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Relativistic Rotation: A Comparison of Theories

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Alternative theories of relativistic rotation considered viable as of 2004 are compared in the light of experiments reported in 2005. En route, the contentious issue of simultaneity choice in rotation is resolved by showing that only one simultaneity choice, the one possessing continuous time, gives rise, via the general relativistic equation of motion, to the correct Newtonian limit Coriolis acceleration. In addition, the widely dispersed argument purporting Lorentz contraction in rotation and the concomitant curved surface of a rotating disk is analyzed and argued to be lacking for more than one reason. It is posited that not by theoretical arguments, but only via experiment can we know whether such effect exists in rotation or not. The Coriolis/simultaneity correlation, and the results of the 2005 experiments, support the Selleri theory as being closest to the truth, though it is incomplete in a more general applicability sense, because it does not provide a global metric. Two alternatives, a modified Klauber approach and a Selleri–Klauber hybrid, are presented which are consistent with recent experiment and have a global metric, thereby making them applicable to rotation problems of all types.

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References

  1. G. Rizzi and Ruggiero M.L, ed., Relativity in Rotating Frames (Kluwer Academic, Dordrecht, The Netherlands, 2004) http://digilander/libero.it/solciclos/

  2. Rizzi G, Ruggiero M.L, Serafini A, (2004). Found. Phys. 34(12): 1835–1887

    Article  MATH  MathSciNet  Google Scholar 

  3. Selleri F, (2005). Found. Phys. Lett. 4(18): 325–339

    Article  MathSciNet  Google Scholar 

  4. Antonini P, Okhapkin M, Göklü E., Schiller S, (2005). Phys. Rev. A 71: 050101 gr-qc/0504109

    Article  ADS  Google Scholar 

  5. Stanwix P.L. et al., (2005). Phys. Rev. Lett. 95: 040404 hep-ph/0506074.

    Article  ADS  Google Scholar 

  6. Herrmann S. et al., (2005). Phys. Rev. Lett. 95: 150401 physics/0508097.

    Article  ADS  Google Scholar 

  7. C. Møller, The Theory of Relativity (Clarendon Press, Oxford, 1969), pp. 223.

  8. J. Stachel, “Einstein and the rigidly rotating disk”, Chapter 1 in Held, General Relativity and Gravitation (Plenum Press, New York, 1980), p. 9; A. Einstein, The Meaning of Relativity (Princeton University Press, 1950), footnote on pg 60.

  9. B. Mashoon, “Gravitation and nonlocality”, gr-qc/0112058; “The hypothesis of locality and its limitations,” Chapter 3 in Ref 1

  10. Ref. 8, p. 7.

  11. Ø. Grøn, Am. J. Phys. 43(10), 869–876 (1975). Grøn’s treatment has become a classic for traditional approach advocates.

  12. Grøn Ø., (1977). Int. J. Theor. Phys. 16(8): 603–614

    Article  Google Scholar 

  13. Ø. Grøn, “Space geometry in rotating frames: A Historical Perspective”, Chapter 15 in Ref 1.

  14. Weber T.A, (1999). Am. J. Phys. 67(2): 159–160

    Article  ADS  Google Scholar 

  15. Weber T.A, (1997). Am. J. Phys. 65(10): 946–953

    Article  ADS  Google Scholar 

  16. Klauber R.D, “Toward a consistent theory of relativistic rotation”, Chapter 6 in Ref 1. physics/0404027

  17. Rizzi G., Tartaglia A, (1999). Found. Phys. Lett. 12(2): 179–186

    Article  MathSciNet  Google Scholar 

  18. Rizzi G., Ruggiero M.L, (2002). Found. Phys. 32: 1525 gr-qc/0207104.

    Article  MathSciNet  Google Scholar 

  19. G. Rizzi and Serafini A, “Synchronization and desynchronization on rotating platforms”, Chapter 5 in Ref 1.

  20. Cranor M.B, Heider E.M, Price R.H, (2000). Am. J. Phys. 68(11): 1016–1020

    Article  ADS  MathSciNet  Google Scholar 

  21. Anandan J, (1981). Phys. Rev. D 24(2): 338–346

    Article  ADS  MathSciNet  Google Scholar 

  22. Ghosal S.K, Raychaudhuri B, Chowdhury A.K, Sarker M, (2004). Found. Phys. Lett. 17, 457

    Article  MATH  MathSciNet  Google Scholar 

  23. Peres A, Phys. Rev. D. 18(6), 2173–2174 (78).

  24. Dieks D, (1991). Eur. J. Phys. 12: 253–259

    Article  Google Scholar 

  25. R. Anderson, I. Vetharaniam, and Stedman G.E, Phys. Rep. 295(3&4), 93–180 (March 1998). Many articles have appeared on this subject. These authors cite virtually all of them prior to 1998.

