arxiv: 2512.15393 · v2 · submitted 2025-12-17 · 🌀 gr-qc · hep-th· quant-ph

Recognition: 2 theorem links

· Lean Theorem

Spontaneous wave function collapse from non-local gravitational self-energy

Kimet Jusufi , Douglas Singleton , Francisco S.N. Lobo

Authors on Pith no claims yet

Pith reviewed 2026-05-16 22:00 UTC · model grok-4.3

classification 🌀 gr-qc hep-thquant-ph

keywords wave function collapseSchrödinger-Newton equationnon-local gravityT-dualityequivalence principlequantum superpositionsemiclassical spacetime

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The pith

Non-local gravitational self-energy destabilizes quantum superpositions, producing spontaneous collapse on a timescale inversely proportional to mass.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper adds a non-local gravitational self-energy term motivated by T-duality to the semiclassical Schrödinger-Newton equation. Spacetime non-locality makes linear superposition only an approximation that fails once gravity is active. Assuming superposition holds at first, the authors show it becomes unstable, with collapse arising from the clash between the equivalence principle and quantum superposition. The resulting collapse time is model-independent and scales inversely with the mass of the system. Wave functions in inertial versus freely falling frames acquire extra phase shifts containing linear, cubic, and constant gravitational corrections.

Core claim

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 spontaneous, model-independent collapse with time inversely proportional to the mass of the system, arising from the tension between the equivalence principle and the superposition principle in semiclassical non-local spacetime.

What carries the argument

Non-local gravitational self-energy term motivated by T-duality, inserted into the Schrödinger-Newton equation to render linear superposition unstable.

Load-bearing premise

The non-local gravitational self-energy term can be consistently added to the semiclassical Schrödinger-Newton equation while initially preserving linear superposition as a valid starting point that later breaks.

What would settle it

Experimental measurement of the collapse time for a known mass that fails to scale inversely with mass, or the absence of any collapse in a regime where the model predicts a measurable effect.

read the original abstract

We incorporate non-local gravitational self-energy, motivated by string-inspired T-duality, into the Schr\"odinger-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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adds T-duality non-locality to the Schrödinger-Newton equation and derives a 1/mass collapse time from inertial vs free-fall phase shifts, but the nonlinearity of the inserted term likely breaks the linear-superposition starting assumption.

read the letter

The main point is that this work inserts a non-local gravitational self-energy term motivated by T-duality into the Schrödinger-Newton equation, assumes linear superposition holds without gravity, and then shows that gravity makes the superposition unstable. The instability comes from a gravitationally induced phase shift between inertial and freely falling frames that includes linear and cubic time terms plus a constant, producing a spontaneous collapse time inversely proportional to mass. The claim is that this tension between the equivalence principle and superposition is model-independent once the non-local term is in place. That specific combination and the frame-based derivation of the scaling look new relative to standard gravitational decoherence papers. The paper does a reasonable job spelling out the logic inversion and tying the phase corrections directly to collapse. The soft spot is exactly the one flagged in the stress test. A non-local self-energy term is generically nonlinear in the wave function, so the full equation is nonlinear from t=0. That makes it hard to treat an exact linear superposition as the initial state whose instability is then derived. The phase-shift calculation therefore sits on an inconsistent background unless the paper shows explicitly how the non-local insertion remains perturbatively linear at early times. Without the explicit form of the non-local term and the step-by-step derivation in the text, it is difficult to judge whether the cubic term emerges cleanly or whether hidden scales enter. The citations follow the usual SN and T-duality lines and do not appear circular on their own. This is for readers working on gravity-induced collapse models and semiclassical quantum gravity who want to see how string-inspired non-locality might alter the Schrödinger-Newton dynamics. A serious referee could usefully check the nonlinearity consistency and the phase calculation. I would send it to peer review rather than desk reject.

Referee Report

2 major / 1 minor

Summary. The paper incorporates a non-local gravitational self-energy term motivated by string-inspired T-duality into the Schrödinger-Newton equation. It inverts the usual logic by assuming the validity of linear superposition as an initial condition and demonstrates that gravitational effects render such superpositions unstable. This instability arises from a phase shift between wave functions computed in inertial and freely falling frames, containing linear and cubic time-dependent terms plus a constant; the resulting spontaneous collapse time scales inversely with the mass of the system and is claimed to be model-independent.

Significance. If the derivation holds without internal inconsistency, the result would supply a concrete, parameter-free mechanism for objective wave-function collapse rooted in the tension between the equivalence principle and quantum superposition within a semiclassical spacetime that carries intrinsic non-locality. This would strengthen the Schrödinger-Newton framework by linking collapse directly to a T-duality-motivated correction rather than an ad-hoc stochastic term, offering falsifiable predictions for collapse timescales in macroscopic superpositions.

major comments (2)

[phase-shift calculation and collapse-time derivation] The phase-shift calculation between inertial and free-falling frames (described in the abstract and the section deriving the collapse time) assumes that linear superposition remains an exact solution at early times. However, the non-local gravitational self-energy term is nonlinear in the wave function; inserting it into the Schrödinger-Newton equation renders the dynamics nonlinear from t=0, so the initial linear superposition is not a solution of the equation being analyzed. This undermines the perturbative consistency of the phase-shift derivation and the claimed collapse-time scaling.
[section introducing the non-local term and final scaling formula] The claim that the collapse time is model-independent and inversely proportional to mass depends on the concrete functional form of the T-duality non-local term. It is not shown whether the non-local length scale is fixed by external string-theory input or effectively fitted to reproduce the desired scaling; if the latter, the result is circular by construction and the 'parameter-free' status does not hold.

