Foundations of Physics

, Volume 29, Issue 10, pp 1499–1520 | Cite as

Classical Roots of the Unruh and Hawking Effects

  • M. Pauri
  • M. Vallisneri
Article

Abstract

Although the Unruh and Hawking phenomena are commonly linked to field quantization in “accelerated” coordinates or in curved space-times, we argue that they are deeply rooted at the classical level. We maintain, in particular, that these effects should be best understood by considering how the special-relativistic notion of “particle” gets blurred when employed in theories including accelerated observers or in general-relativistic theories and that this blurring is an instantiation of a more general behavior arising when the principle of equivalence is used to generalize classical or quantum special-relativistic theories to curved space-times or accelerated observers. A classical analogue of the Unruh effect, stemming from the noninvariance of the notion of “electromagnetic radiation” as seen by inertial and accelerated observers, is illustrated by means of four gedanken-experimente. The issue of energy balance in the various cases is also briefly discussed.

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REFERENCES

  1. 1.
    S. W. Hawking, Commun. Math. Phys. 43, 199–220 (1975).Google Scholar
  2. 2.
    W. G. Unruh, Phys. Rev. D 14, 870 (1976).Google Scholar
  3. 3.
    D. W. Sciama, in Relativity, Quanta and Cosmology in the Development of the Scientific Thought of Albert Einstein, F. de Finis, ed. (Johnson Reprint, New York, 1979).Google Scholar
  4. 4.
    M. Vallisneri, Mutamenti nella nozione di vuoto: elettrodinamica dei sistemi accelerati, radiazione di Unruh-Hawking e termodinamica dei buchi neri, Tesi di Laurea (University of Parma, Parma, Italy, 1997).Google Scholar
  5. 5.
    R. Peierls, Surprises in Theoretical Physics (Princeton University Press, Princeton, NJ, 1979).Google Scholar
  6. 6.
    R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (University of Chicago Press, Chicago, 1994).Google Scholar
  7. 7.
    R. Haag and D. Kastler, J. Math. Phys. 5, 848–861 (1964).Google Scholar
  8. 8.
    P. A. M. Dirac, Quantum Mechanics (Oxford University Press, Oxford, 1958).Google Scholar
  9. 9.
    R. Dawkins, The Selfisch Gene (Oxford University Press, Oxford, 1976).Google Scholar
  10. 10.
    M. Planck, Ann. Phys. 1, 69 (1900).Google Scholar
  11. 11.
    A. Higuchi and G. E. A. Matsas, Phys. Rev. D 48, 689–697 (1993).Google Scholar
  12. 12.
    K. Srinivasan, L. Sriramkumar, and T. Padmanabhan, Phys. Rev. D 56, 6692 (1997).Google Scholar
  13. 13.
    K. Srinivasan, L. Sriramkumar, and T. Padmanabhan, Int. J. Mod. Phys. D 6, 607 (1997).Google Scholar
  14. 14.
    T. W. Marshall, Proc. Roy. Soc. London A 276, 475 (1963).Google Scholar
  15. 15.
    T. W. Marshall, Proc. Cambr. Phil. Soc. 61, 537 (1965).Google Scholar
  16. 16.
    T. H. Boyer, Phys. Rev. D 29, 1089 (1984).Google Scholar
  17. 17.
    V. L. Ginzburg, Sov. Phys. Uspekhi 12, 565–574 (1970), translation by V. L. Ginzburg; Usp. Fiz. Nauk 98, 569-585 (1969).Google Scholar
  18. 18.
    M. Born, Ann. Phys. 30, 1 (1909).Google Scholar
  19. 19.
