Quantum Mechanics, Hidden Variables and Quantum Logic

Roberto Giuntini

Jeffrey Bub

Donald Hockney

Jarosław Pykacz, Emilio Santos

Various impossibility proofs for hidden variables theories produced within the quantum logic approach are analyzed. A very general form of n-term Bell-type inequalities is given. From these inequalities a new impossibly proof for hidden variables theories able to reproduce all numerical results of quantum mechanics follows.

Emilio Santos

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.

Hrvoje Nikolić

We argue that it is logically possible to have a sort of both reality and locality in quantum mechanics. To demonstrate this, we construct a new quantitative model of hidden variables (HV's), dubbed solipsistic HV's, that interpolates between the orthodox no-HV interpretation and nonlocal Bohmian interpretation. In this model, the deterministic point-particle trajectories are associated only with the essential degrees of freedom of the observer, and not with the observed objects. In contrast with Bohmian HV's, nonlocality in solipsistic HV's can be substantially reduced down to microscopic distances inside the observer. Even if such HV's may look philosophically unappealing to many, the mere fact that they are logically possible deserves attention.