Abstract
We examine, in the context of the Einstein-Podolsky-Rosen-Bohm gedankenexperiment, problems associated with state reduction and with nonlocal influences according to different interpretations of quantum mechanics, when attempts are made to apply these interpretations in the relativistic domain. We begin by considering the significance of retrodiction within four different interpretations of quantum mechanics, and show that three of these interpretations, if applied in a relativistic context, can lead to ambiguities in their description of a process. We consider ways of dealing with these ambiguities, in particular focussing on the “preferred frame” hypothesis. We then re-examine an argument involving nonlocal measurements which claimed that the preferred frame hypothesis is not tenable, and show that this argument does not in fact necessitate a rejection of the preferred frame. We then suggest that, to avoid confusion, the preferred frame could be extended to cover unitary interactions as well as state reductions. We conclude with a brief examination of a proposal that state reduction should take effect across the backward light cone of a measurement event.
Similar content being viewed by others
References
Y. Aharonov and D. Z. Albert,Phys. Rev. D 21, 3316 (1980).
Y. Aharonov and D. Z. Albert,Phys. Rev. D 24, 359 (1981).
K. E. Hellwig and K. Kraus,Phys. Rev. D 1, 566 (1970).
N. Bohr,Atomic Physics and Human Knowledge (Science Editions, New York, 1961).
P. A. M. Dirac,The Principles of Quantum Mechanics (Oxford University Press, London, 1958).
J. von Neumann,Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1955).
D. Bohm,Phys. Rev. 85, 166 (1952).
D. Bohm and B. J. Hiley,The Undivided Universe: An Ontological Interpretation of Quantum Mechanics (Routledge, London, 1993).
P. R. Holland,The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).
For a review, see R. Omnès,Rev. Mod. Phys. 64, 339 (1992).
See, for example, M. Gell-Mann, and J. B. Hartle, inProceedings of the 3rd International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, S. Kobayashiet al., eds. (Physical Society of Japan, Tokyo, 1990).
R. B. Griffiths,J. Stat. Phys. 36, 219 (1984).
See ref 8, Chap. 10.
A. Einstein, B. Podolsky, and N. Rosen,Phys. Rev. 47, 777 (1935); D. Bohm,Quantum Theory (Prentice-Hall, Englewood Cliffs, 1951), pp. 611–623.
R. B. Griffiths,Am. J. Phys. 55, 11 (1987).
R. B. Griffiths,Found. Phys. 23, 1601 (1993).
J. S. Bell,Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987).
See, for example, A. Aspect, J. Dalibard, and G. Roger,Phys. Rev. Lett. 49, 1804 (1982).
Y. Aharonov and D. Z. Albert,Phys. Rev. D 29, 228 (1984).
I. Prigogine,From Being to Becoming (Freeman, San Francisco, 1980), p. 207.
J. P. Vigier, “Nonlocal Quantum Potential Interpretations of Relativistic Action at a Distance in Many-Body Problems,” inOpen Questions in Quantum Physics, G. Tarozzi and A. van der Merwe, eds. (Reidel, Dordrecht, 1985).
P. Droz-Vincent,Phys. Rev. D 19, 702 (1979).
K. R. Popper,Quantum Theory and the Schism in Physics (Hutchinson, London, 1982).
A. Valentini,On the Pilot-Wave Theory of Classical, Quantum, and Subquantum Physics, PhD Thesis, International School for Advanced Studies, Trieste (1992).
G. J. Smith and R. Weingard,Found. Phys. 17, 149 (1987).
L. D. Landau and R. Peierls,Z. Phys. 69, 56 (1931).
Y. Aharonov, D. Z. Albert, and L. Vaidman,Phys. Rev. D 34, 1805 (1986).
S. Popescu and L. Vaidman,Phys. Rev. A 49, 4331 (1994).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cohen, O., Hiley, B.J. Retrodiction in quantum mechanics, preferred Lorentz frames, and nonlocal measurements. Found Phys 25, 1669–1698 (1995). https://doi.org/10.1007/BF02057882
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02057882