Measurements and Time Reversal in Objective Quantum Theory

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