einstein & inconsistency in general relativity, by c. y. lo

8/14/2019 Einstein & Inconsistency in General Relativity, by C. Y. Lo

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Inconsistency and Problems in Einsteins General Relativity

Currently, Einsteins general relativity is generally regarded as a top scientific achievement, although it is very dif-

ficult to understand. It is well known that observations accurately confirm the three predictions of Einstein [1, 2],

namely: 1) the gravitational redshifts, 2) the perihelion of Mercury, and 3) the deflection of light. However, the

difficulties in its understanding actually came, at least in part, due to its being not a self-consistent theory [3].

Einsteins three accurate predictions created a faith on general relativity. Because of such a faith, few of his peers

took a critical look of his theory. Although problems were raised by Whitehead [3] and Eddington [4] on Ein-

steins theory of measurements, they are soon forgotten since nobody was able to solve them. Currently, instead of

trying to improve the theory, many theorists tried very hard to make physical sense out of just any solutions of

Einsteins equation [5, 6, 7]. And such efforts often made their works sound more like science frictions than a sci-

entific theory [8]. Unsolved problems were still there after more than 90 years although all the problems seem to

be rectifiable. In other words, general relativity actually has never been well understood.

It should be noted that, in spite of the confirmations of Einsteins predictions, there are problems in verifying Ein-

steins theory as follows:

1)The gravitational redshifts were based on Einsteins 1911 preliminary assumption equivalence between accel-

eration and Newtonian gravity. However, such an assumption is inconsistent with Einsteins equivalence

principle proposed later in 1916 [1, 2]. Fock [9] found that it is impossible to have a metric that is consistent

with Newtonian uniform gravity. This shows that gravitational red shifts can be derived from an invalid the-

ory although the gravitational redshifts can be derived from Einsteins equivalence principle [1, 2].

2) Although Einstein did derive the perihelion of Mercury, Gullstrand [10] pointed out in his report to the NobelCommittee that Einsteins field equation may not be able to produce a solution for a two-body problem. In

other words, Einsteins derivation may not be valid. Because of this, Einstein was awarded a prize for his

work in the photo-electric effects. Moreover, it has been proven that Einsteins field equation indeed cannot

produce a physical solution for a two-body problem [11, 12]. Recently, t Hooft [7] tried to rebuttal this con-

clusion with a counter example of his. However, this only exposed his inadequacy in some aspect of phys-

ics such as that he does not understand Einsteins equivalence principle as well as the principle of causality

[7, 13]. So, the perihelion actually cannot be considered as a verification of Einsteins theory although it doessuggest that his theory would be in the right direction.

3) From both the Schwarzschild and the harmonic solution, Einstein obtained the same first order deflection oflight in terms of the shortest distance r0 from the sun center [1, 2]. Then, in support of his covariance prin-

ciple, Einstein [2] remarked, It should be noted that this result, also, of the theory is not influenced by our

arbitrary choice of a system of coordinates. Obviously, this gauge invariance should have been supported by

all physical quantities in all orders of calculations. Recently, calculation of the deflection angle to the second

order also shows gauge invariance in terms of the impact parameter b [14, 15]. However, careful analysis

shows that this calculation actually implies that the theory is intrinsically not gauge invariant since, for each

gauge, the shortest distance r0 is different from that for another gauge [16]. To defend this inconsistency, the

editorial of the Royal Society claimed [17] only b is a true measurable physical quantity, but r0 is just an ar-

bitrary label, a hypothetical construct. However, this is inconsistent with Einsteins result on the first order

approximation [1, 2]. Thus, the editorial of the Royal Society has not reached the maturity in logic.

Because Einsteins covariance principle is invalid, general relativity of Einstein was not a complete theory. Fortu-

nately, the Maxwell-Newton approximation has been proven as the valid first order approximation for gravity due

to massive sources [18] such that the binary pulsar experiment can be explained satisfactorily [11, 12]. According

to this approximation, r0 is at least accurate to the first order. Moreover, validity of this approximation implies also

that the coupling constants have different signs [11] and thus the physical assumption of unique sign in singularity

theorems of Penrose and Hawking is invalid.

