Current Issues in Quantum Logic PDF
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Current Issues in Quantum Logic ETTORE MAJORANA INTERNATIONAL SCIENCE SERIES Series Editor: Antonino Zichichi European Physical Society Geneva, Switzerland (PHYSICAL SCIENCES) Volume 1 INTERACTING BOSONS IN NUCLEAR PHYSICS Edited by F. lachello Volume 2 HADRONIC MATTER AT EXTREME ENERGY DENSITY Edited by Nicola Cabibbo and Luigi Sertorio Volume 3 COMPUTER TECHNIQUES IN RADIATION TRANSPORT AND DOSIMETRY Edited by Walter R. Nelson and T. M. Jenkins Volume 4 EXOTIC ATOMS '79: Fundamental Interactions and Structure of Matter Edited by Kenneth Crowe, Jean Duclos, Giovanni Fiorentini, and Gabriele Torelli Volume 5 PROBING HADRONS WITH LEPTONS Edited by Giuliano Preparata and Jean-Jacques Aubert Volume 6 ENERGY FOR THE YEAR 2000 Edited by Richard Wilson Volume 7 UNIFICATION OF THE FUNDAMENTAL PARTICLE INTERACTIONS Edited by Sergio Ferrara, John Ellis, and Peter van Nieuwenhuizen Volume 8 CURRENT ISSUES IN QUANTUM LOGIC Edited by Enrico G. Beltrametti and Bas C. van Fraassen Current Issues in Quantum Logic Edited by Enrico G. Beltrametti University of Genoa Genoa, Italy and Bas C. van Fraassen University of Toronto Toronto, Ontario, Canada and University of Southern California Los Angeles, California Plenum Press . New York and London library of Congress Cataloging in Publication Data Workshop on Quantum Logic, Erice, Italy, 1979. Current issues in quantum logic. (Ettore Majorana international science series: Physical sciences; v. 8) Includes index. 1. Logic Symbolic and mathematical-Congresses. 2. Quantum theory-Congresses. I. Beltrametti, Enrico G.III. Van Fraassen, Bastiaan C., 1941- III. Series. QC174.17.M35W67 1979 511.3 80-29505 ISBN-13: 978-1-4613-3230-5 e-ISBN-13: 978-1-4613-3228-2 001: 10.1007/978-1-4613-3228-2 Proceedings of the Workshop on Quantum Logic, held December 2-9, 1979, at the Ettore Majorana Center for Scientific Culture, Erice, Sicily © 1981 Plenum Press, New York Softcover reprint of the hardcover 1st edition 1981 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the publisher FOREWORD These are the proceedings of the Workshop on Quantum Logic held in Erice (Sicily), December 2 - 9, 1979, at the Ettore Hajorana Centre for Scientific Culture. A conference of this sort was originally proposed by Giuliano Toraldo di Francia, who suggested the idea to Antonino Zichichi, and thus laid the foundation for the Workshop. To both of them we express our appreciation and thanks, also on behalf of the other participants, for having made this conference possible. There were approximately fifty participants; their names and institutions are listed in the text. Quantum logic, which has now a history of some forty or more years, has seen remarkable growth during the sixties and seventies. The papers in the present volume presuppose, by and large, some acquaintance with the elements of the subject. These may be found in the well-known books by J.H. Jauch (Foundations of Quantum Hechanics; Reading, 1968), V.S. Varadarajan (Geometry of Quantum Theory: Princeton, 1968), and C. Piron (Foundations of Quantum Theory; New York, 1976). The initial program for the conference listed about twenty-five invited papers. But in the context of a very active and qualified attendance, other contributions were offered. This volume contains all of them. The program listed six main topics: I. Classification or different areas of quantum logic, and open problems. II. Comparison and unification of different approaches to quantum theories; problems of interpretation. III. Formal quantum logic; axiomatics. IV. Hodal interpretations of quantum logic. v vi FOREWORD V. Quantum set theory. VI. Advances concerning mathematical structure; other problems. In retrospect, other topics take on some promise through their appearance in a number of papers, for example, the representation of complex systems, and their relations to their subsystems. But the complexities of cross-classification and overlap will be readily apparent to the reader. We decided therefore to group the papers