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arxiv: 2605.15600 · v1 · pith:2WSISDWTnew · submitted 2026-05-15 · 🌀 gr-qc · quant-ph

The role of Wigner rotation in estimating the specific angular momentum of a Kerr spacetime

F. J. Lobo , M. Rivera-Tapia , G. Rubilar , A. Delgado This is my paper

Pith reviewed 2026-05-20 17:48 UTC · model grok-4.3

classification 🌀 gr-qc quant-ph
keywords Kerr spacetimeWigner rotationpolarization rotationgeodesic interferometerspecific angular momentumMach-Zehnder interferometergravitational time delay
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The pith

A geodesic Mach-Zehnder interferometer with a single photon encodes both gravitational time delay and Wigner rotation, yielding an estimate of Kerr specific angular momentum.

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

The paper investigates polarization rotation due to the gravitational field in Kerr spacetime and explores estimating the specific angular momentum parameter. It models a Mach-Zehnder interferometer whose arms follow null geodesics and tracks a single photon through the setup. The detection probability at the output ports depends on two separate phase differences computed in the slow-rotation and weak-field limits, so the visibility registers both the time-delay effect and the polarization rotation. From this probability the authors derive an estimate for the angular momentum and quantify its uncertainty.

Core claim

In a geodesic interferometer in Kerr spacetime the interferometric visibility is produced by the sum of a gravitational time-delay phase and a Wigner rotation phase of the photon polarization; under the slow-rotation and weak-field approximations this visibility directly supplies an estimate of the specific angular momentum together with its uncertainty.

What carries the argument

Wigner rotation of photon polarization along null geodesics, combined with gravitational time delay in the slow-rotation weak-field Kerr metric.

If this is right

  • The interferometric visibility functions as a combined signature of gravitational time delay and polarization rotation.
  • An estimate of the specific angular momentum follows directly from the observed detection probability.
  • The uncertainty of that estimate is characterized once the two phase contributions are isolated.

Where Pith is reading between the lines

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

  • The same visibility data might separate the two effects more cleanly if independent control over the time-delay term were available.
  • Analogous interferometers in other weak-field metrics could test whether polarization rotation remains measurable when angular momentum is replaced by other parameters.

Load-bearing premise

The phase differences for time delay and polarization rotation can be reliably computed and isolated using only the slow-rotation and weak-field approximations in the Kerr metric, without higher-order corrections or full geodesic integration affecting the estimate.

What would settle it

A measured detection probability that fails to match the predicted function of the two calculated phase differences in a controlled weak-field rotating spacetime would falsify the estimation procedure.

Figures

Figures reproduced from arXiv: 2605.15600 by A. Delgado, F. J. Lobo, G. Rubilar, M. Rivera-Tapia.

Figure 1
Figure 1. Figure 1: FIG. 1: Geodesic interferometer: A single photon emit [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: shows ∆ϑ τ as a function of the initial position of the photon source r2 ∈ [7 × 106 m, 7.5 × 106 m] for a geodesic interferometer with l = 0.3 m and h = 0.7 m for ω1 = 106 Hz, ω2 = 1010 Hz and ω3 = 1012 Hz. Clearly, the phase difference generated by the arrival time difference exhibits very small values in the interval [10−22 , 10−16]. The choice of values allows comparison with the study of the Kerr frame… view at source ↗
Figure 3
Figure 3. Figure 3: shows ∆ϑ as a function of the angular coor￾dinate θ for the case of Earth with REarth ≈ 7 × 106 m and ∆r := r3 − r1 ≈ 1 m with r2 = REarth (red line) and r2 = 2REarth (blue line). As is apparent from this figure, the Wigner phase ∆ϑ reaches values of the order of 10−30, which is several orders of magnitude smaller than the phase shift ∆ϑ τ generated by the arrival time difference. The value of ∆ϑ can be in… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Relative error [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

We study the rotation of the polarization due to the gravitational field in the Kerr spacetime and the possibility of estimating the specific angular momentum that parameterizes this metric. Our approach is based on a geodesic interferometer, that is, a Mach-Zehnder interferometer whose arms are defined by null geodesics, and a single photon propagating within it. We show that the detection probability at the output ports of the interferometer is a function of two phase differences, one arising from the gravitational time delay and the other from the polarization rotation, both computed under the slow rotation and weak field approximations. Thereby, the interferometric visibility is a signature of two relativistic effects. Using the detection probability, we obtain an estimate for the specific angular momentum and characterize its uncertainty.

