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Could Galileo be wrong?

Authors:
  • The Applied and Pure Research Institute

Abstract

The free falling of a neutral capacitor, though more massive after charged, would be slower. Thus, the claim of Galileo that neutral objects of different masses would fall with the same speed at vacuum is not always true. Nevertheless, the equivalence between gravitational and inertial masses would still be valid. Moreover, Einstein's equivalence principle, which has been misrepresented with distortion to become invalid by the Wheeler School, actually is generally valid, although the charge-mass repulsive force unequivocally shows that acceleration is intrinsically not generally just related to attractive gravity. To verify the equivalence of masses, new experiments should be conducted when the charge-mass interaction is present. To this end, first the experimental confirmation of the details, such as the distance dependence, of such a repulsive force between charge and mass is needed; and this is also a crucial test for general relativity. (C) 2011 Physics Essays Publication. [DOI: 10.4006/1.3636395]
APRI-TH-PHY-011-01
Could Galileo Be Wrong?
C. Y. Lo
Applied and Pure Research Institute
7 Taggart Drive, Unit E, Nashua, NH 03060
Physics Essays, 24, 4 (August 2011)
Abstract
The free falling of a neutral capacitor, though more massive after charged, would be slower. Thus, the claim of
Galileo that neutral objects of different masses would fall with the same speed at vacuum is not always true. Neverthe-
less, the equivalence between gravitational and inertial masses would still be valid. Moreover, Einstein’s equivalence
principle, which has been misrepresented with distortion to become invalid by the Wheeler School, actually is generally
valid, although the charge-mass repulsive force unequivocally shows that acceleration is intrinsically not generally just
related to attractive gravity. To verify the equivalence of masses, new experiments should be conducted when the charge-
mass interaction is present. To this end, first the experimental confirmation of the details, such as the distance depen-
dence, of such a repulsive force between charge and mass is needed; and this is also a crucial test for general relativity.
Key Words: repulsive force, charge-mass interaction, charged capacitors, Pioneer Anomaly.
04.20.-q, 04.20.Cv
Science sets itself apart from other paths to truth by recognizing that even its greatest practitioners sometimes err. … We
recognize that our most important scientific forerunners were not prophets whose writings must be studied as infallible
guides—they were simply great men and women who prepared the ground for the better understandings we have now
achieved.” -- S. Weinberg, Physics Today, November 2005.
1. Introduction
Galileo showed that objects of different weight would fall with the same speed toward earth when air resistance and
etc. are negligible. 1) Thus, Aristotle’s thesis that heavier matter always falls faster is wrong. However, as Einstein pointed
out, one cannot prove a theory with experiments. Thus, in principle, it is still not entirely clear whether Galileo’s state -
ment is always true.
Owing to the charge-mass repulsive force [1], Galileo could be wrong since it would be possible that a heavier ob -
ject falls faster or slower. Consider two charged particles such as the electron and the proton. The attractive force toward
the proton is much larger than the attractive force toward the electron since their masses have a difference of about 2000
times. However, the charge-mass repulsive forces toward these particles are the same 2) because they have the same abso-
lute charge [1]. Thus, the lighter electron would fall slower than the heavier proton.
One may note also that a charged particle would emit electromagnetic wave and thus has a radiative reaction force.
However, this force is absent when the acceleration is zero and is negligible for the free fall. This slowing down would
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also make the electron falling slower since the mass of proton is much larger. Moreover, since the neutron has no charge,
it would fall faster than the proton and the electron. 3) For macroscopic objects, which are not strongly subjected to quan-
tum mechanics, the difference due to the effects of the charge-mass interaction should be observable in vacuum.
One may argue that the above cases involve an object with net charges, and thus is beyond the cases that Galileo
considered. However, because of the charge-mass interaction, a capacitor would fall slower after charged although its
mass would have a negligible increment [1].4) Therefore, the claim of Galileo is actually not always valid although his ob-
servation is approximately valid for many cases. In other words, what the 1993 press release of the Nobel Committee [2]
termed “the equivalence principle” (which is only intimately connected with Einstein’s equivalence principle [3; p. 58]) 5),
the identity between gravitational and inertial mass is tested only when the charge-mass interaction is absent.
Einstein [3] once remarked,
“The equality of two (gravitational and inertial) masses, so differently defined, is a fact which is confirmed
by experiments of very high accuracy (experiments of Eötvös), and classical mechanics offers no explana-
tion for this equality. It is, however, clear that science is fully justified in assigning such a numerical equal -
ity only after this numerical equality is reduced to an equality of the real nature of the two concepts.”
Now, we should have a new level of understanding on this equality since it is intimately related to Einstein’s equivalence
principle and is crucial to general relativity; and thus to the modern development of physics.
2. The Equality of Gravitational and Inertial Masses
As Einstein [3] pointed out, “this principle (his “principle of equivalence”) is evidently intimately connected with
the law of the equality between the inert and the gravitational mass, …” And this principle is the foundation of general
relativity that produces the static charge-mass interaction. Validity of the equality between these two masses, is crucial for
general relativity to be a self-consistent theory.
However, the experiments of Eötvös verify this equality only for the case that the charge-mass interaction is ab -
sent. Thus, a new experimental test should be conducted for the case when the charge-mass interaction is present. 6) To
this end, first one must know what the new repulsive force is. It has been found that, for a small particle Q with charge q
and a particle P with mass m separated by a distance r, the static neutral repulsive force derived by Lo [1] to the first or-
der is
F =
3
2
r
mq
, (1)
(in the unit light speed c = 1 and gravitational coupling constant = 1 [4]). However, such a force could be too small to be
measured experimentally with current technology.7)
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Nevertheless, if we consider the repulsive force between a metal ball B with charge q and a test particle P with mass
m, and the distance between the test particle P and the center of the ball B is denoted by r, then the repulsive force is the
same as eq. (1) [5]. As the number of electrons N increased in the ball B, the attractive force due to masses would linearly
increase with number N, but the repulsive force would increase with the square of the number N. Since the charge q for a
metal ball can be considerably large, such a repulsive force is measureable [5]. On the other hand, an increment of charge
would increase the energy, but the weight is reduced. 2) Thus, such a more massive object would fall slower, and thus it
would be unclear that the acceleration mass and the gravitational mass are equivalent.
