Skip to main content

Space Geometry of Rotating Platforms: An Operational Approach

Foundations of Physics volume 32, pages 1525–1556 (2002)Cite this article

Abstract

We study the space geometry of a rotating disk both from a theoretical and operational approach; in particular we give a precise definition of the space of the disk, which is not clearly defined in the literature. To this end we define an extended 3-space, which we call “relative space:” it is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the “physical space of the rotating platform.” Then, the geometry of the space of the disk turns out to be non Euclidean, according to the early Einstein's intuition; in particular the Born metric is recovered, in a clear and self consistent context. Furthermore, the relativistic kinematics reveals to be self consistent, and able to solve the Ehrenfest's paradox without any need of dynamical considerations or ad hoc assumptions.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

REFERENCES

  1. P. Ehrenfest, Phys. Z. 10, 918 (1909).

    Google Scholar 

  2. M. G. Sagnac, C. R. Acad. Sci. (Paris) 157, 708, 1410 (1913).

    Google Scholar 

  3. M. Planck, Phys. Z. 11, 294 (1910).

    Google Scholar 

  4. H. A. Lorentz, Nature 106, 793 (1921).

    Google Scholar 

  5. A. S. Eddington, Mathematical Theory of Relativity (Cambridge University Press, Cambridge, 1922), Space, Time and Gravitation (Cambridge University Press, Cambridge, 1920).

    Google Scholar 

  6. G. L. Clark, Proc. R. Soc. Edinburgh 62A, 434 (1947).

    Google Scholar 

  7. C. W. Berenda, Phys. Rev. 62, 280 (1942).

    Google Scholar 

  8. G. Cavalleri, Nuovo Cimento LIII B(2), 416 (1968).

    Google Scholar 

  9. T. E. Phipps, Jr., Experiment on Relativistic Rigidity of a Rotating Disk, NOLTR 73-9 (Naval Ordnance Laboratory, 1973), p. 47.

  10. A. Brotas, C. R. Acad. Sci. (Paris) 267, 57 (1968).

    Google Scholar 

  11. W. H. McCrea, Nature 234, 399 (1971).

    Google Scholar 

  12. A. Einstein, The Meaning of Relativity (Princeton University Press, Princeton N.J., 1950).

    Google Scholar 

  13. J. Stachel, in General Relativity and Gravitation, A. Held, ed. (Plenum, New York, 1980).

    Google Scholar 

  14. G. Stead and H. Donaldson, Phil. Mag. 20, 92 (1910).

    Google Scholar 

  15. H. E. Ives, J. Opt. Soc. Am. 29, 472 (1939).

    Google Scholar 

  16. A. Eagle, Phil. Mag. 28, 592 (1939).

    Google Scholar 

  17. M. Galli, Rend. Acc. Lincei 12, 569 (1952).

    Google Scholar 

  18. E. L. Hill, Phys. Rev. 69, 488 (1946).

    Google Scholar 

  19. N. Rosen, Phys. Rev. 71, 54 (1947).

    Google Scholar 

  20. H. Arzeliès, Relativistic Kinematics (Pergamon, New York, 1966).

    Google Scholar 

  21. L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, New York, 1971).

    Google Scholar 

  22. C. Møller, The Theory of Relativity (Oxford University Press, Oxford, 1972).

    Google Scholar 

  23. Ø. Grøn, Found. Phys. 9, 353 (1979).

    Google Scholar 

  24. Ø. Grøn, Int. J. Theor. Phys. 16, 603 (1977).

    Google Scholar 

  25. Ø. Grøn, Am. J. Phys. 43, 869 (1975).

