Current Issues in Quantum Logic

477 Pages·1981·11.539 MB·English

by  Peter Mittelstaedt (auth.), Enrico G. Beltrametti, Bas C. van Fraassen (eds.)

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