This logical immaturity also led to supporting [19] to Bondi Pirani & Robin [5] who rejected Einsteins require-

ment on weak gravity since it is inconsistent with Einsteins covariance principle. Nevertheless, prominent theor-

ists such as Straumann [20], Wald [21], and Will [22], who believe in both Einsteins requirement on weak gravity

and his covariance principle, failed responding to this inconsistence [5] discovered since 1959. Moreover, such lo-

gic immaturity is not just isolated incidents of this Royal Society as shown in Hawkings book [23, 24].

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Moreover, although the International Society on General Relativity and Gravitation was formed, founders of the

society such as P. G. Bergmann [25], H. Bondi [5], V. A. Fock [8], J. L. Synge [26], J. A. Wheeler [27], and etc.

have never reached a general consensus on general relativity. Under the auspices of this society, General Relativ-ity and Gravitation is published. Surprisingly, members of the Editorial Board actually do not sufficiently under-

stand physical principles, such as Einsteins equivalence principle and the principle of causality [22-30]. For in-

stance, except in Einstein's original works, there are no textbooks or reference books [28] (including the British

Encyclopedia [2006]) that explained Einstein's equivalence principle correctly although this principle is statedsquarely in page 57 of Einstein's book, The Meaning of Relativity' [2]. They also failed to understand that Ein-

stein has changed his position on E = mc2 to as only conditionally valid [31], and also the experiments of the bin-

ary pulsars. In addition, some of such theorists criticized Einstein without getting the facts straight first [8, 26].

Einsteins difficulties are due to incorrectly adapt the mathematical notion of local distance in Riemannian

geometry as if valid in physics [32]. Moreover, Einsteins theory of measurement is actually based on invalid ap-

plications of special relativity [1]. Whitehead [3, p.83], strongly objected,

By identifying the potential mass impetus of a kinematic element with a spatio-temporal measure-

ment Einstein, in my opinion, leaves the whole antecedent theory of measurement in confusion, when

it is confronted with the actual conditions of our perceptual knowledge. The potential impetus shares

in the contingency of appearances. It therefore follows that measurement on his theory lacks system-

atic uniformity and requires a knowledge of the actual contingent physical field before it is possible.

Unfortunately, Whitehead also rejected Einsteins equivalence principle, which actually rectifies Einsteins theoryof measurement [33]. His theory of measurement is also inconsistent with the observed light bending [34, 35], and

is the root for ambiguity of coordinates and ended up the need of his covariance principle as an interim measure.

Fundamental concepts in a great theory are often difficult to grasp [36]. To mention a few, this happened to

Newton, Maxwell, Planck, Schrdinger, and C. N. Yang [37]. Einstein is simply not an exception. Unlike Newton,

Einstein did not have adequate background in mathematics, and this affects the logical structure of his theory. He

believed the solutions with different gauges as equally valid [2], but did not see that his covariance principle is in-

consistent with his notion of weak gravity [5]. Zhou Pei-Yuan [38, 39] of Peking University was the first who cor-

rectly rejected Einsteins covariance principle but accepted Einsteins equivalence principle. Nevertheless, Ein-

stein is a great theorist since the implications of general relativity such as the need for unification have been dis-

covered and verified [40, 41]. However, theoretical developments [7, 41] and NASAs discovery of the Pioneer

anomaly imply that Einsteins theory is clear inadequate [42, 43].

References:

1. A. Einstein, H. A. Lorentz, H. Minkowski, H. Weyl, The Principle of Relativity (Dover, N. Y., 1952), pp 115-118, p.162; A. Einstein, Ann. Phys. (Leipig) 49, 769-822 (1916).

