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The Sagnac and Hafele–Keating experiments: Two keys to the understanding of space–time physics in the vicinity of the Earth

J. H. Field

Département de Physique Nucléaire et Corpusculaire Université de Genève, 24, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland

E-mail Address: [email protected]

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https://doi.org/10.1142/S0217751X1930014XCited by:3 (Source: Crossref)

Abstract

The role of preferred frames for light propagation and time dilation in the region of a massive, spherical, gravitating bodies, where according to general relativity, space–time curvature is described by the Schwarzschild metric equation, is discussed in the context of the Sagnac effect (for light propagation) and the Hafele–Keating experiment (for time dilation). Predictions for both translational and rotational motion relative to the preferred frame are calculated up to order ${(v / c)}^{3}$ . Different published theoretical calculations of the Sagnac effect are critically reviewed. The conflation in the literature of measured time differences in Sagnac experiments (a classical order $v / c$ effect) and time dilation (a relativistic order ${(v / c)}^{2}$ effect) are also discussed.

Keywords:

PACS: 03.30.+p

References

1. K. Schwarzschild, Sitzungberichte Prüssiche Akademie der Wissenschaften (1916), p. 198. Google Scholar
2. S. Weinberg, Gravitation and Cosmology, Principles and Applications of the General Theory of Relativity (John Wiley, New York, 1972), Chap. 8, Sec. 2. Google Scholar
3. I. I. Shapiro et al., Phys. Rev. Lett. 26, 1132 (1971). Crossref, Web of Science, ADS, Google Scholar
4. G. Sagnac, Comptus Rendus Acad. Sci. 157, 1410 (1913). Google Scholar
5. F. Harress, Die Geschwindigkeit des Lichtes in bewegten Korpen, Dissertation, Universität Jena (1912). Google Scholar
6. J. H. Field, Fundam. J. Mod. Phys. 10, 1 (2017). Google Scholar
7. E. J. Post, Rev. Mod. Phys. 39, 475 (1967). Crossref, Web of Science, ADS, Google Scholar
8. R. D. Klauber, Found. Phys. Lett. 16, 447 (2003). Crossref, Web of Science, Google Scholar
9. F. Zernike, Physica 13, 279 (1947). Crossref, ADS, Google Scholar
10. R. Anderson, H. H. Bilger and G. E. Stedman, Am. J. Phys. 62, 975 (1994). Crossref, Web of Science, ADS, Google Scholar
11. G. B. Malykin, Phys. Usp. 40, 317 (1997). Crossref, ADS, Google Scholar
12. G. B. Malykin, Phys. Usp. 43, 1229 (2000). Crossref, ADS, Google Scholar
13. A. A. Michelson and H. G. Gale, Astrophys. J. 61, 140 (1925). Crossref, ADS, Google Scholar
14. N. Ashby, Phys. Today 55, 41 (2002). Crossref, Web of Science, ADS, Google Scholar
15. R. S. Shankland, Am. J. Phys. 31, 47 (1963). Crossref, Web of Science, ADS, Google Scholar
16. C.-C. Su, Europhys. Lett. 56, 170 (2001). Crossref, ADS, Google Scholar
17. C.-C. Su, Eur. Phys. J. C 21, 701 (2001). Crossref, Web of Science, ADS, Google Scholar
18. H. Poincaré, The Monist 15, 1 (1905). Google Scholar
19. J. C. Hafele and R. E. Keating, Science 177, 166 (1972). Crossref, Web of Science, ADS, Google Scholar
20. J. C. Hafele and R. E. Keating, Science 177, 168 (1972). Crossref, Web of Science, ADS, Google Scholar
21. J. C. Hafele, Am. J. Phys. 40, 81 (1972). Crossref, Web of Science, ADS, Google Scholar
22. J. H. Field, Fundam. J. Mod. Phys. 6, 1 (2013). Google Scholar
23. R. V. Pound and G. A. Rebka, Phys. Rev. Lett. 4, 337 (1960). Crossref, Web of Science, ADS, Google Scholar
24. G. B. Malykin, Radiophys. Quantum Electron. 59, 290 (2015). Crossref, Web of Science, ADS, Google Scholar
