Clarifying the New Problem for Quantum Mechanics: Reply to Vaidman

Roughly, the derivation is: By (B1) and (B4), \({\uparrow _z} \otimes \text {initial} \rightarrow \nu \otimes \psi\) and \({\downarrow _z} \otimes \text {initial} \rightarrow \nu ' \otimes \psi '\). By (B1) and (B3), either \({\uparrow _x} \otimes \text {initial} \rightarrow \mu \otimes \psi\) or \({\uparrow _x} \otimes \text {initial} \rightarrow \mu ' \otimes \psi '\). Either way, we violate Unitarity (B2). For details and a generalization to impure states, see [2, Sect. 4].
This problem of accounting for repeated measurements, the problem of effect [3], is closely related to the control problem, however it is not identical. See also [2, Sect. 4.3].

References

Vaidman, L.: There is no new problem for quantum mechanics. Found. Phys. 50(11), 1728–1734 (2020)
Article MathSciNet Google Scholar
Meehan, A.: A new problem for quantum mechanics. Br. J. Philos. Sci. (forthcoming). https://doi.org/10.1093/bjps/axz053
Maudlin, T.: Three measurement problems. Topoi 14(1), 7–15 (1995)
Article MathSciNet Google Scholar
Dürr, D., Goldstein, S., Zanghí, N.: Quantum equilibrium and the origin of absolute uncertainty. J. Stat. Phys. 67(5–6), 843–907 (1992)
Article ADS MathSciNet Google Scholar
Dürr, D., Goldstein, S., Tumulka, R., Zanghí, N.: On the role of density matrices in Bohmian mechanics. Found. Phys. 35(3), 449–467 (2005)
Article ADS MathSciNet Google Scholar
Norsen, T.: Bohmian conditional wave functions (and the status of the quantum state). J. Phys. 701, 012003 (2016)
Google Scholar
Wessels, L.: The preparation problem in quantum mechanics. In: Earman, J., Norton, J. (eds.) The Cosmos of Science, pp. 243–273. University of Pittsburgh Press, Pittsburgh (1997)
Google Scholar

I thank Hans Halvorson, Laura Ruetsche, Lev Vaidman, and an anonymous referee for their helpful comments and discussion.

Department of Philosophy, Princeton University, 1879 Hall, Princeton, NJ, 08544, USA
Alexander Meehan

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Meehan, A. Clarifying the New Problem for Quantum Mechanics: Reply to Vaidman. Found Phys 51, 17 (2021). https://doi.org/10.1007/s10701-021-00438-9

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