Cover

Half-title

Title page

Copyright information

Dedication

Table of contents

List of contributors

Preface

Acknowledgements

1 Protective measurement: an introduction

1.1 Standard quantum mechanics and impulsive measurement

1.2 Weak measurement

1.3 Protective measurement

1.3.1 Measurements with artificial protection

1.3.2 Measurements with natural protection

1.3.3 Measurements of the wave function of a single system

1.4 Further discussion

References

Part I Fundamentals and applications

2 Protective measurement of the wave function of a single system

2.1 Introduction

2.2 Why I think that the quantum wave function describes a single quantum system (and everything else)

2.3 What is and what is not measurable using protective measurement

2.4 The methods of protective measurements and the information gain

2.5 Protective measurement and postselection

2.6 Critique of protective measurement

References

3 Protective measurement, postselection and the Heisenberg representation

3.1 Introduction

3.2 Classical and quantum ergodicity

3.3 Protective measurement in the Schrödinger and Heisenberg representations

3.4 Statistical mechanics with two-state vectors

3.5 Discussion

Acknowledgements

References

4 Protective and state measurement: a review

4.1 Introduction

4.2 Measurement in general

4.3 Quantum non-demolition measurement

4.3.1 Indirect measurement

4.3.2 QND measurement

4.3.3 No measurement without a measurement

4.4 Protective measurement of the state

4.5 Measurement and reversibility

4.6 Quantum state reconstruction

4.7 Unsharpness and negative quasi-probabilities

4.8 Conclusion

References

5 Determination of the stationary basis from protective measurement on a single system

5.1 Introduction

5.2 Joint protective measurement of several observables

5.3 Protective measurement of the stationary basis

5.4 Summary

References

6 Weak measurement, the energy–momentum tensor and the Bohm approach

6.1 Introduction

6.2 Quantum measurement

6.2.1 von Neumann measurement

6.2.2 Example of weak measurements for spin

6.2.3 Details of the weak measurement of spin

6.2.4 Experimental realization of weak Stern–Gerlachmeasurement using photons

6.2.5 Weak values

6.3 Bilinear invariants

6.3.1 Bilinear invariants of the second kind

6.3.2 The energy–momentum tensor

6.3.3 Weak values and the T [sup(0μ)] (x,t) components of theenergy–momentum tensor

6.4 Weak measurements with photons

6.4.1 The experiment of Kocsis et al.

6.4.2 The meaning of the stream lines

6.4.3 Schrödinger particle trajectories

6.5 Conclusions

Acknowledgments

References

Part II Meanings and implications

7 Measurement and metaphysics

7.1 Introduction

7.2 Bohm’s theory

7.3 Contextual properties

7.4 Ensemble interpretations

7.5 Ensemble properties and individual properties: a blurring of the lines

Acknowledgements

References

8 Protective measurement and the explanatory gambit

8.1 Introduction

8.2 Realisms and non-realisms

8.3 Protective measurement

8.4 The explanatory gambit

References

9 Realism and instrumentalism about the wave function: how should we choose?

9.1 Introduction

9.2 Realism as a stance and its pluralistic consequences

9.3 Realism about configuration space

9.4 The wave function as a nomological entity

9.5 The property-first view of the wave function: dispositionalism

9.6 The PBR theorem

9.7 Conclusion

References

10 Protective measurement and the PBR theorem

10.1 Introduction

10.2 Protective measurement: implications for experiment and theory

10.3 The Pusey–Barrett–Rudolph (PBR) theorem

10.4 Protective measurement, PBR and the reality of |Ψ rangle

Acknowledgements

References

11 The roads not taken: empty waves, wave function collapse and protective measurement in quantum theory

11.1 The explanatory role of empty waves in quantum theory

11.2 Measurement: empty waves vs. wave function collapse

11.3 The art in quantum mechanics: path detection and conceptual precision

11.3.1 Theory of path detection

11.3.2 Realism vs. surrealism

11.4 Evidence for empty waves: retrodiction vs. prediction

11.4.1 A general argument against the observability of empty waves

11.4.2 A stronger argument

11.5 Evidence for empty waves: protective measurement

11.6 Conclusion

References

12 Implications of protective measurement on de Broglie–Bohm trajectories

12.1 Motivation

12.2 A historical review of the pilot-wave interpretation

12.3 The measurement theory and the adiabatic theorem

12.3.1 Einstein’s reaction

12.3.2 Von Neumann’s strong measurements

12.3.3 Protective measurements

12.4 Conclusion

References

13 Entanglement, scaling, and the meaning of the wave function in protective measurement

13.1 Introduction

13.2 Theory of entanglement in protective measurement

13.3 Implications of entanglement in protective measurement

13.4 The scaling problem

13.5 Protective measurement and the quantum formalism

13.6 Concluding remarks

References

14 Protective measurement and the nature of the wave function within the primitive ontology approach

14.1 Introduction

14.2 Primitive ontology and the nature of the wave function

14.2.1 The main motivation for a primitive ontology

14.2.2 The central role of the wave function

14.2.3 Primary and secondary ontology

14.2.4 The nature of the wave function

14.3 Quantum structure

14.3.1 Ontic structural realism and primitive ontology

14.3.2 The wave function as a physical structure

14.3.3 Protective measurements and primitive ontology:probing the quantum structure

14.4 Conclusion and perspectives

Acknowledgements

References

15 Reality and meaning of the wave function

15.1 Introduction

15.2 On the reality of the wave function

15.3 Meaning of the wave function

15.3.1 One-body systems

15.3.2 Many-body systems

15.3.3 Ergodic motion of particles

15.3.4 Interpreting the wave function

15.3.5 On momentum, energy and spin

15.4 Conclusions

Acknowledgments

References

Index