In the conventional approach to quantum mechanics, indeterminism is an axiom and nonlocality is a theorem. We consider inverting the logical order, making nonlocality an axiom and indeterminism a theorem. Nonlocal “superquantum” correlations, preserving relativistic causality, can violate the CHSH inequality more strongly than any quantum correlations.

This book is an introduction to finite model theory which stresses the computer science origins of the area. In addition to presenting the main techniques for analyzing logics over finite models, the book deals extensively with applications in databases, complexity theory, and formal languages, as well as other branches of computer science. It covers Ehrenfeucht-Fraïssé games, locality-based techniques, complexity analysis of logics, including the basics of descriptive complexity, second-order logic and its fragments, connections with finite automata, fixed point logics, finite (...) variable logics, zero-one laws, and embedded finite models, and gives a brief tour of recently discovered applications of finite model theory. This book can be used both as an introduction to the subject, suitable for a one- or two-semester graduate course, or as reference for researchers who apply techniques from logic in computer science. (shrink)

Instead of the usual asymptotic passage from quantum mechanics to classical mechanics when a parameter tended to infinity, a sharp boundary is obtained for the domain of existence of classical reality. The last is treated as separable empirical reality following d'Espagnat, described by a mathematical superstructure over quantum dynamics for the universal wave function. Being empirical, this reality is constructed in terms of both fundamental notions and characteristics of observers. It is presupposed that considered observers perceive the world as a (...) system of collective degrees of freedom that are inherently dissipative because of interaction with thermal degrees of freedom. Relevant problems of foundation of statistical physics are considered. A feasible example is given of a macroscopic system not admitting such classical reality.The article contains a concise survey of some relevant domains: quantum and classical Bell-type inequalities; universal wave function; approaches to quantum description of macroscopic world, with emphasis on dissipation; spontaneous reduction models; experimental tests of the universal validity of the quantum theory. (shrink)

I analyze a number of the quantum no-signalling proofs (Ghirardi et al. 1980, Bussey 1982, Jordan 1983, Shimony 1985, Redhead 1987, Eberhard and Ross 1989, Sherer and Busch 1993). These purport to show that the EPR correlations cannot be exploited for transmitting signals, i.e., are not causal. First, I show that these proofs can be mathematically unified; they are disguised versions of a single theorem. Second, I argue that these proofs are circular. The essential theorem relies upon the tensor product (...) representation for combined systems, which has no physical basis in the von Neumann axioms. Historically, the construction of this representation scheme by von Neumann and Weyl built no-signalling assumptions into the quantum theory. Signalling between the wings of the EPR-Bell experiments is unlikely but is not ruled out empirically by the class of proofs considered. (shrink)