Abstract
We make use of natural induction to propose, following John Ju Sakurai, a generalization of Bell's inequality for two spin s=n/2(n=1,2,...) particle systems in a singlet state. We have found that for any finite integer or half-integer spin Bell's inequality is violated when the terms in the inequality are calculated from a quantum mechanical point of view. In the final expression for this inequality the two members therein are expressed in terms of a single parameter θ. Violation occurs for θ in some interval of the form (α,π/2) where α parameter becomes closer and closer to π/2, as the spin grows, that is, the greater the spin number the size of the interval in which violation occurs diminishes to zero. Bell's inequality is a relationship among observables that discriminates between Einstein's locality principle and the non-local point of view of orthodox quantum mechanics. So our conclusion may also be stated by saying that for large spin numbers the non-local and local points of view agree.
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References
A. Einstein, B. Podolsky, and N. Rosen, “Can quantum mechanical description of physical reality be considered complete?, ” Phys. Rev. 47, 777-780 (1935).
K. Gustafson, “Bell's inequalities and the Accardi–Gustafson inequality, ” May 3, 2002 (arXiv:quant-ph/0205013, 15 pp.).
J. S. Bell, “On the Einstein–Podolsky–Rosen paradox, ” Physics 1, 195-200 (1964).
J. J. Sakurai, Modern Quantum Mechanics, San Fu Tuan, ed. (Benjamin/Cummings, 1993).
E. P. Wigner, “Quantum corrections for thermodynamical equilibrium, ” Phys. Rev. 40, 749-760 (1932).
D. Bohm, Quantum Theory (Prentice–Hall, Englewood Cliffs, NJ, 1951).
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González-Robles, V.M. About a Generalization of Bell's Inequality. Foundations of Physics 33, 839–853 (2003). https://doi.org/10.1023/A:1025605209182
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DOI: https://doi.org/10.1023/A:1025605209182