The Completion of Quantum Mechanics 1926–1941

947 Pages·2001·77.708 MB·English

by  Jagdish Mehra, Helmut Rechenberg (auth.)

The Historical Development
of
Q.uantwn Theory
Volume I
Springer Science+B usiness Media, LLC
Jagdish Mehra
Helmut Rechenberg
The Historical DeveloplDent
of
Q,uantwn Theory
VOLUME 6
The Completion of Quantum Mechanics
1926-1941
Part 2
The Conceptual COJDpletion and the Extensions
of Quantum Mechanics
1932-1941
Epilogue: Aspects of the Further DevelopJDent
of Quantum Theory
1942-1999
Subject Index: VolUJDes 1 to 6
Springer
Library of Congress Cataloging-in-Publication Data
Mehra, Jagdish.
The completion of quantum mechanics, 1926-19411 Jagdish Mehra, Helmut Rechenberg.
p. em. - (The historical development of quantum theory; v. 6)
Includes bibliographical references and index.
ISBN 978-0-387-95182-9 ISBN 978-0-387-21805-2 (eBook)
DOI 10.1007/978-0-387-21805-2
I. Quantum theory-History. I. Rechenberg, Helmut. II. Title.
QCI73.98.M44 vol. 6
530. 12'09-iie2 I 00-040039
Printed on acid-free paper.
First softcover printing. 200/.
© 2001 Springer Science+Business Media New York
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ISBN 978-0-387-95182-9 SPIN 10789559
Contents-Part 2
Chapter IV The Conceptual Completion and the Extensions of
Quantum Mechanics (1932-1941) 671
Introduction 671
IV.l The Causality Debate (1929-1935) 678
(a) Introduction: The Principle of Causality in Quantum Theory 678
(b) Heisenberg's Discussions Concerning the Positivism of the 'Vienna
Circle' (1929-1932) 683
(c) The Indeterminacy Relations for Relativistic Quantum Fields
(1929-1933) 692
(d) The Continuation of the Debate on Causality with the Berlin
Physicists (1929-1935) 703
IV.2 The Debate on the Completeness of Quantum Mechanics and Its
Description of Reality (1931...:.1936) 713
(a) Introduction 713
(b) From Inconsistency to Incompleteness of Quantum Mechanics:
The EPR Paradox (1931-1935) 717
(c) The Response of the Quantum Physicists, Notably, Bohr and
Heisenberg to EPR (1935) 725
(d) Erwin SchrOdinger Joins Albert Einstein: The Cat Paradox (1935-
1936) 738
(e) Reality and the Quantum-Mechanical Description (1935-1936) 747
IV.3 New Elementary Particles in Nuclear and Cosmic-Ray Physics
(1929-1937) 759
(a) Introduction: 'Pure Theory' Versus 'Experiment and Theory' 759
(b) The Theoretical Prediction of Dirac's 'Holes' and 'Monopoles'
(1928-1931) 772
(c) The Discovery of New Elementary Particles of Matter and
Antimatter (1930-1933) 785
(d) Quantum Mechanics of the Atomic Nucleus and Beta-Decay
(1931-1934) 801
(e) Universal Nuclear Forces and Yukawa's New Intermediate Mass
Particle (1933-1937) 822
IVA Solid-State, Low-Temperature, and Relativistic High-Density
Physics (1930-1941) 837
(a) Introduction 837
(b) New American and European Schools of Solid-State Physics
(1933-1937) 840
vi Contents
(c) Low-Temperature Physics and Quantum Degeneracy (1928-1941) 857
(d) Toward Astrophysics: Matter Under High Pressures and High
Temperatures (1926-1939) 877
IV.S High-Energy Physics: Elementary Particles and Nuclear
Reactions (1932-1942) 898
(a) Introduction 898
(b) Between Hope and Despair: Progress in Quantum
Electrodynamics (1930-1938) 902
(c) New Fields Describing Elementary Particles, Their Properties, and
Interactions (1934-1941) 935
(d) Nuclear Forces and Reactions: Transmutation, Fusion, and
Fission of Nuclei (1934-1942) 964
EpUogue: Aspects of the Further Development of Quantum Theory
(1942-1999) 1015
1. The Elementary Constitution of Matter: Subnuclear Particles and
Fundamental Interactions 1020
1.1 Some Progress in Relativistic Quantum Field Theory and the
Formulation of the Alternative S-Matrix Theory (1941-1947) 1024
(a) E. C. G. Stueckelberg: 'New Mechanics (1941), 1024
(b) The Principle of Least Action in Quantum Mechanics (Feynman
and Tomonaga, 1942-1943) 1024
(c) Heisenberg's S-Matrlx (1942-1947) 1030
1.2 The Renormalized Quantum Electrodynamics (1946-1950) 1033
(a) The Shelter Island Conference (1947) 1033
(b) Hans Bethe and the Initial Calculation of the Lamb Shift (1947) 1038
(c) The Anomalous Magnetic Moment of the Electron (1947) 1043
(d) The Pocono Conference (1948) 1051
(e) Vacuum Polarization (1948) 1057
(f) The Michigan Summer School: Freeman Dyson at Julian
Schwinger's Lectures (1948) 1059
(g) The Immediate Impact of Schwinger's Lectures (1948) 1062
(h) Schwinger's Covariant Approach (1948-1949) 1064
(i) Gauge Invariance and Vacuum Polarization (1950) 1074
(j) The Quantum Action Principle (1951) 1081
(k) Tomonaga Writes to Oppenheimer (April 1948) 1085
(I) Tomonaga's Papers (1946-1948) 1086
(m) Feynman's Preparations up to 1947 1088
(n) Richard Feynman after the Shelter Island Conference (1947-
1950) 1091
(0) Freeman Dyson and the Equivalence of the Radiation Theories
