# On Hidden Variables and Quantum Mechanical Probabilities

Chapter

## Abstract

An argument, due originally to J. S. Bell, is somewhat simplified and made more specific. It deals primarily with a quantum mechanical system consisting of the spins of two spin-½ particles. It shows that a description of the quantum mechanical measurement of the spin components of these two particles by means of hidden parameters is impossible if we assume that the parameters determining the outcome of the measurement of the spin of each particle are independent of the direction in which we decide to measure the spin of the other particle. The mathematical reason for the impossibility is analyzed.

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## References

- 2.J. M. Jauch and C. Piron,
*Heiv. Phys. Acta***36**(1963), 827; S. B. Kochen and E. Specker,*J. Math. Mech*.**17**(1967), 59. D. Warrington, to appear shortly. This last paper, though based on Bells observation (Note 3), shares with Von Neumanns argument the necessity to consider a succession of many observations. A rather complete and critical review of the earlier literature was given by J. S. Bell,*Rev. Mod. Phys*.**38**(1966), 447; objections against the articles reviewed were articulated also by D. Bohm and J. Bub,*Rev. Mod. Phys*.**38**(1966), 453.Google Scholar - 3.J. S. Bell,
*Physics***1**(1965), 195. A more quantitative evaluation of Bells result, together with a proposal for an experimental test, was given by J. F. Clauser, M. A. Home, A. Shimony and R. A. Holt,*Phys. Rev. Letters***23**(1969), 880, and this writer is indebted to these authors for having called his attention to Bells article. See also D. Warrington, Note 2.Google Scholar

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