appearing in this volume along the same lines, while realizing that borderlines between these areas are often blurred. The purpose of the initial session was to enable all partici pants, who had approached quantum logic from many different points of view and with different backgrounds, to appreciate the relations among their work and interests. Papers in the initial session were invited in addition to more specific contributions by their authors. As participants in the conference we had a feeling of great vitality of research in the area of quantum logic, and the sense that this feeling is shared by many young researchers today. We hope that the reader will experience some of that feeling through this volume. The Editors CONTENTS PART 1: CLASSIFICATION OF DIFFERENT AREAS OF QUANTUM LOGIC, AND OPEN PROBLEMS Classification of different areas of work afferent to quantum logic . 3 P. Mittelstaedt Assumptions and interpretations of quantum logic • . . . .• 17 Bas C. van Fraassen PART 2: COMPARISON AND UNIFICATION OF DIFFERENT APPROACHES TO QUANTUM THEORIES; PROBLEMS OF INTERPRETATION What are quantum logics and what ought they to be? 35 D. Foulis and C. Randall Charting the labyrinth of quantum logics: a progress report . . . • . . . . . . . . • • . . . .• 53 G.Hardegree and P. Frazer Realism and quantum logic 77 R. loG. Hughes What does quantum logic explain? . • . . . • . . . . . • .. 89 J. Bub A new approach to equivalence in quantum logic . . . . . .. 101 R. Cooke and J. Hilgevoord How to rewrite a stochastic dynamical theory so as to generate a measurement paradox . . . . . 115 J. Dorling The quantum logical and the operational description for physical systems ..••.•.•••....... 119 M. Abbati and A. Mani~ vii viii CONTENTS PART 3: FORMAL QUANTUM LOGIC; AXIOMATICS Partial referential matrices for quantum logics . . . . .. 131 J. Czelakowski Some metalogical pathologies of quantum logic. . . . . .. 147 M. Dalla Chiara Quantum logic as an extension of classical logic . . . .. 161 S. Bernini Sequential quantum logic ............•.. " 173 E. Stachow Entailment and Quantum Logic . . . . . . . . . . • . . .. 193 A. Kron, Z. Maric, and S. Vujosevic Some problems and methods In formal quantum logic . . . .. 209 G. Hardegree PART 4: MODAL INTERPRETATIONS OF QUANTUM LOGIC A modal interpretation of quantum mechanics . . . . . . .. 229 Bas C. Van Fraassen The dialogic approach to modalities In the language . • .. 259 of quantum physics P. Mittelstaedt The inner language of operational quantum mechanics . . .. 283 S. Bugajski PART 5: QUANTUM SET THEORY Quan turn set theory . . . . • . . . . . . . . . . . • . .. 303 G. Takeuti Quantum sets, assemblies and plexi 323 D. Finkelstein Omologic as a Hilbert type calculus . • . . . . . . . . •• 333 G. Kalmbach Measure and integration in quantum set theory . . . . . .. 341 S. Gudder ix CONTENTS PART 6: ADVANCES CONCERNING MATHEMATICAL STRUCTURE; OTHER PROBLEMS Commutativity and generalized transition probability . . .. 355 in quantum logic M. Maczynski Representations of Baer *-semigroups and . . . . . . • . .. 365 quantum logics in Hilbert space S. Gudder A non-standard quantum logic with a strong set . . . . . .. 375 of states R. Greechie Description of compound physical systems and logical interaction of physical systems . . . . . . . .. 381 D. Aerts Products of logics 405 A. Zecca Space time structure from quantum logic . . . . . . . . .. 413 A. Marlow Causal logic of Minkowski space-time . . . • . . . . . . .. 419 W. Cegla Propositional systems in field theories and lattice-valued quantum logics ............. 425 M. Banai Non-linear integration and signed measures on . . . . . .. 437 von Neumann algebras P. Kruszynski On the inter-relations of the three quantal principles . .. 447 P. Lahti On the non-unique decomposability of quantum mixtures 455 E. Beltrametti and G. Cassinelli Motion and form 465 B. Mielnik Participants 479 Author Index 483 Subject Index 489 PART 1: CLASSIFICATION OF DIFFERENT AREAS OF QUANTUM LOGIC, QUANTUM LOGIC, AND OPEN PROBLEMS
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