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

• URL: http://arxiv.org/abs/2102.08620v9
• Date: Thu, 28 Mar 2024 11:08:11 GMT
• Title: 3D-Space and the preferred basis cannot uniquely emerge from the quantum structure
• Authors: Ovidiu Cristinel Stoica,
• Abstract summary: Hilbert-Space Fundamentalism (HSF) states that the only fundamental structures are the quantum state vector and the Hamiltonian. HSF leads to strange effects like "passive" travel in time and in alternative realities, realized simply by passive transformations of the Hilbert space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Generic Hilbert Space Fragmentation in Kogut--Susskind Lattice Gauge Theories [0.0]
  We show that Kogut--Susskind formulations of lattice gauge theories give rise to Hilbert space fragmentation. Our findings serve as a guide to the conditions under which these models can be faithfully used to infer the thermalization properties of quantum chromodynamics.
  arXiv  Detail & Related papers  (2025-02-05T19:00:04Z)
• Geometric monotones of violations of quantum realism [89.99666725996975]
  Quantum realism states that projective measurements in quantum systems establish the reality of physical properties, even in the absence of a revealed outcome. This framework provides a nuanced perspective on the distinction between classical and quantum notions of realism, emphasizing the contextuality and complementarity inherent to quantum systems. We derive geometric monotones of quantum realism using trace distance, Hilbert-Schmidt distance, Schatten $p$-distances, Bures, and Hellinger distances.
  arXiv  Detail & Related papers  (2024-12-16T10:22:28Z)
• Hilbert Subspace Ergodicity [0.0]
  We show how quantum many-body scars and Hilbert space fragmentation can affect Complete Hilbert Space Ergodicity. We find that the presence of these mechanisms leads to CHSE in decoupled subspaces, a phenomenon we call Hilbert Subspace Ergodicity.
  arXiv  Detail & Related papers  (2024-11-21T17:58:50Z)
• Quantum Probability Geometrically Realized in Projective Space [0.0]
  This paper aims to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system. The upshot is that quantum theory is the probability theory of projective subspaces, or equivalently, of quantum events.
  arXiv  Detail & Related papers  (2024-10-23T20:29:15Z)
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity [72.27323884094953]
  We make a conceptual overview of an approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom.
  arXiv  Detail & Related papers  (2024-02-19T19:00:02Z)
• The prince and the pauper. A quantum paradox of Hilbert-space fundamentalism [0.0]
  The quantum world is described by a unit vector in the Hilbert space and the Hamiltonian. This thesis is based on the symmetries of the theory of quantum measurements.
  arXiv  Detail & Related papers  (2023-10-23T16:54:05Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• Refutation of Hilbert Space Fundamentalism [0.0]
  According to the "Hilbert Space Fundamentalism", all features of a physical system, including the 3D-space, uniquely emerge from the state vector and the Hamiltonian alone. I give a simplified account of the proof from arXiv:2102.08620 showing that such emerging structures cannot be both unique and physically relevant.
  arXiv  Detail & Related papers  (2021-03-28T10:35:31Z)
• Emergence of classical behavior in the early universe [68.8204255655161]
  Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
  arXiv  Detail & Related papers  (2020-04-22T16:38:25Z)
• Quantum Mechanical description of Bell's experiment assumes Locality [91.3755431537592]
  Bell's experiment description assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality. This result is complementary to a recently published one demonstrating that non-Locality is necessary to describe said experiment. It is concluded that, within the framework of Quantum Mechanics, there is absolutely no reason to believe in the existence of non-Local effects.
  arXiv  Detail & Related papers  (2020-02-27T15:04:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.