    Google Scholar 

  26. T. A. Weber, Am. J. Phys 65, 946 (1997).

    Google Scholar 

  27. D. Dieks, Eur. J. Phys. 12, 253 (1991).

    Google Scholar 

  28. J. Anandan, Phys. Rev. D 24, 338 (1981).

    Google Scholar 

  29. G. Rizzi and A. Tartaglia, Found. Phys. 28, 1663 (1998).

    Google Scholar 

  30. S. Bergia and M. Guidone, Found. Phys. Lett. 11, 549 (1998).

    Google Scholar 

  31. F. Selleri, Found. Phys. 26, 641 (1996).

    Google Scholar 

  32. F. Selleri, Found. Phys. Lett. 10, 73 (1997).

    Google Scholar 

  33. J. Croca and F. Selleri, Nuovo Cimento B 114, 447 (1999).

    Google Scholar 

  34. F. Goy and F. Selleri, Found. Phys. Lett. 10, 17 (1997).

    Google Scholar 

  35. J. P. Vigier, Phys. Lett. A 234, 75 (1997).

    Google Scholar 

  36. P. K. Anastasowksi et al., Found. Phys. Lett. 12, 579 (1999).

    Google Scholar 

  37. W. A. Rodrigues, Jr. and M. Sharif, Found. Phys. 31, 1767 (2001).

    Google Scholar 

  38. R. D. Klauber, Found. Phys. Lett. 11 (5), 405 (1998).

    Google Scholar 

  39. R. D. Klauber, Am. J. Phys. 67 (2), 158 (1999).

    Google Scholar 

  40. A. Tartaglia, Found. Phys. Lett 12, 17 (1999).

    Google Scholar 

  41. A. Grünbaum and A. J. Janis, Synthèse 34, 281 (1977).

    Google Scholar 

  42. M. Strauss, Int. J. Theor. Phys. 11, 107 (1974).

    Google Scholar 

  43. C. Cattaneo, Introduzione alla teoria einsteiniana della gravitazione (Veschi, Roma, 1961).

    Google Scholar 

  44. C. Cattaneo, Nuovo Cimento 10, 318 (1958).

    Google Scholar 

  45. C. Cattaneo, Nuovo Cimento 11, 733 (1959).

    Google Scholar 

  46. C. Cattaneo, Nuovo Cimento 13, 237 (1959).

    Google Scholar 

  47. C. Cattaneo, Rend. Acc. Lincei 27, 54 (1959).

    Google Scholar 

  48. M. Born, Ann. Phys. Leipzig 30, 1 (1909).

    Google Scholar 

  49. R. H. Boyer, Proc. Roy. Soc. 283, 343 (1965).

    Google Scholar 

  50. W. Pauli, Theory of Relativity (Pergamon, New York, 1958).

    Google Scholar 

  51. F. R. Tangherlini, Nuovo Cimento Supp. 20, 1 (1961).

    Google Scholar 

  52. E. J. Post, Rev. Mod. Phys. 39 (2), 475 (1967).

    Google Scholar 

  53. H. D. Wahlquist and F. B. Estabrook, J. Math. Phys. 7, 894 (1966).

    Google Scholar 

  54. H. D. Wahlquist, J. Math. Phys. 33, 304 (1992).

    Google Scholar 

  55. G. Rizzi and A. Tartaglia, Found. Phys. Lett. 12, 179 (1999).

    Google Scholar 

  56. J. Norton, Found. Phys. 19, 1215 (1989).

    Google Scholar 

  57. H. Reichenbach, The Philosophy of Space and Time (Dover, New York, 1957).

    Google Scholar 

  58. H. Reichenbach, in Albert Einstein: Philosopher-Scientist, P. A. Schilpp, ed. (Open Court, La Salle, IL, 1949).

    Google Scholar 

  59. A. Einstein, in Albert Einstein: Philosopher-Scientist, P. A. Schilpp, ed., Ref. 58.

  60. H. Reichenbach, Axiomatization of the Theory of Relativity (University of California Press, Berkeley and Los Angeles, 1969).

    Google Scholar 

  61. M. A. Abramowicz, B. Carter, and J. P. Lasota, Gen. Rel. Grav. 29, 1173–1183 (1988).

    Google Scholar 

  62. V. Cantoni, Nuovo Cimento B 57, 220 (1968).

    Google Scholar 

  63. T. A. Weber, Am. J. Phys. 67 (2), 159 (1999).

    Google Scholar 

  64. B. Mashhoon, Phys. Lett. A 145, 147 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    Guido Rizzi & Matteo Luca Ruggiero

  2. INFN, Via P. Giuria 1, 10125, Torino, Italy

    Matteo Luca Ruggiero

Authors
  1. Guido Rizzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matteo Luca Ruggiero
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rizzi, G., Ruggiero, M.L. Space Geometry of Rotating Platforms: An Operational Approach. Foundations of Physics 32, 1525–1556 (2002). https://doi.org/10.1023/A:1020427318877

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020427318877

  • special relativity
  • rotating platforms
  • space-geometry
  • Ehrenfest
  • non-time-orthogonal frames