Gravity-Induced Local Collapse

• Gravity-induced local collapse is a phenomenon where gravitational interactions overcome dispersive, thermal, and entropic effects to rapidly localize physical systems.
• Theoretical frameworks like local Hamiltonian formalisms and modified Schrödinger–Newton models link gravitational self-energy with observable collapse thresholds.
• Experimental approaches, including granular material tests and quantum simulations, provide practical signatures that validate gravity-driven localization in both classical and quantum regimes.

Gravity-induced local collapse refers to mechanisms—classical or quantum—by which gravitational effects drive the rapid, local dynamical reduction of a physical system, often suppressing extended superpositions or collective motions and yielding locally concentrated states or events. This phenomenon arises across several domains, from quantum measurement and state reduction models to the classical nonlinear instabilities of self-gravitating astrophysical or granular systems. It is characterized, in both quantum and classical realms, by the dominance of gravitational interactions over dispersive, thermal, or entropic effects, resulting in localized collapse behaviors tied directly to gravity’s universal coupling.

1. Spherically Symmetric Hamiltonians and Local Collapse

In spherically symmetric gravitational collapse, gravity-induced local collapse is elucidated via a local, fully gauge-fixed Hamiltonian formalism derived using Ashtekar variables and geometrodynamical techniques (Gegenberg et al., 2011). Starting from the @@@@1@@@@ decomposition,

$$ds^2 = -N^2 dt^2 + A^2 (dr + N^r dt)^2 + R^2 d\Omega_{D-2}^2$$

and proceeding via a canonical transformation to the mass function $M$ (closely related to the Misner–Sharp mass), the physical evolution is encoded locally. The Hamiltonian density becomes algebraic in the matter fields after gauge-fixing $M = f(r,t)$, and the resulting reduced local Hamiltonian takes a universal simple form: $H_{\text{red}} = -[P_M(M, \phi, \dots)]$ This framework is valid for all gravity theories obeying a Birkhoff theorem and supporting a mass function constant on the vacuum constraint surface (e.g. $p$th order Lovelock gravity, 2D dilaton theories). The result isolates the gravitational “collapse” to local algebraic dynamics, emphasizing the physical role of gravity-induced self-interaction in driving local evolution.

2. Gravity-Driven Collapse in Granular and Astrophysical Systems

In classical granular materials and self-gravitating fluids, gravity-induced local collapse manifests as collective, rapid failure modes when gravitational forces overcome stabilizing mechanisms such as friction or thermal support.

• Granular Columns: Experiments with dry granular columns show free-fall–like and quasi-static (friction-dominated) regimes depending on release velocity (Sarlin et al., 2021). Above a critical velocity $\overline{V} \geq 0.4\sqrt{gH_0}$, grains undergo inertially driven, local collapse, following power-law scaling for the final runout and deposit morphology. Below this threshold, friction controls the collapse, and only part of the mass mobilizes, exemplifying local failure.
• Silos: Collapse of a thin-walled silo under gravity occurs when static friction along the wall is fully mobilized prior to grain sliding (Colonnello et al., 2014). The system locally transitions from elastic to irreversible deformations at a “critical collapse height” $L_c$, driven by the buildup of static frictional stress under gravity, marking a prototypical gravity-induced structural collapse mechanism.
• Thermal Astrophysical Systems: When accounting for thermal energy as gravitational mass via $E=mc^2$, there exists a temperature threshold $T_c$ above which gravitational attraction from thermal (internal) energy overcomes pressure, driving collapse (“collapse under the weight of heat”) (Roupas, 2020). The critical temperature intrinsically ties gravitational collapse to thermal properties:

$$kT_c \simeq mc^2 \left(\frac{R c^2}{G M_{\text{rest}}}\right)$$

illustrating a local collapse instability when effective mass is dominated by self-gravitating thermal energy.

3. Gravity-Induced Quantum State Reduction

Penrose, Diòsi, and related models posit that gravity creates a fundamental instability in spatial superpositions of different mass (thus, curvature) configurations, resulting in local collapse of the quantum state.

• Relativistic Schrödinger–Newton Framework: Incorporating relativistic corrections (e.g., the Grave de Peralta approach), the competition between quantum kinetic and gravitational self-energy is captured by a modified characteristic length,

$$l_D^{(r)} = l_D \sqrt{1 - \left(\frac{\bar{\lambda}_C}{l_D}\right)^2}$$

which vanishes for masses approaching the Planck mass, suggesting that heavy self-gravitating quantum states become perfectly localized and thus collapse under their own gravity (Poveda et al., 2021).

• Gravity as a Driver of State Reduction: In contemporary quantum reduction models, the wavefunction’s instability is set by the gravitational self-energy difference $\Delta U$ between branches:

$T_{\psi} \simeq \frac{\hbar}{|\Delta U|}$

(Belhaj et al., 7 Nov 2024, Laloë, 2019, Gasbarri et al., 2017). This results in rapid, local collapse for macroscopic or spatially separated states, while microscopic systems remain unaffected due to negligible $\Delta U$.

