Skip to main content
SpringerLink
Log in

On the energy-time uncertainty relation. Part I: Dynamical time and time indeterminacy

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The problem of the validity and interpretation of the energy-time uncertainty relation is briefly reviewed and reformulated in a systematic way. The Bohr-Einsteinphoton-box gedanken experiment is seen to illustrate the complementarity of energy andevent time. A more recent experiment with amplitude-modulated Mößbauer quanta yields evidence for the genuine quantum indeterminacy of event time. In this way, event time arises as a quantum observable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Jammer,The Philosophy of Quantum Mechanics (Wiley, New York, 1974).

    Google Scholar 

  2. E. P. Wigner, inAspects of Quantum Theory, A. Salam and E. P. Wigner, eds. (Cambridge University Press, Cambridge, Massachusetts, 1972), p. 237.

    Google Scholar 

  3. P. Busch,Phys. Rev. D 33, 2253 (1986).

    Google Scholar 

  4. P. Busch, inSymposium on the Foundations of Modern Physics, Joensuu 1987, P. J. Lahti and P. Mittelstaedt, eds. (World Scientific, Singapore, 1987), p. 105.

    Google Scholar 

  5. W. Pauli,General Principles of Quantum Mechanics (Springer, Berlin, 1980).

    Google Scholar 

  6. E. B. Davies,Quantum Theory of Open Systems (Academic Press, New York, 1976).

    Google Scholar 

  7. M. D. Srinivas and R. Vijayalakshmi,Pramana 16, 173 (1981).

    Google Scholar 

  8. R. Werner,J. Math. Phys. 27, 793 (1986).

    Google Scholar 

  9. A. S. Holevo,Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).

    Google Scholar 

  10. G. Ludwig,Foundations of Quantum Mechanics II (Springer, Berlin, 1986).

    Google Scholar 

  11. P. Lahti and K. Ylinen,J. Math. Phys. 28, 2614 (1987).

    Google Scholar 

  12. G. R. Allcock,Ann. Phys. (N.Y.) 53, 253–348 (1969).

    Google Scholar 

  13. L. D. Landau and R. Peierls,Z. Phys. 69, 56 (1931).

    Google Scholar 

  14. R. Sorkin,Found. Phys. 9, 173 (1981).

    Google Scholar 

  15. W. Heisenberg,Z. Phys. 43, 172 (1927).

    Google Scholar 

  16. N. Bohr,Naturwissenschaften 16, 245 (1928);Nature Suppl., April 14, p. 580.

    Google Scholar 

  17. V. Fock and N. Krylov,J. Phys. (USSR) 11, 112 (1947).

    Google Scholar 

  18. N. Bohr and L. Rosenfeld,Dan. Vid. Selsk. Mat.-fys. Medd. 12 (8), 1–65 (1933).

    Google Scholar 

  19. Y. Aharonov and D. Bohm,Phys. Rev. 122, 1649 (1961).

    Google Scholar 

  20. K. Kraus, “A note on Zeno's paradox in quantum theory,” preprint, University Texas at Austin, DOE-ER-03992-387 (1980).

  21. Yu. I. Vorontsov,Sov. Phys. Usp. 24, 150 (1981).

    Google Scholar 

  22. S. Stenholm, inQuantum Optics, Experimental Gravitation, and Measurement Theory, P. Meystre and M. O. Scully, eds. (Plenum, New York, 1983), p. 117.

    Google Scholar 

  23. P. Busch,Found. Phys. 20, 33 (1990).

    Google Scholar 

  24. Y. Aharonov and J. L. Safko,Ann. Phys. (N.Y.) 91, 279 (1975).

    Google Scholar 

  25. M. Bauer and P. A. Mello,Ann. Phys. (N.Y.) 111, 38 (1978).

    Google Scholar 

  26. L. D. Landau and E. M. Lifschitz,Quantenmechanik (Akademie, Berlin, 1979).

    Google Scholar 

  27. L. Mandelstam and I. G. Tamm,J. Phys. (USSSR) 9, 249 (1945).

    Google Scholar 

  28. A. Messiah,Quantum Mechanics, Vol. 1 (North-Holland, Amsterdam, 1961), pp. 319–320.

    Google Scholar 

  29. L. F. Cook,Am. J. Phys. 48, 142 (1980).

    Google Scholar 

  30. M. Grabowski,Lett. Math. Phys. 8, 455 (1984).

    Google Scholar 

  31. J. Hilgevoord and J. B. M. Uffink,Found. Phys. 15, 925 (1985).

    Google Scholar 

  32. J. Hilgevoord and J. B. M. Uffink, inMicrophysical Reality and Quantum Formalism, A. van der Merwe, F. Selleri, and G. Tarozzi, eds. (Kluwer Academic, Dordrecht, 1987).

    Google Scholar 

  33. L. Fonda, G. C. Ghirardi, and A. Rimini,Rep. Prog. Phys. 41, 587 (1978).

    Google Scholar 

  34. B. Misra and E. C. G. Sudarshan,J. Math. Phys. 18, 856 (1977).

    Google Scholar 

  35. W. Yourgrau, “A budget of paradoxes in physics,” inProblems in Philosophy of Science, I. Lakatos and A. Musgrave, eds. (North-Holland, Amsterdam, 1968), p. 178.

