Measurements and Time Reversal in Objective Quantum Theory
International Series in Natural Philosophy
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Measurements and Time Reversal in Objective Quantum Theory is a three-chapter book that begins with a discussion on the fundamentals of conventional quantum theory. The second chapter focuses on the time arrow of quantum theory. It specifically presents a schematized account of the results of an interesting paper on time reversal in quantum theory published by Aharonov, Bergmann, and Lebowitz. The last chapter presents the authors' conclusions and additional comments in this field. This book will be valuable to students of wave mechanics and will serve as a supplement to textbooks, which fail to present an appropriate discussion of these matters.
Table of Contents
Preface
The Einstein-Podolsky-Rosen Paradox
The Paradox of Schrödinger's Cat
The Paradox of Wigner's Friend
The Time Arrow of Quantum Theory
The Purpose of this Book
Acknowledgments
1. Measurements in Objective Quantum Theory
1.1 Introduction
1.2 Topics to Be Discussed
1.3 Probabilities and Ensembles
1.4 "Realistic" Theories of Elementary Systems
1.5 Ensembles of What?
1.6 Determinism for Ensembles
1.7 Indeterminism for Elementary Systems
1.8 Eigenstates of Conserved Observables
1.9 Objectivity
1.10 Reality of Nature
1.11 Quantum Theory and Knowledge
1.12 Schrödinger's Cat
1.13 Is Reduction of the State Vector after a Measurement Either Mandatory or Illogical?
1.14 Does Reduction Change the State of any Well-Defined Entity?
1.15 The Time at which a State is Reduced by a Measurement
1.16 Common Objections against the above Conclusions
1.17 Conventional Formalism of the Theory of Measurements
1.18 What Could be Wrong with the Probability Interpretation of the State Vector?
1.19 The Example of Einstein and Bohr
1.20 Wigner's 1963 Example
1.21 Everett's Memory State Vector
1.22 Probability Distribution for Follow-up Measurement
1.23 Visual Recording
1.24 Everett's "Relative States"
1.25 Is There a State Vector for the Universe?
1.26 Objections against Everett's Model
1.27 Conclusion
2. Retrodiction in Objective Quantum Theory
2.1 Introduction
2.2 Use of the Conventional Postulates of Quantum Theory
2.3 Resolution of Mixed States
Example 1
Example 2
Example 3
2.4 Alterations of State during and between Measurements
2.5 Time Reversal in Quantum Theory
2.6 Derivation of Postdictive Probabilities from Predictive Probabilities
2.7 Derivation of the Time-Symmetric Probability Postulate from the Conventional Predictive one
2.8 Tendency toward Asymptotic Garbling of the Quantum State Irreversibility of Our Assumption (52)
2.9 Derivation of the Predictive Probability Rule in "Time-Symmetric" Quantum Theory
2.10 An Example of Valid Retrodiction
2.11 Predictive and Postdictive State Vectors
2.12 The Practical Usefulness of Retrodiction
2.13 Misunderstandings in the Literature
3. Concluding Remarks
3.1 Limits of Validity of Quantum Theory
3.2 The Part Played by Our Mind
3.3 Reducibility after Measurement
3.4 The Time Arrow in Quantum Theory
3.5 Quantum Theory and Philosophy
3.6 Our Mind and Its Workings
3.7 Quantum Theory and God
3.8 Quantum Theory and Realism
Physicists Arui Philosophers
What Observables Can "Have" a Value?
Appendices
Appendix A Position and Momentum according to Park and Margenau
Appendix Β Simultaneous Measurement of Position and Momentum according to Ballentine
Appendix C One of d'Espagnat's "Proofs" That the Result of a Measurement Cannot Be a Mixed State
Appendix D Example of Nonunitary Evolution of the Density Matrix
Appendix E Cloud Chamber Tracks without Reduction of States
Appendix F On the Need for Large Apparatus for Validity of the Conventional Schematization of the Theory of Measurements
Appendix G Density Matrices and Mixed States
Author Index
Subject Index
Other Titles in the Series in Natural Philosophy
Product details
- No. of pages: 162
- Language: English
- Copyright: © Pergamon 1975
- Published: January 1, 1975
- Imprint: Pergamon
- eBook ISBN: 9781483155067
About the Author
F. J. Belinfante
About the Editor
D. Ter Haar
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