while Eq.(2-26) is derived by Eqs. (2-11), (2-12), (2-3), Eqs. (2-11), (2-12), (2-3), (2-7) are all inverse transformation equations, we already assume that the inverse transformation equations should be correct, so Eqs. (2-11), (2-12), (2-3), (2-7) are all correct. Therefore Eq.(2-27) is correct. Hence Eq.(2-32) is not correctonly means that Eq.(2-31) is not correct. While Eq.(2-31) is derived by Eq.(2-3) and Eq.(2-30), Eq.(2-3) is the inverse transformation equation, we already assume that the inverse transformation equations should be correct, so Eq.(2-3) is correct. Hence Eq.(2-31) is not correct means that Eq.(2-30) is not correct. While Eq.(2-30) is derived by Eq.(2-7), Eq.(2-9) and Eq.(2-10), while Eq.(2-7) is the inverse transformation equation, we already assume that Eq.(2-7) is correct, so Eq.(230) is not correct only means that Eq.(2-9) and Eq.(2-10) are not correct.
The results of above discussion show that, between ΣB and ΣC, if Eq.(2-11) and Eq.(2-12) are correct, then Eq.(2-9) and Eq.(2-10) will not be correct. The results of discussion show again that in the two sets of Lorentz transformation equations, if one set are correct, the another set must not be correct.
Synthesizing all the above discussions we can get the conclusions as follows: 1) Between arbitrary two inertial systems running the relative uniform speed translational motion, the transformation equations cannot be mutually inverse. 2) For two arbitrary inertial systems running the relative uniform speed translational motion, they cannot be “Equality (Equal Right)”. If ΣA and ΣB are two inertial systems running the relative uniform speed translational motion, from the principle of relativity we know that, in both of ΣA and ΣB, the laws of physics with the same mathematical form can be established. However, the above two conclusions tell us that, if the temporal and spatial changing rules established in ΣB will agree with the transformation equation established in ΣA, then the temporal and spatial changing rules established in ΣA will not agree with the transformation equation established in ΣB. If the physical state changing rules of a physical system agree with the laws of physics established in a certain inertial system, then we say that this inertial system is the physical system's inertial reference system. (In the past, many people do not know the application conditions of the principle of relativity, so the inertial system and the inertial reference system are not distinguished.) According to the above discussion we can induce as follows: 1) In all the inertial systems running the relative uniform speed translational motion, the laws of physics with identical mathematical form are all established between the physical system and its inertial reference system;
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2) For the two inertial systems ΣA and ΣB, running the relative uniform speed translational motion, if ΣA is the inertial reference system of ΣB, definitely ΣB is not the inertial reference system of ΣA.
These two sections are the application conditions of the principle of relativity. The application conditions of the principle of relativity are not the theoretical foundation, but they are the prerequisite for establishing the theory, before the establishment of theory, we must stress that the theory should be consistent with the application conditions of the principle of relativity, otherwise the theory will not be valuable. According to the above conclusions we can get the following deduces: 1) The temporal and spatial transformations are not from the relative motion of the physical system, but from the motion of the physical system relative to its inertial reference system. 2) The so-called matter space is also the inertial reference system space. 3) The temporal and spatial transformation rules have nothing to do with the relative character of simultaneity. 4) It is wrong to introduce the one-way spreading light signals along with all directions in space into equation.
3 Brief Introduction to “The Matter Space-time Theory of Relativity” “The Matter Space-time Theory of Relativity” (“Matter Theory” for short) is the theory established to solve many unsolved problems in special relativity. “Matter Theory” is based on the matter space only. The principle of constant speed of light, the principle of relativity and other assumptions are no longer needed. “Matter Theory” overcomes almost all the unsolved problems in special relativity, explains all the physical phenomena and experiments that can be explained by special relativity, and presents many new predictions. Here we take the temporal and spatial transformations as examples to explain the following problems. The temporal and spatial transformations of “Matter Theory” show that not only the moving clock will slow down, but also the same inertial system space will have the characteristics of multilevel of space-time. For different levels of space-time, the clock rates are different, the masses are different, and the energies are also different, but there is not the contraction of moving ruler. Although we have the multi-level of space-time, for each level, the space is always three-dimensional, the time is always one-dimensional. The indivisible four-dimensional space-time does not exist in the world of objective reality. Of course, also there are not the phenomena of time-like interval, space-like interval, time sequence reverse, cause and effect reverse, and so on. These errors are the apparent phenomena resulting from special relativity introduced one-way spreading light signals along with all directions in space.
