Paper · Jul 19, 2023

Stochastic Ricci Flow dynamics of the gravitationally induced wave-function collapse

Matteo Lulli, Antonino Marciano, Kristian Piscicchia

gr-qcarXiv:2307.10136
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Abstract

In order to reconcile the wave-function collapse in quantum mechanics with the finiteness of signals' propagation in general relativity, we delve into a stochastic version of the Ricci flow and study its non-relativistic limit in presence of matter. We hence derive the Diósi-Penrose collapse model for the wave-function of a quantum gas. The procedure entails additional parameters with respect to phenomenological models hitherto accounted for, including the temperature of the gas and the cosmological constant, in turn related to the stochastic gravitational noise responsible for the collapse.

Comments: 14 pages

Ricci flowPhysics

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Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Stochastic Quantization of General Relativity à la Ricci-Flow (Matteo Lulli, Antonino Marciano and Xiaowen Shan, 2021)1Lulli 2021 Brownian Motion in the Hilbert Space of Quantum States along with the Ricci Flow and Stochastically Emergent Einstein-Hilbert Action: Formulating a Well-Defined Feynman Path-Integral Measure for Quantum Fields in the Presence of Gravity (A. A. Varshovi, 2022)6Varshovi 2022 General Relativity and the Ricci Flow (Mohammed Alzain, 2022)5Alzain 2022 Quantum Modified Gravity at Low Energy in the Ricci Flow of Quantum Spacetime (M. J. Luo, 2022)4Luo 2022 A path integral formula of quantum gravity emergent from entangled local structures (Jinglong Liu, Stephon Alexander, Antonino Marciano et al., 2023)3Liu 2023 Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and F(R,T,Q,Tₘ) gravity (Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev et al., 2024)8Bubuianu 2024 Noise-induced stabilization of Schwarzschild–AdS black holes under stochastic Ricci flow (Jihui Wang, Matteo Lulli and Antonino Marciano, 2026)2Wang 2026 Entropy and Non-Collapse in Lorentzian Geometry (Rohit Dhormare, 2026)7Dhormare 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Stochastic Quantization of General Relativity à la Ricci-Flow

    Matteo Lulli, Antonino Marciano and Xiaowen Shan PDF

    Topics Physics · Same authors Matteo Lulli, Antonino Marciano · Shared terms “stochastic”, “relativity”, “cosmological constant”

  2. Noise-induced stabilization of Schwarzschild–AdS black holes under stochastic Ricci flow

    Jihui Wang, Matteo Lulli and Antonino Marciano PDF

    Topics Physics · Same authors Matteo Lulli, Antonino Marciano · Shared terms “stochastic Ricci”, “cosmological constant”

  3. A path integral formula of quantum gravity emergent from entangled local structures

    Jinglong Liu, Stephon Alexander, Antonino Marciano et al. PDF

    Topics Physics · Same author Antonino Marciano · Shared terms “procedure”, “relativity”

  4. Quantum Modified Gravity at Low Energy in the Ricci Flow of Quantum Spacetime

    M. J. Luo PDF

    Topics Physics · Shared terms “cosmological constant”

  5. General Relativity and the Ricci Flow

    Mohammed Alzain PDF

    Topics Physics · Shared terms “relativity”

  6. Brownian Motion in the Hilbert Space of Quantum States along with the Ricci Flow and Stochastically Emergent Einstein-Hilbert Action: Formulating a Well-Defined Feynman Path-Integral Measure for Quantum Fields in the Presence of Gravity

    A. A. Varshovi PDF

    Topics Physics · Shared terms “presence”, “cosmological constant”, “gravitational”

  7. Entropy and Non-Collapse in Lorentzian Geometry

    Rohit Dhormare PDF

    Topics Physics · Shared terms “collapse”, “relativity”

  8. Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and gravity

    Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev et al. PDF

    Topics Physics · Shared terms “gravitational”, “relativity”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Physics Ricci flow first appeared in physics, as the leading-order renormalization-group flow of the string sigma model (Friedan, 1980). Start with: Nonlinear Models in 2+ε Dimensions (Friedan, 1980)

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.

  3. 11A.1
    The Equation and Its First SolutionsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A heat equation for the metric: spheres, cylinders and scaling.