Abstract
An apparent paradox proposed by Aharonov and Vaidman in which a single particle can be found with certainty in two (or more) boxes is analyzed by way of a simple thought experiment. It is found that the apparent paradox arises from an invalid counterfactual usage of the Aharonov-Bergmann-Lebowitz (ABL) rule and effectively attributes conflicting properties not to the same particle but no different particles. A connection is made between the present analysis and the consistent histories formulation of Griffiths. Finally, a critique is given of some recent counterarguments by Vaidman against the rejection of the counterfactual usage of the ABL rule.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Y. Aharonov, P. G. Bergman, and J. L. Lebowitz, Phys. Rev. B 134, 1410–1416 (1964).
Y. Aharonov and L. Vaidman, J. Phys. A 24, 2315–2328 (1991).
D. Z. Albert, Y. Aharonov, and S. D’ Amato, Phys. Rev. Lett. 56, 2457 (1986).
O. Cohen, Phys. Rev. A 51, 4373–4380 (1995).
R. B. Griffiths, J. Stat. Phys. 36, 4373 (1984).
R. B. Griffiths, Phys. Rev. A 54, 2759–2774 (1996).
R. B. Griffiths, Phys. Rev. A 57, 1604–1618 (1998).
R. E. Kastner, Stud. Hist. Philos. Modern Phys., quant-ph/9806002 (in press).
D. J. Miller, Phys. Lett. A 222, 31 (1996).
K. R. Popper, The Logic of Scientific Discovery (Routledge, London, 1959).
W. D. Sharp and N. Shanks, Philos. Sci. 60, 488–499 (1993).
R. Stalnaker, in Studies in Logical Theory, N. Rescher, ed. (Blackwell, Oxford, 1968).
L. Vaidman, Found. Phys. 26, 895–906 (1996).
L. Vaidman, Time-symmetrized counterfactuals in quantum theory, preprint, quantph/ 9802042 (1998).
D. Lewis, Philosophical Papers, Vol. II (Oxford University Press, Oxford, 1986).
D. Lewis, Counterfactuals (Harvard University Press, Cambridge, 1973).
Rights and permissions
About this article
Cite this article
Kastner, R.E. The Three-Box “Paradox” and Other Reasons to Reject the Counterfactual Usage of the ABL Rule. Foundations of Physics 29, 851–863 (1999). https://doi.org/10.1023/A:1018865010735
Issue Date:
DOI: https://doi.org/10.1023/A:1018865010735