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We discuss how to embed quantum nonlocality in an approximately classical spacetime background, a question which must be answered irrespective of any underlying microscopic theory of spacetime. We argue that, in deterministic…

We apply the machinery of projection lattices and von Neumann algebras to analyze the question of how modal interpretations can (and do) circumvent von Neumann's infamous 'no-hidden-variables' theorem.

Noncommuting observables cannot be simultaneously measured, however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint…

We consider probabilistic systems with hidden state and unobservable transitions, an extension of Hidden Markov Models (HMMs) that in particular admits unobservable {\epsilon}-transitions (also called null transitions), allowing state…

We adapt the axioms of the quantum mechanics to the quantum Minkowski space-time coordinates and their transformations under the quantum Lorentz group to show how we can formulate the noncommutative special relativity and its quantum…

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…

We prove that all deterministic hidden-variables theories, that reproduce quantum theory for a 'quantum equilibrium' distribution of hidden variables, predict the existence of instantaneous signals at the statistical level for hypothetical…

No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical…

Bell's theorem rests on the following fundamental condition for a local system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a and b are the outcomes respectively for measurements alpha on one side, and beta on the…

In this work, we extend the idea of Quantum Markov chains [S. Gudder. Quantum Markov chains. J. Math. Phys., 49(7), 2008] in order to propose Quantum Hidden Markov Models (QHMMs). For that, we use the notions of Transition Operation…

We introduce for a general correlation scenario a new simulation model, a local quasi hidden variable (LqHV) model, where locality and the measure-theoretic structure inherent to an LHV model are preserved but positivity of a simulation…

Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…

Efforts to construct deeper, realistic, level of physical description, in which individual systems have, like in classical physics, preexisting properties revealed by measurements are known as hidden-variable programs. Demonstrations that a…

An hidden variable (hv) theory is a theory that allows globally dispersion free ensembles. We demonstrate that the Phase Space formulation of Quantum Mechanics (QM) is an hv theory with the position q, and momentum p as the hv. Comparing…

The puzzling properties of quantum mechanics, wave-particle duality, entanglement and superposition, were dissected experimentally at past decades. However, hidden-variable (HV) models, based on three classical assumptions of wave-particle…

We demonstrate how to construct a lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories. The covariant theory that we propose employs a multi-time formalism and a…

Despite claims that Bell's inequalities are based on the Einstein locality condition, or equivalent, all derivations make an identical mathematical assumption: that local hidden-variable theories produce a set of positive-definite…

Bell's theorem proves only that hidden variables evolving in true physical time can't exist; still the theorem's meaning is usually interpreted intolerably wide. The concept of hidden time (and, in general, hidden space-time) is introduced.…

We present a local-hidden-variable model for positive-operator-valued measurements (an LHVPOV model) on a class of entangled generalized Werner states, thus demonstrating that such measurements do not always violate a Bell-type inequality.…

Quantum trajectory theories have not fully reconciled discrete quantum jumps with continuous unitary evolution. We address this challenge by developing a hidden variable formulation that reveals hidden correlations in individual trials. We…