Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-28T18:21:04.363Z Has data issue: false hasContentIssue false

The Nature of the Controversy over Time-Symmetric Quantum Counterfactuals

Published online by Cambridge University Press:  01 January 2022

Abstract

It is proposed that the recent controversy over “time-symmetric quantum counterfactuals” (TSQCs), based on the Aharonov-Bergmann-Lebowitz Rule for measurements of pre- and post-selected systems, can be clarified by taking TSQCs to be counterfactuals with a specific type of compound antecedent. In that case, inconsistency proofs such as that of Sharp and Shanks (1993) are not applicable, and the main issue becomes not whether such statements are true, but whether they are nontrivial. The latter question is addressed and answered in the negative. Thus it is concluded that TSQCs, understood as counterfactuals with a compound antecedent, are true but only trivially so, and provide no new contingent information about specific quantum systems (except in special cases already identified in literature).

Type
Research Article
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The author gratefully acknowledges helpful comments and suggestions from two anonymous referees. This work was supported in part by grant no. SES-0115185 of the National Science Foundation.

References

Aharonov Yakir, Peter G. Bergmann, and Lebowitz, Joel L. (1964), “Time Symmetry in the Quantum Process of Measurement”, Time Symmetry in the Quantum Process of Measurement 134:14101416.Google Scholar
Aharonov, Yakir, and Vaidman, Lev (1990), “Properties of a Quantum System During the Time Interval Between Two Measurements”, Properties of a Quantum System During the Time Interval Between Two Measurements 41:1120.Google ScholarPubMed
Aharonov, Yakir, and Vaidman, Lev (1991), “Complete Description of a Quantum System at a Given Time”, Complete Description of a Quantum System at a Given Time 24:23152328.Google Scholar
Albert, David Z., Aharonov, Yakir, and D’Amato, Susan (1985), “Curious New Statistical Predictions of Quantum Mechanics”, Curious New Statistical Predictions of Quantum Mechanics 54:57.Google Scholar
Albert, David Z., Aharonov, Yakir, and D’Amato, Susan (1986), “Comment on ‘Curious Properties of Quantum Systems Which Have Been Both Preselected and Post-Selected”, Comment on ‘Curious Properties of Quantum Systems Which Have Been Both Preselected and Post-Selected 56: 2427.Google Scholar
Bub, Jeffrey, and Brown, Harvey (1986), “Curious Properties of Quantum Ensembles Which Have Been Both Preselected and Post-Selected”, Curious Properties of Quantum Ensembles Which Have Been Both Preselected and Post-Selected 56:23372340.Google ScholarPubMed
Busch, Paul (1988), “Surprising Features of Unsharp Quantum Measurements”, Surprising Features of Unsharp Quantum Measurements 130:323329.Google Scholar
Cohen, Oliver (1995), “Pre- and Postselected Quantum Systems, Counterfactual Measurements, and Consistent Histories”, Pre- and Postselected Quantum Systems, Counterfactual Measurements, and Consistent Histories 51:43734380.Google ScholarPubMed
Cohen, Oliver (1998), “Reply to ‘Validity of the Aharonov-Bergmann-Lebowitz Rule’”, Reply to ‘Validity of the Aharonov-Bergmann-Lebowitz Rule’ 57:22542255.Google Scholar
Goodman, Nelson (1947), “The Problem of Counterfactual Conditionals”, The Problem of Counterfactual Conditionals 44:113128.Google Scholar
Horwich, Paul (1988), Asymmetries in Time. Cambridge: MIT Press.Google Scholar
