Bell’s arguments (Bell, 1964 and Bell, 1971) against local hidden variable theories proceed by means of inequalities; it is noted in (Koç, 1992) that in these arguments Bell does not consider the geometrical (or, algebraic) properties of the quantum mechanical correlation function (for a system of spin-1/2 particles in the singlet state). It is shown in (Koç, 1992) that, due to the geometry (or, algebraic properties) of the quantum mechanical correlation function, Bell’s arguments in (Bell, 1964 and Bell, 1971) are inconclusive. In addition to this, it is asserted in (Koç, forthcoming) that Wigner’s argument (Wigner, 1970) against local hidden variable theories is similarly inconclusive because of the geometrical (or, algebraic) properties of the quantum mechanical probability functions (for a system of spin-1/2 particles in the singlet state).
Bell, J. S. ‘‘On the Einstein-Podolsky-Rosen Paradox’’, Physics 1 (1964): 195.
Bell, J. S. ‘‘Introduction to the Hidden Variable Question’’ in B. d’Espagnat, ed., Foundations of Quantum Mechanics. Academic Press, 1971.
Koç, Y., ‘‘The Local Expectation Value Function and Bell’s Inequalities’’, Il Nuovo Cimento 107B (1992): 961-971.
Koç, Y. , ‘‘Wigner’s Inequality, Quantum Mechanical Probability Functions and Hidden Variable Theories’’ forthcoming in Il Nuovo Cimento B.
Wigner, E. P., ‘‘On Hidden Variables and Quantum Mechanical Probabilities’’, Amer. J. Phys. 38 (1970): 1005-1009.