    G. A. Schott, Electromagnetic Radiation (Cambridge University Press, London, 1912).Google Scholar
  20. 20.
    G. A. Schott, Phil. Mag. 29, 49–62 (1915).Google Scholar
  21. 21.
    S. R. Milner, Phil. Mag. 41, 405–419 (1921).Google Scholar
  22. 22.
    D. L. Drukey, Phys. Rev. 76, 543-544 (1949).Google Scholar
  23. 23.
    T. C. Bradbury, Ann. Phys. (N.Y.) 19, 323–347 (1962).Google Scholar
  24. 24.
    C. Leibovitz and A. Peres, Ann. Phys. (N.Y.) 25, 400–404 (1963).Google Scholar
  25. 25.
    W. T. Grandy, Jr., Nuovo Cim. A 65, 738–742 (1970).Google Scholar
  26. 26.
    M. von Laue, Relativitäts Theorie ( Vieweg, Braunschweig, Germany, 1919).Google Scholar
  27. 27.
    W. Pauli, in Enzyklopädie der Matematischen Wissenschaften, Vol. V 19 (Teubner, Leipzig, 1921).Google Scholar
  28. 28.
    N. Rosen, Ann. Phys. (N.Y.) 17, 269–275 (1962).Google Scholar
  29. 29.
    M. Bondi and T. Gold, Proc. Roy. Soc. A 229, 416–424 (1955).Google Scholar
  30. 30.
    T. Fulton and F. Rohrlich, Ann. Phys. (N.Y.) 9, 499–517 (1960).Google Scholar
  31. 31.
    F. Rohrlich, Nuovo Cim. 21, 811 (1961).Google Scholar
  32. 32.
    F. Rohrlich, Ann. Phys. (N.Y.) 22, 169–191 (1963).Google Scholar
  33. 33.
    R. A. Mould, Ann. Phys. (N.Y.) 27, 1–12 (1964).Google Scholar
  34. 34.
    A. Kovetz and G. E. Tauber, Am. J. Phys. 37, 382–385 (1969).Google Scholar
  35. 35.
    D. G. Boulware, Ann. Phys. (N.Y.) 124, 169–188 (1980).Google Scholar
  36. 36.
    F. Piazzese and G. Rizzi, Meccanica 20, 199–206 (1985).Google Scholar
  37. 37.
    S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).Google Scholar
  38. 38.
    C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).Google Scholar
  39. 39.
    I. Ciufolini and J. A. Wheeler, Gravitation and Inertia (Princeton University Press, Princeton, NJ, 1995).Google Scholar
  40. 40.
    O. Levin, Y. Peleg, and A. Peres, J. Phys. A 25, 6471–6481 (1992).Google Scholar
  41. 41.
    J. L. Synge, Proc. Royal Irish Acad. A 65, 27–42 (1967).Google Scholar
  42. 42.
    F. Rohrlich, Classical Charged Particles (Addison-Wesley, Reading, MA, 1965).Google Scholar
  43. 43.
    P. A. M. Dirac, Proc. Roy. Soc. A 167, 148 (1938).Google Scholar
  44. 44.
    J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).Google Scholar
  45. 45.
    V. L. Ginzburg, Theoretical Physics and Astrophysics (Pergamon Press, New York, 1979).Google Scholar
  46. 46.
    D. Tagliavini, Nuova derivazione dell'equazione di Dirac-Lorentz e problemi di simmetria temporale in elettrodinamica classica, Tesi di Laurea (University of Parma, Parma, Italy, 1991).Google Scholar
  47. 47.
    D. Tagliavini, personal communication (1997).Google Scholar
  48. 48.
    A. Einstein, Jahrbuch Radioakt. Eletronik. 4, 411–462 (1907).Google Scholar
  49. 49.
    W. G. Unruh and R. M. Wald, Phys. Rev. D 29, 1047–1056 (1984).Google Scholar
  50. 50.
    D. W. Sciama, P. Candelas, and D. Deutsch, Adv. Phys. 30(3), 327–366 (1981).Google Scholar
  51. 51.
    H. B. Callen and T. A. Welton, Phys. Rev. 83, 34–40 (1951).Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • M. Pauri
  • M. Vallisneri

There are no affiliations available

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