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arXiv:1701.02236 · Physical review. D/Physical review. D.

Gravity induced wave function collapse

Giulio Gasbarri, Marko Toroš, Sandro Donadi, Angelo Bassi

Published Nov 13, 2017• 75 citations
arXivHTMLPDF

Abstract

Starting from an idea of S. L. Adler [in Quantum Nonlocality and Reality: 50 Years of Bell's Theorem, edited by M. Bell and S. Gao (Cambridge University Press, Cambridge, England 2016)], we develop a novel model of gravity induced spontaneous wave function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength $\ensuremath{\xi}$ of the complex metric fluctuations with available experimental data. We show that $\ensuremath{\xi}\ensuremath{\ge}{10}^{\ensuremath{-}26}$ in order for the model to guarantee classicality of macro-objects, and at the same time $\ensuremath{\xi}\ensuremath{\le}{10}^{\ensuremath{-}20}$ in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of $\ensuremath{\xi}\ensuremath{\sim}{10}^{\ensuremath{-}21}$.

DOI
10.1103/physrevd.96.104013

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Starting from an idea of S. L. Adler [in Quantum Nonlocality and Reality: 50 Years of Bell's Theorem, edited by M. Bell and S. Gao (Cambridge University Press, Cambridge, England 2016)], we develop a novel model of gravity induced spontaneous wave function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength \ensuremathξ\ensuremath{\xi}\ensuremathξ of the complex metric fluctuations with available experimental data. We show that \ensuremathξ\ensuremath≥10\ensuremath−26\ensuremath{\xi}\ensuremath{\ge}{10}^{\ensuremath{-}26}\ensuremathξ\ensuremath≥10\ensuremath−26 in order for the model to guarantee classicality of macro-objects, and at the same time \ensuremathξ\ensuremath≤10\ensuremath−20\ensuremath{\xi}\ensuremath{\le}{10}^{\ensuremath{-}20}\ensuremathξ\ensuremath≤10\ensuremath−20 in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of \ensuremathξ\ensuremath∼10\ensuremath−21\ensuremath{\xi}\ensuremath{\sim}{10}^{\ensuremath{-}21}\ensuremathξ\ensuremath∼10\ensuremath−21.
I impose the Newtonian criteria of inertial frames on the c.o.m.trajectories of massive objects undergoing spontaneous collapse of their wave function. The corresponding modification of the so far used stochastic Schrödinger equation eliminates the Brownian motion of the c.o.m., and restores the exact inertial motion for free masses. For the collapse of Schrödinger cat states the Born rule is satisfied invariably. The proposed machinery comes from the radical assumption that, in the vicinity of the spontaneously localized mass, the stochastic fluctuations of the c.o.m.—inevitable in the collapse process—would drag the physical inertial frame with themselves. The perspective of a general theory is presented where the spontaneous-collapse-caused breakdown of local energy-momentum conservation could be remedied by altering the metric, resulting in collapse-induced curvature of the space-time. My assumption of frame-drag by quantized masses is independent of the general relativistic frame-drag by classical masses.
Based on the assumption that the standard Schrödinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals have survived from the 1980s. The Schrödinger–Newton equation (1984) provides well-localized solitons for free macro-objects but lacks the mechanism of how extended wave functions collapse on solitons. The gravity-related stochastic Schrödinger equation (1989) provides the spontaneous collapse, but the resulting solitons undergo a tiny diffusion, leading to an inconvenient steady increase in the kinetic energy. We propose the stochastic Schrödinger–Newton equation, which contains the above two gravity-related modifications together. Then, the wave functions of free macroscopic bodies will gradually and stochastically collapse to solitons, which perform inertial motion without momentum diffusion: conservation of momentum and energy is restored.
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.
In a multi-fold universe, gravity emerges from Entanglement through the multi-fold mechanisms. As a result, gravity-like effects appear in between entangled particles that they be real or virtual. Long range, massless gravity results from entanglement of massless virtual particles. Entanglement of massive virtual particles leads to massive gravity contributions at very smalls scales. Multi-folds mechanisms also result into a spacetime that is discrete, with a random walk fractal structure and non-commutative geometry that is Lorentz invariant and where spacetime nodes and particles can be modeled with microscopic black holes. All these recover General relativity at large scales and semi-classical model remain valid till smaller scale than usually expected. Gravity can therefore be added to the Standard Model. This can contribute to resolving several open issues with the Standard Model without new Physics other than gravity. These considerations hints at a even stronger relationship between gravity and the Standard Model.In a multi-fold universe, we predicted that no spontaneous wave function collapse or decoherence is due to gravity induced spacetime or curvature superposition. It was at the difference of a widely held conjecture formalized by Penrose and Diósi. Experimental results seem to confirm that indeed gravity does not induce collapse by curvature superposition, albeit of course fluctuations and interactions could still result in collapse as with any other quantum interactions.
We present a self-consistent stochastic semiclassical framework in which objective localization (collapse) of quantum states induces localized fluctuations in the stress–energy distribution that source causal gravitational wave perturbations via an Einstein–Langevin type equation. The model combines a Lindblad-averaged continuous spontaneous localization (CSL)-like dynamics with a local collapse bookkeeping field that enforces local energy–momentum conservation. Linearized analysis yields a causal wave equation for metric perturbations sourced by a stochastic tensor whose statistics are computable from collapse parameters. We derive scaling laws for expected strain statistics from a localized mass superposition, provide order-of-magnitude estimates and outline experimental strategies and model limitations. The construction avoids standard no-go objections (superluminal signaling and Page–Geilker constraints) at the ensemble level while yielding concrete, testable predictions for future high-sensitivity detectors. This model offers a phenomenological approach that can guide future experiments, assuming advancements in preparing mesoscopic superpositions and detecting subtle gravitational effects.
Gravitational decoherence and gravitational wave function collapse are presented as two related but conceptually distinct ideas. Gravitational decoherence measures the effect of gravitational perturbations on the evolution of quantum systems, in particular their progressive lack of coherence. Gravitational wave function collapse starts with the assumption that the Schr¨odinger equation is not entirely right, and must be supplemented with extra terms, which cause the (random) collapse of the wave function; the collapse is then linked to gravity. Some of the most popular models are reviewed, with an emphasis on their conceptual status, stage of development, and open questions.