Related papers: On Noncontextual, Non-Kolmogorovian Hidden Variabl…
We study hidden-variable models from quantum mechanics, and their abstractions in purely probabilistic and relational frameworks, by means of logics of dependence and independence, based on team semantics. We show that common desirable…
We compare the classical Kolmogorov and quantum probability models. We show that the gap between these model is not so huge as it was commonly believed. The main structures of quantum theory (interference of probabilities, Born's rule,…
We discuss quantum non-locality and contextuality using the notion of transition sets. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear…
This article contains a review of Nelson's analysis of Bell's theorem. It shows that Bell's inequalities can be violated with a theory of local random variables if one accepts that the outcomes of these variables are not predetermined prior…
According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…
We present a discrete model theory similar in structure to ordinary quantum mechanics, but based on a finite field instead of complex amplitudes. The interpretation of this theory involves only the "modal" concepts of possibility and…
The Kochen-Specker theorem, Bell inequalities, and several other tests that were designed to rule out hidden-variable theories, assume the existence of observables having infinitely sharp eigenvalues. A paradigmatic example is spin-1/2. It…
Beginning with the Bell theorem, cyclic systems of dichotomous random variables have been the object of many foundational findings in quantum mechanics. Here, we ask the question: if one chooses a cyclic system "at random" (uniformly within…
We have recently showed that it is possible to deal with collections of indistinguishable elementary particles (in the context of quantum mechanics) in a set-theoretical framework by using hidden variables, in a sense. In the present paper…
The precision with which we can measure operators that do not commute with conserved quantities is limited by the need to preserve the associated global symmetries. We show how to construct a local hidden-variable model that violates Bell…
Bell's theorem guarantees that no model based on local variables can reproduce quantum correlations. Also some models based on non-local variables, if subject to apparently "reasonable" constraints, may fail to reproduce quantum physics. In…
The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable…
The derivation of Bell inequalities for beables is well-known to require a "no-conspiracy" assumption. This assumption is widely accepted, the alternative being correlations between instrument settings and hidden beables. Two further…
Finding quantitative aspects of quantum phenomena which cannot be explained by any classical model has foundational importance for understanding the boundary between classical and quantum theory. It also has practical significance for…
The Kochen-Specker theorem states that noncontextual hidden variable models are inconsistent with the quantum predictions for every yes-no question on a qutrit, corresponding to every projector in three dimensions. It has been suggested [D.…
Einstein, Podolsky and Rosen (EPR) showed that it is possible to predict with certainty the value of a property without disturbing the object in question. In contrast, Quantum Mechanics (QM) holds that if different measurement setups cannot…
Bell nonlocality, the fact that local hidden variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental…
In this paper, we show that Erwin Schroedinger's generalization of the Einstein Podolsky Rosen argument can be connected to certain mathematical theorems - Gleason's and also Kochen and Specker's - in a manner analogous to the relation of…
According to a widespread view, the Bell theorem establishes the untenability of so-called 'local realism'. On the basis of this view, recent proposals by Leggett, Zeilinger and others have been developed according to which it can be proved…
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,…