25. B. Paterson et al., An undergraduate test of gravitational time dilation, arXiv:1710.07838. Google Scholar
26. R. Wang et al., Phys. Lett. A 312, 7 (2003). Crossref, Web of Science, ADS, Google Scholar
27. R. Wang, Y. Zheng and A. Yao, Phys. Rev. Lett. 93, 143901 (2004). Crossref, Web of Science, ADS, Google Scholar
28. Y. Saburi, M. Yamamoto and K. Harada, IEEE Trans. Instrum. Meas. 25, 473 (1976). Crossref, Web of Science, ADS, Google Scholar
29. D. W. Allan, M. A. Weiss and N. Ashby, Science 228, 64 (1985). ADS, Google Scholar
30. G. Petit and P. Wolf, Astron. Astrophys. 286, 971 (1994). Web of Science, ADS, Google Scholar
31. P. Wolf and G. Petit, Phys. Rev. A 56, 4405 (1997). Crossref, Web of Science, ADS, Google Scholar
32. S. Weinberg, Gravitation and Cosmology, Principles and Applications of the General Theory of Relativity (John Wiley, New York, 1972), Chap. 8, Eq. 8.7.4. Google Scholar
33. A. A. Michelson and E. W. Morley, Phil. Mag. 24, 449 (1887). Crossref, Google Scholar
34. I. Newton, The Principia, Translated by I. B. Cohen and A. Whitman (University of California Press, Berkeley, 1999), p. 795. Google Scholar
35. R. J. Kennedy and E. M. Thorndike, Phys. Rev. 42, 400 (1932). Crossref, ADS, Google Scholar
36. R. J. Kennedy, Proc. Natl. Acad. Sci. 12, 621 (1926). Crossref, ADS, Google Scholar
37. K. K. Illingworth, Phys. Rev. 30, 692 (1927). Crossref, ADS, Google Scholar
38. G. Joos, Ann. Phys. 7, 385 (1930). Crossref, Google Scholar
39. D. C. Miller, Rev. Mod. Phys. 5, 203 (1933). Crossref, ADS, Google Scholar
40. R. S. Shankland et al., Rev. Mod. Phys. 27, 16 (1955). Crossref, Web of Science, Google Scholar
41. P. Langevin, Comptes Rendus Acad. Sci. 173, 831 (1921). Google Scholar
42. P. A. M. Dirac, Quantum Mechanics, 4th edn. (Oxford University Press, Oxford, 1958), Chap. 1, Sec. 3. Google Scholar
43. P. H. Brown and R. Q. Twiss, Proc. R. Soc. A 242, 300 (1957). Crossref, ADS, Google Scholar
44. P. H. Brown and R. Q. Twiss, Proc. R. Soc. A 243, 291 (1958). Crossref, ADS, Google Scholar
45. J. Lense and H. Thirring, Phys. Z. 19, 156 (1918). Google Scholar
46. J.-M. Lévy-Leblond and F. Balibar, Quantics, Rudiments of Quantum Physics (North-Holland, Amsterdam, 1990), p. 493. Google Scholar
47. A. Einstein, Ann. Phys. 17, 891 (1905) [English translation: W. Perrett and G. B. Jeffery, The Principle of Relativity (Dover, New York, 1952), p. 37; Einstein’s Miraculous Year (Princeton University Press, Princeton, New Jersey, 1998), p. 123]. Google Scholar
48. A. Dufour and F. Prunier, Comptus Rendus Acad. Sci. 204, 1925 (1937). Google Scholar
49. J. H. Field, The physics of space and time III: Classification of space–time experiments and the twin paradox, arXiv:0806.3671v1. Google Scholar
50. J. H. Field, Primary and reciprocal space–time experiments, relativistic reciprocity relations and Einstein’s train-embankment thought experiment, arXiv:0807.0158v2. Google Scholar
51. P. Harzer, Astrom. Nachr. 198, 378 (1914). ADS, Google Scholar
52. P. Harzer, Astrom. Nachr. 199, 10 (1914). ADS, Google Scholar
53. B. Pognay, Ann. Phys. 80, 217 (1926). Crossref, Google Scholar
54. B. Pognay, Ann. Phys. 85, 244 (1928). Crossref, Google Scholar
55. F. Prunier, Comptus Rendus Acad. Sci. 200, 46 (1935). Google Scholar
56. H. von Laue, Ann. Phys. 23, 989 (1907). Crossref, Google Scholar
57. R. A. Bergh, G. Kotler and H. J. Shaw, Electron. Lett. 16, 260 (1980). Crossref, Web of Science, ADS, Google Scholar
58. P. Langevin, Scientia 10, 31 (1911). Google Scholar
