Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 10

3D-space and the preferred basis cannot uniquely emerge from the quantum structure

Pages: 3895 – 3962

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n10.a12

Author

Ovidiu Cristinel Stoica (Department of Theoretical Physics, Horia Hulubei National Institute of Physics and Nuclear Engineering (NIPNE-HH), Măgurele, Romania)

Abstract

Hilbert-Space Fundamentalism (HSF) states that the only fundamental structures are the quantum state vector and the Hamiltonian, and from them everything else emerge uniquely, including the 3D-space, a preferred basis, and a preferred factorization of the Hilbert space.

In this article it is shown that whenever such a structure emerges from the Hamiltonian and the state vector alone, if it is physically relevant, it is not unique.

Moreover, HSF leads to strange effects like “passive” travel in time and in alternative realities, realized simply by passive transformations of the Hilbert space.

The results from this article affect all theories that adhere to HSF, whether they assume branching or state vector reduction (in particular the version of Everett’s Interpretation coined by Carroll and Singh “Mad-dog Everettianism”), various proposals based on decoherence, proposals that aim to describe everything by the quantum structure alone, and proposals that spacetime emerges from a purely quantum theory of gravity.

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Published 25 March 2024