Table Of ContentDecoherence and the Appearance
of a Classical World in Quantum Theory
Springer-Verlag Berlin Heidelberg GmbH
D. Giulini E. Joos C. Kiefer J. Kupsch
1.-0. Stamatescu H. D. Zeh
Decoherence
and the Appearance
of a Classical World
in Quantum Theory
With 33 Figures
t
Springer
Domenico Giulini
Fakultat fUr Physik, Universitat Freiburg
Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
Erich Joos
Rosenweg 2, D-22869 Schenefeld, Germany
Claus Kiefer
Fakultat ffir Physik, Universitat Freiburg
Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
Joachim Kupsch
Fachbereich Physik, Universitat Kaiserslautern
Erwin-Schriidinger-Strasse, D-67663 Kaiserslautern, Germany
Ion-Olimpiu Stamatescu
Forschungsstatte der Evangelischen Studiengemeinschaft,
Schmeilweg 5, D-69118 Heidelberg
and
Institut flir Theoretische Physik, Universitat Heidelberg
Philosophenweg 16, D-69120 Heidelberg, Germany
H. Dieter Zeh
Institut flir Theoretische Physik, Universitat Heidelberg
Philosophenweg 19, D-69120 Heidelberg, Germany
Library of Congress Cataloging-in-Publication Data. Decoherence and the appearance of a classical world in quantum
theory I D. Giulini ... ret al.J. p. cm. Includes bibliographical references.
ISBN 978-3-662-03265-7 ISBN 978-3-662-03263-3 (eBook)
DOI 10.1007/978-3-662-03263-3
1. Quantum
theory. 2. Quantum field theory. I. Giulini,D. (Domenico), 1959-. QCI74.12.D42 1996 530.1'2-dc20 96-32375
ISBN 978-3-662-03265-7
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© Springer-Verlag Berlin Heidelberg 1996
Originally published by Springer-Verlag Berlin Heidelberg New York in 1996
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Preface
The central theme of this book is the problem of how to explain within quan
tum theory the classical appearance of our macroscopic world. This topic is of
fundamental importance not only for the status of quantum theory but also
for the philosophical discussion concerning our view of the physical world. The
book originated from the regular Workshop on Foundations of Quantum The
ory organized for the past several years at the Forschungsstiitte der Evangeli
schen Studiengemeinschaft (FESt, or Protestant Institute for Interdisciplinary
Research) by one of the authors (LO.S.). These meetings assembled people with
longstanding activities in the field of decoherence and people who within their
fields of research became interested in the decoherence program as a quantitative
approach to basic questions in quantum theory.
Although we have tried to write a "coherent" book, our reader will soon
notice that our conceptions vary on some basic notions. Characteristic are our
different opinions on the relevance of mathematical concepts for the interpreta
tion of quantum mechanics and hence different inclinations to make active use
of these concepts in physical arguments. In some cases this leads us to view or
stress differently some fundamental physical concepts, such as 'state' and 'ob
servable'. As a consequence, the reader will find expressed not only mutually
complementing, but also partially competing views and proposals on certain is
sues. We made no attempt to hide any aspect of our debate, which is fuelled by
our conviction that in any serious attempt to fully understand the physics and
formalism of decoherence one has to address all (or more) of the issues raised in
this book.
Since we agreed that all of us should be given the freedom to choose their own
emphasis and presentation - even at the price of some redundancies - we decided
to indicate the various authorships chapterwise and, where required, sectionwise.
In this sense they should be regarded (and - whenever it appears appropriate -
even quoted) as independent contributions. On the other hand, each single topic
in the book was discussed extensively in content and presentation by all authors
until a certain degree of approval was reached. This makes a mutual influence
clearly apparent at many places. We like to think of the reader as a participant
in our discussion and hope that he or she will benefit from our presentation of
different aspects of a common central theme.
The research project that led to this book was dedicated to a subject that
in the authors' opinion is unduly neglected at German universities and research
institutions. Indeed, this project would not have been possible without the par-
VI Preface
ticipation and support of FESt as part of its interdisciplinary research activity
that promotes projects in various fields. These include research in, and the dia
logue between, natural sciences, humanities, ethics, and theology. We hope that
our efforts will stimulate similar workshops or research programs elsewhere.
We sincerely thank FESt for its unfailing support of, and confidence in, our
work.
We are further indebted to Prof. Wolf Beiglbock, to Dr. Angela Lahee, and
to Tilman Bohn for competent advice and assistence in the completion of the
book and for help in preparing the manuscript.