  26. F. Selleri, “Sagnac effect: end of the mystery”, Chapter 4 in Ref 1.

  27. Selleri F, (1997). Found. Phys. Lett. 10: 73–83

    MathSciNet  Google Scholar 

  28. Sagnac M.G, Comptes Rendus 157, 708–718 (1913); “Effet tourbillonnaire optique. La circulation de l’éther lumineux dans un interférographe tournant,” Journal de Physique Thèorique et Appliqèe Paris, Sociète française de physique, Series 5, 4, (1914), 177–195.

    Google Scholar 

  29. Post E.J, (1967). Rev. Mod. Phys. 39: 475–493

    Article  ADS  Google Scholar 

  30. Ref. 19, pp. 98–99, also Ref. 1, p. 409.

  31. Selleri F, (2004). Found. Phys. Lett. 17: 599–606

    Article  MATH  MathSciNet  Google Scholar 

  32. Klauber R.D, “Non-time-orthogonality, gravitational orbits and Thomas precession”, gr-qc/0007018.

  33. Tartaglia A, (1999). Founds. Phys. Lett. 12(1): 17–28

    Article  MathSciNet  Google Scholar 

  34. Strauss M, (1974). Int. J. Theor. Phys. 11: 107–123

    Article  Google Scholar 

  35. Klauber R.D, Found. Phys. Lett. 16(5), 441–457 (Oct 2003). gr-qc/0206033.

  36. See extensive discussions in Ref. 1.

  37. Born M, Einstein’s Theory of Relativity. (Dover, NY, 1965) pp. 214–216.

  38. Brillet A., Hall J.L, (1979). Phys. Rev. Lett. 42(9): 549–552

    Article  ADS  Google Scholar 

  39. Bel L, “Eppur, si muove!” Chapter 12 in Ref 1.

  40. Klauber R.D, (2004). Found. Phys. Lett. 17(2): 125–147, gr-qc/0210106.

    Article  MATH  Google Scholar 

  41. The texts and articles listed below are among those that discuss physical vector and tensor components. Ref.16, pp. 114–116; D. Savickas, Am. J. Phys. 70, (8), 798–806; Sokolnikoff I.S, Tensor Analysis (Wiley & Sons, NY, 1951) pp. 8, 122–127, 205; G. E. Hay, Vector and Tensor Analysis (Dover, 1953) pp. 184–186; A. J. McConnell, Application of Tensor Analysis (Dover, 1947) pp. 303–311; C. E. Pearson, Handbook of Applied Mathematics (Van Nostrand Reinhold, 1983 2nd ed.), pp. 214–216; M. R. Spiegel, Schaum’s Outline of Vector Analysis (Schaum) p. 172; R. C. Wrede, Introduction to Vector and Tensor Analysis (Dover, 1972), pp. 234–235.

  42. Misner C.W, Thorne K.S, and Wheeler J.A, Gravitation (Freeman, NY, 1973) p. 210.

  43. See Sec. 2.5.2 of Ref. 25 for further discussion and citations of prior work on this topic.

  44. Klauber R.D, Found. Phys. Lett. 11(5), 405–443. qc-gr/0103076. See Sec. 4.1. These relations can be found elsewhere as well.

  45. Bel L, Martin J, Molina A, (1994). J. Phys. Soc. Japan 63(12): 4350–4363

    Article  MATH  MathSciNet  Google Scholar 

  46. L. Bel and A. Molina, “Local anisotropy of space in a frame of reference co-moving with the Earth”, Il Nuovo Cimento 11B(6) (2000) and arXiv: gr-qc/9806099.

  47. Ref. 1, contributions to Dialogues III and IV, pp. 411–437.

  48. Ref. 1, p. 433.

  49. Byl J, Sanderse M, van der Kamp W., (1985). Am. J. Phys. 53(1): 43–45

    Article  ADS  Google Scholar 

  50. Nikolic H, “Proper co-Ordinates of non-inertial observers and rotation”, Chapter 14 in Ref 1.

  51. Ref 50, p. 278.

  52. Klauber R.D, “Non-time-orthogonality and tests of special relativity”, gr-qc/0006023 (2000).

  53. Klauber R.D, “Generalized tensor analysis method applied to non-time-orthogonal coordinate frames”, gr-qc/0107035 (2001).

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    Robert D. Klauber

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Klauber, R.D. Relativistic Rotation: A Comparison of Theories. Found Phys 37, 198–252 (2007). https://doi.org/10.1007/s10701-006-9099-z

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