Max Jammer The Philosophy of Quantum Merchanics: The Interpretations of QM in historical perspective. John Wiley and Sons 1974.com PREFACE Never in the history of science has there been a theory which has had such a profound impact on human thinking as quantum mechanics; nor has there been a theory which scored such spectacular successes in the predic- tion of such an enormous variety of phenomena (atomic physics, solid state physics, chemistry, etc. Furthermore, for all that is known today, quantum mechanics is the only consistent theory of elementary processes. Thus although quantum mechanics calls for a drastic revision of the very foundations of traditional physics and epistemology, its mathematical apparatus or, more generally, its abstract formalism seems to be firmly established.
In fact, no other formalism of a radically different structure has ever been generally accepted as an alternative. The interpretation of this formalism, however, is today, almost half a century after the advent of the theory, still an issue of unprecedented dissension. In fact, it is by far the most controversial problem of current research in the foundations of Copyright O 1974, by John Wiley & Sons, Inc. physics and divides the community of physicists and philosophers of All rights reserved.
Published simultaneously in Canada. science into numerous opposing "schools of thought." Reproduction or translation of any part of this work beyond In spite of its importance for physics and philosophy alike, the in- that permitted by Sections 107 or 108 of the 1976 United States terpretative problem of quantum mechanics has rarely, if ever, been Copyright Act without the permission of the copyright owner studied sine ira et studio from a general historical point of view. The is unlawful. Requests for permission or further information numerous essays and monographs published on this subject are usually should be addressed to the Permissions Department, John Wiley & Sons, Inc.
confined to specific aspects in defense of a particular view. No compre- hensive scholarly analysis of the problem in its generality and historical Library of Congress Cataloging in Publication Data: Perspective has heretofore appeared. The present historico-critical study is Jammer, Max. designed to fill this lacuna.
The philosophy of quantum mechanics. The book is intended to serve two additional purposes. "A Wiley-Interscience publication." Since the book is not merely a chronological catalogue of the various Includes bibliographical references. interpretations of quantum mechanics but is concerned primarily with the 1.
Quantum theory-History. analysis of their conceptual backgrounds, philosophical implications, and I. interrelations, it may also serve as a general introduction to the study of QC173.1'2 74- 13030 the logical foundations and philosophy of quantum mechanics. Although ISBN 0-47 1-43958-4 for a deeper understanding of modern theoretical physics, Printed in the United States of America this subject is seldom given sufficient consideration in the usual textbooks and lecture courses on the theory.
The historical approach, moreover, has v www.com 1t 1 and encouraged me to write this book. Finally, I wish to thank my colleagues Professors Marshall Luban and Paul Gluck for their critical reading of the typescript of the book. Needless to say, the responsibility for any errors or misinterpretations rests entirely upon me. CONTENTS Bar-Ilan Unioers@y Ramat-Can, Israel and Cily Unioersiry of New York 1 Formalism and Interpretations September 1974 1.2 Interpretations Appendix Selected Bibliography I Selected Bibliography I1 2 Early Semiclassical Interpretations 2.1 The conceptual situation in 1926/ 1927 2.2 Schrodinger's electromagnetic interpretation 2.4 Born's original probabilistic interpretation 2.5 De Broglie's double-solution interpretation 2.6 Later semiclassical interpretations 3 The Indeterminacy Relations 3.1 The early history of the indeterminacy relations 3.3 Subsequent derivations of the indeterminacy relations 3.5 Later developments 4 Early Versions of the Complementarity Interpretation 4.1 Bohr's Como lecture 4.3 "Parallel" and "circular" complementarity 4.4 Historical precedents www.com Contents 5 The Bohr-Einstein Debate 108 9 Stochastic Interpretations 5.1 The Fifth Solvay Congress 109 9.2 Early discussions between Bohr and Einstein 121 9.2 Early stochastic interpretations 5.3 The Sixth Solvay Congress 132 9.4 Later discussions on the photon-box experiment and the time-energy relation 136 10 Statistical Interpretations 5.5 Some evaluations of the Bohr-Einstein debate 156 10.1 Historical