E.J. is indebted to his wife for her consistent, unwavering support and en
couragement during the dark times.
Heidelberg Domenico Giulini
April 1996 Erich Joos
Claus Kiefer
Joachim Kupsch
Ion-Olimpiu Stamatescu
H. Dieter Zeh
Table of Contents
1. Introduction
E. Joos 1
2. The Program of Decoherence: Ideas and Concepts
H.D. Zeh ......................... . 5
2.1 The Phenomenon of Decoherence 5
2.1.1 Superpositions . . . . . . . 5
2.1.2 Superselection Rules . . . . 7
2.1.3 Decoherence by "Measurements" 9
2.2 Observables as a Derived Concept . . 12
2.3 The Measurement Problem ..... 16
2.4 Density Matrix, Coarse Graining, and "Events" 27
3. Decoherence Through Interaction with the Environment
E. Joos ............................... 35
3.1 The General Mechanisms of Decoherence 40
3.1.1 Dynamics of Quantum Correlations 40
3.1.2 Scattering Processes . . . . . . . . 47
3.1.3 Environment-Induced Superselection Rules 49
3.2 Localization of Objects ............ 54
3.2.1 Localization Through Ideal Measurements 56
3.2.1.1 Spatial Decoherence . . . 56
3.2.1.2 Equation of Motion 61
3.2.1.3 Decohering Wave Packets 66
3.2.1.4 More General Recoil-Free Decoherence 68
3.2.2 Decoherence and Dissipation 69
3.2.2.1 Quantum Brownian Motion 69
3.2.2.2 Ehrenfest Theorems . . . . 77
3.2.2.3 Decoherence Versus Friction 79
3.2.3 Wigner Function Description of Decoherence 81
3.2.4 Molecular Structure . . . . 89
3.3 General Dynamical Consequences . . . . . 96
3.3.1 The Quantum Zeno Effect . . . . . . 96
3.3.1.1 Phenomenological Description 97
VIII Table of Contents
3.3.1.2 An Experimental Test . . . . . . . . 102
3.3.1.3 Models for the Quantum Zeno Effect 105
3.3.2 Master Equations .............. 109
3.3.2.1 Pauli Equation ........... 109
3.3.2.2 Lindblad's Form of Master Equations 111
3.3.2.3 Null Measurements, Histories and Quantum Jumps 114
3.3.3 Dynamical Stability of States ............ 125
3.3.3.1 Sensitivity to the Presence of an Environment 125
3.3.3.2 Quantum Nondemolition Measurements 135
4. Decoherence in Quantum Field Theory
C. Kiefer .................. . 137
4.1 Decoherence in Quantum Electrodynamics 137
4.1.1 "Measurement" of Charges by Fields 138
4.1.2 "Measurement" of Electromagnetic Fields by Charges 143
4.2 Emergence of Classical Spacetime . . . . . . . . . . . . . 146
5. Consistent Histories and Decoherence
C. Kiefer ................ . 157
5.1 Influence Functional and Its Application
to Quantum Brownian Motion . . . . . 159
5.2 Definition and Properties of Consistent Histories 167
5.3 Reduced Density Matrix and Decoherence .... 176
5.4 Consistent Histories, Arrow of Time, and Quantum Gravity 179
6. Superselection Rules and Symmetries
D. Giulini ................. . 187
o
6.1 States, bservables , and Superselection Rules 187
6.2 Symmetries of the Physical State Space (J. Kupsch) 194
6.3 Physical Symmetries and Redundancy of Description 199
6.3.1 Configuration Spaces and Spaces of State ... 199
6.3.2 Symmetries and Redundant State Spaces 201
6.3.3 Symmetries, Redundancies, and Superselection Rules 207
6.3.4 A Heuristic Discussion of Field-Theoretical Examples 212
6.4 Decoherence and Charge Superselection Rules ..... . 219
7. Open Quantum Systems
J. Kupsch .......... . 223
7.1 Formalisms for Open Systems 223
7.2 Projection Methods ..... 225
7.3 Generalized Master Equations 229
7.4 Markov Approximation and Semigroups 233
7.5 Quantum Stochastic Processes 236
7.6 Induced Superselection Sectors 242
Table of Contents IX
8. Stochastic Collapse Models
1.-0. Stamatescu ....... . 249
8.1 The Question of State Vector Reduction 249
8.1.1 Decoherence and Collapse 249
8.1.2 Approaches to Collapse 251
8.2 Spontaneous Collapse Models . 256
8.2.1 Spontaneous Localization by a Jump Process 257
8.2.2 Continuous Spontaneous Localization . . . . 260
8.3 Spontaneous Localization, Quantum State Diffusion,
and Decoherence ................. . ........ 264
9. Related Ideas and Concepts
H.D. Zeh ............ . 269
9.1 Phase Averaging in Ensembles ("Dephasing") 269
9.2 Stochastic Forces (E. Joos) ........ . 271