2. A. Einstein, The Meaning of Relativity (Princeton Univ. Press, 1954), p. 63, p. 87 & p.. 93.

3. A. N. Whitehead, The Principle of Relativity (Cambridge Univ. Press, Cambridge, 1922).

4. A. S. Eddington, The Mathematical Theory of Relativity (1923) (Chelsa, New York, 1975), p. 10.

5. H. Bondi, F. A. E. Pirani & I. Robinson, Proc. R. Soc. London A 251, 519-533 (1959).

6. Penrose R., Rev. Mod. Phys. 37 (1), 215-220 (1964).

7. C. Y. Lo, The Principle of Causality and the Cylindrically Symmetric Metrics of Einstein & Rosen, Bulletin ofPure and Applied Sciences, 27D (2), 149-170 (2008).

8. K. S. Thorne,Black Holes and Time Warps (Norton, New York, 1994), pp. 105, 456.

9. V. A. Fock, The Theory of Space Time and Gravitation, translated by N. Kemmer (Pergamon Press, 1964),pp 6, 111, 119, 228-233

10. A. Gullstrand, Ark. Mat. Astr. Fys. 16, No. 8 (1921); ibid, Ark. Mat. Astr. Fys. 17, No. 3 (1922).

11. C. Y. Lo, Einstein's Radiation Formula and Modifications to the Einstein Equation, Astrophysical Journal 455,421-428 (Dec. 20, 1995).

12. C. Y. Lo, On Incompatibility of Gravitational Radiation with the 1915 Einstein Equation, Phys. Essays 13 (4),527-539 (December, 2000).

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13. C. Y. Lo, Special Relativity, Misinterpretation of E = Mc2, and Einsteins Theory of General Relativity, inProc. IX International Scientific Conference on Space, Time, Gravitation, August 7-11, 2006, Saint-Peters-

burg, Russian Academy of Sciences.

14. J. Bodenner & C. M. Will, Am. J. Phys. 71 (8), 770 (August 2003).

15. J. M. Grard & S. Piereaux, The Observable Light Deflection Angle, arXiv:gr-qc/9907034 v1 8 Jul 1999.

16. C. Y. Lo, The Deflection of Light to Second Order and Invalidity of the Principle of Covariance, Bulletin ofPure and Applied Sciences, 27D (1), 1-15 (2008).

17. Louise Gardner, Editorial Coordinator, the Royal Society, A Board Members Comments (Feb. 25, 2009).

18. C. Y. Lo, Compatibility with Einstein's Notion of Weak Gravity: Einstein's Equivalence Principle and the Ab-sence of Dynamic Solutions for the 1915 Einstein Equation, Phys. Essays 12 (3), 508-526 (Sept. 1999).

19. Pring F, The Royal Society, Board Member's Comments (Jan. 8, 2007).

20.N. Straumann, General Relativity and Relativistic Astrophysics (Springer, New York, 1984).

21. R. M. Wald, General Relativity (The Univ. of Chicago Press, Chicago, 1984).

22. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge. Univ. 1981).

23. S. Hawking, A Brief History of Time (Bantam Books, New York, 1988).

24. (2006 6 19 ) www5.chinesenewsnet.com/MainNews/Opinion.

25. P. G. Bergman,Introduction to the Theory of Relativity (Dover, New York, 1976).

26. J. L. Synge,Relativity; The General Theory (North-Holland, Amsterdam, 1971).

27. C. W. Misner, K. S. Thorne, & J. A. Wheeler,Gravitation (Freeman, San Francisco, 1973).

28. C. Y. Lo, Einsteins Principle of Equivalence, and the Einstein-Minkowski Condition, Bulletin of Pure andApplied Sciences, 26D (2), 73-88 (2007d).

29. C. Y. Lo, The Gravitational Plane Waves of Liu and Zhou and the Nonexistence of Dynamic Solutions forEinsteins Equation, Astrophys. Space Sci., 306: 205-215 (2006 (DOI 10.1007/s10509-006-9221-x).