Further experimental verification for details of this force such as the distance dependence is important because it is
the only confirmation of general relativity with a non-massive source, and thus is beyond the Maxwell-Newton Approxi-
mation. After the formula (1) for the neutral repulsive force is confirmed, we would be ready to do improved experiments
of Eötvös that is based on a charged metal ball. A difficulty is that a charged metal ball is not neutral.
A easier confirmation of the force (without clear distance-dependence) would be to weight the charged capacitors
[1]. According to special relativity, the change of mass of a particle is related to the change of energy ΔE are related by
ΔE = Δmc2 (2)
although eq. (2) is not generally true for any energy [1].7) For a capacitor of 200µF charged to 1000 volt, the related
mass increment would be about 10-12 gram, and the mass increment of a charged capacitor is negligible. Note also
that the increment of energy is not purely electromagnetic since the electron has mass. In fact, as observed, the increment
of the attractive force to the neutral capacitor due to the increment of mass is far smaller than the repulsive force [1].
3. Validity of Einstein’s Equivalence Principle and its Misrepresentations
Although most theorists agree with Einstein [3, 6] that his equivalence principle is the foundation of general relativ-
ity, there is no book or reference, other than Einstein’s own work, that can state and explain his principle correctly. In par-
ticular, they often confused the principle with Einstein’s 1911 assumption of equivalence [7], which has been proven in-
valid by experiments such as the bending of light. Another source of confusion is that many theorists, including Nobel
Laureate ‘t Hooft [8],8) still have mistaken Pauli’s invalid version [9] as Einstein’s equivalence principle although Ein-
stein has made clear it as a misinterpretation [10]. This manifests that many physicists have a tradition of inadequate
background in pure mathematics. Many rely on only the opinions of the so-called “authorities”,9) and thus here a more
detailed analysis is provided for those who failed to understand Einstein’s equivalence principle [8].
In the book ‘Gravitation” [4] of Misner, Thorne and Wheeler, there is no reference to Einstein’s equivalence princi-
ple (i. e. [3] and [6]). Instead, they misleadingly refer to Einstein’s invalid 1911 assumption [7] and Pauli’s invalid ver -
sion [9]. (As shown in their eq. (40.14), they also failed to understand the local time of a particle at free fall [4].) Due to
their influence, Einstein’s equivalence principle was often mistakenly regarded the same as the 1911 assumption. 9) More-
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over, many simply cannot tell the difference between the principle of 1916 and the assumption of 1911 [11-13]. 10)
In view of the charge-mass interaction, Einstein’s equivalence principle is clearly inadequate [1, 14]. Thus, one may
wonder whether Einstein’s equivalence principle is generally valid. The answer is that it is because a uniform gravity in
the equivalence principle is not generated by a massive source, but is generated by acceleration [13]. In an isolated gravi -
tational field generated by acceleration, there is no charge-mass interaction for a charge; whereas in a gravitational field
generated by masses, there is a charge-mass interaction for a charge [1].
Einstein’s equivalence principle [3, 6] leads to the Einstein-Minkowski condition, on which the time dilation and
space contractions are based. On his equivalence principle, Einstein [3] wrote:
‘Let now K be an inertial system. Masses which are sufficiently far from each other and from other bodies are
then, with respect to K, free from acceleration. We shall also refer these masses to a system of co-ordinates K’,
uniformly accelerated with respect to K. Relatively to K’ all the masses have equal and parallel accelerations;
with respect to K’ they behave just as if a gravitational field were present and K’ were unaccelerated. Overlook-
ing for the present the question as to the “cause” of such a gravitational field, which will occupy us latter, there is
nothing to prevent our conceiving this gravitational field as real, that is, the conception that K’; is “at rest” and a
gravitational field is present we may consider as equivalent to the conception that only K is an ”allowable” sys-
tem of co-ordinates and no gravitational field is present. The assumption of the complete physical equivalence of
the systems of coordinates, K and K’, we call the “principle of equivalence;” this principle is evidently intimately
connected with the law of the equality between the inert and the gravitational mass, and signifies an extension of
the principle of relativity to coordinate systems which are non-uniform motion relatively to each other.’
Later, Einstein made clear that a gravitational field is generated from a space-time metric. What is new in Einstein’s
equivalence principle in 1916 is the claim of the Einstein-Minkowski condition as a consequence for gravity.
The Einstein-Minkowski condition has its foundation from mathematical theorems [14] as follows:
Theorem 1. Given any point P in any Lorentz manifold (whose metric signature is the same as a Minkowski
space) there always exist coordinate systems (x
µ
) in which
g
µν
/
x
λ
= 0 at P.
Theorem 2. Given any time-like geodesic curve
Γ
there always exists a coordinate system (the so-called Fermi
coordinates) (xµ) in which
g
µν
/
x
λ
= 0 along
Γ
..
In these theorems, the local space of a particle is locally constant, but not necessarily Minkowski. However, after some
algebra, a local Minkowski metric exists at any given point and along any time-like geodesic curve Γ. In a uniformly ac-
celerated frame, the local space in a free fall is a Minkowski space according to special relativity.
What Einstein added is that physically such a locally constant metric must be Minkowski. Such a condition is needed
for special relativity as a special case [13]. However, these theorems imply only that the local metric is locally constant at
a given point P. Thus, in general, gravity may not be transformed away in a small region by a coordinate transformation
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although the changes of the local metric would be very small within such a small region if the metric at P is a continuous
function. In fact, Einstein [6; p.144] remarked with a counter example, “For it is clear that, e.g., the gravitational field
generated by a material point in its environment certainly cannot be ‘transformed away’ by any choice of the system of
coordinates…“ 11) Nevertheless, both Pauli [9] and Will [15, 16] overlooked (or disagreed with) the remark of Einstein.
Consequently, Pauli’s version [9] is a simplified but corrupted version of these theorems as follows:
“For every infinitely small world region (i.e. a world region which is so small that the space- and time-vari-
ation of gravity can be neglected in it) there always exists a coordinate system K 0 (X1, X2, X3, X4) in which
gravitation has no influence either in the motion of particles or any physical process.”
