## Abstract

Bell’s Theorem is one of the most profound results in physics of the twentieth century. Not only does it have a significant impact on natural philosophy and on the true meaning of quantum mechanics, it also has stimulated important and practical new research in quantum optics. In 1972 at the CQ03 Rochester conference, in response to a number of disturbing issues and challenges then raised by Ed Jaynes concerning the foundations of quantum electrodynamics, I introduced the quantum optics community to Bell’s Theorem and a few of the associated mysteries manifest in quantum entanglement. Given the widespread belief that the foundations of quantum mechanics were then well understood, needless to say, my 1972 talks were then met with considerable skepticism. Eventually, however, the importance of Bell’s Theorem gained full acceptance, so that now it is discussed in many recent quantum mechanics and quantum optics textbooks. Similarly, my first experimental test (with Stuart Freedman in 1972) of the Bell-Clauser-Horne-Shimony-Holt prediction has since then been repeated and confirmed literally dozens of times, and that prediction now provides a standard quantitative measure of entanglement. Moreover, the fundamental ideas underlying Bell’s Theorem have been found to be sufficiently useful and important, that it is doubtful that the parallel conference ICQI-2001 would have occurred without them. This article recounts the important historical events behind the development of Bell’s Theorem.

## Keywords

Quantum Mechanic Hide Variable Coincidence Rate Optical Photon CHSH Inequality## Preview

