Bell's theorem and an explicit stochastic local hidden-variable model

Luis de la Peña, Ana Marı́a Cetto, Thomas A. Brody

Parker Emmerson

Bell’s theorem presents a fundamental limit on the correlations achievable by any local hidden variable theory, seemingly precluding such models from reproducing quantum mechanical predictions. In this paper, we introduce a local hidden variable model based on phenomenological velocity and curvature operator techniques. By constructing a mathematical framework that maintains locality and realism, we demonstrate that it is possible to reproduce the quantum mechanical correlation functions that violate Bell’s inequalities. This challenges the conventional understanding imposed by Bell’s theorem and suggests the need for a re-examination of the foundational assumptions in quantum mechanics.

Louis Vervoort

Usually the 'hidden variables' of Bell's theorem are supposed to describe the pair of Bell particles. Here a semantic shift is proposed, namely to attach the hidden variables to a stochastic medium or field in which the particles move. It appears that under certain conditions one of the premises of Bell's theorem, namely 'measurement independence', is not satisfied for such 'background-based' theories, even if these only involve local interactions. Such theories therefore do not fall under the restriction of Bell's no-go theorem. A simple version of such background-based models are Ising models, which we investigate here in the classical and quantum regime. We also propose to test background-based models by a straightforward extension of existing experiments. The present version corrects an error in the preceding version.

H. E. Andås

Geoffrey Paul Hellman

Virendra Singh

We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and then analyse it's weakness in terms of Bell's explicit hidden variable model of spin one-half particles. We next discuss Gleason's theorem and Kochen-Specker theorem and bring out the troublems with non contextual hidden variable theories. An important role is played by Einstein locality in the discussion of hidden variable theories as was first brought out by Einstein, Podolsky and Rosen. We elaborate it's various implications such as Bell's theorem in terms of Bell's inequalities as well as later work in which Bell's theorem follows without using inequalities.