Related papers: Von Neumann's 'No Hidden Variables' Proof: A Re-Ap…
Most of the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory. We show that these proofs contain mathematical steps that cannot be reconciled with the Kolmogorov axioms. Specifically we demonstrate…
By implicitly assuming that all measurements occur simultaneously, Bell's Theorem only applied to local theories that violated Heisenberg's Uncertainty Principle. By explicitly introducing time into our derivation of Bell's theorem, an…
Loophole-free violations of Bell inequalities imply that at least one of the assumptions behind local hidden-variable theories must fail. Here, we show that, if only one fails, then it has to fail completely, therefore excluding models that…
While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and non-locality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the…
A local hidden variable model with pseudo-functional density function restricted to a binary probability event space is demonstrated to be able to reproduce the quantum correlation in an Einstein Podolsky Rosen Bohm and Aharonov type of…
The hidden-variables premise is shown to be equivalent to the existence of generic filters for algebras of commuting propositions and for certain more general propositional systems. The significance of this equivalence is interpreted in…
By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by 't Hooft. We view these…
This paper addresses arguments that "separability" is an assumption of Bell's theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as "holism") will allow us to restore a…
I review the relation of the Bell inequalities - characteristic of (classical) probabilities defined on Boolean logics - with noncontextual and local hidden variables theories of quantum mechanics and with quantum information.
From its earliest days nearly a century ago, quantum mechanics has proven itself to be a tremendously accurate yet intellectually unsatisfying theory to many. Not the least of its problems is that it is a theory about the results of…
A recent proposal for a superdeterministic account of quantum mechanics, named Invariant-set theory, appears to bring ideas from several diverse fields like chaos theory, number theory and dynamical systems to quantum foundations. However,…
Recently, Roger Colbeck and Renato Renner (C&R) have claimed that '[n]o extension of quantum theory can have improved predictive power'. If correct, this is a spectacular impossibility theorem for hidden variable theories, which is more…
It is generally assumed that {\em local realism} represented by a noncontextual and local hidden-variables model in $d=4$ such as the one used by Bell always gives rise to CHSH inequality $|\langle B\rangle|\leq 2$. On the other hand, the…
A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-like proof involving just two observers. On one hand, this new approach allows us to derive…
Selection artefacts are common in science. A method of selecting samples from a larger population may produce bias, in either direction. It may induce correlations between variables independent in the full population, or mask correlations…
Three classes of local hidden-variable models that violate both Bell and Leggett inequalities are presented. The models, however, do not reproduce the quantum mechanical predictions, hence they are experimentally testable. It is concluded…
It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping…
The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long lasting debate. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical…
We show that the projection postulate plays a crucial role in the discussion on the so called "quantum nonlocality", in particular in the EPR-argument. We stress that the original von Neumann projection postulate was crucially modified by…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…