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arxiv: 2601.17849 · v2 · pith:ZFPMOW3Fnew · submitted 2026-01-25 · ✦ hep-th · gr-qc· hep-ph

Geometric noise spectrum in interferometers

Laurent Freidel , Robin Oberfrank This is my paper

Pith reviewed 2026-05-22 11:36 UTC · model grok-4.3

classification ✦ hep-th gr-qchep-ph
keywords quantum gravityinterferometersmetric perturbationsWightman functionpower spectral densitygraviton fluctuationsUV divergencesPlanck scale
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The pith

The power spectral density of time delay fluctuations in interferometers, derived from the Wightman function of linear metric perturbations, is ultraviolet finite and remains suppressed by the Planck scale across vacuum, thermal, squeezed,

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

The paper sets out to compute the power spectral density of time delay fluctuations induced by quantum metric perturbations as a possible low-energy signature of quantum gravity. It begins with a general formula that expresses this spectrum in terms of the Wightman function of linear metric perturbations and then evaluates the expression for graviton fluctuations in the vacuum, in thermal states, and in squeezed states, as well as for the vacuum stress-energy of a massless scalar field. The resulting spectra contain no ultraviolet divergences. A sympathetic reader would care because the calculation supplies an explicit, finite observable that could in principle be accessed with existing interferometer technology rather than requiring Planck-scale energies.

Core claim

The central claim is that the power spectral density of time delay fluctuations is given directly by an integral involving the Wightman function of linear metric perturbations; when this expression is evaluated for intrinsic graviton fluctuations in the vacuum, thermal, and squeezed states and for vacuum fluctuations of a massless scalar field, the spectra are ultraviolet finite and, although thermal and squeezed states provide amplification, they remain suppressed by the Planck scale.

What carries the argument

The power spectral density of time delay fluctuations expressed via the Wightman function of linear metric perturbations, which converts two-point correlations of quantum gravitational fluctuations into a finite frequency spectrum for each state considered.

If this is right

  • The spectra remain free of ultraviolet divergences for graviton fluctuations in vacuum, thermal, and squeezed states.
  • Thermal and squeezed graviton states amplify the fluctuations while preserving Planck-scale suppression.
  • Vacuum stress-energy fluctuations of a massless scalar field produce similarly finite and suppressed spectra.
  • The general expression supplies a concrete low-energy quantum-gravitational observable for interferometer experiments.

Where Pith is reading between the lines

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

  • The same formalism could be applied to existing large-scale interferometers to place experimental bounds on the size of the predicted Planck-suppressed noise.
  • Including interactions between metric perturbations and additional matter fields would generate further testable corrections to the spectra.
  • The absence of divergences suggests that a full nonlinear treatment might still yield finite results at the scales probed by current detectors.

Load-bearing premise

Time delay fluctuations in a real interferometer are accurately captured by the Wightman function of linear metric perturbations without higher-order or nonlinear gravitational effects becoming important.

What would settle it

A laboratory measurement of the time-delay power spectrum in an interferometer that either exhibits ultraviolet divergences at high frequencies or shows amplitudes exceeding the Planck-scale suppression would falsify the central claim.

Figures

Figures reproduced from arXiv: 2601.17849 by Laurent Freidel, Robin Oberfrank.

Figure 1
Figure 1. Figure 1: Spacetime diagram of a null ray crossing the interferometer in the [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Plot of the dimensionless function Fh(x) from (3.18) that determines the frequency￾dependence of the noise spectral density according to (3.17). We also show its large-frequency envelope (3xπ) −1 . From the closed-form expression and the plot, several characteristic features of the spectrum can be identified: • Behavior in the limits. Both the x → 0 and the x → ∞ limits are finite and tend to zero. For low… view at source ↗
Figure 3
Figure 3. Figure 3: Plot of the dimensionless function FH(x) from (4.30) that determines the frequency￾dependence of the noise spectral density of the induced metric fluctuations according to (4.29). We also show its envelope x(5 · 1280π 3 ) −1 . The dominant oscillation comes from the cos(2x) term with amplitude. The leading upper and lower envelopes are therefore F max H (x) ∼ x 6400π 3 , F min H (x) ∼ x 19200π 3 . (4.33) w… view at source ↗
read the original abstract

We study the power spectral density of time delay fluctuations in an interferometer as a potential low-energy quantum gravitational observable. We derive a general expression for the spectrum in terms of the Wightman function of linear metric perturbations, which we then apply to a variety of cases. We analyze the intrinsic graviton fluctuations in the vacuum, thermal, and squeezed states, as well as the fluctuations induced by the vacuum stress-energy of a massless scalar field. We find that the resulting spectra are free of ultraviolet divergences and that, while thermal and squeezed states provide a natural amplification mechanism, the spectra remain suppressed by the Planck scale.

