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arxiv: 2512.16667 · v3 · submitted 2025-12-18 · 🌀 gr-qc · hep-th· quant-ph

Field Quantisations in Schwarzschild Spacetime: Theory versus Low-Energy Experiments

Viacheslav A. Emelyanov This is my paper

Pith reviewed 2026-05-16 21:13 UTC · model grok-4.3

classification 🌀 gr-qc hep-thquant-ph
keywords quantum field theory in curved spacetimeSchwarzschild spacetimeHawking radiationpropagatorpath-integral formalismgravitational interferencefree fall
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The pith

The propagator for a Hawking particle in Schwarzschild spacetime differs from the path-integral propagator that matches low-energy gravity experiments.

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

Non-relativistic quantum mechanics with Newton's potential describes free fall and gravity-induced interference experiments on Earth. Quantum field theory in curved spacetime offers a more fundamental treatment by embedding gravity through general covariance, yet leaves the notion of a particle ambiguous. The paper computes the propagator for a Hawking particle in the far-horizon region of Schwarzschild spacetime within this framework. The result does not coincide with the propagator obtained from the path-integral formalism that successfully reproduces the low-energy experiments.

Core claim

We compute the propagator for a Hawking particle in the far-horizon region of Schwarzschild spacetime and find that it differs from the propagator that follows from the path-integral formalism, the latter being the object that adequately describes both free fall and quantum interference induced by gravity.

What carries the argument

The propagator of the Hawking particle obtained from field quantisation in Schwarzschild spacetime.

If this is right

  • The path-integral approach used for terrestrial gravity experiments may not be derivable from quantum field theory in curved spacetime without additional assumptions.
  • Consistency between high-energy and low-energy descriptions of gravity requires identifying which propagator governs actual particle motion near a horizon.
  • Low-energy quantum mechanics with Newtonian gravity may need revision if the curved-spacetime propagator is taken as fundamental.
  • Hawking radiation calculations could be affected by the choice of propagator when extended to regions far from the horizon.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The discrepancy could be tested by comparing predictions for atom interferometry in Earth's gravity against curved-spacetime calculations in a weak-field limit of Schwarzschild.
  • If the difference is general, it may indicate that standard quantisation procedures in curved spacetime require modification to recover the correct non-relativistic limit.
  • This raises the possibility that the ambiguity in defining particles in curved spacetime affects even low-energy regimes previously thought to be unproblematic.

Load-bearing premise

The propagator computed for a Hawking particle in the far-horizon region can be directly compared with the path-integral propagator used for non-relativistic particles in weak gravitational fields.

What would settle it

An experiment that measures the phase shift or probability amplitude for a quantum particle in free fall or interference that matches one propagator but not the other.

Figures

Figures reproduced from arXiv: 2512.16667 by Viacheslav A. Emelyanov.

Figure 1
Figure 1. Figure 1: FIG. 1. Numerical computations of ( [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Numerical computations of the gray-body factor Γ( [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Left column: Numerical computations of [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Left column: Numerical computations of [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Numerical computations of [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Numerical computations of [PITH_FULL_IMAGE:figures/full_fig_p027_6.png] view at source ↗
read the original abstract

Non-relativistic quantum particles in the Earth's gravitational field are successfully described by the Schr\"{o}dinger equation with Newton's gravitational potential. Particularly, quantum mechanics is in agreement with such experiments as free fall and quantum interference induced by gravity. However, quantum mechanics is a low-energy approximation to quantum field theory. The latter is successful by the description of high-energy experiments. Gravity is embedded in quantum field theory through the general-covariance principle. This framework is known in the literature as quantum field theory in curved spacetime, where the concept of a quantum particle is, though, ambiguous. In this article, we study in this framework how a Hawking particle moves in the far-horizon region of Schwarzschild spacetime by computing its propagator. We find this propagator differs from that which follows from the path-integral formalism -- the formalism which adequately describes both free fall and quantum interference induced by gravity.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript computes the propagator for a Hawking particle in the far-horizon region of Schwarzschild spacetime within the framework of quantum field theory in curved spacetime (QFTCS) and reports that this propagator differs from the one obtained via the path-integral formalism, which is stated to successfully describe low-energy experiments such as free fall and gravitational quantum interference for non-relativistic particles in weak gravitational fields.

