Chen, Eddy Keming and Tumulka, Roderich (2025) Typical Quantum States of the Universe are Observationally Indistinguishable. [Preprint]
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Abstract
We establish three new impossibility results regarding our knowledge of the quantum state of the universe---a central object in quantum theory. We show that, if the universal quantum state is a typical unit vector from a high-dimensional subspace H_0 of Hilbert space H (such as the one defined by a low-entropy macro-state as prescribed by the Past Hypothesis), then no observation can determine or just significantly narrow down which vector it is. In other words, the overwhelming majority of possible state vectors are observationally indistinguishable from each other (and from the density matrix of H_0). Moreover, we show that for any observation that isn't too unlikely and most pairs of unit vectors from H_0, the observation will not significantly favor one vector over the other. We further show that the uniform distribution over the unit sphere in H_0, after Bayesian updating in the light of any observation that isn't too unlikely, is still extremely close to uniform. Our arguments rely on a typicality theorem from quantum statistical mechanics. We also discuss how theoretical considerations beyond empirical evidence might inform our understanding of this fact and our knowledge of the universal quantum state.
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Typical Quantum States of the Universe are Observationally Indistinguishable. (deposited 23 Oct 2024 17:45)
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