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

1 major / 1 minor

Summary. The manuscript derives a general expression for the power spectral density of time-delay fluctuations in an interferometer in terms of the Wightman function of linearized metric perturbations h_μν. It applies this formula to graviton fluctuations in vacuum, thermal, and squeezed states as well as to fluctuations induced by the vacuum stress-energy of a massless scalar field, concluding that the resulting spectra are ultraviolet-finite and remain suppressed by the Planck scale, with thermal and squeezed states providing a natural amplification mechanism.

Significance. If the linear-perturbation framework is justified, the work supplies a concrete, parameter-free route to a low-energy quantum-gravitational observable in interferometers. The direct use of the Wightman function, the reported absence of UV divergences, and the identification of amplification channels in non-vacuum states are genuine strengths that could guide future experimental searches.

major comments (1)
  1. [Derivation of the spectrum (general expression in terms of the Wightman function)] The central expression for the time-delay power spectrum is obtained by inserting the two-point Wightman function of linearized metric perturbations into the proper-time integral. This step implicitly assumes that quadratic and higher-order graviton self-interactions, stress-energy back-reaction, and non-linear coordinate effects remain negligible at the relevant frequencies. No estimate or bound on the size of these corrections is provided; if they generate additional UV-sensitive contributions that survive the same filtering, the claimed UV finiteness and strict Planck suppression would be modified. A quantitative assessment of the linear regime’s domain of validity is therefore required to support the main conclusions.
minor comments (1)
  1. [Abstract] The abstract states that the spectra are “free of ultraviolet divergences” without indicating whether this finiteness follows from the linear approximation, from the specific frequency window, or from an explicit cancellation; a brief clarifying sentence would help readers.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive major comment. We address the point regarding the linearised framework below and have revised the manuscript to include additional discussion on its domain of validity.

read point-by-point responses

  1. Referee: [Derivation of the spectrum (general expression in terms of the Wightman function)] The central expression for the time-delay power spectrum is obtained by inserting the two-point Wightman function of linearized metric perturbations into the proper-time integral. This step implicitly assumes that quadratic and higher-order graviton self-interactions, stress-energy back-reaction, and non-linear coordinate effects remain negligible at the relevant frequencies. No estimate or bound on the size of these corrections is provided; if they generate additional UV-sensitive contributions that survive the same filtering, the claimed UV finiteness and strict Planck suppression would be modified. A quantitative assessment of the linear regime’s domain of validity is therefore required to support the main conclusions.

    Authors: We agree that the central expression is derived within the linearised gravity approximation, treating h_μν as a free field (or in the specified quantum state) whose Wightman function enters the proper-time integral. This is the standard approach for computing Planck-suppressed observables in the low-energy effective theory. Higher-order graviton self-interactions and back-reaction effects enter at higher orders in the gravitational coupling and are therefore further suppressed by additional powers of the Planck scale relative to the leading linear term. Non-linear coordinate effects are likewise higher order in the weak-field expansion. While a fully quantitative bound on these corrections would require a separate calculation of loop or non-linear contributions (which lies outside the present scope), we have added a new paragraph in the revised manuscript (in the discussion following Eq. (main expression)) that outlines the regime of validity: for interferometer frequencies far below the Planck scale, the linear term dominates and the reported UV finiteness together with the overall Planck suppression remain intact. This clarification supports the main conclusions without altering the computed spectra. revision: partial

standing simulated objections not resolved
  • A fully quantitative numerical estimate of the magnitude of higher-order corrections would require an independent calculation involving graviton loops or non-linear metric effects, which is beyond the scope of this work.

Circularity Check

0 steps flagged

Derivation of time-delay spectrum from Wightman function is self-contained with no reduction to inputs by construction

full rationale

The paper derives a general expression for the power spectral density of time-delay fluctuations directly from the two-point Wightman function of linearized metric perturbations h_μν and then evaluates this expression for vacuum, thermal, squeezed graviton states and for the stress-energy of a massless scalar. No step equates a fitted parameter to a prediction, renames a known result, or relies on a load-bearing self-citation whose content is itself unverified. The reported absence of UV divergences and Planck-scale suppression follow from the standard properties of the Wightman function together with the interferometer's frequency filtering; these are independent of the final observable and do not collapse to a tautology or to prior work by the same authors. The derivation therefore remains non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; ledger entries are inferred from the stated approach and therefore provisional.

axioms (1)
  • domain assumption Linear metric perturbations and their Wightman function suffice to describe the relevant low-energy quantum-gravitational fluctuations in an interferometer.
    Central to the general expression for the spectrum derived from metric perturbations.

pith-pipeline@v0.9.0 · 5616 in / 1197 out tokens · 51354 ms · 2026-05-22T11:36:58.536350+00:00 · methodology

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Forward citations

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