Measurements and Time Reversal in Objective Quantum Theory (eBook)

Front Cover 1
Measurements and Time Reversal in Objective Quantum Theory 4
Copyright Page 5
Table of Contents 6
PREFACE 10
The Einstein-Podolsky-Rosen paradox 10
The paradox of Schrödinger's cat 14
The paradox of Wigner's friend 14
The time arrow of quantum theory 16
The purpose of this book 16
ACKNOWLEDGEMENTS 20
CHAPTER 1. MEASUREMENTS IN OBJECTIVE QUANTUM THEORY 22
1.1. Introduction 22
1.2. Topics to be discussed 26
1.3. Probabilities and ensembles 29
1.4. "Realistic" theories of elementary systems 30
1.5. Ensembles of what? 32
1.6. Determinism for ensembles 33
1.7. Indeterminism for elementary systems 33
1.8. Eigenstates of conserved observables 34
1.9. Objectivity 35
1.10. Reality of nature 36
1.11. Quantum theory and knowledge 37
1.12. Schrödinger's cat 39
1.13. Is reduction of the state vector after a measurement either mandatory or illogical? 43
1.14. Does reduction change the state of any well-defined entity? 44
1.15. The time at which a state is reduced by a measurement 45
1.16. Common objections against the above conclusions 47
1.17. Conventional formalism of the theory of measurements 47
1.18. What could be wrong with the probability interpretation of the state vector? 51
1.19. The example of Einstein and Bohr 53
1.20. Wigner's 1963 example 57
1.21. Everett's menfiory state vector 58
1.22. Probability distribution for follow-up measurement 63
1.23. Visual recording 65
1.24. Everett's ''relative states" 65
1.25. Is there a state vector for the universe? 68
1.26. Objections against Everett's model 70
1.27. Conclusion 73
CHAPTER 2. RETRODICTION IN OBJECTIVE QUANTUM THEORY 76
2.1. Introduction 76
2.2. Use of the conventional postulates of quantum theory 77
2.3. Resolution of mixed states 79
2.4. Alterations of state during and between measurements 83
2.5. Time reversal in quantum theory 87
2.6. Derivation of postdictive probabilities from predictive probabilities 92
2.7. Derivation of the time-symmetric probability postulate from the conventional predictive one 94
2.8. Tendency toward asymptotic garbling of the quantum state 95
2.9. Derivation of the predictive probability rule in "time-symmetric" quantum theory 101
2.10. An example of valid retrodiction 103
2.11. Predictive and postdictive state vectors 106
2.12. The "practical" usefulness of retrodiction 107
2.13. Misunderstandings in the literature 108
CHAPTER 3. CONCLUDING REMARKS 111
3.1. Limits of validity of quantum theory 111
3.2. The part played by our mind 112
3.3. Reducibility after measurement 113
3.4. The time arrow in quantum theory 116
3.5. Quantum theory and philosophy 117
3.6. Our mind and its workings 118
3.7. Quantum theory and God 119
3.8. Quantum theory and realism 120
APPENDICES 124
APPENDIX A: POSITION AND MOMENTUM ACCORDING TO PARK AND MARGENAU 124
APPENDIX .: SIMULTANEOUS MEASUREMENT OF POSITION AND MOMENTUM ACCORDING TO BALLENTINE 126
APPENDIX C: ONE OF D'ESPAGNAT's "PROOFS" THAT THE RESULT OF A MEASUREMENT CANNOT BE A MIXED STATE 131
APPENDIX D: EXAMPLE OF NONUNITARY EVOLUTION OF THE DENSITY MATRIX 140
APPENDIX .: CLOUD CHAMBER TRACKS WITHOUT REDUCTION OF STATES 141
APPENDIX F: ON THE NEED FOR LARGE APPARATUS FOR VALIDITY OF THE CONVENTIONAL SCHEMATIZATION OF THE THEORY OF MEASUREMENTS 142
APPENDIX G: DENSITY MATRICES AND MIXED STATES 144
AUTHOR INDEX 148
SUBJECT INDEX 150
OTHER TITLES IN THE SERIES IN NATURAL PHILOSOPHY 162