The special relativity is a systematic theory, so “Matter Theory” is also a systematic theory, and covers a wide range, besides this paper, other results can be found in reference [1].
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Reference 1 Duan Zhongxiao, The Matter Space-time Theory of Relativity, Matter Regularity, 2012, Vol.12, No.5, Sum No.53, 30-63
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Shortcomings and Applicable Scopes of Special and General Theory of Relativity Fu Yuhua (Beijing relativity theory research federation, Beijing, 100049, China)(E-mail: fuyh1945@sina.com)
Abstract: The 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 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, establishing 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. Some wrong results caused by the theory of relativity (including the Lorentz transformation) are pointed out, such as the problems caused relativity is in a sad plight that the sonic speed in vacuum permanently is equal to zero, the twin paradox that the two brothers' state of motion are quite same, and so on. Moreover, in this paper not only solving the problem of a body’s restrained motion in gravitational field such as a small ball rolls along an incline that cannot be solved by relativity, but also with the help of relativity deriving the improved Newton’s universal gravitation formula that gives the same results as given by general relativity for the problem of Mercury’s advance of perihelion and the problem of gravitational defection of a photon orbit around the sun. This paper proposes that taking law (principle) of conservation of energy as the interdisciplinary grand unified theory to unified process all the problems related to energy in physics, astronomy, mechanics, chemistry, biology, medicine, engineering and so on; taking the unified variational principle for quantization in dynamic Smarandache multi-space and the fractal method as the interdisciplinary grand unified method; and taking the “science of conservation of energy” to replace or partially replace the theory of relativity. Keywords:Special and general theory of relativity, shortcomings, applicable scope, science of conservation of energy
Introduction People generally believe that Einstein is the greatest scientist in the 20th century, and his
achievement is only next to Newton. At the same time, the scientific circles generally thought the theory of relativity is one of
the greatest scientific achievements in the 20th century.
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But on the other hand, since the 1920s, Einstein and the theory of relativity have been gradually held in both hands to the god world.
Enter into the 21st century, the situation has changed, Einstein and the theory of relativity already start to go down the god world.
The Chinese renowned scientist Academician Song Jian boldly questions Einstein, and calls the young scientists dare to innovate. He read out the science report entitled “Astronautics, Astronavigation and Light Barrier” in the 242nd Xiangshan conference. Pointed out that, 100 years ago, Einstein, in his paper about special relativity that shocked the scientific circles, proposed a famous saying, it is impossible to exist any movement to travel faster than the speed of light. The present scientific circles name this phenomenon “light barrier”. However, this “extrapolation” certainly hasn’t been proven by any direct experiment.
Many men of insight already pointed out that, taking the research and challenge to the theory of relativity as the turning point, will have the possibility to lead more scientists to occupy the more and more scientific peaks gradually.
As we analyze the theory of relativity, besides the positive, remorseless, careful and valuable consideration, also emphasize and give prominence to the aspects of philosophy and critique. All of these provide the beneficial imagination space for surmounting Einstein and the theory of relativity. The people are not difficult to understand that, from the angle of natural sciences theory to criticize the theory of relativity, is an extremely difficult matter, this paper truly involves many contents about this aspect, however the effects will wait for the reader to comment; Whereas, from the angle of philosophy to challenge and criticize the theory of relativity, will have the possibility to let the reader easy to understand, and may extrapolate, positively join the beneficial exploration.
The rivers and mountains breed the talent person from generation to generation. Einstein and the theory of relativity will be surpassed; this is the matter of sooner or later.
Recently, some scientists pointed out, the theory of relativity had not considered temperature factor, this is a big flaw. While considering the temperature factor, the theory of relativity inevitably must be rebuilt.
