Table Of ContentQUANTUM MECHANICS, A HALF CENTURY LATER
EPISTEME
A SERIES IN THE FOUNDATIONAL,
METHODOLOGICAL, PHILOSOPHICAL, PSYCHOLOGICAL,
SOCIOLOGICAL AND POLITICAL ASPECTS
OF THE SCIENCES, PURE AND APPLIED
Editor: MARIO BUNGE
Foundations and Philosophy of Science Unit, McGill University
Advisory Editorial Board:
RUTHERFORD ARIS, Chemistry, University of Minnesota
DANIEL E, BERLYNE, Psychology, University of Toronto
HUBERT M. BLALOCK, Sociology, University of Washington
GEORGE BUGLIARELLO, Engineering, Polytechnic Institute of New York
NOAM CHOMSKY, Linguistics, MIT
KARL W. DEUTSCH, Political science, Harvard University
BRUNO FRITSCH, Economics, E.T.H. Zurich
ERWIN HIEBERT, History of science, Harvard University
ARISTID LINDENMA YER, Biology, University of Utrecht
JOHN MYHILL, Mathematics, SUNY at Buffalo
JOHN MA YN ARD SMITH, Biology, University of Sussex
RAIMO TUOMELA, Philosophy, University of Helsinki
VOLUME 5
QU ANTUM MECHANICS,
A HALF CENTURY LATER
PAPERS OF A COLLOQUIUM
ON FIFTY YEARS OF QUANTUM MECHANICS,
HELD AT THE UNIVERSITY LOUIS PASTEUR,
STRASBOURG, MAY 2-4, 1974
Edited by
JOSE LEITE LOPES
Universite Louis Pasteur, Strasbourg
and
MICHEL PATY
Centre de Recherches Nucleaires et Universite Louis Pasteur, Strasbourg
D. REIDEL PUBLISHING COMPANY
DORDRECHT-HOLLAND/BOSTON-U.S.A.
Library of Congress Cataloging in Publication Data
Colloquium on Fifty Years of Quantum Mechanics,
University Louis Pasteur, 1974.
Quantum mechanics.
(Episteme ; v. 5)
Bibliography: p.
Includes index.
1. Quantum theory-Congresses. I. Lopes, Jose
Leite. II. Paty, Michel, 1938- III. Title.
QCI73.96.C64 1974 530.1'2 77-8178
ISBN -13: 978-94-010-1198-3 e-ISBN -13: 978-94-010-1196-9
DOl: 10.1007/978-94-010-1196-9
Published by D. Reidel Publishing Company,
P.O. Box 17, Dordrecht, Holland
Sold and distributed in the U.S.A., Canada, and Mexico
by D. Reidel Publishing Company, Inc.
Lincoln Building, 160 Old Derby Street, Hingham,
Mass. 02043 U.S.A.
All Rights Reserved
Copyright © 1977 by D. Reidel Publishing Company, Dordrecht, Holland
and copyrightholders as specified on appropriate pages
Softcover reprint of the hardcover 1st edition 1977
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any informational storage and
retrieval system, without written permission from the copyright owner
T ABLE OF CONTENTS
FOREWORD VII
PREFACE a
J. A. WHEELER / Include the Observer in the Wave Function? 1
A. FRENKEL / On the Possible Connections between Quantum
Mechanics and Gravitation 19
J. M. JAUCH / The Quantum Probability Calculus 39
G. CASSINELLI and E. G. BELTRAMETTI / Quantum Logics and
Ideal Measurements of the First Kind 63
c. PIRON / A First Lecture on Quantum Mechanics 69
s. P. SHUSHURIN / Essay on the Development of the Statistical
Theory of the Calculus of Probability 89
M. MUGUR-SCHACHTER / The Quantum Mechanical One-
System Formalism, Joint Probabilities and Locality 107
B. D'ESPAGNAT/On Propositions and Physical Systems 147
J.-M. LEVY-LEBLOND / Towards a Proper Quantum Theory 171
D. BOHM and B. HILEY I On the Intuitive Understanding of
Non-Locality as Implied by Quantum Theory 207
R. LESTIENNE / Four Ideas of David Bohm on the Relationship
between Quantum Mechanics and Relativity 227
R. DAUDEL / The Role of Quantum Mechanics in the Set-up of a
Mathematical Government among Molecular Populations 237
G. LOCHAK / Hidden Parameters, Hidden Probabilities 245
M. P AT Y / The Recent Attempts to Verify Quantum Mechanics 261
M. LAMEHI-RACHTI and w. MITTIG / Spin Correlation
Measurement in Proton-Proton Scattering and Comparison
with the Theories of the Local Hidden Variables 291
INDEX 305
FOREWORD
The articles collected in this volume were written for a Colloquium on
Fifty Years of Quantum Mechanics which was held at the University
Louis Pasteur of Strasbourg on May 2-4, 1974, in commemoration of
the original work by De Broglie in 1924.