30. C. Y. Lo, Einsteins Equivalence Principle, the Principle of Causality, and Plane-Wave Solutions, Phys. Essays20 (3) (Sept. 2007).

31. A. Einstein, E= mc2 (1946), inIdeas and Opinions(Crown, New York, 1954), p. 337.

32. C. Y. Lo, Misunderstandings Related to Einsteins Principle of Equivalence, and Einsteins Theoretical Errorson Measurements, Phys. Essays 18 (4), 547-560 (December, 2005).

33. C. Y. Lo, Space Contractions, Local Light Speeds, and the Question of Gauge in General Relativity, ChineseJ. of Phys. (Taipei), 41 (4), 233-343 (August 2003).

34. C. Y. Lo, On Criticisms of Einsteins Equivalence Principle, Phys. Essays 16 (1), 84-100 (March 2003).

35. C. Y. Lo, On Interpretations of Hubble's Law and the Bending of Light, Progress in Phys., Vol. 1, 10 (2006).

36. L. Motz & J. H.. Weaver, The Story of Physics (Avon, New York, 1989).

37. C. N. Yang, Phys. Rev. Lett. 33, 445 (1974).

38. Zhou (Chou) Pei-Yuan, On Coordinates and Coordinate Transformation in Einsteins Theory of GravitationinProc. of the Third Marcel Grossmann Meetings on Gen. Relativ., ed. Hu Ning, Science Press & North

Holland. (1983), 1-20.

39. Zhou Pei-Yuan, Further Experiments to Test Einsteins Theory of Gravitation,International Symposium onExperimental Gravitational Physics (Guangzhou, 3-8 Aug. 1987), edited by P. F. Michelson, 110-116 (World

Sci., Singapore).

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http://www5.chinesenewsnet.com/MainNews/Opinion/2006_6_24_19_43_16_133.htmlhttp://www5.chinesenewsnet.com/MainNews/Opinion/2006_6_24_19_43_16_133.html


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40. C. Y. Lo, The Necessity of Unifying Gravitation and Electromagnetism and the Mass-Charge Repulsive Ef-fects in Gravity, Physical Interpretation of Relativity Theory: Proceedings of International Meeting. Moscow,

2 5 July 2007/ Edited by M.C. Duffy, V.O. Gladyshev, A.N. Morozov, P. Rowlands. Moscow: BMSTU,

2007, p. 82.

41. C. Y. Lo, Limitations of Einsteins Equivalence Principle and the Mass-Charge Repulsive Force, Phys. Essays

21 (1), 44-51 (March 2008).

42. S. G. Turgshev, V. Toth, L. R. Kellogy, E. L. Lau, and K. J. Lee, The Study of the Pioneer Anomaly: NewData Objectives for New Investigation arXIV: gr-gc/0512121v2, 6 Mar. 2006.

43. C. Y. Lo, The Mass-Charge Repulsive Force and Space-Probes Pioneer Anomaly, in preparation.

Dear Mr. Yen:

I have read carefully your article of 2005 on interviewing me regarding the work of Zhou and

general relativity. You are correct that some of the contents in your article need updated since

three years have passed.

To this end, I have written a short article, ,on this subject. My goal is the get the readers being aware of that general relativity is far from

perfect as some media advocated. I hope this article would be useful to you.

Sincerely yours,

C. Y. Lo

p.s. I attached also a Chinese translation of my paper of 2003.