minor comments (1)

[Abstract] The abstract states the central claims at a high level but contains no equations, explicit form of the non-local operator, or derivation steps, which makes immediate technical assessment difficult.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major point below with clarifications and indicate the revisions that will be incorporated.

read point-by-point responses

Referee: [phase-shift calculation and collapse-time derivation] The phase-shift calculation between inertial and free-falling frames (described in the abstract and the section deriving the collapse time) assumes that linear superposition remains an exact solution at early times. However, the non-local gravitational self-energy term is nonlinear in the wave function; inserting it into the Schrödinger-Newton equation renders the dynamics nonlinear from t=0, so the initial linear superposition is not a solution of the equation being analyzed. This undermines the perturbative consistency of the phase-shift derivation and the claimed collapse-time scaling.

Authors: We agree that the full dynamics are nonlinear due to the gravitational self-energy. Our approach begins with an initial linear superposition prepared in the absence of gravity and treats the non-local term as inducing a perturbative phase accumulation between frames. The derivation is valid in the early-time regime where gravitational effects have not yet caused significant deviation from linearity. We will revise the manuscript to explicitly state this perturbative approximation, define the regime of validity, and clarify that the initial state is an approximate solution prior to collapse onset. This strengthens the presentation without altering the scaling result. revision: partial
Referee: [section introducing the non-local term and final scaling formula] The claim that the collapse time is model-independent and inversely proportional to mass depends on the concrete functional form of the T-duality non-local term. It is not shown whether the non-local length scale is fixed by external string-theory input or effectively fitted to reproduce the desired scaling; if the latter, the result is circular by construction and the 'parameter-free' status does not hold.

Authors: The non-local length scale is fixed by the T-duality radius from string theory, an external input unrelated to collapse phenomenology. The inverse-mass scaling follows from dimensional analysis of the non-local self-energy combined with the equivalence-principle mismatch and holds for any non-local term characterized by such a fixed scale. In the revision we will add an explicit derivation demonstrating the robustness of this scaling for general non-local forms with externally fixed length, confirming the parameter-free status without circularity. revision: yes

Circularity Check

0 steps flagged

No significant circularity: collapse time derived from phase-shift instability in modified SN equation

full rationale

The derivation chain begins with an externally motivated non-local gravitational self-energy term (T-duality), inserts it into the semiclassical Schrödinger-Newton framework, assumes linear superposition as an initial approximation, and computes a gravitationally induced phase shift (linear + cubic in t plus constant) between inertial and free-fall frames. This produces an instability yielding a collapse time scaling as 1/mass. No equation reduces by construction to a fitted parameter, no self-citation chain bears the central load, and the result is explicitly labeled model-independent. The non-local term is treated as an input motivated outside the present work; the phase-shift calculation follows from the modified Hamiltonian without renaming or smuggling an ansatz that presupposes the target scaling. The paper therefore remains self-contained against external benchmarks (equivalence principle, linear Schrödinger dynamics at early times).

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 1 invented entities

The central claim rests on inserting a non-local gravitational self-energy term motivated by T-duality into the Schrödinger-Newton equation, assuming linear superposition holds initially, and then showing gravitational instability. The non-local scale is not specified as derived or fitted in the abstract.

axioms (3)

domain assumption Linear superposition principle remains valid as an initial assumption even when gravity is present
Explicitly invoked when the authors 'invert the logic' and assume superposition to demonstrate instability.
domain assumption Semiclassical spacetime background with intrinsic non-locality from T-duality
The non-local gravitational self-energy is motivated by string-inspired T-duality and inserted into the semiclassical Schrödinger-Newton equation.
domain assumption Equivalence principle holds in the semiclassical regime
The tension between equivalence principle and superposition is stated as the source of collapse.

invented entities (1)

Non-local gravitational self-energy term no independent evidence
purpose: To render spacetime intrinsically non-local and induce spontaneous collapse when added to the Schrödinger-Newton equation
Introduced as the key modification; no independent evidence or falsifiable prediction outside the model is stated in the abstract.

pith-pipeline@v0.9.0 · 5441 in / 1344 out tokens · 29684 ms · 2026-05-16T22:00:22.205888+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We incorporate non-local gravitational self-energy, motivated by string-inspired T-duality, into the Schrödinger–Newton equation... τcollapse ∼ ℏ / ΔEGSE ... inversely proportional to the mass
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

non-local gravitational self-energy term... EGSE = −1/2 ∫ VG(x) ρbare(x) d³x ... modified Schrödinger–Newton equation (7)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Gravitationally induced wave-function collapse from dynamical bifurcation
quant-ph 2026-04 unverdicted novelty 6.0

Gravitational self-interaction induces deterministic collapse as a bifurcation selecting stable localized states from unstable extended ones in a regularized nonlinear Schrödinger equation.

Reference graph

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