Significance. If the discrepancy is shown to survive a controlled weak-field limit with matched vacua and normalizations, the result would indicate that the particle concept in QFTCS does not reduce to the effective non-relativistic description used for terrestrial gravity experiments, with implications for the consistency of quantum mechanics and general relativity at low energies. The attempt to perform an explicit propagator comparison is a positive step toward falsifiable contact between the two frameworks.

major comments (2)
  1. [Abstract] The central claim requires that the QFTCS propagator (obtained from the appropriate two-point function or Bogoliubov-transformed modes for a Hawking particle) coincides with the path-integral propagator in the appropriate limit; however, the abstract provides no derivation steps, explicit mode expansions, or error estimates for this comparison, making it impossible to verify whether the reported difference follows from the field equations or from an unstated choice of vacuum or normalization.
  2. [Comparison of formalisms] The comparison assumes direct equivalence between the Hawking-particle propagator in the asymptotically flat far region and the non-relativistic path-integral propagator used for weak static potentials; this equivalence is not automatic because Hawking modes carry thermal correlations from the global Kruskal vacuum while the low-energy treatment employs local positive-frequency modes with no horizon, and the manuscript does not demonstrate that these distinctions vanish in the relevant limit.
minor comments (1)
  1. [Abstract] The abstract contains minor grammatical issues ('by the description of high-energy experiments' should read 'in the description'; 'by computing its propagator' is awkward) that should be corrected for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and for recognizing the potential implications of our work. We address each major comment below and have revised the manuscript to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract] The central claim requires that the QFTCS propagator (obtained from the appropriate two-point function or Bogoliubov-transformed modes for a Hawking particle) coincides with the path-integral propagator in the appropriate limit; however, the abstract provides no derivation steps, explicit mode expansions, or error estimates for this comparison, making it impossible to verify whether the reported difference follows from the field equations or from an unstated choice of vacuum or normalization.

    Authors: We agree that the abstract was too concise. In the revised version we have expanded it to outline the Bogoliubov transformation from the Kruskal vacuum, the explicit mode expansions employed in the far-horizon region, and the leading-order error estimates used in the weak-field comparison. These additions make the origin of the reported discrepancy traceable to the field equations and the chosen vacuum. revision: yes

  2. Referee: [Comparison of formalisms] The comparison assumes direct equivalence between the Hawking-particle propagator in the asymptotically flat far region and the non-relativistic path-integral propagator used for weak static potentials; this equivalence is not automatic because Hawking modes carry thermal correlations from the global Kruskal vacuum while the low-energy treatment employs local positive-frequency modes with no horizon, and the manuscript does not demonstrate that these distinctions vanish in the relevant limit.

    Authors: We acknowledge that an explicit demonstration was missing. The revised manuscript now contains a dedicated paragraph showing that, for non-relativistic energies far below the Hawking temperature and in the asymptotically flat far region, the thermal correlations are exponentially suppressed. With this suppression the Bogoliubov coefficients reduce to the Minkowski limit, so the distinction between global and local positive-frequency modes becomes negligible. The remaining discrepancy therefore survives this controlled limit and cannot be attributed to an inconsistent choice of vacuum. revision: yes

Circularity Check

0 steps flagged

No circularity: direct QFTCS propagator computation compared to path-integral result

full rationale

The paper computes the propagator for a Hawking particle in the far-horizon region of Schwarzschild spacetime within the QFTCS framework and reports a difference from the path-integral propagator. No load-bearing step reduces by construction to a fitted input, self-definition, or self-citation chain; the derivation is presented as an explicit calculation of the two-point function or mode-sum propagator. The comparison rests on stated assumptions about the Hawking state and asymptotic region rather than tautological renaming or imported uniqueness theorems. This is the most common honest finding for a computational paper whose central claim is a reported mismatch between two formalisms.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the QFT-in-curved-spacetime propagator for a Hawking particle is the correct object to compare with the non-relativistic path-integral propagator; no free parameters are mentioned, but the choice of vacuum and the precise definition of the particle state function as axioms.

axioms (2)
  • domain assumption The concept of a quantum particle remains well-defined in the far-horizon region of Schwarzschild spacetime
    Invoked when the author computes the propagator for a Hawking particle
  • domain assumption The path-integral formalism used for low-energy gravity experiments is the appropriate benchmark for comparison
    Stated in the abstract as the formalism that adequately describes free fall and interference

pith-pipeline@v0.9.0 · 5451 in / 1390 out tokens · 31621 ms · 2026-05-16T21:13:02.862388+00:00 · methodology

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