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the equivalence principle， the covarianc,the equivalence principle, the covariance principleandthe question of self-consistency in general relativity内容丰富，建议下载阅览。①页数 42②字数 10884③ 摘要 the equivalence prin...
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The Equivalence Principle, the Covariance Principleand
the Question of Self-Consistency in General Relativity
内容丰富，建议下载阅览。
①页数 42
②字数 10884
③ 摘要
The equivalence principle, which states the local equivalence between acceleration and gravity, requires that a free falling observer must result in a co-moving local Minkowski space. On the other hand, covariance principle assumes any Gaussian system to be valid as a space-time coordinate system. Given the mathematical existence of the co-moving local Minkowski space along a time-like geodesic in a Lorentz manifold, a crucial question for a satisfaction of the equivalence principle is whether the geodesic represents a physical free fall. For instance, a geodesic of a non-constant metric is unphysical if the acceleration on a resting observer does not exist. This analysis is modeled after Einstein illustration of the equivalence principle with the calculation of light bending. To justify his calculation rigorously, it is necessary to derive the Maxwell-Newton Approximation with physical principles that lead to general relativity. It is shown, as expected, that the Galilean transformation is incompatible with the equivalence principle. Thus, general mathematical covariance must be restricted by physical requirements. Moreover, it is shown through an example that a Lorentz manifold may not necessarily be diffeomorphic to a physical space-time. Also observation supports that a spacetime coordinate system has meaning in physics. On the other hand, Pauli version leads to the incorrect speculation that in general relativity space-time coordinates have no physical meaning
④关键字 the Covariance Principl
⑥参考文献
1. D. Kramer, H. Stephani, E. Herlt, & M. MacCallum, Exact Solutions of Einstein Field Equations, ed. E. Schmutzer (Cambridge Univ. Press, Cambridge, 1980), pp 19-24.
2. A. Einstein, Analen der Physik, 49, 769-822 (1916); also (Leipzig, 1916); A. Einstein, H. A. Lorentz, H. Minkowski, H. Weyl, The Principle of Relativity (Dover, New York, 1952), p. 115, p. 118 & p. 162.
3. A. Einstein, The Meaning of Relativity (Princeton Univ. Press, 1954), pp. 63, 87, 90-93, & 129.
4. Y. Bruhat, he Cauchy Problem,' in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
5. W. B. Bonnor, J. B. Griffiths & M. A. H. MacCallum, Gen. Rel. & Gravitation, 26, 7, 1994.
6. C. Y. Lo, in Proc. Sixth Marcel Grossmann Meeting On General Relativity, 1991, ed. H. Sato & T. Nakamura, 1496 (World Sci., Singapore, 1992).
7. C. Y. Lo, Astrophys. J., 455: 421-428 (Dec. 20, 1995).
8. C. Y. Lo, Phys. Essays, 10 (3), 424-436 (Sept. 1997); ibid., Phys. Essays, 12 (2), 226-241 (June 1999).
9. C. Y. Lo, Phys. Essays, 11 (2), 264-272 (June 1998).
10. W. Pauli, Theory of Relativity (Pergamon, London, 1958), p. vi & p. 145.
11. A. S. Eddington, The Mathematical Theory of Relativity (Chelsa, New York, 1975), p. 10 & p. 129.
12. S. Weinberg, Gravitation and Cosmology (John Wiley Inc., New York, 1972), p. 3.
13. C. W. Misner, K. S. Thorne, & J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), p. 386 & p. 172.
14. P. G. Bergmann, Introduction to the Theory of Relativity (Dover, New York, 1976), p. 159.
15. Liu Liao, General Relativity (High Education Press, Shanghai, China, 1987), pp 13-16.
16. C. Y. Lo, Phys. Essays, 7 (4), 453-458 (Dec., 1994).
17. E. Kretschmann, Ann. Phys., Lpz., 53, 575 (1917).
18. S. W. Hawking, A Brief History of Time (Bantam, New York, 1988), pp 24, 50 & 143-152.
19. J. L. Synge, Relativity (North-Holland, Amsterdam, 1956), pp IX-X.
20. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge Univ. Press, 1981).
21. R. M. Wald, General Relativity (The Univ. of Chicago Press, 1984), p. 438 & p. 441.
22. H. C. Ohanian & R. Ruffini, Gravitation and Spacetime (Norton, New York, 1994), p.xi, p.54, and back cover.
23. Yu Yun-qiang, An Introduction to General Relativity (Peking Univ. Press, Beijing, 1997).
24. V. A. Fock, Rev. Mod. Phys. 29, 345 (1957).
25. A. Gullstrand, Ark. Mat. Astr. Fys. 16, No. 8 (1921).
26. A. Gullstrand, Ark. Mat. Astr. Fys. 17, No. 3 (1922).
27. A. Einstein, elativity and the Problem of Space (1954)' in Ideas and Opinions (Crown, 1982).
28. A. Einstein, eometry and Experience (1921)' in Ideas and Opinions (Crown, New York, 1982).
29. A. Einstein, hat is the Theory of Relativity? (1919)' in Ideas and Opinions (Crown, New York, 1982).
30. J. Norton, hat was Einstein Principle of Equivalence?" in Einstein Studies Vol. 1: Einstein and the History of General Relativity, Eds. D. Howard & J. Stachel (Birkh酳ser, 1989).
