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Nonlocality and conservation laws in hidden variable theories

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Abstract

It is shown that any hidden variable model that reproduces quantum mechanics for a single particle must either be nonlocal or violate conservation of momentum. This is established by deriving an inequality which must hold in any local, momentum-conserving hidden variable model for a modified form of the double-slit experiment. It is then shown that any hidden variable model that reproduces quantum mechanics must violate the inequality. The inconsistency between the classical and quantum views of the world is therefore demonstrated in a new way.

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References

  1. A. Einstein, B. Podolsky, and N. Rosen,Phys. Rev. 47, 777 (1935).

    Article  ADS  Google Scholar 

  2. J. Von Neumann,Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1955), pp. 323ff. The loophole in this proof (and in other proofs) exploited by Bohm's model has been discussed by Bell. See. J. S. Bell,Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 29.

    MATH  Google Scholar 

  3. L. de Broglie,Non-linear Wave Mechanics: A Causal Interpretation (Elsevier, Amsterdam, 1960).

    MATH  Google Scholar 

  4. D. Bohm,Phys. Rev. 85, 166 (1952).

    Article  ADS  MathSciNet  Google Scholar 

  5. D. A. Rice,Am. J. Phys. 65, 144 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  6. J. S. Bell,Physics 1, 195 (1964), reprinted in J. S. Bell,Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 14.

    Google Scholar 

  7. S. M. Tan, D. F. Walls, and M. J. Collett,Phys. Rev. Lett. 66, 252 (1991). See also B. J. Oliver and C. R. Stroud,Phys. Lett. A 135, 407 (1989), who derived essentially the same result except they did not useindependent oscillators.

    Article  ADS  Google Scholar 

  8. A. Peres,Phys. Rev. Lett. 74, 4571 (1995); L. Vaidman,Phys. Rev. Lett. 75, 2063 (1995); D. M. Greenberger, M. A. Horne, and A. Zeilinger,Phys. Rev. Lett. 75, 2064 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  9. L. Hardy,Phys Rev. Lett. 73, 2279 (1994).

    Article  ADS  Google Scholar 

  10. Quoted from M. L. G. Redhead,Incompleteness, Nonlocality, and Realism: a Prolegomenon to the Philosophy of Quantum Mechanics (Oxford University Press, Oxford, 1987), p. 82.

    MATH  Google Scholar 

  11. N. Bohr, inAlbert Einstein: Philosopher-Scientist, P. A. Schilpp, ed. (Opencourt, Evanston, 1949), p. 200; W. K. Wootters and W. H. Zurek,Phys. Rev. D 19, 473 (1979).

    Google Scholar 

  12. D. Bohm and B. J. Hiley,The Undivided Universe: An Ontological Interpretation of Quantum Theory (Routledge, London, 1993).

    Google Scholar 

  13. P. R. Holland,The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics (Cambridge University Press, Cambridge, 1993).

    Google Scholar 

  14. Ref., pp. 119–120.

    Google Scholar 

  15. Note that this does not contradict Ehrenfest's theorem. Ehrenfest's theorem shows that conservation of momentum holds for theexpectation value of momentum. It is still possible, in a hidden variable theory, for conservation of momentum at the hidden variables level to be violated, yet at the statistical level of many events for the expectation value of momentum to be conserved.

  16. Ref. 13, pp. 176ff.

    Google Scholar 

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Rice, D.A. Nonlocality and conservation laws in hidden variable theories. Found Phys 27, 1345–1353 (1997). https://doi.org/10.1007/BF02551516

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  • DOI: https://doi.org/10.1007/BF02551516

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