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Mixture equivalence principles and postquantum theories of gravity

Samuel Fedida1 and Adrian Kent1,2

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Phys. Rev. D 111, 126016 – Published 20 June, 2025

DOI: https://doi.org/10.1103/pttr-6kj7

Abstract

We examine the mixture equivalence principle (MEP), which states that proper and improper mixed states with the same density matrix are always experimentally indistinguishable, and a weaker version, which states that this is sometimes true in gravity theories. We point out that Møller-Rosenfeld semiclassical gravity violates the weak MEP and that nonlinear extensions of quantum mechanics violate the MEP. We further demonstrate that modifications of the Born rule in quantum theory also typically violate the MEP. We analyze such violations in the context of thermal baths, where proper and improper thermal states induce different physical situations. This has significant implications in the context of black hole physics. We argue that Møller-Rosenfeld semiclassical gravity is not the semiclassical limit of quantum gravity in the context of black hole spacetimes, even in the presence of N≫1 matter fields.

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Phys. Rev. D 111, 126016– Published 20 June, 2025
  • Received 18 December 2024
  • Accepted 3 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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