Proceedings of the Conference Foundations of Probability and Physics : Växjö, Sweden, 25 November-1 December, 2000

In this volume, leading experts in experimental as well as theoretical physics (both classical and quantum) and probability theory give their views on many intriguing (and still mysterious) problems regarding the probabilistic foundations of physics. The problems discussed during the conference include Einstein-Podolsky-Rosen paradox, Bell's inequality, realism, nonlocality, role of Kolmogorov model of probability theory in quantum physics, von Mises frequency theory, quantum information, computation, "quantum effects" in classical physics. Contents: Locality and Bell's Inequality (L Accardi & 2 Interpretations of Probability3 The Axioms of Probability; 4 Probability in Quantum Mechanics; 5 Conclusions; References; Forcing Discretization and Determination in Quantum History Theories; 1 Introduction; 2 Outcome determination via contextual models; 3 Unitary ortho- and projective structure; 4 Representing quantum history theory; 5 Further discussion; Acknowledgments; References; Interpretations of Quantum Mechanics and Interpretations of Violation of Bell's Inequality; 1 Realist and empiricist interpretations of quantum mechanics; 2 EPR experiments and Bell experiments 11 Bell's inequalities and the chamaleon effect12 Physical implausibility of Bell's argument; 13 The role of the single probability space in CHSH's proof; 14 The role of the counterfactual argument in CHSH's proof; 15 Physical difference between the CHSH's and the original Bell's inequalities; References; Refutation of Bell's Theorem; 1 Introduction; 2 The EPRB gedanken experiment; 3 The 'CHSH' function; 4 Strongly objective interpretation; 5 Weakly objective interpretation; 6 Conclusion; References; Probability Conservation and the State Determination Problem; 1 Introduction 2 Conservation of Probability3 Determination of the phase function; 4 Validity and range of applicability; 5 Evolution of a Gaussian Wave Packet; 6 Operational Issues; Acknowledgments; References; Extrinsic and Intrinsic Irreversibility in Probabilistic Dynamical Laws; 1 Introduction; 2 Ontic and epistemic descriptions; 3 Breaking Time-Reversal Symmetry: Extrinsic Irreversibility; 4 Breaking Time-Reversal Symmetry: Intrinsic Irreversibility; 5 Summary and Open Questions; Acknowledgments; References; Interpretations of Probability and Quantum Theory; 1 Introduction Foreword; Contents; Preface; Locality and Bell's Inequality; 1 Inequalities among numbers; 2 The Bell inequality; 3 Implications of the Bell's inequalities for the singlet correlations; 4 Bell on the meaning of Bell's inequality; 5 Critique of Bell's ""vital assumption""; 6 The role of the counterfactual argument in Bell's proof; 7 Proofs of Bell's inequality based on counting arguments; 8 The quantum probabilistic analysis; 9 The realism of ballot boxes and the corresponding statistics; 10 The realism of chameleons and the corresponding statistics 3 Bell's inequality in quantum mechanics4 Bell's inequality in stochastic and deterministic hidden-variables theories; 5 Analogy between thermodynamics and quantum mechanics; 6 Conclusions; References; Discrete Hessians in Study of Quantum Statistical Systems: Complex Ginibre Ensemble; 1 Introduction; 2 The Ginibre ensembles; Acknowledgements; References; Some Remarks on Hardy Functions Associated with Dirichlet Series; 1 Introduction; 2 ""Hardyfication"" of Dirichlet series; 3 Factorization of n; 4 Applications; References In this section we summarize some elementary inequalities among numbers, which correspond to different forms of the Bell inequality one meets in the literature. Ensemble Probabilistic Equilibrium and Non-Equilibrium Thermodynamics without the Thermodynamic Limit