(CYLo)Applied and Pure Research Institute

17 Newcastle Drive, Nashua, NH 03060, USA

The Chinese Journal of Physics, Vol. 41, No. 4, 233-243 (Schwarzschild)

04.20.-q , 04.20.Cv

1.4


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1921 "The Meaning of Relativity [1]" ( (Schwarzschild) ) [1,2] [1]

, 1)

[2] Galilean() K (x, y, z, t)

ds2 = c2dt2 dx2 - dy2- dz2, (1)

ds2 = c2 dt2 dr2 - r2 d2 - dz2, x = r cos , y = r sin , (1)

, c 3x1010 cm/sec K'(x', y', z', t') K z z' 2) K x-y K' x'-y' = +t [3-5] K'

ds2 = (c2 - 2r2) dt2 dr2 - (1 - 2r2/c2)-1r2 d2 dz2, (2)

x = r cos , y = r sin , r = [x2 + y2]1/2, 2r2/2c2 [2]

K' [1,2] (2) , (2)

, (Riemannian) 3) Eq. (2) Eq. (2) () Eq. (2)

(pseudo-Riemannian) ,,,,

M [ 6 ],

ds2 = [(1 M/2r)2/(1 + M/2r)2]dt2 (1 + M/2r)4(dx2 + dy2 + dz2), (3)

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r = [x2 + y2 + z2]1/2 r, (x,y, z) (3) (Pythagoras (3) ) , (x, y, z) r = [x2 + y2 + z2]1/2-, (3)

[1,2]

[3-8] 4)

[1,2] K'(x, y, z, t),

ds2 = (1 2M/)dt2 (1 2M/)-1d2 2d2 2 sin2 d2, (4)

2 = x2 + y2 + z2, x = sin cos, y = sin sin z = cos ( 3 ) ( 4 )

= r (1 + M/2r)2

, > 2M. (5)

[6] (3) (4) 5) (diffeomorphic) [9]

2. , 1919 [10], (Eddington) [11] 1915 [1,2] gab

Gab Rab R gab = K T(m)ab , (6)

Rab Ricci; T(m)ab - gab ,

aGab 0. (7)

(6),

: i)[7] ii) [9](Eddington) [11][12-14]

2) [15,16] [6]

ds2 = F(r) c2dt2 D(r) dr2 C(r)(r2d2 + r2 sin2 d2) . (8)

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C (r) D (r) F (r) D (r) = C (r) (3) C (r) = 1 , (x, y, z,t) (4) ( r )

r

(3) ( 4 ) , (3) (4) ()

,1916 22[2] x()ds2 = 1;dx2 = dx3 = dx4 = 0. 1 = g11 dx12 x (70) g11= (1 + a/r) dx = 1 a/2r

(4) [1, p.91]

1911 (3) (4) , ( 6)) [8] (Whitehead) [17]

,6)

7) ,

M

dt

d 21= ,

M

dt

d1 . (9)

- (Michelson-Morley) [18]

3. S PM1 B1M2 B2M1 P d1M2P d2 cu chcu r

( ) M1 ()

7

M1

up

M2P

S

B2 B1


8/12

t1 PM1P t1 = 2d1/cu t2P M2P t2= 2 d2/ch

==

uh c

d

c

dttt 1212 2 (10)

M2() t2 PM2 Pt2 = 2d2/cu t1 PM1 P t1 = 2d1/ch

==

hu c

d

c

dttt 1212 2''' . (11)

,

hu

uh

cc

ccddttT

+== )(2' 21 (12)

(

vu

vh

c

)

c

cddTcd

+= )(2 21 , hcc = uc . (13)

uh ccc = = 0,

228

8

e

e

e R

GM

c

R

R

M

c

v

==

, Re = 6.378x106 meters, (14)

M G 9.8 m/sec2

v/c = 6.96x10-10

5000 d 500 [18]Michelson-Morley

(d1 + d2) 36 meters. (15)

vu[1]

4.- ( [11])[19]probe-B [20] 1915 [15], (Schwarzschild) [1,6-8] [8,9] (2)

(2) ( 2 ) Sagnac [21]()

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( 7.3 x 10-5/sec ) 2Re2/2c2 Mk/Re 1.7 x10-3[6]

[22]