It is our hope that this volume will convey to the reader the idea
that quantum mechanics, besides being a fundamental tool for scien
tific workers today, is also a source of a number of questions and
thoughts about the interpretation of the foundation of quantum
mechanics itself. This gives rise to problems of a philosophical and
logical character and has repercussions on other domains such as the
theory of gravitation.
Besides the papers presented at the Colloquium, an article has been
included by D. Bohm and B. Hiley. This compensates, perhaps, for
the article of S. Kochen, whose manuscript unfortunately did not
reach us in time for inclusion in ~his volume. A few months after this
Colloquium we learned of the death of Professor Jauch, who had taken a
lively and crucial part in its discussions. We have been extremely
saddened by the news of his death, and would like to express our long
standing indebtedness to him as a physicist.
We are grateful to Professor B. d'Espagnat who kindly helped us in
organizing the Colloquium meetings and to Professor G. Ourisson
who, as President of the Louis Pasteur University, gave us en
couragement and support to our enterprise. We would further like to
express our thanks to all those who have contributed to the work
involved in the Colloquium and the publication of this book, and
especially to Dr J. Simmons who agreed to check the English version
of several contributions.
J. LEITE LOPES
M. PATY
PREFACE
A few years ago, H. Barreau, G. Monsonego, M. Paty and myself
organized the Seminar on the Foundations of Science at the U niver
sity Louis Pasteur of Strasbourg.
Modern society recognizes the importance of science in the world
through its technological applications and the multitude of appliances,
gadgets and mechanisms which fill and often invade our daily life.
Scientists, dominated by the spirit of competition in their respective
fields of specialization, often pass too quickly from one interpretation
scheme to another and thus may stifle their research work by being
over-anxious to publish more and more.
It would therefore be beneficial to organize in the universities,
parallel to the different specialized seminars on recent experimental
work and theoretical models, seminars on the foundation of science,
its historical evolution, and the description and genesis of its ideas.
That is what we have tried to set up at Strasbourg over the past few
years; it is with this motivation that the Conference 'A Half Century
of Quantum Mechanics' was organized, and these papers collected
and published.
It is already fifty years ago that the intuition of De Broglie laid the
foundation stone of the theoretical structure that houses the funda
mental laws of atomic, nuclear and sub-nuclear phenomena.
As everybody knows, some fundamental notions of quantum
mechanics put forward by De Broglie himself and by Einstein and
Niels Bohr, amongst others, are still open to further discussion. It is
true that perhaps a great majority of physicists remain content in
calculating the effective cross-sections of collisions and reactions and
the energy levels of physical systems etc ... with the help of quantum
mechanics. However, others try in addition to examine thoroughly its
physical and philosophical significance, and are sometimes led to
modify some basic ideas of the theory.
Such discussions may indeed contribute to the progress of scientific
thought. We hope that this collection of papers which has been
x PREFACE
requested on the occasion of the 50th anniversary of the thesis of
Louis De Broglie, will contribute to that aim.
We regret the recent death of Leon Rosenfeld, the eminent physi
cist, who was one of the prominent members of the Copenhagen
school, and who came several times to Strasbourg to participate in the
seminars on the Foundations of Science.
Let us dedicate this work to the memory of L. Rosenfeld.
J. LEITE LOPES
JOHN ARCHIBALD WHEELER*
INCLUDE THE OBSERVER IN
THE WAVE FUNCTION?
