Book contents
- Frontmatter
- Contents
- Foreword
- Preface
- 1 Historical perspective
- 2 Present situation, remaining conceptual difficulties
- 3 The theorem of Einstein, Podolsky, and Rosen
- 4 Bell theorem
- 5 More theorems
- 6 Quantum entanglement
- 7 Applications of quantum entanglement
- 8 Quantum measurement
- 9 Experiments: quantum reduction seen in real time
- 10 Various interpretations
- 11 Annex: Basic mathematical tools of quantum mechanics
- Appendix A Mental content of the state vector
- Appendix B Bell inequalities in non-deterministic local theories
- Appendix C An attempt for constructing a “separable” quantum theory (non-deterministic but local)
- Appendix D Maximal probability for a state
- Appendix E The influence of pair selection
- Appendix F Impossibility of superluminal communication
- Appendix G Quantum measurements at different times
- Appendix H Manipulating and preparing additional variables
- Appendix I Correlations in Bohmian theory
- Appendix J Models for spontaneous reduction of the state vector
- Appendix K Consistent families of histories
- References
- Index
Appendix E - The influence of pair selection
Published online by Cambridge University Press: 05 September 2012
- Frontmatter
- Contents
- Foreword
- Preface
- 1 Historical perspective
- 2 Present situation, remaining conceptual difficulties
- 3 The theorem of Einstein, Podolsky, and Rosen
- 4 Bell theorem
- 5 More theorems
- 6 Quantum entanglement
- 7 Applications of quantum entanglement
- 8 Quantum measurement
- 9 Experiments: quantum reduction seen in real time
- 10 Various interpretations
- 11 Annex: Basic mathematical tools of quantum mechanics
- Appendix A Mental content of the state vector
- Appendix B Bell inequalities in non-deterministic local theories
- Appendix C An attempt for constructing a “separable” quantum theory (non-deterministic but local)
- Appendix D Maximal probability for a state
- Appendix E The influence of pair selection
- Appendix F Impossibility of superluminal communication
- Appendix G Quantum measurements at different times
- Appendix H Manipulating and preparing additional variables
- Appendix I Correlations in Bohmian theory
- Appendix J Models for spontaneous reduction of the state vector
- Appendix K Consistent families of histories
- References
- Index
Summary
In the proof of the Bell theorem, we have assumed that all pairs of particles emitted by the source are actually detected, whatever choice is made for the measurement settings a and b; within local realism, the Bell inequalities are then obeyed, which means that it is impossible to reproduce the a and b dependence (4.9) of the correlation function predicted by quantum mechanics (since it allows violations of the Bell inequalities). In this appendix, we examine what happens when the detection process introduces a selection in the ensemble of emitted pairs; in a first step (§E.1), we assume that this selection is independent of a and b, and in a second step (§E.2), we generalize to include a possible dependence. In the latter case, we will see that it then becomes possible to reproduce any variation of the correlation rate as a function of a and b, including the prediction (4.9) in cos(a−b) of quantum mechanics, while remaining within local realism; this is the origin of the “loophole” discussed in §4.5.1.a.
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- Do We Really Understand Quantum Mechanics? , pp. 336 - 340Publisher: Cambridge University PressPrint publication year: 2012