6.96x10-10

[22] 8) 1990 10-9 Fabry-Perot [23]

1979 (Yilmaz) [24]9) Michelson-Morley L L [23,25]

[23]

10 ) [26] [4] [5, p. 58] 11)

[17] [12-16,27]

The author is grateful for stimulating discussions with Professors A. J. Coleman, P. Morrison, A. Napier, and

W. Oliver. The author is also grateful to the referees for their valuable comments and suggestions. In particular,

the author appreciates very much the information about the Sagnac effect and the work of Yilmaz. Special thanks

are due to Mr. J. Markovitch for useful suggestions on the presentation. This work is supported in part by Innotec

Design, Inc., USA.

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1) -(-)M g Minkowski(+, , , ) (M, g) Lorentz g Lorentzian [8] Lorentz [1,2]

2) [15,16], (diffeomorphic) [1-9]

3) [2]

4) () [3]

5) Lorentz f: (M, g)(M, g) C Cf(diffeomorphism) M M(diffeomorphic)[9],

6)

7) Minkowski

8) H(Yilmaz)

9) (Yilmaz) Michelson-Morley

10)[22] [6], [27](asymptotically flat)

11) Maxwell-Newton [15,28], [29]

1. A (, 1954), p. 63 p. 87 p. 93 2. A, HA, H, H, (Dover,, 1952), pp. 115-118 3. YB. Zel'dovich ID (Dover,1996), pp. 7-16 4. (, , 1987), pp. 26-30 5., (,, 1997), pp. 63-66 6. S (,, 1972)7. VA, , N (Pergamon , 1964), pp. 6, 111, 119, 228-

2338. HC R, (Norton,, 1994), p. xi, p. 54, 9. RM, (,, 1984), p. 84-88

10


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10. A,? (1919), (,, 1982)11. AS, (1923) (Chelsa,, 1975), p. 10 12. DHE M, , E(,, 1980)

13. , Phys, 7 (4), 453 (1994); , Phys, 11 (2), 264-272 (1998)

14. WBJB MA H Gen. Rel. Gravitation, 26, 7, 1994 15. , Phys, 12 (3), 508-526 (1999 9 )16. , Phys, 13 (4), 527-539 (2000 12 )17. AN, (,, 1922)18. JD, (,, 1966), pp. 350-352 19. CW,KS, JA, (WH,, 1973)20. C. W. F. Everitt et al. in Proc. Seventh Marcel Grossmann Meeting on Gen. Relativ., Stanford, July 1994, ed.

R. Jantzen & M. Keiser, Ser. ed. R. Ruffini, 1533 (World Sci., Singapore, 1996).

21. EJ, ,39, 475-493 (1967); http://www.mathpages.com/rr/s2-07/2-07.htm

22. 23.,, ,

, ,,, 1990 8 13-17 , 2, 1155-1159 24. H, Hadronic J.,2, 997-1020 (1979)25. A JL , Phys., 42, 549 (1979)26. , (,

1987 8 3-8 ),F, 110-116 (,)27., Commun. Theor. Phys. (), 31, 13-20 (1999)28. , Astrophys. J., 455: 421-428 (1995 12 20 )29. ,

REFERENCES

1. A. Einstein, The Meaning of Relativity (Princeton Univ. Press, 1954), p. 63, p. 87 & p. 93.

2. A. Einstein, H. A. Lorentz, H. Minkowski, H. Weyl, The Principle of Relativity (Dover, N. Y., 1952), pp 115-118,

p.162; A. Einstein, Ann. Phys. (Leipig) 49, 769-822 (1916).

3. Y. B. Zeldovich & I. D. Novikov,Stars and Relativity (Dover, New York 1996), pp 7-16.

4. Liu Liao, General Relativity (High Education Press, Shanghai, 1987), pp 26-30.

5. Yu Yun-qiang,An Introduction to General Relativity (Peking Univ. Press, Beijing, 1997), pp 63-66.

6. S. Weinberg, Gravitation and Cosmology (John Wiley, New York, 1972).

7. V. A. Fock, The Theory of Space Time and Gravitation, translated by N. Kemmer (Pergamon Press, 1964), pp 6,

111, 119, 228-233.

