Let A 1 , A 2 , A 3 A 4 be four observables, the compatible observables among them being (A 1 , A 3 ), (A 1 , A 4 ), (A 2 , A 3 ), (A 2 , A 4 ). In order that the empirical data be reproducible by a quantum or a classical theory, the two-point correlation functions $$\{ C_{ij} = \left\langle {A_i A_j } \right\rangle :i,j a compatible pair\} $$ must necessarily satisfy $$|X_{13} X_{14} (...) - X_{23} X_{24} | \leqslant \left( {1 - X_{13} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - X_{14} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \left( {1 - X_{23} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - X_{24} ^2 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} (*)$$ where Xij=CijC ii −1/2 C jj −1/2 . In the case ofGaussian data, this inequality is alsosufficient; If (*) holds, there is a Gaussian joint distribution for A 1 , A 2 , A 3 , A 4 which reproduces the Gaussian data for compatible pairs. It follows that Bell's inequality is satisfied by all true-false propositions about the Gaussian data. A further consequence of the analysis is thatquantum Gaussian fields satisfy Bell's inequality for all true-false propositions aboutfield measurements.The maximum violation of (*) corresponds to Rastall's example in the case of two-valued observables. (shrink)

** The primary topic of this dissertation is the study of the relationships between parts and wholes as described by particular physical theories, namely generalized probability theories in a quasi-classical physics framework and non-relativistic quantum theory. ** A large part of this dissertation is devoted to understanding different aspects of four different kinds of correlations: local, partially-local, no-signaling and quantum mechanical correlations. Novel characteristics of these correlations have been used to study how they are related and how they can be (...) discerned via Bell-type inequalities that give non-trivial bounds on the strength of the correlations. ** The study of quantum correlations has also prompted us to study a) the multi-partite qubit state space with respect to its entanglement and separability characteristics, and b) the differing strength of the correlations in separable and entangled qubit states. Results include a novel classification of multipartite (partial) separability and entanglement, strong constraints on the monogamy of entanglement and of non-local correlations, and many new entanglement detection criteria that are directly experimentally accessible. ** Because of the generality of the investigation these results also have strong foundational as well as philosophical repercussions for the different sorts of physical theories as a whole; notably for the viability of hidden variable theories for quantum mechanics, for the possibility of doing experimental metaphysics, for the question of holism in physical theories, and for the classical vs. quantum dichotomy. (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)

The discussion of whether quantum theory is compatible with the locality idea that no causal influence can act outside the forward light cone has recently been tightly linked to the corresponding question for a much simpler model theory that enjoys all of the pertinent properties of quantum theory but is much easier to fully comprehend. It is shown here that, contrary to recent claims, the model theory is incompatible with the locality idea mentioned above. The logical structure of the argument, (...) which is similar to the one employed for quantum theory, is discussed. (shrink)