Abstract
I revisit the paper ‘Two dogmas about quantum mechanics,’ co-authored with Itamar Pitowsky, in which we outlined an information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. Following the analysis by Frauchiger and Renner of ‘encapsulated’ measurements (where a super-observer, with unrestricted ability to measure any arbitrary observable of a complex quantum system, measures the memory of an observer system after that system measures the spin of a qubit), I show that the Everett interpretation leads to modal contradictions. In this sense, the Everett interpretation is inconsistent.
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Notes
- 1.
This conceptual picture applies to quantum mechanics on a finite-dimensional Hilbert space. A restriction to ‘normal’ quantum states is required for quantum mechanics formulated with respect to a general von Neumann algebra, where a generalized Gleason’s theorem holds even for quantum probability functions that are not countably additive. Thanks to a reviewer for pointing this out.
- 2.
- 3.
Aage Petersen (Petersen 1963, p. 12): ‘When asked whether the algorithm of quantum mechanics could be considered as somehow mirroring an underlying quantum world, Bohr would answer, “There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.”
- 4.
Thanks to Renato Renner for pointing this out.
- 5.
In Bub and Stairs (2014), Allen Stairs and I proposed this as a consistency condition to avoid potential contradictions in quantum interactions with closed timelike curves.
- 6.
The standard axiom system for the modal logic of the operator ‘I am certain that’ includes the axiom ‘if I am certain that A, then it is not the case that I am certain that not-A’ (assuming the accessibility relation is serial and does not have any dead-ends). Thanks to Eric Pacuit for pointing this out.
- 7.
Thanks to Veronika Baumann for clarifying this.
- 8.
Thanks to Renato Renner for this observation.
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Acknowledgements
Thanks to Veronika Baumann, Michael Dascal, Allen Stairs, and Tony Sudbery for critical comments on earlier drafts.
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Bub, J. (2020). ‘Two Dogmas’ Redux. In: Hemmo, M., Shenker, O. (eds) Quantum, Probability, Logic. Jerusalem Studies in Philosophy and History of Science. Springer, Cham. https://doi.org/10.1007/978-3-030-34316-3_8
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