Questioning Nonlocality: An Operational Critique to Bell’s Theorem

Federico Laudisa

Douglas L. Hemmick, Asif M. Shakur

Paul G. Kwiat

Ghenadie N. Mardari

Euclidean theorems are indisputable in flat spaces, but do not hold in curved spaces. Likewise, Bell’s Theorem is true for jointly distributed variables in Kolmogorov probability spaces. Yet, quantum spin variables are not jointly distributed and cannot coexist in Kolmogorov spaces. They have different qualities and operate by different rules. Therefore, Bell’s Theorem does not entail that quantum theory is non-local. The question remains: what is the origin of quantum contextuality? Other theories (not quantum theory) need nonlocality or super-determinism to make similar predictions, because they cannot violate Bell-type inequalities, but why is quantum theory different? The answer is found in the analysis of quantum superposition, in the context of a much older debate about the ontology of linear wave superposition.

Abner Shimony

Section 5.1 considers the question, Why Was Bell the Discoverer of Bell's Theorem?, and proposes his moral character as an answer. Section 5.2 gives three reminiscences of encounters with Bell. Section 5.3 proposes that the nonlocality exhibited by Bell's Theorem and the Bell-inspired experiments is best understood in the framework of the pregeometry of Michael Heller and collaborators, which is based upon the noncommutative geometry of Alain Connes.

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.