Thus, Pauli regards the equivalence principle as merely the existence of locally constant spaces, which may not be
locally Minkowski. Thus, the physical content of Einstein’s principle has been removed. (Mathematically, if for
each point, there is a small world region in which gravitation has no influence, then gravity has no influence, i.e.,
special relativity.)8) Therefore, Einstein’s claim of Pauli’s version as being a misinterpretation [10] is well justified
Moreover, Einstein’s equivalence principle is often misinterpreted. Will [15] claimed “’Equivalence’ came
from the idea that life in a free falling laboratory was equivalent to life without gravity.” The British Encyclopedia
also stated Einstein’s Equivalence Principle incorrectly and ignored the Einstein-Minkowski condition [13].
Apparently, Pauli [9] and the Wheeler School failed to understand the mathematics of the above theorems.
Misner et al. [4] claimed that Einstein’s equivalence principle is as follows: -
“In any and every local Lorentz frame, anywhere and anytime in the universe, all the (non-gravitational) laws
of physics must take on their familiar special-relativistic form. Equivalently, there is no way, by experiments
confined to infinitestimally small regions of spacetime, to distinguish one local Lorentz frame in one region of
spacetime frame from any other local Lorentz frame in the same or any other region.”
They even claimed the above as Einstein’s equivalence principle in its strongest form. However, this version makes es -
sentially another form of the misinterpretation of Pauli [9]. Since a local Lorentz frame may have only one point with a
local Minkowski metric, the local Lorentz frames are distinguishable. Therefore, as Einstein pointed out [6], gravitation
is not generally equivalent to acceleration. Thus, they made the combined errors of Pauli and the 1911 assumption.12)
To be specific, the phrase, “must take on” should be changed to “must take on approximately” Also, the phrase, “ex-
periments confined to infinitesimally small regions of spacetime” does not make sense since experiments can be con -
ducted only in a finite region. Moreover, in their eq. (40.14) they got an incorrect local time of the earth.13) Thus, clearly
these three theorists [4] failed to understand the basics of general relativity [3, 6, 9].9)
Thorne [17; p. 105] even criticized the distortion of Will [15], who ignored tidal gravitational force, as if Einstein’s
equivalence principle. However, Einstein has already explained these problems to Rehtz [10] as follows:
“The equivalence principle does not assert that every gravitational field (e.g., the one associated with the Earth)
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can be produced by acceleration of the coordinate system. It only asserts that the qualities of physical space, as
they present themselves from an accelerated coordinate system, represent a special case of the gravitational field.”
Moreover, Einstein [10] explained to Laue, “What characterizes the existence of a gravitational field, from the empirical
standpoint, is the non-vanishing of the Γlik (field strength), not the non-vanishing of the Riklm.” This allows Einstein to
conclude that the geodesic equation is also the equation of motion of a massive particle under gravity.
Following the misidentification of Fock [18], the Wheeler School [16] also claimed that Einstein’s equivalence
principle invalid.5) Although Einstein’s equivalence principle was clearly illustrated only recently [19], 14) the Wheeler
School should bear the responsibility of their misinformation on this principle [4] by ignoring both crucial work of Ein-
stein, i. e., references [3] and [6]. Their main problem, among others, is the lack of rigor in logic. Moreover, since the
Wheeler School did not even state the facts correctly, they are very far away from being authoritative. 15) In fact,
many probably need the help from the physics community.
4. The Conflict between Einstein’s Covariance Principle and his Equivalence Principle.
A problem in general relativity is that Einstein’s covariance principle is actually in conflict with his equivalence prin-
ciple. The covariance principle implies that he time dilation and the space contractions can be measured [1, 6], and there-
fore should be unique for a given frame of reference. On the other hand, the covariance principle would imply different
gauges (such as the Schwarzschild and the harmonic gauges of the same frame) as equivalent in physics. However, if one
reads carefully, Einstein only assumed, but did not prove his equivalence principle to be valid for the gauge considered.
Hence, it is possible that only one gauge is valid for the equivalence principle.
This is a major problem because the covariance principle is Einstein’s remedy for his theory of measurement. For its
justification Einstein had used special relativity, and this probably was why Whitehead’s criticisms of Einstein’s theory of
measurement being invalid in physics, was rejected [20]. This would explain also that many still believed in Einstein’s
covariance principle, in spite of experimental and theoretical evidences against it [21]. The problem is finally settled after
it is discovered that Einstein’s justifications were actually based on invalid applications of special relativity [20].
Major sources of errors are not only the incorrect rejection of Einstein’s equivalence principle, but the acceptance of
Einstein’s invalid covariance principle [21]. In addition to the usual mistake due to a failure in distinguishing physics
from mathematics, the Wheeler School has a special need because the covariance principle is crucial for their theory of
black holes [4, 5, 19, 20]. However, they probably were aware of the inconsistency between Einstein’s covariance princi-
ple and Einstein’s equivalence principle [22] since they used a different approach to derive light bending.
Ironically, the Wheeler School also inadvertently provides probably the earliest counter example for the covariance
principle. Will [4; p. 1067] found that Whitehead’s theory is invalid; but the solution of Whitehead is diffeomorhpic to
Einstein’s solutions [23].16) This example illustrates also a failure on their logical consistency in thinking.
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5. Conclusions and Remarks
Based on evidences, we conclude:
1) All the mass fall in the same way in vacuum only if the mass-charge interaction is absent.
2) The inertial and gravitational masses are equivalent, and this should be further verified with experiments.
3) Einstein’s equivalence principle is inadequate [1], but generally valid. The attempt of the Wheeler School to re-
place Einstein’s equivalence principle with the invalid equivalence of gravity and acceleration is incorrect.
Moreover, errors in general relativity are related to misinterpretation of Einstein’s equivalence principle [19]. The influ -
ence of the Wheeler School leads many theorists, including Eric J. Weinberg, editor of Physical Review D, to claim that
there is no difference in physics between Einstein’s and Pauli’s versions [24]. 17) Thus, it is necessary to rectify the dam-
ages done to general relativity by the Wheeler School and associates [5, 16, 17, 20, 25]. 16) The rectification of this main
stream of errors is urgent since they have already dominated the 1993 Nobel Committee [2].