The purpose of this paper is to discuss the shortcomings and applicable scopes of special and general theory of relativity
1 Shortcomings of special and general theory of relativity The first basic shortcoming of the special and general theory of relativity is that they do
not conform to the truth uniqueness. In the natural sciences domain, as dealing with a specific issue, should only have one
truth. But, the two basic principles of special theory of relativity are the special principle of
relativity and the principle of constant speed of light; the two basic principles of general theory of relativity are the principle of equivalence and the principle of general covariance; In
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other words, the special theory of relativity has two truths; the general theory of relativity also has two truths; while in the entire theory of relativity, altogether has four truths. These obviously do not conform to the truth uniqueness.
For the reason to disobey the truth uniqueness, between the two basic principles of special theory of relativity, as well as between the two basic principles of general theory of relativity, inevitably will appear the contradictions which are unable to solve.
The second basic shortcoming of the special and general theory of relativity is that, 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. Therefore it is wrong to take them as the general truth.
This certainly doesn’t mean that, the special theory of relativity and general theory of relativity are completely wrong. For some partial questions, the special theory of relativity and general theory of relativity also may produce the correct conclusions or the approximate results.
The third basic shortcoming of the special and general theory of relativity is that, to establish the physical theory from the mathematical principle instead of the physical principle.
If this road is correct, then the mathematicians will have the ability to govern physics and nearly all natural sciences. But this obviously is not impossible.
In the physics domain, to command physics with mathematics, instead of command mathematics with physics, this is the biggest misguide to physics given by Einstein. As a result of this kind of misguide, besides some individual success, the innumerable time and energy of many people with outstanding ability (including Einstein himself) have been wasted.
2 Contradictions between the basic principles of special and general theory of relativity Firstly we discuss the contradictions between the two basic principles of special theory
of relativity. The special principle of relativity states that physical laws should be the same in all
inertial reference frames. The principle of constant speed of lightstates thatlight is propagated in empty space in
straight lines with a velocity c= 300,000 km/s. Einstein firstly noted the apparent incompatibility of the law of propagation of light with
the principle of relativity. It can be stated briefly as follows [1]. As such a system let us again choose our embankment. If a ray of light be sent along the
embankment, the tip of the ray will be transmitted with the velocity c relative to the embankment. Now let us suppose that our railway carriage is again traveling along the railway lines with the velocity v, and that its direction is the same as that of the ray of light. Let us inquire about the velocity of propagation of the ray of light relative to the carriage, w is the required velocity of light with respect to the carriage, and we have
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w = c−v. The velocity of propagation of a ray of light relative to the carriage thus comes cut smaller than c. But this result comes into conflict with the principle of relativity. For, like every other general law of nature, the law of the transmission of light in vacuum must, according to the principle of relativity, is the same for the railway carriage as reference body as when the rails are the body of reference. For this apparent incompatibility, Einstein proposed two kinds of choices: (1) abandon either the principle of relativity or the law of the propagation of light in vacuum; (2) systematically holding fast to both these laws a logically rigid theory could be arrived at. This theory has been called the special theory of relativity, which was established by Einstein according to the second choice. Now we must discuss the question that, whether or not the special theory of relativity can truly solve the contradiction between the law of propagation of light and the special principle of relativity. Our answer is that it cannot. Considering all the possible situations, the people cannot help to ask: As deriving the Lorentz transformation, why only the principle of invariance of light speed was used? Why didn't consider the principle of invariance of other speed? Obviously, for the principle of invariance of other speed, combining with the special theory of relativity, similarly may obtain other one kind of transformation relations. Thus inevitably appears the irreconcilable contradiction. Then, whether or not the principle of invariance of other speed is existed? The answer is affirmative. For example, in all the reference frames at the vacuum state, the sound propagation velocity is zero. In addition, we also may find many examples that the conclusions of special theory of relativity (including the Lorentz transformation) bring on the wrong results, see below. Therefore, the special theory of relativity doesn’t successfully solve the contradiction between the law of propagation of light and the special principle of relativity. Whether has the other way to successfully solve this contradictory? The answer is affirmative. For the apparent incompatibility of the law of propagation of light with the principle of relativity, besides the two kind of choices proposed by Einstein, still may simultaneously give up the special principle of relativity and the law of propagation of light in vacuum, and choose another principle or law (for example, the law of conservation of energy) as the only truth, to establish the new physical system. This choice may be considered as a correct way to surmount or replace the theory of relativity. Certainly, it is very difficult to reach this achievement. Secondly we discuss the contradictions between the two basic principles of general theory of relativity. Einstein stated that, The Equality of Inertial and Gravitational Mass as an Argument for
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the General Postulate of Relativity. Its main content is as follows[1]. We imagine a large portion of empty space, as reference body let us imagine a spacious
chest resembling a room with an observer inside who is equipped with apparatus. Gravitation
， naturally does not exist for this observer. To the middle of the lid of the chest is fixed
externally a hook with rope attached, and now a “being” begins pulling at this with a constant force. The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion. He is then standing in the chest in exactly the same way as anyone stands in a room of a home on our earth. If he releases a body which he previously had in his land, the body will approach the floor of the chest with an accelerated relative motion. Relying on his knowledge of the gravitational field, the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time. Of course he will be puzzled for a moment as to why the chest does not fall in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest is suspended at rest in the gravitational field.