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 / 2 minor

Summary. The manuscript studies polarization rotation in Kerr spacetime via a geodesic Mach-Zehnder interferometer using a single photon. It claims that the output-port detection probability depends on two distinct phase differences—one from gravitational time delay and one from Wigner/polarization rotation—both evaluated in the slow-rotation and weak-field limits. The resulting interferometric visibility therefore encodes both effects, permitting an estimate of the specific angular momentum a together with its uncertainty.

Significance. If the claimed phase separation holds, the work offers a concrete interferometric route to extract the Kerr parameter a from combined time-delay and frame-dragging signatures. This is potentially useful for precision tests of general relativity with quantum light. The explicit linkage of visibility to two relativistic phases is a clear conceptual contribution, though its quantitative impact remains limited by the absence of displayed derivations and validation.

major comments (2)
  1. [Abstract / phase definitions] Abstract and central derivation: the detection probability is asserted to be a function of two separable phases whose a-dependence can be inverted, yet no explicit expressions for either phase or for P are supplied. Without these formulas it is impossible to verify that the Wigner-rotation contribution is cleanly isolated from the time-delay term at the order kept in the slow-rotation expansion.
  2. [Approximations and phase computation] Approximations section: the slow-rotation and weak-field expansions are used to truncate the null-geodesic and parallel-transport equations. The manuscript does not quantify the size of the omitted cross terms (frame-dragging corrections that enter both coordinate time and polarization transport at the same order in a). For interferometer baselines or frequencies where these terms are comparable to the leading a contribution, the claimed estimator for a would be biased.
minor comments (2)
  1. [Notation] Clarify the precise definition of the specific angular momentum a (including units and normalization) and how it appears in each phase expression.
  2. [Uncertainty analysis] Provide a brief error-propagation formula or Monte-Carlo procedure used to characterize the uncertainty in the extracted value of a.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We respond to each major comment below, indicating the changes we will make in the revised version.

read point-by-point responses

  1. Referee: [Abstract / phase definitions] Abstract and central derivation: the detection probability is asserted to be a function of two separable phases whose a-dependence can be inverted, yet no explicit expressions for either phase or for P are supplied. Without these formulas it is impossible to verify that the Wigner-rotation contribution is cleanly isolated from the time-delay term at the order kept in the slow-rotation expansion.

    Authors: The explicit expressions for the gravitational time-delay phase, the Wigner-rotation phase, and the resulting detection probability P are derived in the main text under the slow-rotation and weak-field approximations. To address the referee's concern and allow direct verification without consulting the body of the paper, we will incorporate the key formulas into the abstract of the revised manuscript. revision: yes

  2. Referee: [Approximations and phase computation] Approximations section: the slow-rotation and weak-field expansions are used to truncate the null-geodesic and parallel-transport equations. The manuscript does not quantify the size of the omitted cross terms (frame-dragging corrections that enter both coordinate time and polarization transport at the same order in a). For interferometer baselines or frequencies where these terms are comparable to the leading a contribution, the claimed estimator for a would be biased.

    Authors: We agree that an explicit estimate of the neglected cross terms would strengthen the presentation. In the consistent expansion we employ, these terms appear at higher order and remain small for the weak-field, slow-rotation regime considered. We will add a short discussion in the revised manuscript that quantifies their relative magnitude for representative interferometer baselines and frequencies, thereby clarifying the domain of validity of the estimator. revision: yes

Circularity Check

0 steps flagged

No circularity: estimator obtained by inverting derived probability expression

full rationale

The paper derives the two phase differences (gravitational time delay and Wigner/polarization rotation) from the Kerr metric under explicit slow-rotation and weak-field approximations, then writes the output-port detection probability as an explicit function of those phases. The estimate for specific angular momentum a is obtained by algebraic inversion of that probability formula together with an uncertainty characterization; the abstract and reader's summary present this as a forward computation followed by inversion rather than a parameter that is fitted to data containing the same a or redefined by construction. No self-citation chain, ansatz smuggling, or renaming of a known result is indicated as load-bearing for the central claim. The derivation therefore remains self-contained against the stated approximations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard general-relativistic approximations and the existence of well-defined null geodesics forming a closed interferometer; no new entities are postulated and no free parameters are introduced beyond the Kerr angular-momentum parameter itself.

axioms (1)
  • domain assumption Slow rotation and weak field approximations suffice to compute the gravitational time delay and polarization rotation phases in Kerr spacetime.
    Explicitly invoked to obtain the two phase differences that enter the detection probability.

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