Up to 1990, Zhou Pei-Yuan of Peking University probably was the only theorist, who took the view of rejecting the
covariance principle but accepting Einstein’s equivalence principle [26, 27]. Moreover, Zhou could have discovered that
linearization to obtain an approximate wave solution is invalid 18) if his student and friends had not made surprising mis-
takes [28, 29]. However, the works of Zhou was misunderstood as an incorrect coordinate dependent theory, 19) and thus
nobody would continue the experiments on local light speeds that Zhou initiated [27, 30]. 20) Apparently, Zhou [27] agrees
with Einstein that the Michelson-Morley experiment does not provide a firm foundation for special relativity. Zhou is
right since the light speeds may not be isotropic although the data exclude the Galileo transformation.
Thus, the misinterpretations of the Wheeler School are the obstacles that would prevent the progress in relativity not
only in the US and Europe but also in China [31]. Their misinterpretations created a distortion of the Einstein-Minkowski
condition, the so-called “local Lorentz invariance” [32]. This would unfairly give a further destructive damage to the reputation of
Einstein. A problem is that many blindly accept invalid claims and misinterpretations [19, 21, 33, 34].8)
In short, a crucial issue is the details of the static repulsive force [1, 35-38] since it would also confirm the static
Einstein equation. Currently, the string theory was assured by the positive mass theorem [33, 34] as would be a theory for
everything. However, such a theorem is also based on an invalid assumption of a unique coupling sign [39], whose ac-
ceptance was due to mistakenly considered E = mc 2 as unconditionally valid for any energy. Thus, investigating the
charge-mass interaction [5] and the equivalence of the inertial and gravitational masses seems more urgent. 21)
Acknowledgments:
Special Thanks are to the referees for valuable comments and useful suggestions. This work is supported in part by
Innotec Design, Inc., U. S. A. and the Chan Foundation.
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Endnotes:
1) What Galileo claimed is that a neutral body, independent of its weight, would have the same acceleration for a free
fall in vacuum. A free fall in vacuum would eliminate all effects due to other near by particles and air resistance.
2) The effect of such a repulsive force [5] was inadvertently detected by Tsipenyuk & Andreev [38]. They discovered
that the weight of a metal ball is reduced after it is irradiated with high energy electrons. However, they could not
explain this phenomenon because they did not know the repulsive force discovered in 1997 [40]. Thus, this experi-
ment shows that this new force cannot be explained in terms of electromagnetism or attractive gravitation, and that
electromagnetic energy is a source of gravity but is not equivalent to mass.
3) Any neutral object is in a bounded state and the electrons and the protons are not at rest. Note that the current-mass
interaction would normally cancel the static charge-mass repulsive forces [1]; as suggested by a charged capacitor.
4) Experiments on the weight reduction of a capacitor after charged have a very long history that can be traced back
to before 1960 [35-37]. However, since this weight reduction cannot be explained in term of electromagnetism or
attractive gravitation, they remain to be mysteries before the charge-mass interaction was discovered [40].
5) Ohanian & Ruffini and Wheeler [25] and etc. have mistaken Einstein’s equivalence assumption of 1911 as Ein -
stein’s equivalence principle of 1916 [3] just as Fock [18] did. The misidentification has unfairly projected an im-
age of Einstein as an obstinate old man since the 1911 assumption has been proven incorrect by observations. Ap-
parently, the Nobel Committee was unaware of the experimental supports of Einstein’s equivalence principle [19].
One can invent his own principle, but he should make clear the advantage of his version over Einstein’s. Other -
wise, anybody has the right to call it as a misinterpretation [9].
6) The charge-mass interaction was over looked because E = mc2 was mistakenly considered as unconditional [19].
7) The repulsive force between a charge and a spherical distributed mass is complicated due to the 1/r 3 dependency
[1]. However, such a force between a mass and a charge metal ball is far simpler [5]. This force further confirms
that Einstein’s proof of E = mc2 is incomplete [19, 40-42]. Although it is known that the electromagnetic energy is
not equivalent to mass, it was not clear a direct experimental confirmation have been obtained.
8) A common problem of Pauli [9], ‘t Hooft [8], and Misner et al. [4] is inadequate background in mathematics. How-
ever, Fields medalists, S. T. Yau and E. Witten fail to see their mathematical errors on Einstein’s equivalence prin-
ciple probably due to careless reading. They also made other claims [33, 34] based on an invalid assumption on
unique sign of couplings [19, 39]. These theorems are cited as one of the reasons for awarding the Fields Medals to
them [43]. Many rejected the claim of Zhou [27], but accepted Yau’s that the Wheeler School approved.
9) Fock [18] and the Wheeler School [25] claimed that it is impossible to express a uniform gravity in terms of a
spacetime metric, and that Einstein’s equivalence principle is invalid. They are proven wrong [13].
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10) In the book of Liu [11], although he refers to Einstein [6], he also refers to others who misinterpreted Einstein’s
equivalence principle [13]. He also claimed that Einstein’s equivalence principle is not rigorously valid. In the pa-
per of Huang [12], he used conflicting references, since he refers to both Einstein (his ref. [1] therein) and Ohanian
(his ref. [21] therein) as if the same. Like Pauli’s, Huang also made a principle without valid contents. Note that
open-mindedness means only giving different views a due consideration that need not be acceptance.
11) In effect, Einstein pointed out that the versions of both Misner et al [4] and Pauli [9] are impossible in physics.
12) Their influence has altered MIT open course phys. 8.033 to include errors in general relativity again in 2006 [13, 19, 22, 41]. I
discovered these problems [41] and have reported them with adequate details directly to MIT in 2010.
13) Liu [11], Wald [20] and Weinberg [44] do not make the same mistake, but Ohanian & Ruffini [25] do.
14) Hsu & Hsu [45] failed to get a transformation between an inertial frame and a uniformly accelerated frame.
15) Institutes such as the Princeton University, the Royal Society, and etc. are normally considered as authoritative.
