Frontiers of Nonequilibrium Statistical Physics pp 131-138 | Cite as

# How To Make Quantum Mechanics Look Like A Hidden-Variable Theory and Vice Versa

Chapter

## Abstract

Conventional quantum mechanics is a superb calculational tool. It has successfully solved mysteries ranging from macroscopic superconductivity^{1(a)} to the microscopic theory of the electron^{1(b)} and has provided deeper insight into the nature of the vacuum^{1(c)} on the one hand and the description of the nucleon^{1(d)} on the other. Whole new fields^{2(a)−2(b)} such as quantum optics and quantum electronics owe their very existence to this body of knowledge.

## Keywords

Quantum Mechanic Quantum Theory Hide Variable Quantum Distribution Polarization Correlation
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## References

- 1.(a) J. Bardeen, L. Cooper, and J. Schrieffer,
*Phys. Rev*. 108, 1175 (1957); (b) P. Dirac,*Quantum Mechanics*(Oxford University, London, 1935); (c) W. Lamb and R. Retherford, Phys. Rev. 72, 241 (1947); (d) see, for example, K. Huang,*Quarks, Leptons and Gauge Fields*(World Scientific, Singapore, 1982).MathSciNetADSzbMATHCrossRefGoogle Scholar - 2.(a)
*Quantum Optics and Electronics*, 1964 Les Houches Lectures, edited by C. DeWitt, A. Blandin, and C. Cohen- Tannoudji (Gordon and Breach, New York, 1965); (b) M. Lax, in*Brandeis University Summer Lectures*, edited by M. Chretien, S. Deser, and E. Gross (Gordon and Breach, New York, 1966); (c) H. Haken,*Handbuch Der Physik*(Springer, Berlin, 1920), Vol. 25/2C; (d) W. H. Louisell,*Quantum Statistical Properties of Radiation*(Wiley, New York, 1973); (e) R. Loudon,*The Quantum Theory of Light*(Oxford University, London, 1973); (f) M. Sargent, M. Scully, and W. Lamb,*Laser Physics*(Addison-Wesley, Reading, Mass., 1974).Google Scholar - 3.A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47,
*111*(1935). The present spin-y example is due to D. Bohm. In this regard B. Hiley quotes Dirac and FeynmanCrossRefGoogle Scholar - 4.F. Belinfante,
*A Survey of Hidden-Variable Theories*(Pergamon, New York, 1973); J. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).Google Scholar - 5.J. Bell, Rev. Mod. Phys. 38, 447 (1966).ADSzbMATHCrossRefGoogle Scholar
- 6.A good summary of experimental tests up to 1978 is given by Clauser and Shimony in Ref. 4. The recent work of Aspect is especially interesting in this regard, see A. Aspect, P. H. Grangier and G. Roger, Phys. Rev. Lett. 49, 91 (1982).Google Scholar
- 7.B. Hiley, New Sci. 6, 17 (1983).Google Scholar
- 8.See, for example, the review article by M. Hillery, R. O’Connell, M. Scully, and E. Wigner (unpublished).Google Scholar
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- 10.F. Belinfante, in Ref. 4, p. 279.Google Scholar
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- 12.See, for example, C. Cantrell and M. Scully, Phys. Rep. 43C, 499(1978).ADSCrossRefGoogle Scholar
- 13.The work of Belinfante referred to here actually involves photon polarization correlations rather than the spin correlations which we deal with. However, the two problems are holo- morphic and we present here the arguments couched in spin- y language. We emphasize however the intellectual content of the arguments is credited to Belinfante. In fact we have even trial to use his phraseology where appropriate in order to remain faithful to his logic.Google Scholar
- 14.See especially R. Glauber, in Ref. 2(a) and L. Mandel and E. Wolf, Rev. Mod. Phys. 32, 231 (1965).MathSciNetADSCrossRefGoogle Scholar
- 15.For a nice overview of the subject, see E. Hahn in
*NMR Grundlagen und Fortschritte*(Springer, Berlin), Vol. 13.Google Scholar - 16.A. Barut, P. Meystre, and M. Scully (unpublished).Google Scholar

## Copyright information

© Plenum Press, New York 1986