origins 6 The Incompleteness Objection and Later Versions of the 10.2 Ideological reasons Complementarity Interpretation 159 10.3 From Popper to LandC 10.4 Other attempts The interactionality conception of microphysical attributes 160 The prehistory of the EPR argument 166 11 Theories of Measurement The EPR incompleteness argument 181 Early reactions to the EPR argument 189 1 1.1 Measurement in classical and in quantum physics The relational conception of quantum states 197 11.2 Von Neumann's theory of measurement Mathematical elaborations 21 1 1 1.3 The London and Bauer elaboration Further reactions to the EPR argument 225 11.4 Alternative theories of measurement The acceptance of the complementarity interpretation 247 11.6 Many-world theories 7 Hidden-Variable Theories 252 Motivations for hidden variables 253 Appendix: Lattice Theory Hidden variables prior to quantum mechanics 257 Early hidden-variable theories in quantum mechanics 261 Index Von Neumann's "impossibility proof" and its repercussions 265 The revival of hidden variables by Bohm 278 The work of Gleason, Jauch and others 296 Bell's contributions 302 Recent work on hidden variables 312 The appeal to experiment 329 8 Quantum Logic 340 8.1 The historical roots of quantum logic 341 8.2 Nondistributive logic and complementarity logic 346 8.3 Many-valued logic 36 1 8.4 The algebraic approach 379 8.5 The axiomatic approach 384 8.6 Quantum logic and logic 399 8.com 1 2 Fonnaliim and Interpretations I 1.
THE FORMALISM A Hilbert space X , as abstractly defined by von Neumann, is a linear strictly positive inner product space (generally over the field 3 of complex The purpose of the first part of this introductory chapter is to present a -- which is complete with respect to the metric generated by the brief outline of the mathematical formalism of nonrelativistic quantum inner product and which is separable. Its elements are called uectors, mechanics of systems with a finite number of degrees of freedom. This usually denoted by #, 9,., and their inner or scalar product is denoted by formalism, as we have shown elsewhere,' was the outcome of a compli- (cp,#),whereas the elements of 9are called scalars and usually denoted by cated conceptual process of trial and error and it is hardly an overstate- a, b,. In his work on linear integral equations (1904-1910) David Hilbert ment to say that it preceded its own interpretation, a development almost had studied two realizations of such a space, the Lebesgue space C2 of unique in the history of physical science.
Although the reader is assumed (classes of) all complex-valued Lebesgue measurable square-integrable to be acquainted with this formalism, its essential features will be reviewed, functions on an interval of the real line R (or R itself), and the space l2 of without regard to mathematical subtleties, to introduce the substance and sequences of complex numbers, the sum of whose absolute squares con- terminology needed for discussion of the various interpretations. Impressed by the fact that by virtue of the Riesz-Fischer theorem Like other physical theories, quantum mechanics can be formalized in these two spaces can be shown to be isomorphic (and isometric) and terms of several axiomatic formulations. The historically most influential hence, in spite of their apparent dissimilarity, to be essentially the same and hence for the history of the interpretations most important formalism space, von Neumann named all spaces of this structure after Hilbert. The was proposed in the late 1920s by John von Neumann and expounded in fact that this isomorphism entails the equivalence between Heisenberg's I his classic treatise on the mathematical foundations of quantum matrix mechanics and Schrodinner's - wave mechanics made von Neumann I mechanics 2 aware of the importance of Hilbert spaces for the mathematical formula- In recent years a number of excellent texts3 have been published which tion of quantum mechanics.
discuss and elaborate von Neumann's formalism and to which the reader is To review this formulation let us recall some of its fundamental notions. referred for further details. A (closed) subspace S of a Hilbert space X is a linear manifold of vectors Von Neumann's idea to formulate quantum mechanics as an operator (i., closed under vector addition and multiplication by scalars) which is calculus in Hilbert space was undoubtedly one of the great innovations in closed in the metric and hence a Hilbert space in its own right. The modern mathematical physim4 orthogonal complement S L of S is the set of all vectors which are ortho- gonal to all vectors of S.