However, due to their reputations of excellence, errors relating to such institutes are often overlooked by many edi -
tors, and a paper criticizing such errors would often be rejected. Consequently, errors accumulated and ironically
they become the usual sources of errors in general relativity [12, 19, 21, 22, 24, 46].
16) As Feynman [47] pointed out, many theorists in gravitation are incompetent. An example of logical deficiency is
Will [4; p. 1067] showed Whitehead’s theory is invalid while concurrently believing the covariance principle [23].
A crucial error is the failure to see the impossibility to have a bounded dynamic solution [19]. Misner et al. [4]
claim that there is a bounded “plane wave” form,
( )
222222222
dzedyeLdxdtcds
ββ
+=
where L=L(u),
β
=
β
(u), u = ct – x, and c is the light speed. This form satisfies the Einstein equation, which at vacuum is reduced
to d2L/du2 + L(d
β
/du)2 = 0. However, this equation actually has no bounded weak solution (i.e.,
4
1L
and
21e
β
±
). Note that – L’(u) is a monotonic increasing function in any finite interval of u since
β
’(u) = 0 means L’ = 0, i.e.,
no wave. In turn, this implies that L(u) is an unbounded function of u since
β
’(u) is a periodic function [4].
17) Eric J. Weinberg won prizes (1992, 1995, 2000) from “Gravity Research Foundation” that has undisclosed judges.
18) ‘t Hooft [41, 48] and also Hehl [49] believe that linearization is unconditionally valid. The error is originated from
Christodoulou & Klainerman [46], who claimed the existence of dynamic solutions with an invalid proof [50-52].
19) There is a couplet that portrays some theorists. It runs:The reed growing on the wall--top-heavy, thin-stemmed
and shallow of root; The bamboo shoot in the hills--sharp-tongued, thick-skinned and hollow inside” [53]. Richter
[54] comments, “ I think some of what passes for the most advanced theory these days is not really science.”
Historically, self-interest sometimes could be a deciding factor for maintaining incorrect views in physics [55].
Many Chinese theorists have not been able to be out from their past errors [10, 11, 31, 56]. Yu follows the errors of
Misner et al. [4], and he claims [31; p. 57] that a measurable physical quantity must be a scalar. In 1993 I have al-
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ready reported the non-existence of dynamic solution for the Einstein equation in Hong Kong [57]. However, theo-
rists were still unable to understand the subsequent paper [39] because they did not know the earlier errors [34, 35].
20) C. N. Yang opposed Zhou’s view because Yang still misunderstood that a gauge theory must be gauge invariant
[21, 58] although Pauli has pointed out such gauge invariance cannot be accomplished in physics [59].
21) The repulsive force has shaken the foundation of the theory of black holes, that gravity is always attractive.
References:
1. C. Y. Lo, Physics Essays 21 (1), 44-51 (March 2008).
2. The 1993 Press Release of the Nobel Prize Committee (The Royal Swedish Academy of Sciences, Stockholm, 1993).
3. A. Einstein, The Meaning of Relativity (Princeton Univ. Press 1954).
4. C. W. Misner, K. S. Thorne, & J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
5. C. Y. Lo & C. Wong, Bulletin of Pure and Applied Sciences, 25D (2), 109-117 (2006).
6. A. Einstein, The foundation of the general theory of relativity (translated from), Annalen der Physik, 49, 769-822
(1916); A. Einstein, H. A. Lorentz, H. Minkowski, & H. Weyl, The Principle of Relativity (Dover, 1923).
7. A. Einstein, On the influence of Gravitation on the propagation of light, Annalen der Physik, 35, 898-908 (1911).
8. ‘t Hooft still considers Misner et al. [4] valid on the equivalence principle (private communication, May 30, 2011).
9. W. Pauli, Theory of Relativity (Pergamon Press, London, 1971).
10. J. Norton, “What was Einstein’s Principle of Equivalence?” in Einstein’s Studies Vol.1: Einstein and the History of
General Relativity, Eds. D. Howard & J. Stachel (Birkhäuser, Boston, 1989).
11. Liu Liao, General Relativity (High Education Press, Shanghai, China, 1987).
12. Y.-S. Huang, Physics Essays 4 (1), 68-75 (March 1991).
13. C. Y. Lo, Bulletin of Pure and Applied Sciences, 26D (2): 73-88 (2007).
14. J. L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1971), pp. IX–X.
15. C. M. Will, Was Einstein Right?” (Basic Books, New York, 1986), p. 20.
16. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge Univ. 1981).
17. K.S. Thorne, Black Holes and Time Warps (Norton, New York, 1994), p. 105.
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Résumé
« La chute libre d’un capaciteur neutre bien qu’étant plus massif après avoir été chargé, serait plus lente. Par conséquent,
la proposition de Galilée, comme quoi les objets neutres de masses différentes tomberaient à la même vitesse dans le
vide, n’est pas toujours exact. Néanmoins, l’équivalence entre les masses gravitationnelles et inertes resterait valable. De
plus, le principe d’équivalence d’Einstein, qui a été représenté faussement avec distortion pour devenir non valable selon
l’Ecole Wheeler est en fait généralement valable bien que la force de répulsin charge-masse démontre sans équivoque
que l’accélération est intrinsèquement non pas simplement rattachée à la gravité d’attraction généralement. Pour vérifier
l’équivalence des masses, de nouvelles expériences devraient être entreprises où l’interaction de la charge-masse est pré-
sente. Dans ce but, en premier lieu la confirmation expérimentale des détails, tels que la dépendance de la distance, d’une
telle force de répulsion entre la charge et la masse est nécessaire ; et ceci est également un test crucial pour la relativité
générale. »
12
... The existence of such a force on a capacitor was first verified by Liu [5] 20) although the weight reduction of charged capacitors has been found much earlier [53]. Thus, it is found that a weight reduction of a neutral object may not be due to a reduction of mass, but a neutral repulsive force, which was unknown to Einstein [54]. ...
... However, one can show experimentally the mass is still essentially the same. This can be done by measuring the period of a pendulum [54]. The period will not change if the mass is reduced. ...
