INTRODUCTION Computer scientists should have a knowledge of abstract statistical thermodynamics. First, computer systems are dynamical systems, much like physical systems, and therefore an important first step in their characterization is in finding properties and parameters that are constant over time (i.e., constants of motion). Second, statistical thermodynamics successfully reduces macroscopic properties of a system to the statistical behavior of large numbers of microscopic processes. As computer systems become large assemblages of small components, an explanation of their macroscopic behavior may also be obtained as the aggregate statistical behavior of its component parts. If not, the elegance of the statistical thermodynamical approach can at least provide inspiration for new classes of models. 1 Third, the components of computer systems are approaching the same size as the microscopic pr

Hidden-variable models of quantum mechanics (QM) are complete descriptions of quantum phenomena. These models have been analyzed under conditions such as locality (Bell [1, 1964]) and non-contextuality (Kochen-Specker [20, 1967]). We give a uniform presentation of six underlying properties that can be asked of hidden-variable models and show all the relationships among them (as depicted in Figure 1.1). Two positive existence theorems are given which show that hidden-variable models of certain types always exist. We follow this with a unified treatment of the “no-go ” theorems of Einstein-Podolsky-Rosen [15, 1935], Bell [1, 1964], and Kochen-Specker [20, 1967]. Within our six-property classification scheme, we are able to give a complete picture of hidden-variable models.

We examine the prevalent use of the phrase “local realism ” in the context of Bell’s Theorem and associated experiments, with a focus on the question: what exactly is the ‘realism ’ in ‘local realism ’ supposed to mean? Carefully surveying several possible meanings, we argue that all of them are flawed in one way or another as attempts to point out a second premise (in addition to locality) on which the Bell inequalities rest, and (hence) which might be rejected in the face of empirical data violating the inequalities. We thus suggest that the phrase ‘local realism’ should be banned from future discussions of these issues, and urge physicists to revisit the foundational questions behind Bell’s Theorem. KEY WORDS: quantum mechanics; local realism; Bell’s theorem; EPR; quantum non-locality

Hidden-variable models of quantum mechanics (QM) are complete descriptions of quantum phenomena. These models have been analyzed under conditions such as locality (Bell [1, 1964]) and non-contextuality (Kochen-Specker [20, 1967]). We give a uniform presentation of six underlying properties that can be asked of hidden-variable models and show all the relationships among them (as depicted in Figure 1.1). Two positive existence theorems are given which show that hidden-variable models of certain types always exist. We follow this with a unified treatment of the “no-go ” theorems of Einstein-Podolsky-Rosen [15, 1935], Bell [1, 1964], and Kochen-Specker [20, 1967]. Within our six-property classification scheme, we are able to give a complete picture of hidden-variable models. 1

Quantum-like formalism for cognitive measurements

A very simple proof of Bell’s theorem is presented, in which neither the assumption that there is a well-defined space of complete states λ of the particle pair and well-defined probability distribution ρ(λ) over this space nor the use of counterfactuals is necessary.