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arXiv:1910.00647 · Quantum Reports

Spontaneous Wave Function Collapse with Frame Dragging and Induced Gravity

Lajos Diósi

Published Dec 4, 2019• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3390/quantum1020025

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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 incorporate non-local gravitational self-energy, motivated by string-inspired T-duality, into the Schrödinger-Newton equation. In this framework spacetime has an intrinsic non-locality, rendering the standard linear superposition principle only an approximation valid in the absence of gravitational effects. We then invert the logic by assuming the validity of linear superposition and demonstrate that such superpositions inevitably become unstable once gravity is included. The resulting wave-function collapse arises from a fundamental tension between the equivalence principle and the quantum superposition principle in a semiclassical spacetime background. We further show that wave functions computed in inertial and freely falling frames differ by a gravitationally induced phase shift containing linear and cubic time contributions along with a constant global term. These corrections produce a global phase change and lead to a spontaneous, model-independent collapse time inversely proportional to the mass of the system.
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 $\ensuremath{\xi}\ensuremath{\sim}{10}^{\ensuremath{-}21}$.
A relativistic collapse model for distinguishable particles is presented. Position and time, for each particle, are the fundamental operators of the theory. The Schrödinger equation is of the continuous spontaneous localization form, with a Hermitian Hamiltonian and an anti-Hermitian, white-noise dependent, Hamiltonian. It generates state vector evolution parametrized by an “evolution parameter.” It is shown how this can be interpreted as an evolving state in spacetime with collapses satisfying Born rule probabilities, and how certain choices of collapse generating operators lead to states of definite mass and definite configuration in spacetime. The model is Poincaré covariant and conserves energy in expectation.
Gravity-induced entanglement has been proposed as a method for testing the non-classical nature of gravity via tabletop experiments. While most existing proposals are restricted to the Newtonian limit, the frame dragging effect offers access to genuinely post-Newtonian features of the gravitational interaction and remains comparatively less explored. Here, we study gravity-induced entanglement generated by frame dragging in an interferometric setting and compute the entanglement phase between the rotational degrees of freedom of a source mass and the paths of a particle in two complementary ways: (i) via Schrödinger evolution with a quantized Lense-Thirring Hamiltonian in the large angular momentum limit, and (ii) via the on-shell action of linearized quantum gravity within the stationary phase approximation. Both approaches yield the same entanglement phase, consistent with the proper time difference between the interferometer arms. The path integral derivation further reveals how gravitational retardation modifies the entanglement phase, thereby making the local, relativistically causal linearized-gravity description explicit. Under the standard locality/mediator assumptions used in existing arguments, the resulting entanglement would witness non-classicality of the gravitational interaction.
Abstract This paper proposes a parameter-free objective reduction theory where wavefunction collapse is induced by gravitational self-energy differences between mass distributions. Unlike Continuous Spontaneous Localization (CSL) models, which rely on phenomenological parameters, the collapse rate in this model (Γ = Eg/ħ) is uniquely determined by universal constants G and ħ. Key Highlights: Dynamical Derivation of the Born Rule: The model demonstrates that the Born probability rule emerges naturally from the martingale property of the stochastic dynamics, rather than being postulated. Experimental Consistency: The theory is shown to be consistent with current laboratory constraints, including double-slit interference experiments with large molecules (mcrit ≈ 10⁻¹⁴ kg) and loophole-free Bell inequality tests. Astrophysical Stability: Analysis confirms the stability of compact objects like neutron stars and the preservation of primordial fluctuations in the Cosmic Microwave Background (CMB). Relativistic Extension: A Lorentz-covariant field-theoretic generalization is provided, using the energy-momentum tensor to source collapse noise while respecting microcausality. The results suggest a self-contained, falsifiable framework for the transition from quantum to classical spacetime without the need for adjustable parameters.