... Galileo Galilei originally carried out the experiment to find the value of the Earth's gravitational acceleration in 1602 and expressed the acceleration of gravity with a mathematical pendulum (Delti, 2022). In his mathematical pendulum experiment, Galileo noticed that if released simultaneously from rest, all objects tend to land simultaneously, concluding that the fall time does not depend on the object's mass (Lo, 2011). In the experiment of measuring the gravitational acceleration using the mathematical pendulum method, errors often appear when determining the pendulum's angle, which is inconsistent and too large so that sin θ = θ does not apply. ...
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This study aims to examine the effect of altitude on the acceleration of gravity with the help of smartphone acoustic sensors. The altitude varies from the interval 100-1061 MASL (Mean Above Sea Level), located around the Special Region of Yogyakarta. An iron ball is dropped from a certain height, and the time it falls is observed using an acoustic sensor in Phypox, and the results are used to determine the acceleration value due to gravity (g) through the equation g = 2h/t2. Fitting data from measurements of the four altitude variations are shown in the polynomial equation y = 0.000003x2 – 0.0035x+10.718 m/s2 with a regression number R2 = 1,000. This equation shows that the acceleration value due to gravity will decrease quadratically with each increase in the altitude per meter above sea level.
... It has been verified by Liu [29] that the mass is essentially the same as Einstein [2] and Lo [30] predicted, but the period is extended after being heated-up. Thus, from the above weight reduction experiments [3,4], the repulsive gravitational force must exist. ...
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Galileo and Newton considered gravity to be independent of temperature, while Einstein claimed that the weight of metal will increase as temperature increases. Further, Maxwell maintained that charge is unrelated to gravity. Experiments show, however, that the weight of a metal piece is reduced as its temperature increases. Thus, charge-initiated repulsive gravitation exists. In fact, repulsive gravity has been demonstrated by the use of a charged capacitor hovering over Earth. Further, it is expected that a piece of heated metal would fall more slowly than a feather in a vacuum. Einstein developed an invalid notion of gravitational mass, and failed to establish the unification of gravitation and electromagnetism since he overlooked repulsive gravitation. Moreover, photons are a combination of the gravitational wave and the electromagnetic wave. For electromagnetic energy is invalid, and is in conflict with the Einstein equation. The non-linear Einstein equation has no bounded dynamic solution, Space-time singularity theorems are based on an invalid implicit assumption that all the couplings have a unique sign. Since gravity is no longer always attractive, the existence of black holes is questionable. The fact that Penrose was awarded the 2020 Nobel Prize in Physics for the derivation of black holes is due to that the Nobel Prize Committee for Physics did not sufficiently understand the physics of general relativity. A distinct characteristic of Penrose's work, as usual, is that it is not verifiable.
... An experimental consequence is that a charged capacitor would fall slower. And an electron would fall slower than a proton falling toward the earth [57]. ...
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General relativity is incomplete since it does not include the gravitational radiation reaction force and the interaction of gravitation with charged particles. General relativity is confusing because Einstein's covariance principle is invalid in physics. Moreover, there is no bounded dynamic solution for the Einstein equation. Thus, Gullstrand is right and the 1993 Nobel Prize for Physics press release is incorrect. Moreover, awards to Christodoulou reflect the blind faith toward Einstein and accumulated errors in mathematics. Note that the Einstein equation with an electromagnetic wave source has no valid solution unless a photonic energy-stress tensor with an anti-gravitational coupling is added. Thus, the photonic energy includes gravitational energy. The existence of anti-gravity coupling implies that the energy conditions in space-time singularity theorems of Hawking and Penrose cannot be satisfied, and thus are irrelevant. Also, the positive mass theorem of Yau and Schoen is misleading, though considered as an achievement by the Fields Medal. E = mc2 is invalid for the electromagnetic energy alone. The discovery of the charge-mass interaction establishes the need for unification of electromagnetism and gravitation and would explain many puzzles. Experimental investigations for further results are important.
... Experimentally, however,six kinds of heated-up metals have reduced weight [22]. Because a charged capacitor has reduced weight, it will fall slower than other neutral objects [32]. Thus, Einstein's unification would affect many areas of physics. ...
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The Biefeld-Brown (B-B) effect consists of two parts: 1) the initial thrust is due to the electric potential that moves the electrons to the positive post; and 2) the subsequent lift is due to the separate concentration of the positive and the negative charges. The weight reduction of a charged capacitor is due to a repulsive charge-mass interaction, which is normally cancelled by the attractive current-mass interaction. In a charged capacitor, some electrons initially moving in the orbits become statically concentrated and thus a net repulsive force is exhibited. Based on observations, it is concluded that a repulsive charge-mass interaction is proportional to the charge density square and diminishes faster than the attractive gravitational force, and that the current-mass force is perpendicular to the current. This charge-mass interaction is crucial to establish the unification of electromagnetism and gravitation. To confirm general relativity further, experimental verification of the details of this mass-charge repulsive force is recommended. Moreover, general relativity implies that the photons must include gravitational energy and this explains that experiments show that the photonic energy is equivalent to mass although the electromagnetic energy-stress tensor is traceless. In general relativity,it is crucial to understandnon-linear mathematics and that the Einstein equation has no bounded dynamic solutions. However, due to following Einstein's errors, theorists failed in understanding these and ignored experimental facts on repulsive gravitation. Since the charge-mass interaction occurs in many areas of physics, Einstein's unification is potentially another revolution in physics. Moreover, the existence of a repulsive gravitation implies the necessity of re-justifying anew the speculation of black holes.
... Moreover, this can be verified by simply weighing a capacitor before and after being charged [31,32]. Some experimental consequences are that a charged capacitor would fall slower than a stone [39] and there are capacitor lifters [31]. ...
... Aristotle's incorrect theory was discredited by Galileo's landmark experiment, where according to legend, Galileo dropped balls of different densities and masses from the tower of Pisa. Galileo noticed that if released simultaneously from rest, all objects tend to land at the same time, concluding that time of fall is independent of the object mass [3]. In the last few decades, and as a result of many advancements in science and technology, many techniques have been proposed to provide very precise and accurate measurement of the acceleration due to gravity [4][5][6][7][8][9][10][11][12][13]. ...
