## Proceedings of the Conference Foundations of Probability and Physics: Vaxjo, Sweden, 25 November-1 December 2000In 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 EinsteinOCoPodolskyOCoRosen paradox, Bell's inequality, realism, nonlocality, role of Kolmogorov model of probability theory in quantum physics, von Mises frequency theory, quantum information, computation, OC quantum effectsOCO in classical physics. Contents: Locality and Bell's Inequality (L Accardi & M Regoli); Refutation of Bell's Theorem (G Adenier); Forcing Discretization and Determination in Quantum History Theories (B Coecke); Some Remarks on Hardy Functions Associated with Dirichlet Series (W Ehm); Ensemble Probabilistic Equilibrium and Non-Equilibrium Thermodynamics without the Thermodynamic Limit (D H E Gross); An Approach to Quantum Probability (S Gudder); Innovation Approach to Stochastic Processes and Quantum Dynamics (T Hida); Origin of Quantum Probabilities (A Khrennikov); OC ComplementarityOCO or Schizophrenia: Is Probability in Quantum Mechanics Information or Onta? (A F Kracklauer); A Probabilistic Inequality for the KochenOCoSpecker Paradox (J-A Larsson); Quantum Stochastics. The New Approach to the Description of Quantum Measurements (E Loubenets); Is Random Event a Core Question? Some Remarks and a Proposal (P Rocchi); Quantum Cryptography in Space and Bell's Theorem (I Volovich); and other papers. Readership: Graduate students and researchers in quantum physics, mathematical physics, theoretical physics, stochastic processes, and probability & statistics." |

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### Contents

Refutation of Bells Theorem | 29 |

Extrinsic and Intrinsic Irreversibility in Probabilistic Dynamical Laws | 50 |

Interpretations of Probability and Quantum Theory | 71 |

Forcing Discretization and Determination in Quantum History | 85 |

Complex | 115 |

Ensemble Probabilistic Equilibrium and NonEquilibrium | 131 |

An Approach to Quantum Probability | 147 |

Innovation Approach to Stochastic Processes and Quantum | 161 |

Is Probability in Quantum | 219 |

A Probabilistic Inequality for the KochenSpecker Paradox | 236 |

Abstract Models of Probability | 257 |

Quantum KSystems and their Abelian Models | 274 |

Scattering in Quantum Tubes | 303 |

Is Random Event the Core Question? Some Remarks and a Proposal | 321 |

Constructive Foundations of Randomness | 337 |

Structure of Probabilistic Information and Quantum Laws | 350 |

Origin of Quantum Probabilities | 180 |

Nonconventional Viewpoint to Elements of Physical Reality Based | 201 |

Quantum Cryptography in Space and Bells Theorem | 364 |

### Common terms and phrases

abelian model algebra algorithm analysis approach assumption axioms Bell Bell experiments Bell's inequality Bell's theorem CHSH classical commute complex condition consider context correlation corresponding defined definition denote density derived described deterministic dynamical entropy elements ensemble epistemic equation ergodic event evolution example exists expectation value experiments finite formalism given hidden variables Hilbert space history theories interpretations of probability K-system Khrennikov Kolmogorov linear macroscopic macrostate Math mathematical measurement results microstate observables obtain ontic operator outcomes p-adic parameter particle pairs phase space Phys physical reality possible probabilistic rule probability distribution probability set probability theory problem proof properties quantum measurement quantum mechanics quantum probabilistic quantum probability quantum system quantum theory random variables rational numbers realistic relation relative frequencies representation respect Schrodinger semigroup sequence spin statistical ensemble statistical stabilization stochastic process structure subalgebra thermodynamics topology transformation vector wave function weakly objective white noise zero

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Page 7 - But on one supposition we should, in my opinion, absolutely hold fast: the real factual situation of the system 52 is independent of what is done with the system Si, which is spatially separated from the former.

Page 7 - In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote.

Page 7 - On leave of absence from SLAC and CERN 196 JS BELL Vol. 1, No. 3 A(l, A) = ±1, B(l, A) = ±1. (1) The vital assumption [2] is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on...