8. H. C. Ohanian & R. Ruffini, Gravitation and Spacetime (Norton, New York, 1994), p. xi, p. 54, and back cover.

9. R. M. Wald, General Relativity (The Univ. of Chicago Press, Chicago, 1984), p. 84-88.

10. A. Einstein, 'What is the Theory of Relativity? (1919), in Ideas and Opinions (Crown, New York, 1982).

11. A. S. Eddington, The Mathematical Theory of Relativity (1923) (Chelsa, New York, 1975), p. 10.

12. D. Kramer, H. Stephani, E. Herlt, & M. MacCallum,Exact Solutions of Einstein's Field Equations, ed. E.Schmutzer (Cambridge Univ. Press, Cambridge, 1980).

13. C. Y. Lo, Phys. Essays, 7 (4), 453 (1994); C. Y. Lo, Phys. Essays, 11 (2), 264-272 (1998).

14. W. B. Bonnor, J. B. Griffiths & M. A. H. MacCallum, Gen. Rel. & Gravitation, 26, 7, 1994.

15. C. Y. Lo, Phys. Essays, 12 (3), 508-526 (Sept., 1999).

16. C. Y. Lo, Phys. Essays, 13 (4), 527-539 (Dec., 2000).

17. A. N. Whitehead, The Principle of Relativity (Cambridge Univ. Press, Cambridge, 1922).

18. J. D. Jackson, Classical Electrodynamics (John Wiley, New York, 1966), pp. 350-352.

19. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973).

20. C. W. F. Everitt et al. in Proc. Seventh Marcel Grossmann Meeting on Gen. Relativ., Stanford, July 1994, ed. R.

Jantzen & M. Keiser, Ser. ed. R. Ruffini, 1533 (World Sci., Singapore, 1996).

21. E. J. Post, Reviews of Modern Physics, Vol. 39, 475-493 (1967). See alsohttp://www.mathpages.com/rr/s2-07/2-

07.htm.

22. C. Y. Lo & C. Wong, On Experimental Test of the Gauge in General Relativity, in preparation.

11
http://www.mathpages.com/rr/s2-07/2-07.htmhttp://www.mathpages.com/rr/s2-07/2-07.htmhttp://www.mathpages.com/rr/s2-07/2-07.htmhttp://www.mathpages.com/rr/s2-07/2-07.htmhttp://www.mathpages.com/rr/s2-07/2-07.htm


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23. Li Yonggui, Zhao Zhiqiang, Zhou Xiaofan, Zhou Peiyuan, Measurement of the Relative Difference of Light Velo-

city in the Horizontal and Vertical Directions on the Earths Surface, Proceeding of the Fourth Asia Pacific Phys-

ics Conference, Seoul, Korea, August 13-17, 1990, 2, 1155-1159.

24. H. Yilmaz, Hadronic J., Vol. 2, 997-1020 (1979).

25. A. Brillet & J. L. Hall, Phys. Rev. Letters, 42, 549 (1979).

26. Zhou Pei-yuan, Further Experiments to Test Einsteins Theory of Gravitation, International Symposium on Ex-

perimental Gravitational Physics (Guangzhou, 3-8 August 1987), edited by Peter F. Michelson, 110-116 (WorldScientific, Singapore).

27. Peng Huangwu, Commun. Theor. Phys. (Beijing), 31, 13-20 (1999).

28. C. Y. Lo, Astrophys. J., 455: 421-428 (Dec. 20, 1995).

29. C. Y. Lo, On Criticisms of Einsteins Equivalence Principle, in preparation.

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einstein & inconsistency in general relativity, by c. y. lo

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