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In this paper, we present a new technique to study the dynamics of a free-falling object in a lab setting and to measure the acceleration due to gravity g using a simple and economic setup. The precise measurement of time taken for an object to fall freely passing an infrared (IR) transceiver is utilized to deduce the acceleration due to gravity. The reflected IR intensity from a free-falling 0.19 m rod of equally spaced white stripes of 0.01 m is detected and sent to a digital oscilloscope to observe and record the falling time period of each stripe. By fitting recorded elapsed falling times to the well-known quadratic equation of motion under constant acceleration, an accurate value of the acceleration due to gravity of g = 9.8092 ± 0.0384 m s−2 is obtained. In addition to its accuracy, the proposed technique is safer and more economic than most of the other currently used setups to determine g in undergraduate teaching labs. This study may provide undergraduate lab instructors with an efficient teaching technique for a traditional classroom experiment.
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Simulation shows that general relativity would lead to the existence of black holes if gravitation is always attractive. However, although we observed an invisible and extremely heavy object governs the orbits of stars at the center of our galaxy, we still cannot determine the existence of a black hole. Thus, one may ask whether black holes actually exist. Einstein’s general relativity has been established, because its prediction on the bending of light rays has been confirmed by observation. However, Einstein’s prediction on the increment of weight for a piece of metal as the temperature increases is proven incorrect by experiments, which actually show a reduction of weight. This leads to the necessary existence of repulsive gravitational force, which has been demonstrated by a charged capacitor hovering above the earth. Thus, Einstein, Newton, Galileo, and Maxwell all made the error of overlooking the repulsive gravitational charge-mass interaction. Thus, it is necessary to rejustify the existence of black holes, because gravity is not always attractive. Moreover, repulsive gravitational force makes it necessary to extend general relativity to a five-dimensional theory. Thus, to find out whether black holes exist, it is necessary to investigate the repulsive gravitation and a five-dimensional space.
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We use a torsion balance scale to measure the attraction between two large lead balls and two smaller brass balls, connected with an up-side down T bar that is hung with a string. The vertical part of the T bar is attached with a mirror that reflects a laser beam to provide a light spot that shows how much the T bar has turned. It is observed that the gravitational forces between the lead balls and the brass balls are reduced when the temperature of the lead balls increased. Thus, this experiment shows clearly the existence of a repulsive gravitational force that increases as the temperature of the lead balls increase. This supports that the charge-mass interaction is the reason that the theories of Galileo, Newton, and Einstein failed to explain the Anomaly of the Space-Probes and flybys, and the fact that not all the neutral subjects necessarily fall with the same acceleration. In other words, the Newtonian law of gravitation is only approximately valid. Thus, the attempts such as J. Luo (罗俊)’s to obtain an accurate gravitational coupling constant with just improved skill are futile. The physical picture of Galileo, Newton, and Einstein on gravitation needs extension beyond the Standard Model (SM).
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Here we present a new physical quantity with the aim of unifying the structure of physics. The basic assumption starts with a reduction of all natural forces into a single force. As a first step, we combine Coulomb's law and the law of gravity into a single law. Astonishingly, this new law introduces a force never before described, which takes the form of a mass-charge force. This new force may be responsible for holding together the atomic nucleus, counteracting the Coulomb repulsive force. As such, this nuclear force could also be integrated into the new force law. A reduction of the natural forces into a single force would also reduce the number of conservation laws. The discussion herein focuses only on whether gravitational and inertial masses are identical or have different properties: if velocity increases, inertial mass also increases, but gravitational mass appears to remain constant. Furthermore, this may make it possible to measure absolute gamma factors which are given by the quotient of the inertial and gravitational masses. If true, this would invalidate one of the postulates of the theory of special relativity, leaving the theory of relativity open to new interpretation. Introduction of the new quantity, the complex number consisting of charge and mass(bq, m(0)), would not, however, invalidate other well-known formulas of physics, for the following reasons: with respect to all equations relating to gravitational mass, the charges usually sum to zero, yielding q = 0 and (bq, m(0)) congruent to m, leading to no inconsistencies; with respect to all equations relating to charge, the en-or would similarly be negligible, since charge changes through m only by adding the summand m/b. Since the gravitational mass of an electron is very small, precise measurements are needed to verify this proposed complex relationship. The inertial mass would remain as has been established. (C) 2013 Physics Essays Publication. [http://dx.doi.org/10.4006/0836-1398-26.1.120]
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Christodoulou and Klainerman claimed the existence of "dynamic" solutions for the vacuum Einstein equation of 1915. However, their so-called dynamic solutions are merely constructed from their presumed strong asymptotically flat (SAP) "initial data sets" without showing the physical relevance. They have not shown the existence of a case other than the static solutions. Moreover, they have not related any of their dynamic solutions to dynamic sources. Thus, their claim of the existence of a dynamic solution is invalid simply because it has not been proven. It is shown that for a presumed dynamic solution, an SAF initial data set is incompatible with the Maxwell-Newton approximation, the linear field equation for weak gravity, which is due to the equivalence principle. It is proven also that a dynamic SAF initial data set is inconsistent with Einstein's radiation formula, which is supported by experiments. It is concluded that the only physically valid SAF initial data sets are the static solutions.
