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.
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.
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.
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.
The continuous spontaneous localization (CSL) theory of dynamical wave-function collapse is an experimentally testable alternative to nonrelativistic quantum mechanics. In it, collapse occurs because particles interact with a classical random field. However, particles gain energy from this field, i.e., particle energy is not conserved. Recently, it has been shown how to construct a theory dubbed ``completely quantized collapse'' (CQC) which is predictively equivalent to CSL. In CQC, a quantized random field is introduced, and CSL's classical random field becomes its eigenvalue. In CQC, energy is conserved, which allows one to understand that energy is conserved in CSL, as the particle's energy gain is compensated by the random field's energy loss. Since the random field has energy, it should have gravitational consequences. For that, one needs to know the random field's energy density. In this paper, it is shown how to construct a symmetric, conserved, energy-momentum-stress-density tensor associated with the quantized random field, even though this field obeys no dynamical equation and has no Lagrangian. Then, three examples are given involving the random field's energy density. One considers interacting particles, the second treats a ``cosmological'' particle creation model, the third involves the gravity of the random field.
Careful monitoring of harmonically bound (or as a limiting case, free) masses is the basis of current and future gravitational wave detectors, and of nanomechanical devices designed to access the quantum regime. We analyze the effects of stochastic localization models for state vector reduction, and of related models for environmental decoherence, on such systems, focusing our analysis on the non-dissipative forced harmonic oscillator, and its free mass limit. We derive an explicit formula for the time evolution of the expectation of a general operator in the presence of stochastic reduction or environmentally induced decoherence, for both the non-dissipative harmonic oscillator and the free mass. In the case of the oscillator, we also give a formula for the time evolution of the matrix element of the stochastic expectation density matrix between general coherent states. We show that the stochastic expectation of the variance of a Hermitian operator in any unraveling of the stochastic process is bounded by the variance computed from the stochastic expectation of the density matrix, and we develop a formal perturbation theory for calculating expectation values of operators within any unraveling. Applying our results to current gravitational wave interferometer detectors and nanomechanical systems, we conclude that the deviations from quantum mechanics predicted by the continuous spontaneous localization (CSL) model of state vector reduction are at least five orders of magnitude below the relevant standard quantum limits for these experiments. The proposed LISA gravitational wave detector will be two orders of magnitude away from the capability of observing an effect.
We propose an effective non-relativistic framework in which wave-function collapse emerges as a deterministic dynamical instability induced by gravitational self-interaction and regulated by short-distance repulsion. The dynamics is described by a nonlinear Schrödinger equation supplemented by a phenomenological repulsive sector ensuring regularity at high densities. Using a variational Gaussian ansatz, we derive an explicit effective energy functional and show that extended quantum states lose stability beyond a critical mass scale. This loss of stability is associated with a bifurcation in the reduced dynamical system governing the wave-function width, leading to the emergence of stable localized configurations. Within this picture, collapse corresponds to the dynamical selection of one of these localized attractors, driven by infinitesimal asymmetries in the initial state and occurring without stochastic noise or environmental coupling. The mechanism provides a controlled and quantitative realization of gravity-induced localization, extending Schrödinger--Newton-type models while avoiding their pathological short-distance behavior. Possible implications for mesoscopic systems probing the quantum-to-classical transition are briefly discussed.
Collapse models describe phenomenologically the quantum-to-classical transition by adding suitable nonlinear and stochastic terms to the Schr\"odinger equation, thus (slightly) modifying the dynamics of quantum systems. Experimental bounds on the collapse parameters have been derived from various experiments involving a plethora of different systems, from single atoms to gravitational wave detectors. Here, we give a comprehensive treatment of the continuous spontaneous localization (CSL) model, the most studied among collapse models, for Fermi liquids. We consider both the white and non-white noise case. Application to various astrophysical sources is presented.