Quantum mechanics, non-locality, and the space discreteness hypothesis

• URL: http://arxiv.org/abs/2508.14836v1
• Date: Wed, 20 Aug 2025 16:39:04 GMT
• Title: Quantum mechanics, non-locality, and the space discreteness hypothesis
• Authors: W. A. Zúñiga-Galindo,
• Abstract summary: The discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances.<n>We consider the time as a real variable, using the formalism of Dirac-von Neumann.<n>We also discuss a model for the two-slit experiment, where bright and dark states of light naturally occur.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space $\mathcal{X}$ as a model for the space. However, we consider the time as a real variable. In this framework, the formalism of Dirac-von Neumann can be used. This discreteness hypothesis implies that given two different points in space, there is no continuous curve (a world line) joining them. Consequently, this hypothesis is not compatible with the theory of relativity. We propose $\mathbb{R}\times(\mathbb{R}\times\mathcal{X})^{3}$ as a model of a space-time. For simplicity, we work out our models using $\mathbb{R}\times(\mathbb{R}\times\mathcal{X})$ as the configuration space. Quantum mechanics (QM), in the sense of Dirac-von Neumann, on the Hilbert space $L^{2}(\mathbb{R}\times\mathcal{X})$ is a non-local theory: the Hamiltonians are non-local operators, and thus, spooky action at a distance is allowed. The paradigm asserting that the universe is non-locally real implies that the proposed version of QM admits realism. This version of QM can be specialized to standard QM by using Hamiltonians acting on wavefunctions supported on the region $\mathbb{R}\times\mathbb{R}$. We apply the developed formalism to the measurement problem. We propose a new mechanism for the collapse of the wavefunction. The mechanism resembles the one proposed by Ghirardi, Ramini, and Weber, but there are significant differences. The most important feature is that the Schr\"{o}dinger equation describes the dynamics at all times, even at the moment of measurement. We also discuss a model for the two-slit experiment, where bright and dark states of light (proposed recently) naturally occur.

Related papers

• Obstructions to Unitary Hamiltonians in Non-Unitary String-Net Models [0.0]
  We prove that the Yang-Lee fusion rules admit no unitary solution to the pentagon equations.<n>We invoke the theory of $mathcalPT$-symmetric quantum mechanics to interpret the non-Hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2026-01-11T09:10:03Z)
• Discrete symmetries in classical and quantum oscillators [51.56484100374058]
  We show the eigenfunctions $_n=zn$ of the quantum Hamiltonian in the complex Bargmann-Fock-Segal representation.<n>The superposition $=sum_n c_n_n$ arises only with incomplete knowledge of the initial data for solving the Schrdinger equation.
  arXiv  Detail & Related papers  (2026-01-05T10:04:39Z)
• 2-Adic quantum mechanics, continuous-time quantum walks, and the space discreteness [0.0]
  We show that a large class of 2-adic Schr"odinger equations is the scaling limit of certain continuous-time quantum Markov chains (CTQMCs)<n>We construct new types of continuous time quantum walks (CTQWs) on graphs using two symmetric matrices.
  arXiv  Detail & Related papers  (2025-02-23T03:10:55Z)
• Two types of quantum chaos: testing the limits of the Bohigas-Giannoni-Schmit conjecture [0.8287206589886881]
  There are two types of quantum chaos: eigenbasis chaos and spectral chaos. The Bohigas-Giannoni-Schmit conjecture asserts a direct relationship between the two types of chaos for quantum systems with a chaotic semiclassical limit. We study the Poissonian ensemble associated with the Sachdev-Ye-Kitaev (SYK) model.
  arXiv  Detail & Related papers  (2024-11-12T21:10:04Z)
• Klein-Gordon oscillators and Bergman spaces [55.2480439325792]
  We consider classical and quantum dynamics of relativistic oscillator in Minkowski space $mathbbR3,1$. The general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic functions on the K"ahler-Einstein manifold $Z_6$.
  arXiv  Detail & Related papers  (2024-05-23T09:20:56Z)
• Small-time controllability for the nonlinear Schr\"odinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
  We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields. In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
  arXiv  Detail & Related papers  (2023-07-28T21:30:44Z)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• Heisenberg versus the Covariant String [0.0]
  A Poincar'e multiplet of mass eigenstates $bigl(P2 - m2bigr)Psi = 0$ cannot be a subspace of a space with a $D$-vector position operator $X=(X_0,dots X_D-1)$: the Heisenberg algebra $[Pm, X_n] = i deltam_n$ implies by a simple argument that each Poincar'e multiplet of definite mass vanishes.
  arXiv  Detail & Related papers  (2022-12-14T14:46:00Z)
• Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension [0.0]
  We study massless 1-dimensional Dirac-Coulomb Hamiltonians, that is, operators on the half-line of the form $D_omega,lambda:=beginbmatrix-fraclambda+omegax&-partial_x.
  arXiv  Detail & Related papers  (2021-07-08T11:48:57Z)
• Phase Space Formulation of Quantum Mechanics as an Hidden Variables Theory [0.0]
  We demonstrate that the Phase Space formulation of Quantum Mechanics is an hv theory with the position q, and momentum p as the hv. We identify the assumption that led von Neumann to the Hilbert space formulation of QM which precludes global dispersion free ensembles within the theory.
  arXiv  Detail & Related papers  (2021-05-01T13:19:55Z)
• Perelman's Ricci Flow in Topological Quantum Gravity [62.997667081978825]
  In our quantum gravity, Perelman's $tau$ turns out to play the role of a dilaton for anisotropic scale transformations. We show how Perelman's $cal F$ and $cal W$ entropy functionals are related to our superpotential.
  arXiv  Detail & Related papers  (2020-11-24T06:29:35Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [41.94295877935867]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations.<n>This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry.<n>We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)

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.