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A gravitational wave, as Hogarth (Ph.D. thesis, University of London, 1953) pointed out in 1953, necessarily implies a nonzero energy-stress tensor at vacuum. Thus for the dynamic case, the Einstein equation violates the principle of causality and cannot have a dynamic solution. Nobel Laureates and Field Medalists failed to see this and thus overlooked that, for the dynamic case, the linearization to obtain an approximation is invalid in mathematics. To support the errors of the 1993 Nobel Committee, 't Hooft claimed that his "cylindrical symmetric wave" would challenge this nonexistence of dynamic solutions. This paper shows, however, that the more general metric form of the Einstein-Rosen type violates the principle of causality. Thus, his solution is invalid in physics. Moreover, there are two errors in his construction, namely, (1) the plane-wave has been extended beyond its physical validity as an idealization and (2) the integration over the angle is not a wave packet and cannot be justified with any physical process. His invalid interpretation of the principle of causality is due to a failure in distinguishing the differences between mathematics and physics. According to Einstein, just as many others, 't Hooft also misinterpreted Einstein's equivalence principle. (C) 2011 Physics Essays Publication. [DOI: 10.4006/ 1.3528716]
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Although Einstein insisted on the fundamental importance of his equivalence principle, many did not understand its solid foundation in mathematics and physics and had mistaken his principle to be the same as Pauli's version or the 1911 preliminary assumption of equivalence. It is shown that the limitation of Einstein's equivalence principle is revealed by the Reissner-Nordstrom metric of a charged particle because this metric necessarily implied the existence of a charge-mass repulsive force. For two pointlike particles having a relative distance r, the repulsive force would be m q2 / r3 where m and q are, respectively, the mass of one particle and the charge of the other. Thus, the equation of motion as the geodesic equation+the Lorentz force is inadequate, and a unification of gravitation and electromagnetism is necessary. However, if one extends the equivalence principle to a five-dimensional space, the repulsive force would be included in a five-dimensional relativity. Experimental verification of this fifth force is proposed, and it would provide evidence for Einstein's belief, the conditional validity of E=m c2.
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We present atom-interferometer tests of the local Lorentz invariance of post-Newtonian gravity. An experiment probing for anomalous vertical gravity on Earth, which has already been performed, uses the highest-resolution atomic gravimeter so far. The influence of Lorentz violation in electrodynamics is also taken into account, resulting in combined bounds on Lorentz violation in gravity and electrodynamics. Expressed within the standard model extension or Nordtvedt’s anisotropic universe model, we limit 12 linear combinations of seven coefficients for Lorentz violation at the part per billion level, from which we derive limits on six coefficients (and seven when taking into account additional data from lunar laser ranging). We also discuss the use of horizontal interferometers, including atom-chip or guided-atom devices, which potentially allow the use of longer coherence times in order to achieve higher sensitivity.
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Einstein's 1911 preliminary application of the equivalence between acceleration and Newtonian uniform gravity to derive gravitational redshifts was commonly but mistakenly regarded to be the same as Einstein's principle of equivalence, which has its foundation in theorems of Riemannian geometry and special relativ-ity. Consequently, limitations due to Newtonian gravity shown in such derivations were incorrectly believed as meaning that Einstein's equivalence principle should not only be inadequate to derive the bending of light, but also have questionable validity itself. Moreover, in Einstein's theory of measurements, his instruments, being in free-fall states, are incorrectly ignored. Consequently, there are theoreti-cal errors and inconsistency, for example, as shown in the case of Einstein's uni-formly rotating disk. However, after the theoretical errors are identified and rec-tified, the uniformly rotating disk will be an example that illustrates the impor-tance of Einstein's equivalence principle and the inadequacy of Pauli's version. The crucial role of Einstein's equivalence principle in time dilation and space contractions is thus illustrated.
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Einstein's radiation formula is supported by the Taylor-Hulse experiment, but its derivation is not self-consistent. Furthermore, as discovered by Einstein, his radiation formula is not compatible with his field equation. As suggested by Einstein's own remark, modifications to the source tensor are necessary. Based on the Taylor-Hulse experiment, in this paper a theory is developed within the theoretical framework of general relativity within which the radiation formula remains the same for binary stars. Concurrently, it is determined that, because of radiation, the source tensor is not zero in a vacuum. Antigravity coupling, suggested by Pauli as a possibility, is a necessary feature. In addition, it is shown that the current theory of linearized gravity is not valid for radiation.
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It is pointed out that all the gauge theories in physics actually are not gauge invariant. Calculation of the deflection angle to the second order shows that general relativity is also not gauge invariant since the shortest distance from the Sun center is different for each gauge. Further, different "de Sitter" precession formulas of the first order are obtained for different gauges. Thus, Einstein's covariance principle is intrinsically invalid. This invalidity would imply also that Einstein's theory of measurement is invalid, since his covariance principle is the remedy for his theory of measurement. Nevertheless, since the Maxwell-Newton approximation has been proven as the first order of a physical metric, the second order approximation of deflection angle can be obtained from measuring the shortest distance from the Sun center. Concurrently, it is shown that the so-called "genuinely measurable quantities," which could be used to make gauge invariant measurements, actually do not exist. As shown in the 1993 press release of the Nobel Committee, many still do not understand Einstein's equivalence principle. Validity of the harmonic metric to the first order and validity of Einstein's equivalence principle can be directly tested by measuring the local light speeds.
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It is pointed out that the usual principle of invariance under isotopic spin rotation is not consistant with the concept of localized fields. The possibility is explored of having invariance under local isotopic spin rotations. This leads to formulating a principle of isotopic gauge invariance and the existence of a b field which has the same relation to the isotopic spin that the electromagnetic field has to the electric charge. The b field satisfies nonlinear differential equations. The quanta of the b field are particles with spin unity, isotopic spin unity, and electric charge +/-e or zero.
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An overdue critical analysis of Einstein's general relativity is provided. For the dynamic case, the Einstein equation is invalid since it is impossible to have a physical solution. For the static case, Einstein's covariance principle has been proven invalid. This error comes from Einstein's theory of measurement which adapts the notion of distance in Riemannian geometry as if it were valid in physics. It is shown that such a theory was not used in Einstein's predictions and its supporting arguments are actually based on invalid applications of special relativity. Nevertheless, Einstein's equivalence principle plays a crucial role in rectifying the shortcomings of his theory of measurement. Moreover, the Maxwell-Newton approximation for massive sources is proven to be independently valid for the dynamic cases. Then, to explain the binary pulsar experiments, the Einstein equation needs to be modified with an additional source of the gravitational stress-energy tensor with a different coupling sign. After E=mc(2) is shown to be only conditionally valid, the charge-mass interaction is discovered, and its existence is experimentally verified. Thus, the unification of gravitation and electromagnetism is necessary. This new force explains the characteristics of NASA's Pioneer anomaly. Moreover, since a photon must include gravitational energy, particle physics cannot be fully understood without taking gravity into consideration. (C) 2010 Physics Essays Publication. [DOI: 10.4006/1.3359739]