Kastner, Ruth E. (1999a), “Time-Symmetrized Quantum Theory, Counterfactuals, and ‘Advanced Action’”, Time-Symmetrized Quantum Theory, Counterfactuals, and ‘Advanced Action’ 30:237259.Google Scholar
Kastner, Ruth E. (1999b), “The Three-Box Paradox and Other Reasons to Reject the Counterfactual Usage of the ABL Rule”, The Three-Box Paradox and Other Reasons to Reject the Counterfactual Usage of the ABL Rule 29:851863.Google Scholar
Kastner, Ruth E. (1999c), “TSQT ‘Elements of Possibility’?”, TSQT ‘Elements of Possibility’? 30:399402.Google Scholar
Kastner, Ruth E. (2001), “Comment on ‘What Quantum Mechanics is Trying to Tell Us,’ by Ulrich Mohrhoff”, Comment on ‘What Quantum Mechanics is Trying to Tell Us,’ by Ulrich Mohrhoff 69:860863.Google Scholar
Mermin, N. David (1997), “How to Ascertain the Values of Every Member of a Set of Observables That Cannot All Have Values”, in Cohen, R. S. et al. (eds.), Potentiality, Entanglement and Passion-at-a-Distance, Dordrecht: Kluwer Academic Publishers, 149157.CrossRefGoogle Scholar
Miller, D. J. (1996), “Realism and Time Symmetry in Quantum Mechanics”, Realism and Time Symmetry in Quantum Mechanics 222: 31.Google Scholar
Mohrhoff, Ulrich (2000), “What Quantum Mechanics is Trying to Tell Us”, What Quantum Mechanics is Trying to Tell Us 68:728745.Google Scholar
Mohrhoff, Ulrich (2001), “Objective Probabilities, Quantum Counterfactuals, and the ABL Rule—a response to R. E. Kastner”, Objective Probabilities, Quantum Counterfactuals, and the ABL Rule—a response to R. E. Kastner 69:864873.Google Scholar
Sharp, W. David, and Shanks, Niall (1989), “The Curious Quantum Statistics in the Interval Between Measurements”, The Curious Quantum Statistics in the Interval Between Measurements 138:451453.Google Scholar
Sharp, W. David, and Shanks, Niall (1993), “The Rise and Fall of Time-Symmetrized Quantum Mechanics”, The Rise and Fall of Time-Symmetrized Quantum Mechanics 60:488499.Google Scholar
Vaidman, Lev (1996a), “Defending Time-Symmetrized Quantum Theory”, Tel-Aviv University preprint, quant-phys/9609007.Google Scholar
Vaidman, Lev (1996b), “Weak-Measurement Elements of Reality”, Weak-Measurement Elements of Reality 26:895906.Google Scholar
Vaidman, Lev (1997), “Time-Symmetrized Quantum Theory”, invited lecture, Fundamental Problems in Quantum Theory workshop, University of Maryland Baltimore County, Aug. 4–7, 1997; quant-ph/9710036.Google Scholar
Vaidman, Lev (1998a), “On the Validity of the Aharonov-Bergmann-Lebowitz Rule”, On the Validity of the Aharonov-Bergmann-Lebowitz Rule 57:22512253.Google Scholar
Vaidman, Lev (1998b), “Time-Symmetrical Quantum Theory”, Time-Symmetrical Quantum Theory 46:729739.Google Scholar
Vaidman, Lev (1999a), “Defending Time-Symmetrized Quantum Counterfactuals”, Defending Time-Symmetrized Quantum Counterfactuals 30:373397; e-print version, quant-ph/9811092.Google Scholar
Vaidman, Lev (1999b), “Time-Symmetrized Counterfactuals in Quantum Theory”, Time-Symmetrized Counterfactuals in Quantum Theory 29:755765.Google Scholar
Vaidman, Lev (1999c), “The Meaning of Elements of Reality and Quantum Counterfactuals—Reply to Kastner”, The Meaning of Elements of Reality and Quantum Counterfactuals—Reply to Kastner 29:865876.Google Scholar
Vaidman Lev, Yakir Aharonov, and Albert, David (1987), “How to Ascertain the Values of σx, σy, and σz of a Spin- $\frac{1}{2}$ Particle”, Physical Review Letters 58:13851387.CrossRefGoogle Scholar
von Neumann, John (1955), Mathematical Foundations of Quantum Mechanics. Translated by Beyer, R.T., Princeton: Princeton University Press.Google Scholar