the Question of Self-Consistency in General Relativity
内容丰富，建议下载阅览。
①页数 42
②字数 10884
③ 摘要
The equivalence principle, which states the local equivalence between acceleration and gravity, requires that a free falling observer must result in a co-moving local Minkowski space. On the other hand, covariance principle assumes any Gaussian system to be valid as a space-time coordinate system. Given the mathematical existence of the co-moving local Minkowski space along a time-like geodesic in a Lorentz manifold, a crucial question for a satisfaction of the equivalence principle is whether the geodesic represents a physical free fall. For instance, a geodesic of a non-constant metric is unphysical if the acceleration on a resting observer does not exist. This analysis is modeled after Einstein illustration of the equivalence principle with the calculation of light bending. To justify his calculation rigorously, it is necessary to derive the Maxwell-Newton Approximation with physical principles that lead to general relativity. It is shown, as expected, that the Galilean transformation is incompatible with the equivalence principle. Thus, general mathematical covariance must be restricted by physical requirements. Moreover, it is shown through an example that a Lorentz manifold may not necessarily be diffeomorphic to a physical space-time. Also observation supports that a spacetime coordinate system has meaning in physics. On the other hand, Pauli version leads to the incorrect speculation that in general relativity space-time coordinates have no physical meaning
④关键字 the Covariance Principl
⑥参考文献
1. D. Kramer, H. Stephani, E. Herlt, & M. MacCallum, Exact Solutions of Einstein Field Equations, ed. E. Schmutzer (Cambridge Univ. Press, Cambridge, 1980), pp 19-24.
2. A. Einstein, Analen der Physik, 49, 769-822 (1916); also (Leipzig, 1916); A. Einstein, H. A. Lorentz, H. Minkowski, H. Weyl, The Principle of Relativity (Dover, New York, 1952), p. 115, p. 118 & p. 162.
3. A. Einstein, The Meaning of Relativity (Princeton Univ. Press, 1954), pp. 63, 87, 90-93, & 129.
4. Y. Bruhat, he Cauchy Problem,' in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
5. W. B. Bonnor, J. B. Griffiths & M. A. H. MacCallum, Gen. Rel. & Gravitation, 26, 7, 1994.
6. C. Y. Lo, in Proc. Sixth Marcel Grossmann Meeting On General Relativity, 1991, ed. H. Sato & T. Nakamura, 1496 (World Sci., Singapore, 1992).
7. C. Y. Lo, Astrophys. J., 455: 421-428 (Dec. 20, 1995).
8. C. Y. Lo, Phys. Essays, 10 (3), 424-436 (Sept. 1997); ibid., Phys. Essays, 12 (2), 226-241 (June 1999).
9. C. Y. Lo, Phys. Essays, 11 (2), 264-272 (June 1998).
10. W. Pauli, Theory of Relativity (Pergamon, London, 1958), p. vi & p. 145.
11. A. S. Eddington, The Mathematical Theory of Relativity (Chelsa, New York, 1975), p. 10 & p. 129.
12. S. Weinberg, Gravitation and Cosmology (John Wiley Inc., New York, 1972), p. 3.
13. C. W. Misner, K. S. Thorne, & J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), p. 386 & p. 172.
14. P. G. Bergmann, Introduction to the Theory of Relativity (Dover, New York, 1976), p. 159.
15. Liu Liao, General Relativity (High Education Press, Shanghai, China, 1987), pp 13-16.
16. C. Y. Lo, Phys. Essays, 7 (4), 453-458 (Dec., 1994).
17. E. Kretschmann, Ann. Phys., Lpz., 53, 575 (1917).
18. S. W. Hawking, A Brief History of Time (Bantam, New York, 1988), pp 24, 50 & 143-152.
19. J. L. Synge, Relativity (North-Holland, Amsterdam, 1956), pp IX-X.
20. C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge Univ. Press, 1981).
21. R. M. Wald, General Relativity (The Univ. of Chicago Press, 1984), p. 438 & p. 441.
22. H. C. Ohanian & R. Ruffini, Gravitation and Spacetime (Norton, New York, 1994), p.xi, p.54, and back cover.
23. Yu Yun-qiang, An Introduction to General Relativity (Peking Univ. Press, Beijing, 1997).
24. V. A. Fock, Rev. Mod. Phys. 29, 345 (1957).
25. A. Gullstrand, Ark. Mat. Astr. Fys. 16, No. 8 (1921).
26. A. Gullstrand, Ark. Mat. Astr. Fys. 17, No. 3 (1922).
27. A. Einstein, elativity and the Problem of Space (1954)' in Ideas and Opinions (Crown, 1982).
28. A. Einstein, eometry and Experience (1921)' in Ideas and Opinions (Crown, New York, 1982).
29. A. Einstein, hat is the Theory of Relativity? (1919)' in Ideas and Opinions (Crown, New York, 1982).
30. J. Norton, hat was Einstein Principle of Equivalence?" in Einstein Studies Vol. 1: Einstein and the History of General Relativity, Eds. D. Howard & J. Stachel (Birkh酳ser, 1989).