• Bohmian and GBC Models: Models where gravity sources from Bohmian positions (rather than quantum mass density) predict deterministic but locally sensitive collapses. The interaction between mass density in configuration space and the gravitational field produces an antihermitian term in the dynamical equation, favoring localization at the branch correlated with the Bohmian positions and suppressing “empty” branches (Laloë, 2022, Laloë, 2019).
• Collapse Time and Induced Observables: For superposed charged states, gravity-induced collapse can, in principle, induce tiny electric currents (with $I_{\text{eff}} \sim Q_y / T_y$), though their detection is beyond current experimental capabilities (Belhaj et al., 7 Nov 2024).

4. Nonlocality, Locality, and Witnesses of Quantum Gravity

• Collapse-Based Models and Nonlocality: Collapse-based models such as the Diòsi–Penrose paradigm implement gravity-driven reduction via continuous mass-density monitoring governed by stochastic master equations with nonlocal kernels,

$$d\rho/dt \sim -\int dr ds\,\frac{G}{4|r-s|}\, [\hat{h}_\sigma(r), [\hat{h}_\sigma(s), \rho]]$$

(Feng et al., 25 Mar 2025). This intrinsic nonlocality means that any observed entanglement generated via these collapse dynamics does not imply fully classical gravity, as the hidden quantum process is nonlocal and violates strict locality.

• Entanglement-Based Witnesses: The entanglement-based witness (GWT) states that if two systems become entangled via a mediator, that mediator must be at least partly non-classical. Collapse-based models that predict such entanglement are thus not implementing genuinely classical gravity but rather nonlocal dynamical processes, reaffirming the validity of the GWT (Feng et al., 25 Mar 2025).
• Local, Parameter-Free Models: Newer proposals seek genuinely local, parameter-free mechanisms: by enforcing product states between matter and gravity throughout evolution, the collapse is driven by minimizing the deviation from Schrödinger evolution (measured by a “residual” norm $||R||$). Collapse occurs when the gravitational phase separation surpasses a threshold, with no stochastic noise but with superdeterministic hidden variables introduced to maintain statistical consistency with Born’s rule (Hossenfelder, 13 Oct 2025). This ensures local, testable, and parameter-free predictions, marking a conceptual advance over stochastic, nonlocal earlier models.

5. Simulating and Testing Gravity-Induced Collapse

Advances in quantum simulation enable controlled exploration of gravity-induced collapse models.

• Quantum Computing Simulations: Simulation of mass-dependent decoherence channels, e.g. $p(m) = 1 - \exp(-k m^\alpha)$, yields qualitative collapse signatures—such as rapid, nonlinear parity decay in GHZ states or loss of quantum advantage in Grover’s search—distinguishable from constant-rate dephasing (Balaji et al., 14 Aug 2025). Such protocols define baseline signatures: if future experiments with mesoscopic “mass” show concordant scaling, this would suggest a contribution from gravitationally induced collapse mechanisms.
• Experimental Proposals: Designs include creation of large-mass (or large-qubit) GHZ states, branch-mass-selective interference, and superposed charged systems measured for induced currents or radiation. For parameter-free, local models, collapse times for nanogram-scale superpositions (with femtometer separations) are predicted to be on the order of seconds, a regime accessible to next-generation optomechanical experiments (Hossenfelder, 13 Oct 2025).

6. Universal Aspects and Applicability

Unified features across diverse domains are:

• The existence of a gravitational self-interaction threshold, above which localization—or local collapse—occurs irrespective of specifics (quantum, granular, or thermal).
• The emergence of parameter-free or universal scaling relations, linking collapse time or observable decay rates directly to gravitational quantities (mass, gravitational self-energy).
• The centrality of localization in both state reduction and classical collapse ergodicity breaking, driven by gravity.

Modern theories formulate collapse within a local Hamiltonian framework (when possible), or otherwise recognize that nonlocal features (e.g., in non-linear master equations) necessarily imply the mediator must be non-classical.

7. Implications for the Quantum–Classical Boundary

Gravity-induced local collapse is at the forefront of understanding the quantum–classical transition. In quantum gravitational reduction models, gravity is hypothesized to set the “classicality” scale by enforcing localization of macro-superpositions, while leaving microscopic quantum systems untouched. In classical and semiclassical contexts, gravity’s universal reach underpins the transition from stable, extended states to highly localized, collapsed configurations, whether in astrophysical cores or granular aggregates.

Furthermore, the experimental discrimination between gravity-induced, mass-dependent decoherence and standard environmental noise, supported by quantum computing simulations, offers a practical path for future validation or falsification of theoretical models.

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Gravity-induced local collapse encompasses a broad set of phenomena in which gravity, through fundamentally local or universal mechanisms, enforces the suppression of extended, delocalized, or unstable states—from quantum superpositions to mechanical structures—by driving the system into rapidly evolving, locally concentrated configurations. This concept integrates advances in canonical Hamiltonian gravity, quantum state reduction models, laboratory and geophysical collapse observations, and modern quantum technology, providing a cohesive framework for understanding gravity’s role in localization and the onset of classicality.