Guided by this example, Einstein attempted to point out that, our extension of the principle of relativity implies the necessity of the law of the equality of inertial and gravitational mass.
Here Einstein attempted to explain that the two basic principles of general theory of relativity (the principle of equivalence and the principle of general covariance) do not have contradictory. But this endeavor is a futile effort.
Einstein said that, our extension of the principle of relativity implies the necessity of the law of the equality of inertial and gravitational mass.
According to this viewpoint, how to process the temperature mass and electromagnetic mass, friction mass and so on? Whether or not our extension of the principle of relativity implies the necessity of the law of the equality of the three of temperature, inertial and gravitational mass?
If the three masses are not equal, then between “the principle of equivalence” (at present it should be the equality of the three of temperature, inertial and gravitational mass) and the principle of relativity (the principle of general covariance) the contradiction is appeared.
If the three masses are equal, then it is a wrong conclusion. Because as the object temperatures are different, it will contain the different thermal energy. According to the special theory of relativity, the energy may be translated into mass, thus for the same object, when its temperatures are different, its masses are different. But the reason for this mistake is the supposition that the two basic principles of general theory of relativity (the principle of equivalence and the principle of general covariance) do not have contradictory. Therefore this supposition is wrong.
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It should be noted that, because the temperature, inertial and gravitational mass are not equal, in passing we find another example that between the special theory of relativity and the general theory of relativity the contradictory is appeared.
3 Mistakes of the basic principles of special and general theory of relativity Firstly we discuss the mistakes of the two basic principles of special theory of relativity. According to the special principle of relativity, physical laws are the same in all inertial
reference frames. If the meaning of “same” is “completely equal”, then the special principle of relativity
has the question in the philosophy. In the world never have two completely equal leaves. For any two reference frames (coordinate systems), the descriptions to some physical
laws impossibly to be completely same. Regarding the different reference-bodies (or their state of motion), at least we may say, the convenient degrees to describe “the law of nature” are different. That is the reason that the rectangular coordinates and polar coordinates are more universal (or more predominant) than other coordinates.
Especially, if these physical laws refer to the quantity relations, or for the reason that some conditions are different, the descriptions for them may be completely dissimilar.
For example, for the law of sound velocity, we may say that, “on the earth's surface with air temperature is 15℃, the sound velocity is 340m/s”.
But, for the airplane flying with the sound velocity, if its flight direction is consistent with the sound propagation direction, then the sound velocity is 0m/s. If its flight direction is opposite to the sound propagation direction, then the sound velocity is 680m/s.
Moreover, for the coordinate systems in vacuum state, among them the sound simply cannot propagate, thus the sound velocity is 0m/s forever. Please note this conclusion, because we can see later that no other than this conclusion, will cause the Lorentz transformation to induce the wrong result.
The reader may display own imagination as far as possible, to find more misgivings about the special principle of relativity.
According to the principle of constant speed of light, light is propagated in empty space in straight lines with a velocity c= 300,000 km/s.
For the experimental confirmations to the principle of constant speed of light, we should say that the experiments are extremely limited, many factors have not considered. For example, under the strong heat source radiation, whether or not the speed of light is the same as no heat source radiation?