59. N. D. Mermin, Am. J. Phys. 51, 1130 (1983). Crossref, Web of Science, ADS, Google Scholar
60. N. D. Mermin, Am. J. Phys. 52, 119 (1984). Crossref, Web of Science, ADS, Google Scholar
61. P. Ehrenfest, Phys. Z. 10, 918 (1909). Google Scholar
62. A. Einstein, Relativity, the Special and the General Theory (Princeton University Press, Princeton, 1955), p. 59 [The Meaning of Relativity, 5th edn., English translation: R. W. Lawson (Methuen, London, 1960), p. 82]. Google Scholar
63. J. H. Field, Fundam. J. Mod. Phys. 2, 139 (2011). Google Scholar
64. J. H. Field, Fundam. J. Mod. Phys. 4, 1 (2012). Google Scholar
65. W. Nawrot, Phys. Essays 17, 518 (2004). Crossref, ADS, Google Scholar
66. G. Sagnac, J. Phys. Radium 4, 177 (1914). Google Scholar
67. J. Anandan, Phys. Rev. D 24, 338 (1981). Crossref, Web of Science, ADS, Google Scholar
68. A. A. Logunov and V. Chugreev, Sov. Phys. Usp. 31, 861 (1988). Crossref, ADS, Google Scholar
69. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th edn. (Pergamon Press, Oxford, 1975), p. 254. Google Scholar
70. P. Langevin, Comptus Rendus Acad. Sci. 200, 49 (1935). Google Scholar
71. P. Langevin, Comptus Rendus Acad. Sci. 205, 304 (1937). Google Scholar
72. N. Ashby, Relativity in Rotating Frames, eds. G. Rizzi and M. L. Ruggiero (Kluwer Academic Publishers, Dordrecht, 2004), p. 15. Google Scholar
73. M. G. Trocheris, Phil. Mag. Ser. 40, 1143 (1949). Crossref, Google Scholar
74. D. Dieks and G. Nienhaus, Am. J. Phys. 58, 650 (1990). Crossref, Web of Science, ADS, Google Scholar
75. D. Dieks, Found. Phys. Lett. 4, 347 (1990). Crossref, Web of Science, Google Scholar
76. D. Dieks, Eur. J. Phys. 12, 253 (1991). Crossref, Google Scholar
77. A. Sommerfeld, Optics (Academic Press, New York, 1954). Google Scholar
78. P. W. Forder, J. Phys. A: Math. Gen. 17, 1343 (1984). Crossref, ADS, Google Scholar
79. W. W. Chow et al., Rev. Mod. Phys. 57, 61 (1985). Crossref, Web of Science, ADS, Google Scholar
80. N. Ashby, Living Rev. Rel. 6, 1 (2003). Crossref, ADS, Google Scholar
81. P. Holland and H. R. Brown, Am. J. Phys. 67, 204 (1999). Crossref, Web of Science, ADS, Google Scholar
82. D. M. Greenberger, Phys. Rev. Lett. 87, 100405 (2001). Crossref, Web of Science, ADS, Google Scholar
83. H. Hernandez-Coronado Unstable particle in non-relativistic quantum mechanics?, arXiv:1106.3757v1. Google Scholar
84. G. B. Malykin, Phys. Usp. 45, 907 (2002). Crossref, Web of Science, ADS, Google Scholar
85. J. Bailey et al., Nature 268, 301 (1977). Crossref, Web of Science, ADS, Google Scholar
86. R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948). Crossref, Web of Science, ADS, Google Scholar
87. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, Massachusetts, 1965). Google Scholar
88. J. H. Field, Ann. Phys. (N.Y.) 321, 627 (2006). Crossref, Web of Science, ADS, Google Scholar
89. J. H. Field, Eur. J. Phys. 34, 1507 (2013). Crossref, Web of Science, Google Scholar
90. R. P. Feynman, Phys. Rev. 76, 749 (1949). Crossref, Web of Science, ADS, Google Scholar
91. F. Hasselbach and M. Nicklaus, Phys. Rev. A 48, 143 (1993). Crossref, Web of Science, ADS, Google Scholar
92. M. Dresden and C. N. Yang, Phys. Rev. D 20, 1846 (1979). Crossref, Web of Science, ADS, Google Scholar
93. J. J. Sakurai, Phys. Rev. D 21, 2993 (1980). Crossref, Web of Science, ADS, Google Scholar
94. W. Ehrenberg and R. E. Siday, Proc. R. Soc. B 62, 8 (1949). ADS, Google Scholar
95. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959). Crossref, Web of Science, ADS, Google Scholar
96. J. H. Field, Eur. J. Phys. 33, 63 (2011). Crossref, Web of Science, Google Scholar