Critique of Home and Sengupta's derivation of a Bell inequality

Dipankar Home, S. Sengupta

Colin James

Andrew Elby

John S. Bell

a) Bell tries to formulate more explicitly a notion of “local causality”: correlations between physical events in different space-time regions should be explicable in terms of physical events in the overlap of the backward light cones. It is shown that ordinary relativistic quantum field theory is not locally causal in this sense, and cannot be embedded in a locally causal theory. b) Clauser, Home and Shimony criticize several steps in Bell's argument that any theory of local “beables” is incompatible with quantum mechanics. It is contended that the Clauser-Horne derivation of a Bell-type inequality circumvents his weak steps. The Clauser-Horne derivation must assume that there are no undetected correlations between choices of controllable variables in two space-like separated regions. Methodological considerations support this assumption. c) In response to criticism by Shimony, Home, and Clauser, Bell tries to clarify the argument of “The theory of local beables”, and to defend as permissible the hypothesis of free variables. d) Bell's reply to an earlier criticism by Shimony, Clauser, and Home is answered. The convergence of Bell's position towards theirs is noted.

Pierre A. Millette

M. R. Clover

By implicitly assuming that all possible Bell-measurements occur simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty Principle. This assumption is made in the original form of Bell's inequality, in Wigner's probability inequalities, and in the ``nonlocality without inequalities'' arguments. The introduction of time into derivations of these variants of Bell's theorem results in extra terms related to the time order of the measurements used in constructing correlation coefficients. Since the same locality assumptions are made in the Heisenberg-compliant derivations of this paper, only time-independent classical local hidden variable theories are forbidden by violations of the original Bell inequalities; time-dependent quantum local hidden variable theories can satisfy this new bound and agree with experiment. We further point out that factorizable wavefunctions have been used to describe some EPR experiments and can be used to describe others. These will generate local de Broglie-Bohm trajectories in the description of the data. This second, independent, line of argument also shows that violation of Bell's inequality is only evidence that Heisenberg's Uncertainty Principle cannot be ignored.