Advertisement

Celestial Mechanics and Dynamical Astronomy

, Volume 77, Issue 2, pp 107–126 | Cite as

Superluminal Kinematics in the Milne Universe: Causality in the Cosmic Time Order

  • Roman Tomaschitz
Article

Abstract

The causality of superluminal signal transfer in the galaxy background is scrutinized. The cosmic time of the comoving galaxy frame determines a distinguished time order for events connected by superluminal signals. Every observer can relate his rest frame to the galaxy frame, and compare so the time order of events in his proper time to the cosmic time order. In this way all observers arrive at identical conclusions on the causality of events connected by superluminal signals. The energy of tachyons (superluminal particles) is defined in the comoving galaxy frame analogous to the energy of subluminal particles. It is positive in the galaxy frame and bounded from below in the rest frames of geodesically moving observers, so that particle-tachyon interactions can be based on energy-momentum conservation. We study tachyons in a Robertson-Walker cosmology with linear expansion factor and open, negatively curved 3-space (Milne universe). This cosmology admits globally geodesic rest frames for uniformly moving observers, synchronized by Lorentz boosts. In this context we show that no signals can be sent into the past of observers. If an observer emits a tachyonic signal, then the response of a second observer can never reach him prior to the emission, i.e., no predetermination can occur. The proof is based on the positivity of tachyonic energy.

tachyons superluminal signals cosmic time causality Robertson-Walker cosmology hyperbolic space 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aharanov, Y., Reznik, B. and Stern, A.: 1998, Phys. Rev. Lett. 81, 2190.CrossRefADSGoogle Scholar
  2. Anderson, R., Vetharaniam, I. and Stedman, G. E.: 1998, Phys. Rep. 295, 93.MathSciNetCrossRefGoogle Scholar
  3. Bahcall, N. A. et al.: 1999, Science 284, 1481.CrossRefADSGoogle Scholar
  4. Balazs, N. L. and Voros, A.: 1986, Phys. Rep. 143, 109.MathSciNetCrossRefADSGoogle Scholar
  5. Bilaniuk, O. M. P., Deshpande, V. P. and Sudarshan, E. C. G.: 1962, Am. J. Phys. 30, 718.MathSciNetCrossRefADSGoogle Scholar
  6. Chaliasos, E.: 1987, Physica A 144, 390.zbMATHMathSciNetCrossRefADSGoogle Scholar
  7. Davies, P. C. W.: 1975, Nuovo Cimento B 25, 571.ADSGoogle Scholar
  8. Dirac, P. A. M.: 1973, in: J. Mehra (ed.), The Physicist's Conception of Nature, Reidel, Dordrecht, p. 45.Google Scholar
  9. Dyson, F. J.: 1972, in: A. Salam and E. P. Wigner (eds), Aspects of Quantum Theory, Cambridge Univ. Press, p. 213.Google Scholar
  10. Dyson, F. J.: 1979, Rev. Mod. Phys. 51, 447.CrossRefADSGoogle Scholar
  11. Feinberg, G.: 1967, Phys. Rev. 159, 1089.CrossRefADSGoogle Scholar
  12. Feinberg, G.: 1970, Sci. Am. 222(2), 69.CrossRefGoogle Scholar
  13. Feinberg, G.: 1978, Phys. Rev. D 17, 1651.CrossRefADSGoogle Scholar
  14. Fenchel, W.: 1989, Elementary Geometry in Hyperbolic Space, de Gruyter, Berlin.zbMATHGoogle Scholar
  15. Ford, L. H.: 1995, Phys. Rev. D 51, 1692.MathSciNetCrossRefADSGoogle Scholar
  16. Fuller, R. W. and Wheeler, J. A.: 1962, Phys. Rev. 128, 919.zbMATHMathSciNetCrossRefADSGoogle Scholar
  17. Hoyle, F. and Narlikar, J. V.: 1995, Rev. Mod. Phys. 67, 113.MathSciNetCrossRefADSGoogle Scholar
  18. Infeld, L. and Schild, A.: 1945, Phys. Rev. 68, 250.MathSciNetCrossRefADSGoogle Scholar
  19. Milne, E. A.: 1932, Nature 130, 9.zbMATHADSGoogle Scholar
  20. Milne, E. A.: 1948, Kinematic Relativity, Clarendon, Oxford.zbMATHGoogle Scholar
  21. Newton, R.: 1970, Science 167, 1569.ADSGoogle Scholar
  22. Parker, L.: 1969, Phys. Rev. 188, 2287.CrossRefADSGoogle Scholar
  23. Pirani, F. A. E.: 1970, Phys. Rev. D 1, 3224.CrossRefADSGoogle Scholar
  24. Sandage, A.: 1988, Annu. Rev. Astron. Astrophys. 26, 561.CrossRefADSGoogle Scholar
  25. Smoot, G. F. and Scott, D.: 1998, in C. Caso et al., Eur. Phys. J. C 3, 1.Google Scholar
  26. Tanaka, S.: 1961, Progr. Theoret. Phys. 24, 171.CrossRefADSGoogle Scholar
  27. Terletsky, Ya. P.: 1961, Sov. Phys. Dokl. 5, 782.ADSGoogle Scholar
  28. Tomaschitz, R.: 1997a, Chaos, Solitons & Fractals 8, 761.zbMATHMathSciNetCrossRefADSGoogle Scholar
  29. Tomaschitz, R.: 1997b, Int. J. Bifurcation & Chaos 7, 1847.zbMATHMathSciNetCrossRefADSGoogle Scholar
  30. Tomaschitz, R.: 1998a, Int. J. Theoret. Phys. 37, 1121.zbMATHMathSciNetCrossRefGoogle Scholar
  31. Tomaschitz, R.: 1998b, Int. J. Mod. Phys. D 7, 279.zbMATHCrossRefADSGoogle Scholar
  32. Tomaschitz, R.: 1998c, Astrophys. & Space Sci. 259, 255.zbMATHCrossRefADSGoogle Scholar
  33. Tomaschitz, R.: 1998d, Chaos, Solitons & Fractals 9, 1199.zbMATHMathSciNetCrossRefADSGoogle Scholar
  34. Tomaschitz, R.: 1999a, Int. J. Mod. Phys. A 14, 4275, ibid. A 14, 5137.zbMATHMathSciNetCrossRefADSGoogle Scholar
  35. Tomaschitz, R.: 1999b, Class. Quant. Grav. 16, 3349.zbMATHMathSciNetCrossRefADSGoogle Scholar
  36. Tomaschitz, R.: 2000a, Astrophys. & Space Sci. 271, 181.zbMATHCrossRefADSGoogle Scholar
  37. Tomaschitz, R.: 2000b, Int. J. Mod. Phys. A 15, 3019.zbMATHMathSciNetCrossRefADSGoogle Scholar
  38. Tomaschitz, R.: 2000c, Eur. Phys. J. B 17, 523.MathSciNetCrossRefADSGoogle Scholar
  39. Wheeler, J. A. and Feynman, R. P.: 1945, Rev. Mod. Phys. 17, 157.CrossRefADSGoogle Scholar
  40. Whittaker, E.: 1951, A History of the Theories of Aether and Electricity, Thomas Nelson & Sons, London.zbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Roman Tomaschitz
    • 1
  1. 1.Department of PhysicsHiroshima UniversityHiroshimaJapan

Personalised recommendations