ABSTRACT. The classical dynamics of Einstein's closed universe (idealized for
simplicity to be empty except as excited by gravitational waves) is analyzed in no way
more economically than by the standard Hamilton-Jacobi method. In it the essential
ideas are (1) a spacelike 3-geometry, (3)'9; (2) an infinite-dimensional superspace 9', each
point (or collection of equivalent points) of which stands for one and only one (3)'9; (3)
a Hamilton-Jacobi function S (dimensions of action) or wave-phase S/h (measured in
radians) that propagates through superspace, S = S«3)'9), according to the standard
Einstein-Hamilton-Jacobi equation of A. Peres; (4) a 'constructive interference'
between this family of wave crests and other families of wave crests (obeying the same
EHJ equation) that picks out (U. Gerlach) 'Yes' points (constructive interference) in
superspace from 'No' points (destructive interference); (5) definition through these
'Yes' points of a 'leaf of history' slicing through superspace; and (6) identification of
this leaf of history with a particular spacetime (4)'9 that satisfies Einstein's field
equation. Thus, every spacelike slice through this (4)'9 is a 'Yes' (3)'9, and conversely.
When one goes from classical theory to quantum theory, one goes from S«3)'9) to ",«3)'9),
with the approximate correspondence:
'" - (slowly varying amplitude) exp (is/h).
When one enriches the content of the theory from pure Einstein geometrodynamics to
geometry plus particle-fields and other fields, one still has every degree of freedom of
the universe included in the independent variables upon which", depends. Therefore
the observer himself would seem to be included in ",. However, so to 'include the
observer in' makes insuperable difficulties of principle, which are described. One has to
accept that physics never permits a complete prediction, but only a forecast of a
correlation between events (E. P. Wigner). One is led to recognize that a wave function
'encompassing the whole universe' is an idealization, formalistically perhaps a con
venient idealization, but an idealization so strained that it can be used only in part in
any forecast of correlations that makes' physical sense. For making sense it seems
essential most of all to 'leave the observer out of the wave function'.
1. PRELIMINARY SURVEY OF THE ISSUE
Physics treats everything as a dynamic system, even the universe.
Moreover, it describes the state of every dynamic system, not
deterministically, but in probability terms, by a state function. Thus
the consistent carrying out of the scheme of physics as one under
stands it today leaves no alternative but to assign a probability
J. Leite Lopes and M. Paty (eds.), Quantum Mechanics. a Half Century Later, 1-18. All Rights Reserved.
Copyright © 1977 by D. Reidel Publishing Company. Dordrecht·Holland
2 J. A. WHEELER
amplitude to the state of the universe. Yet, Wigner reasons, there is
no such thing as the state function of the. universe. A state function is
only useful insofar as it describes correlations between observations -
and there is no place for any 'observer' to stand 'outside' the
universe to observe it. There has to be a wave function for the
universe but there can't be a wave function for the universe: that is
the dilemma.
How does the 'dilemma of a wave function for the universe' arise?
Why is it important? What changed view does it suggest of the nature
of physics? Geometrodynamics? These issues about the reasonable
ness - and unreasonableness - of a 'quantum mechanics of the universe'
are of concern today. There is no better occasion to survey them than
this 50th anniversary of Louis de Broglie's discovery of the connection
between quantum states and waves.
2. THE ISSUE MORE SHARPLY FOCUSSED: DOES SOME
RELEVANT FEATURE OF CONSCIOUSNESS FALL OUTSIDE
THE DOMAIN OF PHYSICS?
The methods of quantum mechanics allow us to treat the machinery of
observation. Do they also allow us to analyze the observer?
We have no trouble of quantum-mechanics principle to apply the
idea of 'wave function' when a particle passes through a cloud
chamber. Nor when that particle ionizes a nitrogen molecule. Nor at
later stages down the road: ion nucleating droplet; droplet scattering
photon; and photon operating phototube. And does the idea of
'probability amplitude' make difficulty for us when the phototube
operates a digital display? When a photon from the display enters the
eye? When an impulse from the retina passes along the optic nerve?
No, and again, no. Then why not also use probability amplitude to
describe the state of the consciousness of the observer? In brief, does
it make sense to 'include the observer in the wave function'? And if
not, why not?
No question in physics is the takeoff point for a greater variety of
considerations. They range from 'Schrodinger's (1935) cat' and 'Wig
ner's (1963) friend' to Everett's 'relative state' or 'many-universes'
description of quantum mechanics [Everett (1957, 1973); DeWitt and
Graham (1973); Cooper and Van Vechten (1969)] and from the