of Schwinger, Tomonaga, and Feynman (1949-1952) 1099
(p) The Impact of Dyson's Work 1104
(q) Feynman and Schwinger: Cross Fertilization 1106
1.3 New Elementary Particles and Their Interactions (1947-1964) 1107
1.4 The Problems of Strong-Interaction Theory: Fields, S-Matrix,
Currents, and the Quark Model (1952-1969) 1118
vii
Contents
1125
1.5 The 'Standard Model' and Beyond (1964-1999)
II 26
(a) The 'Electroweak Theory' (1964-1983)
1126
(al) The 'Intermediate Weak Boson'
(a2) Spontaneous Symmetry-Breaking and the Higgs Mechanism 1127
(a3) The Weinberg-Salam Model and Its Renormalization 1127
(a4) Neutral Currents and the Discovery of the Weak Bosons Il28
(b) Quantum Chromodynamics (QCD) (1965-1995) 1130
(bl) The Discovery of Physical Quarks 1130
(b2) Asymptotic Freedom of Strong Interaction Forces 1131
(b3) Quantum Chromodynamics 1132
(b4) The Completion of QCD 1133
(c) Beyond the Standard Model (1970-1999) 1134
2. Quantum Effects in the Physical Laboratory and in the Universe 1138
2.1 The Industrial and Celestial Laboratories (1947-1957) 1139
(a) The Transistor in the Industrial Laboratory (1947-1952) 1139
(b) The Celestial Laboratory (1946-1957) 1143
2.2 The Application of Known Quantum Effects (1947-1995) 1145
(a) The Casimir Effect and Its Applications (1947-1978) 1145
(b) The Maser and the Laser (1955-1961) 1153
(c) The Bose-Einstein Condensation (1980-1995) 1156
2.3 Superfiuidity, Superconductivity, and Further Progress in
Condensed Matter Physics (1947-1974) 1159
(a) Rotons and Other Quasi-Particles (1947-1957) 1159
(b) The Solution of the Riddle of Superconductivity (1950-1959) 1163
(c) Critical Phenomena and the RenormaJization Group (1966-1974) 1170
2.4 New Quantum Effects in Condensed Matter Physics (1958-1986) II 73
(a) The MOssbauer Effect (1958) 1173
(b) Experimental Proof of Magnetic Flux Quantization (1961) 1175
(c) The Josephson Effect (1962) 1176
(d) Superfluid Helium III: Prediction and Verification (1961-1972) II 77
(e) The Quantum Hall Effect and Lower Dimensional Quantization
(1980) 1179
(f) High-Temperature Superconductors (1986) 1181
2.5 Stellar Evolution, the Neutrino Crisis, and 3 K Radiation (1957-
1999) Il83
(a) Stellar Evolution and New Types of Stars (1957-1971) Il85
(b) The Solar Neutrino Problem and the Neutrino Mass (1964-1999) Il87
(c) 3 K Radiation and the Early Universe (1965-1990) 1190
3. New Aspects of the Interpretation of Quantum Mechanics 1193
3.1 The Copenhagen Interpretation Revisited and Extended (1948-
1966) 1197
3.2 Causality, Hidden Variables, and Locality (1952-1968) 1208
(a) The Hidden Variables and von Neumann's Mathematical
Disproof Revisited (1952-1963) 1212
viii Contents
(b) The EPR Paradox Revisited, Bell's Inequalities, and Another
Return to Hidden Variables (1957-1968) 1216
(c) The Aharonov-Bohm Effect (1959-1963) 1222
3.3 Further Interpretations and Experimental Confirmation of the
Standard Quantum Mechanics (1957-1999) 1224
(a) The Many-World Interpretation and Other Proposals (1957-1973) 1224
(b) Tests of EPR-Type Gedankenexperiments: Hidden Variables or
Nonlocality (1972-1986) 1229
(c) The Process of Disentanglement of States and SchrOdinger's Cat:
An Experimental Demonstration (1981-1999) 1235
Conclusion: Four Generations of Quantum Physicists 1244
References 1255
Author Index 1441
Subject Index for Volumes 1 to 6 1469
Chapter IV
The Conceptual Completion and the Extensions of
Q.uantUDl Mechanics (1932-1941)
Introduction
The invention of quantum and wave mechanics and the great, if not complete,
progress achieved by these theories in describing atomic, molecular, solid-state
and-to some extent-nuclear phenomena, established a domain of microphysics
in addition to the previously existing macrophysics. To the latter domain of clas
sical theories created since the 17th century applied-principally, the mechanics of
Newton and his successors, and the electrodynamics of Maxwell, Hertz, Lorentz,
and Einstein. The statistical mechanics of Maxwell, Boltzmann, Gibbs, Einstein,
and others indicated a transition to microphysics; when applied to explain the
behaviour of atomic and molecular ensembles, it exhibited serious limitations of
the classical approach. Classical theories were closely connected with a continuous
description of matter and the local causality of physical processes. The micro
scopic phenomena exhibited discontinuities, 'quantum' features, which demanded
changes from the classical description. In the standard scheme of quantum theory
that emerged between 1926 and 1928, notably in Gottingen, Cambridge, and
Copenhagen, the following description arose:
(i) Microscopic natural phenomena could be treated on the basis of the theories of
matrix and wave mechanics, i.e., formally different but mathematically equiva
lent algebraic and operator formulations.