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## References

- 1.J. F. Clauser and A. Shimony, Rep. Prog. Phys. (1978)
**41**1881–1927.ADSCrossRefGoogle Scholar - 2.
*Epistemological Letters*(Association Ferdinand Gonseth, Institut de la Methode, Case Postale 1081, CH-2501, Bienne.) This newspaper was somewhat unique for its time, in that it openly proclaimed that the usual stigma against hidden-variable theories, and the like, was to be absent for publications within it.Google Scholar - 3.J. S. Bell,
*Speakable and unspeakable in quantum mechanics*, (Cambridge Univ. Press, Cambridge, 1987).zbMATHGoogle Scholar - 5.Max Jammer, in Sect. 4.2 of his book,
*The Conceptual Development of Quantum Mechancs*, (McGraw-Hill, New York, 1966) argues that Bohr’s denial of realism was in response to his being strongly influenced by the contemporary philosophers, Kierkegaard and Høffding.Google Scholar - 6.J. von Neumann,
*Mathematische Grundlagen der Quantenmechanic*, (Springer-Verlag, 1932). English translation:*Mathematical Foundations of Quantum Mechanics*, (Princeton University Press, 1955).Google Scholar - 7.A. Einstein, B. Podolsky, and N. Rosen (1935), Phys. Rev.
**47**, 777–80.ADSzbMATHCrossRefGoogle Scholar - 8.
- 10.E. Schrödinger, Proc. Camb. Phil. Soc.
**31**, 555 (1935).ADSCrossRefGoogle Scholar - 11.W. H. Furry, Phys. Rev.
**49**, 393 (1936); Phys. Rev.**49**, 476 (1936). The second paper emphasizes the differences between his and Schrödinger’s views of this result.ADSzbMATHCrossRefGoogle Scholar - 13.A. H. Compton and A. W. Simon, Phys. Rev.
**26**, 289–299 (1925). This experiment is a more precise repetition of an earlier experiment by W. Bothe and H. Geiger, Zeits. für Physik,**26**, 44 (1924). Schrödinger, however, subsequently found a semi-classical explanation of this experiment, and went on to propose an important relevant experiment. See “Splitting photons?”.ADSCrossRefGoogle Scholar - 14.N. Bohr, H. A. Kramers, and J. C. Slater, Phil. Mag. [6]
**47**, 785–802 (1924).Google Scholar - 15.J. S. Bell,
*Phys. World*, Aug. 33–40 (1990).Google Scholar - 16.D. Bohm,
*Quantum Theory*, (Prentis Hall, Englewood Cliffs, NJ, 1950).Google Scholar - 17.D. Bohm and Y. Aharonov, Phys. Rev.
**108**, 1070 (1957).MathSciNetADSCrossRefGoogle Scholar - 18.C. S. Wu and I. Shaknov, Phys. Rev.
**77**, 136 (1950).ADSCrossRefGoogle Scholar - 19.D. Bohm, Phys. Rev.
**85**, 169 (1952). See also, D. Bohm and 1. P. Vigier, Phys. Rev.**96**, 208 (1954). Fortunately, this work was published before the APS policy had been formulated. Presumably, it would have not passed muster under that policy.ADSGoogle Scholar - 20.L. deBroglie,
*Nonlinear Wave Mechanics*, (Elsevier, Amsterdam, 1960);*Ondes Electromagnetiques et Photons*, (Gauthier-Villars, Paris, 1968); and*Introduction to the Vigier Theory of Elementary Particles*, (Elsevier, Amsterdam, 1963).Google Scholar - 21.J. S. Bell, Revs. Mod. Phys.
**38**, 447 (1965).ADSCrossRefGoogle Scholar - 23.J. S. Bell, Physics,
**1**, 195 (1964).Google Scholar - 24.John Bell confesses in the preface to his book,
*Speakable and unspeakale in quantum mechanics*, to being similarly enamored with these features of pilot-wave theories.Google Scholar - 25.C. A. Kocher and E. D. Commins, Phys. Rev. Lett.,
**18**, 575 (1969).ADSCrossRefGoogle Scholar - 26.According to David Wick [
*The Infamous Boundary — Seven Decades of Controversy in Quantum Physics*, Birkhäuser, Boston, 1995], my 1969 letter was the first response to his 1964 paper that Bell had receivedCrossRefGoogle Scholar - 27.J. F. Clauser, Bull. Amer. Phys. Soc.
**14**, 578 (1969).Google Scholar - 29.J, F, Clauser, M. A. Home, A. Shimony, and R. A. Holt, Phys. Rev. Lett.,
**23**, 880 (1969). This paper first coined the term “Bell’s Theorem”.ADSCrossRefGoogle Scholar - 30.S. J. Freedman and J. F. Clauser, Phys. Rev. Lett.
**28**, 938 (1972).ADSCrossRefGoogle Scholar - 31.J. F. Clauser, Phys. Rev. Lett.,
**36**, 1223, (1976).ADSCrossRefGoogle Scholar - 32.J. F. Clauser, Il Nuovo Cimento,
**33B**, 740 (1976).ADSGoogle Scholar - 33.E. S. Fry and R. C. Thompson, Phys. Rev. Lett.
**37**, 465 (1976).ADSCrossRefGoogle Scholar - 34.J. F. Clauser and M. A. Home, Phys. Rev. D
**10**, 526–535 (1974).ADSCrossRefGoogle Scholar - 35.Shortly following CHSH, Bell did extend the range of applicability of the CHSH result further to include the effects of additional hidden variables in each apparatus. [J. S. Bell,
*Introduction to the hidden-variables question*, in Foundations of Quantum Mechanics,*Proceedings of the International School of Physics, “Enrico Fermi”*, B. d’ Espagnat, ed. (Academic Press, New York, 1971), pp. 170–194]. However, in doing so he adds no new premises to Bell’ s Theorem in this new derivation, and similarly explicitly assumes determinism to hold.Google Scholar - 36.J. S. Bell, Science,
**177**, 880 (1972).CrossRefGoogle Scholar - 40.E. S. Fry, T. Walther, and S. Li, Phys. Rev. A,
**52**, 4381–4395 (1995).MathSciNetADSCrossRefGoogle Scholar - 43.A. Aspect, P. Grangier and G. Roger, Phys. Rev. Lett.,
**49**, 91 (1982).ADSCrossRefGoogle Scholar - 44.J.S. Bell,
*Communication at the 6th Gift Conf. Jaca, June 1975*, Res Th 2053-CERN. Perhaps, Bell’s reason for not publishing this result in 1975 is that he may have been afraid that doing so might warrant his being branded a quack, given the then existing stigma against such work.Google Scholar - 46.See, J. S. Bell, A. Shimony, M. A. Home, and J. F. Clauser, Dialectica,
**39**, pp.85–110, (1985), for a republication of this interchange that also includes Bell’s “Beablesrd paper.MathSciNetCrossRefGoogle Scholar - 47.See also, A. Shimony,
*Search for a Naturalistic World*, (Cambridge Univ. Press, Cambridge, 1993). More recently, the importance of these concepts was independently rediscovered by J. Jarrett [Noûs,**18**,569 (1984)].CrossRefGoogle Scholar - 48.W. E. Lamb and Scully, in
*Polarization: Matière et Rayonnement*, (Presses Universitaires de France, Paris, 1969), edited by Société Française de de Physique.Google Scholar - 49.P. A. Franken, in
*Atomic Physics: Pooceedings of the 1st International Conference on Atomic Physics*, (Plenum, New York, 1968) V. Hughes*et al*. eds., p.377.Google Scholar - 52.E, T. Jaynes and Cummings, Proc. IEEE
**51**, 89 (1963); C. R. Stroud, Jr. and E. T. Jaynes, Phys. Rev. A**1**,106 (1970); M. D. Crisp and E. T. Jaynes, Phys. Rev.**179**, 1253 (1969);**185**, 2046 (1969). See also, P. A. Nesbet, Phys. Rev. A**4**, 259 (1971).CrossRefGoogle Scholar - 53.J. F. Clauser, Phys. Rev. A,
**6**, 49 (1972).ADSCrossRefGoogle Scholar - 54.The proceedings of this conference are in
*Coherence and Quantum Optics*, (Plenum Press, New York, 1973) L. Mandel and E. Wolf, eds.Google Scholar - 57.J. M. Jauch and F. Rohrlich,
*The Theory of Photons and Electrons*(Addison-Wesley, Reading, MA, 1955).Google Scholar - 58.J. M. Jauch,
*Dialogue on the Question ARE QUANTA REAL?*(Univ. of Geneva, preprint, 1971).Google Scholar - 59.E. Schrödinger, Physikalische Zeits.
**23**, 301–303 (1922); Die Naturwissenschaften**12**, 720-724 (1924); Il Nuovo Cimento**9**,162-170 (1958).Google Scholar - 60.A. Ádám, L. Jánnosy and P. Varga, Acta Phys. Hung.,
**4**, 301 (1955); Ann. Physik,**16**, 408, (1956).CrossRefGoogle Scholar - 62.J. F. Clauser, Phys. Rev. D,
**9**, 853 (1974).ADSCrossRefGoogle Scholar - 63.P. Grangier, G. Roger, and A. Aspect, Europhys. Lett.,
**20**, 1061 (1986).Google Scholar - 64.A. Aspect, J. Dalibard and G. Roger, Phys. Rev. Lett.,
**49**, 1804 (1982).MathSciNetADSCrossRefGoogle Scholar