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arXiv:2411.04883

On Gravity Implication in the Wavefunction Collapse

A. Belhaj, Salah Eddine Ennadifi

Published Nov 7, 2024• 0 citations
arXivHTMLPDF

Abstract

Inspired by an ontic view of the wavefunction in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates. We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states. Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.

DOI
10.48550/arxiv.2411.04883

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Inspired by an ontic view of the wavefunction in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates. We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states. Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.
Abstract Inspired by an ontic view of the wave function in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state , depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates . We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states . Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.
A new approach to wavefunction collapse is prepared by an analysis of semiclassical gravity. The fact that, in semiclassical gravity, superposed states must share a common classical spacetime geometry, even if they prefer (according to general relativity) differently curved spacetimes, leads to energy increases of the states, when their mass distributions are different. If one interprets these energy increases divided by Planck's constant as decay rates of the states, one obtains the lifetimes of superpositions according to the Diosi-Penrose criterion and reduction probabilities according to Born's rule. The derivation of Born's rule for two-state superpositions can be adapted to the typical quantum mechanical experiments with the help of a common property of these experiments. It is that they lead to never more than two different mass distributions at one location referring e.g. to the cases that a particle "is", or "is not", detected at the location. From the characteristic energy of the Diosi-Penrose criterion, an action is constructed whose relativistic generalisation becomes obvious by a decomposition of the Einstein-Hilbert action to the superposed states. In Part 2, semiclassical gravity is enhanced to the so-called Dynamical Spacetime approach to wavefunction collapse, which leads to a physical mechanism for collapse.
Some collapse models proposed that gravitational effects cause the instability of mass distribution superpositions, leading to wave function collapse. In this paper, we utilize the quantum Boltzmann equation (QBE) to analyze the behavior of a fermion in a spatial superposition under graviton emission. We introduce a quantitative measure that links the stability of the superposition to the spatial separation, particle mass, and gravitational coupling. By examining the collision term in the QBE, we derive the decoherence rate and show how it depends on these parameters. Our results provide a detailed framework for understanding gravity induced decoherence, bridging the gap between quantum field theory and collapse models. We also discuss the implications of these findings for experimental tests of gravitationally induced wave function collapse and the broader class of collapse models known as dissipative continuous spontaneous localization (CSL) model.
We propose a novel semiclassical mechanism to unify quantum mechanics and general relativity, where wave function collapse in a superposition state induces a rapid change in the energy-momentum tensor, triggering spacetime dynamics that propagate at the speed of light. Unlike models assuming superposed spacetimes, we posit that the superposition yields a single, continuous classical spacetime driven by the expectation value of the energy-momentum tensor. Upon collapse, the abrupt shift modifies the spacetime metric via Einstein's field equations, respecting causality. We explore this for a particle in a spatial superposition, propose detailed experimental designs with numerical simulations of gravitational perturbations, address potential theoretical challenges, and discuss implications for existing quantum-gravity theories. This framework offers a pathway to reconcile quantum and gravitational dynamics without quantizing spacetime, with testable signatures in future experiments.
FINDING: Penrose's core thesis is that quantum mechanics must be modified to incorporate gravity's *objective* wavefunction collapse, not merely quantize gravity; the criterion involves gravitational self-energy difference between superposed mass distributions. MATH: The key quantity is the gravitational self-energy EΔ=14πG∫(∇Φ1−∇Φ2)2 d3x E_\Delta = \frac{1}{4\pi G} \int ( \nabla \Phi_1 - \nabla \Phi_2 )^2 \, d^3x EΔ​=4πG1​∫(∇Φ1​−∇Φ2​)2d3x, where Φ1,Φ2\Phi_1, \Phi_2Φ1​,Φ2​ are Newtonian potentials of the two superposed states. The collapse time is τ≈ℏ/EΔ \tau \approx \hbar / E_\Delta τ≈ℏ/EΔ​. For a nucleon, EΔ∼Gm2/r∼10−45 JE_\Delta \sim G m^2 / r \sim 10^{-45} \, \text{J}EΔ​∼Gm2/r∼10−45J, giving τ∼107 s\tau \sim 10^7 \, \text{s}τ∼107s; for a microtubule (~10910^9109 tubulins), EΔ∼10−28 JE_\Delta \sim 10^{-28} \, \text{J}EΔ​∼10−28J, giving τ∼10−2 s\tau \sim 10^{-2} \, \text{s}τ∼10−2s — matching neural timescales. No explicit golden ratio appears in the derivation; the mathematics is purely Newtonian potential theory. CONNECTION: The microtubule geometry (hollow cylinder, 13 protofilaments, 5-start helix) e Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com