    Google Scholar 

  36. J. B. M. Uffink,Phys. Lett. A 108, 59 (1985).

    Google Scholar 

  37. F. E. Schroeck, inThe Physics of Phase Space. Proceedings, College Park, Maryland, 1986, Y. S. Kim and W. W. Zachary, eds. (Springer, Berlin, 1987), p. 426.

    Google Scholar 

  38. H. J. Landau and H. O. Pollak,Bell Syst. Tech. J. 40, 65 (1961).

    Google Scholar 

  39. M. Moshinsky,Am. J. Phys. 44, 1037 (1976).

    Google Scholar 

  40. E. P. Wigner,Rev. Mod. Phys. 29, 255 (1957); reprinted inSymmetries and Reflections (Bloomington, London, 1967), p. 51.

    Google Scholar 

  41. H. Salecker and E. P. Wigner,Phys. Rev. 109, 571 (1957).

    Google Scholar 

  42. L. de Broglie, inPerspectives in Quantum Theory, W. Yourgrau and A. van der Merwe, eds. (MIT Press, Cambridge, Massachusetts, 1971).

    Google Scholar 

  43. A. Peres,Am. J. Phys. 48, 552 (1980).

    Google Scholar 

  44. P. Busch and P. Lahti,Ann. Physik (Leipzig)47, (1990).

  45. N. Bohr, inAlbert Einstein: Philosopher-Scientist, P. A. Schilpp, ed. (Open Court, LaSalle, Illinois, 1949), p. 201.

    Google Scholar 

  46. W. K. Wootters and W. H. Zurek,Phys. Rev. D 19, 473 (1979).

    Google Scholar 

  47. P. Mittelstaedt, A. Prieur, and R. Schieder,Found. Phys. 17, 891 (1987).

    Google Scholar 

  48. E. Prugovecki,Stochastic Quantum Mechanics and Quantum Spacetime, corrected printing (Reidel, Dordrecht, 1986).

    Google Scholar 

  49. P. Busch, Dissertation, University of Cologne, 1982.

  50. P. Busch,Int. J. Theor. Phys. 24, 63 (1985).

    Google Scholar 

  51. F. E. Schroeck,J. Math. Phys. 22, 2562 (1981).

    Google Scholar 

  52. H. J. Treder, inPerspectives in Quantum Theory, W. Yourgrau and A. van der Merwe, eds. (MIT Press, Cambridge, Massachusetts, 1971), p. 17.

    Google Scholar 

  53. H. J. Treder,Found. Phys. 5, 135 (1975).

    Google Scholar 

  54. A. Landé,New Foundations of Quantum Mechanics (Cambridge University Press, Cambridge), Massachusetts (1965), pp. 122–123.

    Google Scholar 

  55. P. Mittelstatedt,Philosophical Problems of Modern Physics (Reidel, Dordrecht, 1976).

    Google Scholar 

  56. J. Hilgevoord and J. B. M. Uffink,Eur. J. Phys. 6, 165–170 (1985).

    Google Scholar 

  57. U. Hauser, W. Neuwirth, and N. Thesen,Phys. Lett. A 49, 57 (1974).

    Google Scholar 

  58. N. Thesen, Dissertation University of Cologne, 1974.

  59. G. Badurek, H. Rauch, and D. Tuppinger,Phys. Rev. A 34, 2600–26008 (1986).

    Google Scholar 

  60. A. S. Wightman,Rev. Mod. Phys. 34, 845 (1962).

    Google Scholar 

  61. J. M. Jauch and C. Piron,Helv. Phys. Acta 40, 559–570 (1967).

    Google Scholar 

  62. S. T. Ali and G. G. Emch,J. Math. Phys. 15, 176 (1974).

    Google Scholar 

  63. D. P. L. Castrigiano,Lett. Math. Phys. 6, 261–269 (1982).

    Google Scholar 

  64. R. Arshansky, L. P. Horwitz, and Y. Lavie,Found. Phys. 13, 1167 (1983).

    Google Scholar 

  65. R. E. Collins and J. R. Fanchi,Found. Phys. 8, 851 (1978).

    Google Scholar 

  66. A. S. Holevo,Rep. Math. Phys. 13, 379 (1978).

    Google Scholar 

  67. L. P. Horwitz and Y. Rabin,Lett. Nuovo Cimento 17, 501 (1976).

    Google Scholar 

  68. J. Kijowski,Rep. Math. Phys. 6, 361 (1974).

    Google Scholar 

  69. Y. S. Kim and M. E. Noz,Found. Phys. 9, 375.

  70. Y. S. Kim and M. E. Noz,Theory and Applications of the Poincaré Group (Reidel, Dordrecht, 1986).

    Google Scholar 

  71. C. Piron,Foundations of Quantum Physics (Benjamin, Reading, Massachusetts).

  72. E. Prugovecki,Found. Phys. 12, 555 (1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, D-5000, Köln 41, Federal Republic of Germany

    Paul Busch

Authors
  1. Paul Busch
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to my parents on the occasion of their 60th birthdays.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Busch, P. On the energy-time uncertainty relation. Part I: Dynamical time and time indeterminacy. Found Phys 20, 1–32 (1990). https://doi.org/10.1007/BF00732932

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00732932

Keywords

Search

Navigation