(ii) The quantum-mechanical theories satisfied the known conservation principles of
energy, momentum, angular momentum, electric charge and current, etc.
(iii) The visualizable (anschauliche) particle and wave pictures of the classical theories
had to be replaced by 'dualistic' or 'complementary' aspects of microscopic
objects which exhibited simultaneous particle and wave features.
(iv) The causal structure known from the classical laws-i.e., the differential equa
tions-remained valid for the quantum-mechanical laws, but the behaviour of
quantum-mechanical objects deviated from those of classical ones.
(v) Based on Born's statistical interpretation of the wave function and Heisenberg's
uncertainty (or indeterminacy) relations, Bohr (on the physical side) and von
Neumann (on the mathematical side) proposed a subtle formalism that ac
counted for the measurement of microscopic properties by macroscopic instru
ments (and observers), in which the classical subject-object relation introduced
300 years earlier by Rene Descartes was replaced by a different one.
The completed physical theory of microscopic phenomena that thus arose, and
was soon characterized as the 'Copenhagen interpretation of quantum mechanics,'
J. Mehra et al., The Completion of Quantum Mechanics 1926–1941
© Springer Science+Business Media New York 2001
672 Chapter IV The Conceptual Completion and the Extensions of Quantum Mechanics
was by no means accepted by all physicists, not even by all quantum physicists
universally. Especially in Middle Europe, a lively debate arose from the late 1920's
onward concerning several characteristic aspects of this interpretation. We have
mentioned in Chapter II that already since the origin of the complementarity view,
Erwin Schrodinger and Albert Einstein vigorously attacked the validity of its very
basis, namely, Heisenberg's uncertainty relations. While Bohr and his associates,
in particular Heisenberg and Pauli, had emerged victorious in this debate on
the uncertainty relations-by demonstrating that the quantum-mechanical scheme
was fully consistent as a mathematical theory and gave an adequate description of
microscopic phenomena-a new debate started around 1930 (Le., after the defeat
of Einstein's arguments by Bohr et al. at the sixth Solvay Conference on Physics)
about the consequences from the uncertainty relations for the principle of cau
sality in quantum mechanics. Now Planck and Schrodinger argued vigorously
against renouncing the (classical) causality concept, which had formed the basis
of all previous successful physical theories and beyond. On the other hand, a
powerful philosophical movement in Germany and its vicinity, notably positivism
and the related views of the 'Vienna Circle,' supported, more or less fully, the
Copenhagen interpretation. Simultaneously with these epistemological debates,
certain theoreticians worked on the problem of whether the uncertainty relations
would not break down when one would seek to extend quantum mechanics to
relativistic phenomena. These investigations, carried out between 1930 and 1933,
ended with the result that uncertainty relations existed also for relativistic fields;
hence, the Copenhagen interpretation remained valid also in this domain.797 The
debate on causality and the extension of the uncertainty relations will be dealt with
in Section IV.I.
In spite of his defeat in 1930, Einstein would not yield to the claim of the
validity of the quantum-mechanical description of microscopic processes. After
several years of preparation, he would publish with two collaborators a new and,
as he believed, decisive blow: the so-called 'Einstein-Podolsky-Rosen (EPR) para
dox' did not argue against the consistency of the modem quantum theory (in
volving, especially, the validity of the uncertainty relations) but rather attempted
to show that the entire, though so successful, scheme violated the very essence of
a physical theory, namely, to describe the 'reality' of nature completely. Bohr,
Heisenberg, and others hurried to reply to Einstein's accusations by demonstrating
that the view of physical reality assumed by their distinguished colleague simply
did not apply to the microscopic domain. At the same time, Erwin SchrOdinger
analyzed, partly independently of Einstein, the intuitive (anschauliche) content of
quantum mechanics and published his famous 'cat paradox.' This nonrelativistic
example addressed the same reality problem which had been discussed by Einstein
and his quantum-mechanical opponents in the relativistic example of EPR. We
shall treat the purely epistemological debate between Einstein and SchrOdinger, on
797We recall from Section 11.7 that the most eminent quantum-mechanical experts were ready to
accept a breakdown of their theory in the domain of relativistic and nuclear physics.