Quantum Mechanics from General Relativity and the Quantum Friedmann Equation

• URL: http://arxiv.org/abs/2411.07961v2
• Date: Wed, 12 Feb 2025 15:54:36 GMT
• Title: Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
• Authors: Marco Matone, Nikolaos Dimakis,
• Abstract summary: We show that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General Relativity and Quantum Mechanics, pointing towards a unified framework.
• Score: 0.0
• License:
• Abstract: We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General Relativity and Quantum Mechanics, pointing towards a unified framework. Solutions of this equation are built in terms of a scale factor encapsulating quantum effects on a free-falling particle. The quantum scale factor reshapes cosmic dynamics, resolving singularities at its vanishing points. As an explicit example, we consider the radiation-dominated era and show that the quantum equation is dual to the one in Seiberg-Witten formulation, recently applied to black holes, and incorporates resurgence phenomena and complex metrics, as developed by Kontsevich, Segal, and Witten. This links to the invariance of time parametrization under $\Gamma(2)$ transformations of the dual wave function.

Related papers

• Scaled quantum theory. The bouncing ball problem [0.0]
  The standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. The quantum-classical transition of the density matrix is described by the linear scaled von Neumann equation for mixed states.
  arXiv  Detail & Related papers  (2024-10-14T10:09:48Z)
• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Quantum Isotropic Universe in RQM Analogy: the Cosmological Horizon [0.0]
  We investigate the quantum dynamics of the isotropic Universe in the presence of a free massless scalar field. We show how the introduction of a "turning point" in the Universe evolution allows to overcome an intrinsic ambiguity in representing the expanding and collapsing Universe.
  arXiv  Detail & Related papers  (2024-04-10T14:45:56Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
  It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
  arXiv  Detail & Related papers  (2021-01-04T16:09:10Z)
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
  Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
  arXiv  Detail & Related papers  (2020-12-11T12:55:17Z)
• Quantum potential in dust collapse with a negative cosmological constant [0.0]
  We obtain the wave function describing collapsing dust in an anti-de Sitter background, as seen by a co-moving observer. We perform a causal de Broglie-Bohm analysis, and obtain the corresponding quantum potential. An initially collapsing solution with a negative cosmological constant bounces back after reaching a minimum radius.
  arXiv  Detail & Related papers  (2020-07-21T17:43:02Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Singularity resolution depends on the clock [0.0]
  We study the quantum cosmology of a flat Friedmann-Lemaitre-Robertson-Walker universe filled with a (free) massless scalar field and a perfect fluid that represents radiation or a cosmological constant whose value is not fixed by the action, as in unimodular gravity.
  arXiv  Detail & Related papers  (2020-05-11T18:06:59Z)
• Quantum fluctuations of the compact phase space cosmology [0.0]
  This article applies effective methods to extract semi-classical regime of quantum dynamics. We find a nontrivial behavior of the fluctuations around the recollapse of the universe. An unexpected relation between the quantum fluctuations of the cosmological sector and the holographic Bousso bound is shown.
  arXiv  Detail & Related papers  (2020-03-18T10:08:11Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.