9.3 Ergodic Behaviour and Irreversible Amplification 274
9.4 Dressing of States . 275
9.5 Complex Potentials 276
9.6 Collective Motion 277
Appendix
AI. Derivation of the Equation of Motion of a Mass Point (E. Joos) 285
A2. Solutions for the Equation of Motion of a Mass Point (E. Joos) 288
A2.1 Gaussian Density Matrices 288
A2.2 Green Functions . . . . 291
A2.3 Some Derived Quantities 292
A3. Quantum Correlations . . . . 295
A3.1 Elementary Properties of Composite Systems
in Quantum Mechanics (D. Giulini) . . . . . 295
A3.1.1 The Composite System Is in a Pure State . 295
A3.1.2 The Composite System Is in a Mixed State 299
A3.2 Observations in Correlated Systems (1.-0. Stamatescu) 302
A4. Spaces of Linear Operators (J. Kupsch) . . . . . . . . . . . 306
A5. Hamiltonian Formulation of Quantum Mechanics (D. Giulini) 309
A6. Galilean Symmetry of Non-relativistic Quantum Mechanics
(D. Giulini) .............. 314
A7. Stochastic Processes (1.-0. Stamatescu) 320
A 7.1 General Definitions 320
A7.2 Markov Chains 321
A7.3 Stochastic Processes 323
A7.4 The Fokker-Planck Equation 324
A7.5 Stochastic Differential Equations 325
A8. Stochastic Schrodinger Equations (J. Kupsch) 330
References . . . . . . . . . . . . . . . . . . . 335
1. Introduction
E. Joos
What distinguishes classical from quantum objects? What is the precise struc
ture of the transition from quantum to classical? Is this transition smooth and
harmless, or does it rather involve a sudden, abrupt change of concepts?
The efforts to find an unambiguous and clear-cut answer to these questions
have persisted since the formulation of the theory in the mid-twenties.1 While
quantum mechanics was originally conceived as a theory of atoms, it has shown
an ever increasing range of applicability, making it more and more evident that
the formalism describes some "true" and general properties of Nature. Today
there seem to be no phenomena which contradict quantum theory - perhaps
with the sole exception that there are definite ("classical") phenomena at all!
Despite this spectacular success of quantum theory, there is still no consensus
about its interpretation. The main problems center around the notions of "obser
vation" and "measurement". The founders of quantum mechanics insisted that
measurement results had necessarily to be expressed in classical ("everyday")
terms. How can this be reconciled with a description in terms of wave functions
(quantum states)? Where is the borderline between the two kinematical con
cepts (if any)? The early Bohr-Einstein debate showed that - because of the
uncertainty relations - the kinematical concepts of classical mechanics cannot
be generally applied to quantum objects. Therefore they have no direct coun
terpart in quantum mechanics; in particular, there are no classical trajectories.
On the other hand, the validity of the uncertainty relations was required also
in the macroscopic domain in order to save the theory from Einstein's attacks.
The orthodox interpretation thus uses two incompatible kinematical concepts
for the description of physical systems - an unacceptable state of affairs in view
of the fact that macro-objects are believed to be made out of atoms! From a
conservative point of view such a theory may well be called inconsistent.
Obviously, the problem of the "classical limit" is at the heart of the inter
pretation problem. Most textbooks suggest that classical mechanics is in some
sense contained in quantum mechanics as a special case, similar to the limit of
small velocities in relativity. Then, for example, the center-of-mass motion of a
macroscopic body would be described by a narrow wave packet, well localized
in both position and momentum. The spreading of the wave packet according to
the Schrodinger equation is indeed negligible for large masses, so that the Ehren
fest theorems seem to allow a derivation of Newtonian mechanics as a limiting
1 An anthology including many essays of considerable interest has been compiled by
Wheeler and Zurek (1983). Other recommended reviews are Jammer (1974) and
d'Espagnat (1995).