For the light propagation, if on a certain point to project two lights along the opposite direction at the same time, then the speed for these two lights to be mutually far away no longer is a speed of light, but is two times of speed of light. In other words, if taking one of these two lights as the reference system, then the speed of another light is -2c. Not only this
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example indicates that the principle of constant speed of light is wrong, but also demonstrates the contradiction between the special principle of relativity and the principle of constant speed of light.
Moreover, Einstein also pointed out that, one of the significant inferences from the general principle of relativity is: in general, rays of light are propagated curvilinearly in gravitational fields. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Therefore the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light).
Here we have a problem immediately: Only in the gravitational field could the light be curving?
Be careful, Einstein wrote that, the special theory of relativity cannot claim an unlimited domain of validity. In other words, this is another example that between the special theory of relativity and the general theory of relativity the contradictory is appeared.
Second we discuss the mistakes of the two basic principles of general theory of relativity.
Now we discuss the question of the principle of equivalence (inertia mass and gravitational mass are equal). Still consider the temperature question. For the heavenly body moves around the sun, if the sun does not radiate the heat energy, then the principle of equivalence may be correct. But, the sun radiates the heat energy. Front already has said, as the object temperatures are different, then its masses are also different, therefore, the inertia mass under one kind of temperature is not the same as the gravitational mass under another kind of temperature.
Thus it can be seen, the principle of equivalence at least should be revised as follows: Under the same temperature the inertial mass and the gravitational mass are equal.
But another question will be coming, the masses of some objects also could be changed in the electromagnetic field, thereupon the principle of equivalence should be revised again as follows: Under the same temperature and the same electromagnetic field situation the inertial mass and the gravitational mass are equal.
To this analogizes, when will such revisions be finished? As for the question of principle of relativity (the principle of general covariance), it does not need us to point out, Einstein himself already revised his original viewpoint. In other words, to withdraw a stride from his originally proposed principle of relativity (the principle of general covariance). In reference [1] Einstein pointed out that, the following statement corresponds to the fundamental idea of the general principle of relativity: “All Gaussian coordinate systems are essentially equivalent for the formulation of the general laws of nature”. Here, Einstein already has obviously drawn back a step, from “All coordinate systems are essentially equivalent for the formulation of the general laws of nature”, drew back to be
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restricted in “all Gaussian coordinate systems” only. As for the reason to draw back this step, we cannot find the explanation. A logical explanation is that the general principle of relativity has encountered the
problem. Moreover, it also has another question: Why has to draw back to “all Gaussian
coordinate systems”? We cannot find the explanation also. A logical explanation is that, because the general theory of relativity used the Gaussian coordinate systems, therefore it could not draw back further.
It is difficult to understand that, the Einstein already discarded the general principle of relativity, i.e., “All coordinate systems are essentially equivalent for the formulation of the general laws of nature” (or similar statement), but at present it still be used in many textbooks!
Here we present an example to show that all coordinate systems are not essentially equivalent for the formulation of the general laws of nature.
As well-known, the fractal distribution reads
C N = rD
The fractal distribution is a straight line only in the double logarithmic coordinates. Therefore, if some law of nature conforms to the fractal distribution rule, then the law that “the change of this natural phenomenon conforms to the linear rule” is only correct in the double logarithmic coordinates.
4 Applicable scopes of special and general theory of relativity Firstly we discuss the applicable scope of special theory of relativity. Because the two basic principles of special theory of relativity are the special principle
of relativity and the principle of constant speed of light, we may say that, in the case that these two principles are correct simultaneously, generally the special theory of relativity is applicable.
For the experiment of Fizeau, these two principles are correct simultaneously. It should be noted that, in special case, even if these two principles are correct simultaneously, it also possibly causes the wrong result. For example the Lorentz transformation may cause the wrong result. Secondly we discuss the applicable scope of general theory of relativity. Because the two basic principles of general theory of relativity are the principle of equivalence and the principle of general covariance, we may say that, in the case that these two principles are correct simultaneously, generally the general theory of relativity is applicable.
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For the problems of the motion of the perihelion of Mercury, deflection of light by a gravitational field, displacement of spectral lines towards the red and so on, these two principles are correct simultaneously.
Similarly, in special case, even if these two principles are correct simultaneously, it also possibly causes the wrong result.
