Foundations of Probability and Physics: Proceedings of the Conference PDF
Preview Foundations of Probability and Physics: Proceedings of the Conference
PQ-QP: Quantum Probability and WItite Noise Analysis Volume XIII ^ ^ Proceedings of the Conference Foundations of p robability and physics Edited by A Khrennikov World Scientific ^ ^ Proceedings of the Conference foundations of Probability and physics P Q - Q P : Quantum Probability and White Noise Analysis Managing Editor: W. Freudenberg Advisory Board Members: L. Accardi, T. Hida, R. Hudson and K. R. Parthasarathy PQ-QP: Quantum Probability and White Noise Analysis Vol. 13: Foundations of Probability and Physics ed. A. Khrennikov QP-PQ Vol. 10: Quantum Probability Communications eds. R. L. Hudson and J. M. Lindsay Vol. 9: Quantum Probability and Related Topics ed. L. Accardi Vol. 8: Quantum Probability and Related Topics ed. L. Accardi Vol. 7: Quantum Probability and Related Topics ed. L. Accardi Vol. 6: Quantum Probability and Related Topics ed. L. Accardi PQ-QP: Quantum Probability and White Noise Analysis Volume XIII Proceedings of the Conference foundations of probability and physics Vaxjo, Sweden 25 November - 1 December 2000 Edited by A Khrennikov University of Vaxjo, Sweden |5% World Scientific m New JerJseerys e• Ly'oLnodnodno n• 'SSiinnggaappoorree *• Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. FOUNDATIONS OF PROBABILITY AND PHYSICS PQ-QP: Quantum Probability and White Noise Analysis - Vol. 13 Copyright © 2001 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-02-4846-6 Printed in Singapore by World Scientific Printers (S) Pte Ltd V Foreword With the present proceedings of a conference on "Foundations of Probability and Physics" we continue the QP series — the first volume of which appeared more than twenty years ago. The series had its origin in proceedings of con- ferences and workshops on quantum probability and related topics. Initially published by Springer-Verlag, World Scientific has now been the publisher for about ten years. Much has changed in the world of quantum probability in the last two decades. Quantum probabilistic methods became a mature subject in mathematics and mathematical physics. The number of well-established scien- tists who have turned their scientific interest to the field of quantum probability is impressively increasing. Scientifically and numerically strong schools of quan- tum probability evolved in the past years. Moreover, the highly interdisciplinary character of quantum probability became more and more evident. Especially, the close connections to white noise analysis aroused the interest of classical and quantum probabilists and stimulated mutual exchange and cooperation fruitful for both parties. Taking into account this development, during the previous QP conferences we discussed comprehensively and in detail the future profile and main goals of the series. Some changes in the alignment and the objectives of the series re- sulted from these discussions. First of all the new title reflects the intention to unify white noise analysis and quantum probability. It is important and essen- tial to bring together classical and quantum probabilists, and the success of the World Scientific journal "Infinite Dimensional Analysis, Quantum Probability and Related Topics" shows that such an alliance will benefit both parties. Fur- thermore, we should be open to a wide audience of scientists and to a broad spectrum of themes. The present volume represents such a field being not very closely connected to quantum probability and white noise analysis but of general interest to the readership of the series. Future volumes of the series will include proceedings of conferences or work- shops, lecture notes of schools but also monographs on topics in quantum prob- ability and white noise analysis. Finally, we would like to thank all former editors of the series for their excellent job they did. We especially appreciate the enthusiastic commitment of Luigi Accardi who initiated the series and was the responsible editor for many years. Wolfgang Freudenberg \ VII Contents Foreword v Preface xi Locality and Bel's Inequality 1 L. Accardi and M. Regoli Refutation of Bel's Theorem 29 G. Adenier Probability Conservation and the State Determination Problem 39 S. Aerts Extrinsic and Intrinsic Ireversibility in Probabilistic Dynamical Laws 50 H. Atmanspacher, R. C. Bishop and A. Amann Interpretations of Probability and Quantum Theory 71 L. E. Ballentine Forcing Discretization and Determination in Quantum History Theories 85 B. Coecke Interpretations of Quantum Mechanics, and Interpretations of Violation of Bel's Inequality 95 W. M. De Muynck Discrete Hessians in Study of Quantum Statistical Systems: Complex Ginibre Ensemble 15 M. M. Duras Some Remarks on Hardy Functions Asociated with Dirichlet Series 121 W. Ehm Ensemble Probabilistic Equilibrium and Non-Equilibrium Thermodynamics without the Thermodynamic Limit 131 D. H. E. Gross An Aproach to Quantum Probability 147 S. Gudder Innovation Approach to Stochastic Processes and Quantum Dynamics 161 T. Hida Statistics and Ergodicity of Wave Functions in Chaotic Open Systems 170 H. Ishio Origin of Quantum Probabilities 180 A. Khrennikov Nonconventional Viewpoint to Elements of Physical Reality Based on Nonreal Asymptotics of Relative Frequencies 201 A. Khrennikov "Complementarity" or Schizophrenia: Is Probability in Quantum Mechanics Information or Onta? 219 A. F. Kracklauer A Probabilistic Inequality for the Kochen-Specker Paradox 236 J.-A. Larsson Quantum Stochastics. The New Approach to the Description of Quantum Measurements 246 E. Loubenets Abstract Models of Probability 257 V. M. Maximov Quantum K-Systems and their Abelian Models 274 H. Narnhofer Scatering in Quantum Tubes 303 B. Nilsson Position Eigenstates and the Statistical Axiom of Quantum Mechanics 314 L. Polley Is Random Event the Core Question? Some Remarks and a Proposal 321 P. Rocchi Constructive Foundations of Randomnes 35 V. I. Serdobolskii ix Structure of Probabilistic Information and Quantum Laws 350 J. Summhammer Quantum Cryptography in Space and Bel's Theorem 364 /. Volovich Interacting Stochastic Proces and Renormalization Theory 373 Y. Volovich
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