The prince and the pauper. A quantum paradox of Hilbert-space fundamentalism

• URL: http://arxiv.org/abs/2310.15090v2
• Date: Thu, 26 Oct 2023 17:53:27 GMT
• Title: The prince and the pauper. A quantum paradox of Hilbert-space fundamentalism
• Authors: Ovidiu Cristinel Stoica
• Abstract summary: The quantum world is described by a unit vector in the Hilbert space and the Hamiltonian. This thesis was previously refuted in (arXiv:2102.08620) in full generality. Here I show that concrete physically distinct worlds can be described by the same unit vector and evolve according to the same law.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum world is described by a unit vector in the Hilbert space and the Hamiltonian. Do they, as abstract basis-independent objects, give a complete description of the physical world, or should we include observables like positions and momenta and the decomposition into subsystems? According to "Hilbert-space fundamentalism" they give a complete description, and all other features of the physical world emerge from them (Carroll, arXiv:2103.09780). This thesis was previously refuted in (arXiv:2102.08620) in full generality. But being an abstract non-uniqueness proof, and not a constructive one, it may not be convincing enough to the busy reader who wants to avoid mathematical details. Here I give a simpler, intuitive and constructive refutation, by showing that concrete physically distinct worlds can be described by the same unit vector and evolve according to the same law.

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