5 From mathematics principle or physical principle to establish the physical theory Einstein thought that [1], every general law of nature must be so constituted that it is
transformed into a law of exactly the same form when, instead of the space-time variables x, y, z, t of the original coordinate system K, we introduce new space-time variables x', y', z', t' of a coordinate system K'. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or in brief: General laws of nature are covariant with respect to Lorentz transformations. This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature.
This speech extremely and clearly indicated the viewpoint that to command physics with mathematics, instead of command mathematics with physics. This really is Einstein’s biggest misleading to the physics.
Every general law or principle of physics must automatically satisfy the covariance in some significance (but it is not the covariance in the significance of theory of relativity), or it is correct for all coordinate systems (but it doesn’t have the completely same forms). For example, the law of conservation of energy may automatically satisfy the covariance in some significance, namely it is correct for all coordinate systems. But it doesn’t have the completely same forms, for different coordinate systems, the sizes of conservation are different.
Therefore, it completely is unnecessary to propose the explicit mathematical condition to the physical law in advance. The physical theory should be established from the physical principle.
It should be noted that, Newton and Einstein formed a sharp contrast. As well-known, Newton was the greatest mathematician, while Einstein wasn’t a mathematician. But as establishing the physical theory, Newton simply didn’t apply the profound mathematical tool. The Newton’s first law and third law nearly didn’t apply mathematics. The second law only applied the multiplication operation. The law of universal gravitation also only applied the multiplication, division and square operation. Newton’s rich and profound mathematical knowledge only was applied to realize the utilization of the simple and important physical laws.
6 Wrong results caused by Lorentz transformation
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First example, suppose we have two reference systems at the vacuum state and their relative speed isn’t equal to zero, there is an alarm clock in a reference system, because it is at the vacuum state, the sound propagation speed is equal to zero. According to the Lorentz transformation, in the second reference system the sound propagation speed will not be equal to zero. This obviously is wrong.
Second example, from the Lorentz transformation expression we may see that, the speed of light is the limit of speed. Once appear the speed faster than light, the Lorentz transformation either is not correct, or will cause the wrong conclusion.
But we already said in front, if on a certain point to project two lights along the opposite direction at the same time, then the speed for these two lights to be mutually far away is two times of speed of light. In other words, in this case, the Lorentz transformation will obtain the speed for these two lights to be mutually far away is still equal to the speed of light. That is wrong.
The Lorentz transformation causes the wrong conclusions that certainly are not limited in these two examples, the reader may try to propose other examples.
7 Other mistakes caused by theory of relativity and some questions cannot be solved by theory of relativity
The phenomena of “rods look shorter and clocks look slower” derived by theory of relativity can be stated as follows.
The rigid rod is shorter when in motion in the direction of its length than when at rest, and the more quickly it is moving, the shorter is the rod.
As a consequence of its motion the clock goes more slowly than when at rest. Now we consider the phenomenon of “clocks look slower”, the purpose is to present a wrong conclusion derived by theory of relativity. As well-known, the phenomenon of “clocks look slower” causes the twin paradox: According to theory of relativity, supposing there are pair of twins, the younger brother keeps on the Earth, the elder brother roams through the outer space as an astronaut. As the elder brother returns to the Earth, he will be much younger than his younger brother. The twin paradox means: Because the movement is relative, also may think the younger brother is carrying on the space navigation, therefore the younger brother should be much younger than the elder brother. Such two conclusions mutually conflict. There are many explanations given by theory of relativity to this twin paradox (some of them even use general theory of relativity to carry on the complex computation), but their basic starting point is as follows: Two brothers' states of motion are different. Thereupon we may make another special twin paradox that two brothers’ states of motion are quite same. If the younger brother doesn’t keep on the Earth, but the elder brother and the younger brother all ride their respective high speed airships, facing the completely opposite directions to navigate from the identical time and the identical site with the same speed along a straight
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line, after a quite long period they begin to decelerate simultaneously until static, then they turn around to navigate again along the same straight line with the manner of front to front, finally simultaneously return to the starting point. From the younger brother's viewpoint that, according to the theory of relativity, the elder brother should be much younger than the younger brother; Similarly, from the elder brother's viewpoint that, according to the theory of relativity, the younger brother should be much younger than the elder brother. Who is much younger to the end?