A mapping #-+cp= A# of a linear manifold 9, 'M. Jammer, The Conceptual Development of Quantum Mechanics (McGraw-Hill, New York, into X is a linear operator A, with domain 9, , if A (a#, + N 2 )= aA#l + 1966, 1968, 1973): RyOshi Riki-gaku Shi (Tokyo Tosho, Tokyo, 1974). bA#, for all #,,#, of 9,and all a,b of 9. The image of 9,under A is 2J.
von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932, the range $itAof A. The linear operator A is continuous if and only if i t is 1969; Dover, New York, 1943); Les Fondements Mathdmatiques de la Mdcanique Quantique (Alcan, Paris, 1946); Fundamentos Matemciticos de l a Mecanica Cucintica (Instituto Jorge Juan, bounded [i., if and only if IA#II/II$II is bounded, where II$II denotes the Madrid, 1949); Mathematical Foundations of Quantum Mechanics (Princeton University Press, norm (#,J,)'/~ of #]. A ' is an extension of A, or A ' > A, if it coincides with A Princeton, N., 1955); MatematiEeskije Osnmi Koantmoj Mekhaniki (Nauka, Moscow, 1964). Since every bounded linear operator has a unique 'G.
Fano, Metodi Matematici della Meccanica Quantistica (Zanichelli, Bologna, 1967); continuous extension to 3C,its domain can always be taken as X. Mathematical Methodr of Quantum Mechanics (McGraw-Hill, New York, 1971).-Nagy, The adjoint A + of a bounded linear operator A is the unique operator Spektraldarstellung linearer Transformationendes Hilbertschen Raumes (Springer, Berlin, Hei- delberg, New York, 1967); J. Jauch, Foundations of Quantum Mechanics (Addison-Wesley, A which satisfies (cp, A#) = (A +cp,#) for all rp, # of 3C.A is self-adjoint if + Reading, Mass. Lengyel, "Functional analysis for quantum theorists," Adoances A = A +.A is unitary if AA = A +A = I, where I is the identity operator.
If + in Quantum Chemistry 1968, 1-82; J. Soult, Linear Operators in Hilbert Space (Gordon and is a subspace of X , then every vector # can uniquely be written Breach, New York, 1968); T. Jordan, Linear Operators for Quantum Mechanics (Wiley, VJ'#;#~L, where #S is in S and qSl is in S L , so that the mapping New York, 1969); E. PrugoveEki, Quantum Mechanics in Hilbert Space (Academic Press, New York, London, 1971).y# defines the projection P,, as a bounded self-adjoint idempo- 4For the history of the mathematical background of this discovery see Ref., P:= Ps) linear operator.
conversely, if a linear operator P is Bernkopf, "The development of function spaces with particular reference to their origins in integral equation theory," Archiw for History of Exact Sciences 3, 1-96 (1966); "A history of Mathematics (Hawthorn, New York, 1970), pp. Kline, Mathematical Thought infinite matrices," ibid. Kramer, The Nature and Growth of Modern & from Ancient to Modern Times (Oxford Unlverslty Press, New York, 1972), pp.com 4 Formalism and Interpretations bounded, self-adjoint, and idempotent, it is a projection. Projections and ,,ondegenerate if the subspace formed by the eigenvectors belonging to this subspaces correspond one to one.
The subspaces S and T are orthogonal eigenvalue is one-dimensional.' Every A in the point spectrum of A is an [i., (q,\C/)=Ofor all q of S and all \C/ of TI, in which case we also say that eigenvalue of A. If the spectrum of A is a nondegenerate point spectrum P, and P, are orthogonal if and only if P,P, = P,P, = O (null operator); Aj(j = l,2,.), then the spectral decomposition (6) of A reduces to A = Zh,P,, and Zy=,Pq is a projection if and only if PJ;PSk=O for jf k.