With the theory of relativity, how to explain this special twin paradox that two brothers’ states of motion are quite same?
According to the kinetic energy formula of special theory of relativity, when the speed v approaches speed of light c, the kinetic energy approaches infinity; when the speed v is greater than speed of light c, the kinetic energy is an imaginary number. But, it already pointed out in reference [2] that there is no speed barrier in the universe. We also pointed out that, if on a certain point to project two lights along the opposite direction at the same time, then the speed for these two lights to be mutually far away no longer is a speed of light, but is two times of speed of light. In this case, can we have the imaginary number kinetic energy? We cannot. Here the wrong result is derived by the kinetic energy formula of special theory of relativity.
We already pointed out that, the two basic principles of special theory of relativity, in certain situations, will not be correct. Therefore, all conclusions of special theory of relativity, in certain situations also are not correct. The most famous formula in theory of relativity, E=mc2, also is not exceptional, it needs to be revised in certain situations. Some of the revised formula may be found in the related literature or on the internet.
Einstein believed that, there is no more common−place statement than that the world in which we live is a four-dimensional space-time continuum.
Space is a three-dimensional continuum. By this we mean that it is possible to describe the position of a point (at rest) by means of three numbers (coordinates) x, y, z, and that there is an indefinite number of points in the neighborhood of this one, which may be as near as we choose to the respective values of the coordinates x, y, z, of the first point.
Minkowski thought that the “world” is naturally four dimensional. For it is composed of individual events, each of which is described by four numbers, namely, three space coordinates x, y, z, and a time coordinate, the time value t.
The four-dimensional mode of consideration of the “world” is natural on the theory of relativity, since according to this theory time is robbed of its independence.
But, in many situations, it is not enough to describe the movement of an event in space by means of three numbers (coordinates) x, y, z. For example, for the planet movement around the sun, it needs six coordinates (other three coordinates are those to determine the planet rotation around x, y, z axis). In fact, in the engineering, those six coordinates have already been used. For example, in finite element structure analysis, as well as in ship
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movement analysis. Now we have this question: How many coordinates are needed to describe the movement
of an event in space? Six coordinates are sufficient? As if we may say that, the coordinate numbers to describe the movement of an event in
space should not be fixed. For different question, should have the different solution. For example regarding certain questions, if facilitates, we may again add the temperature coordinate, mass coordinate and so on.
In fact, at present many physical theories have already been established in higher dimensional space. Such as the string theory and so on, they must be established in the space higher than nine-dimension, some even in 26-dimensional space.
As for time, it also does not need to define as one-dimensional. At present, the time was four-dimensional, three-dimensional, six-dimensional and so on already are proposed. Now we derive one kind of three-dimensional time according to the related formula of Lorentz transformation.
Choosing two different reference systems S and S', their coordinates are x, y, z and x', y', z' respectively. At beginning S and S' are superposition, in system S there is a radial line r to pass the origin of coordinates O, the angles between r and x, y, z are α,β,γ respectively. The corresponding radial line in system S' is r'. Then the origin of coordinates O' of system S' moves with uniform speed V along the direction of radial line r, and x', y', z' are always paralleled with x, y, z respectively. The signs tx,ty,tzand trdenote the times in the directions
of x, y, z respectively in system S, the signs t'x' , t' y' , t'z' and t'r' denote the times in the
directions of x’, y’, z’ respectively in system S’.
Suppose the system S is absolutely at rest, then we have
（ ） t x = t y = tz = tr = t 1
For the theory of relativity, suppose system S' is transmitted along x-axis, then the time transformation formula in Lorentz transformation reads
（ ） t'=
t − (V (1 − V 2
/ /
c2 )x c 2 )1/2
2
According to this, suppose system S' is transmitted along the direction of r, then the time transformation formula in the direction of r’ reads
（ ） t'r'
=
t − (V (1 − V 2
/ /
c2 )r c 2 )1/2
3
To project it into the directions of x', y', z', we obtain the times of t'x' , t' y' , t'z' along the
directions of x', y', z' in system S' are as follows
（ ） t'x' = t'r' cosα 4
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