Multi-wavelength polarization observations of astrophysical sources can test the Einstein equivalence principle (EEP) through the parametrized difference Δγp\Delta\gamma_p between the two photon polarization modes: the associated differential Shapiro delay rotates the observed polarization angle with a characteristic 1/λ1/\lambda dependence, ϕobs(λ)=ϕ0+A/λ+Bλ2\phi_{\mathrm{obs}}(\lambda)=\phi_0+A/\lambda+B\lambda^2, where A≡πc ΔtgraA\equiv\pi c\,\Delta t_{\mathrm{gra}} encodes the EEP-violating delay and BB is the rotation measure. Yi, Zou, Wei & Zhou (2020) applied this model to 60 radio sources from the Australia Telescope 20 GHz (AT20G) survey and 29 optical stars, obtaining Δγp\Delta\gamma_p limits of order 10−2610^{-26}–10−2010^{-20}, but stressed that these must be treated as upper limits: opacity effects, differential Faraday rotation, and multi-component rotation measures can mimic or mask the A/λA/\lambda signature; some catalogue polarization angles lack published uncertainties; the Laniakea supercluster potential was approximated as a Keplerian point mass; and the method cannot discriminate among specific metric gravity theories. The open problem is whether the EEP-induced 1/λ1/\lambda signature can be isolated from these propagation and gravitational systematics at realistically achievable multi-wavelength polarimetry, so that polarimetric Δγp\Delta\gamma_p becomes a systematics-controlled measurement with demonstrated power to discriminate among metric gravity theories. No published work has yet modelled these effects in the polarization-angle channel; the field's methodological response has moved to gauge-consistent fast-radio-burst and gravitational-wave channels, leaving this polarimetric core open.

Background

The Einstein equivalence principle (EEP) states that all non-gravitational physics is locally independent of position and of the velocity and internal state of freely falling test bodies; a photon-sector violation can be parametrized by letting the parametrized post-Newtonian (PPN) parameter γ\gamma (equal to 1 in general relativity), which measures the curvature of space produced by rest mass and governs how strongly gravity deflects light, differ between the two photon polarization modes, Δγp=γ1−γ2\Delta\gamma_p=\gamma_1-\gamma_2. Because γ\gamma also controls the Shapiro delay — the extra light-travel time accumulated when light crosses a gravitational potential — a nonzero Δγp\Delta\gamma_p produces a differential delay Δtgra\Delta t_{\mathrm{gra}} between the two polarization modes, which manifests as a rotation of the observed linear-polarization angle that grows with photon energy, i.e. proportional to 1/λ1/\lambda. The competing, mundane effect is Faraday rotation: linearly polarized radiation propagating through a magnetized plasma has its polarization angle rotated by an angle proportional to λ2\lambda^2, with proportionality constant the rotation measure (RM), RM=0.81∫neB∥ dl\mathrm{RM}=0.81\int n_e B_\parallel\,dl in conventional units. Yi, Zou, Wei & Zhou (2020) therefore fitted the three-parameter model ϕobs(λ)=ϕ0+A/λ+Bλ2\phi_{\mathrm{obs}}(\lambda)=\phi_0+A/\lambda+B\lambda^2 (with A≡πc ΔtgraA\equiv\pi c\,\Delta t_{\mathrm{gra}}) to multi-frequency polarization angles of 60 radio-bright active galactic nuclei from the Australia Telescope 20 GHz (AT20G) survey (at 20, 8.6, and 4.8 GHz; some sources lack published data in one or more of these bands) and of 29 optical stars in the field of the open star cluster NGC 6250 (each observed simultaneously in the five optical UBVRI photometric bands), using Markov-chain Monte Carlo sampling, and converted limits on AA into limits on Δγp\Delta\gamma_p of order 10−2610^{-26}–10−2310^{-23} (radio) and 10−2310^{-23}–10−2010^{-20} (optical), with the Laniakea supercluster — the supercluster hosting the Milky Way — modeled as a Keplerian point mass of about 101710^{17} solar masses at a characteristic scale of about 77 Mpc to fix the line-of-sight gravitational potential. The paper itself flagged the limitations that define the present problem. First, complex propagation effects were not modeled: opacity (frequency-dependent transparency, e.g. synchrotron self-absorption, so that different wavebands sample different regions of the source), differential Faraday rotation (spatially varying Faraday depth across an extended emitting region, which produces rotations and depolarization that do not follow a simple λ2\lambda^2 law), and multiple rotation-measure components along the line of sight can each imprint non-trivial wavelength dependence on the polarization angle and thus mimic or mask an A/λA/\lambda signature, biasing AA and the derived Δγp\Delta\gamma_p; the constraints are consequently upper limits. Second, some radio catalogue polarization angles used in the fits were published without angle uncertainties, weakening the uncertainty propagation. Third, the Keplerian point-mass treatment of Laniakea neglects the true, uncertain mass distribution and potential along each line of sight, a systematic in mapping Δtgra\Delta t_{\mathrm{gra}} to Δγp\Delta\gamma_p; independently, it has been argued (Minazzoli, Johnson-McDaniel & Sakellariadou 2019) that one-way Shapiro delays of cosmological sources are not directly observable and are gauge or model dependent, so the remedy is not merely a better mass model. Fourth, a bound on Δγp\Delta\gamma_p alone cannot distinguish general relativity from alternative metric theories with different coupling structures — the paper explicitly defers developing such theory-discriminating tests. Subsequent literature sharpens rather than resolves these concerns: the review of Wei & Wu (2021) reproduces the polarization results while emphasizing the poorly known local potential and the model dependence of cosmological Shapiro-delay tests; gauge-consistent reanalyses of equivalence-principle tests with fast radio bursts (FRBs, millisecond-duration radio transients of mostly extragalactic origin; Reischke, Hagstotz & Lilow 2022; Reischke & Hagstotz 2023) explicitly note that the relative Shapiro delay is not gauge independent on the background level, and that earlier analyses were affected by this confusion; and new equivalence-principle channels (the test of Li, Zhao & Cai 2021 based on the black-hole photon ring, the strongly lensed ring of light produced by photons orbiting near a black hole's horizon; gravitational-wave tests such as Wang, Yang & Han 2025) pursue different observables entirely. No work has yet upgraded the polarization-angle channel itself.

Problem Statement

Determine whether the EEP-induced 1/λ1/\lambda polarization-angle signature (the parameter A≡πc ΔtgraA\equiv\pi c\,\Delta t_{\mathrm{gra}} in ϕobs(λ)=ϕ0+A/λ+Bλ2\phi_{\mathrm{obs}}(\lambda)=\phi_0+A/\lambda+B\lambda^2) can be isolated from realistic propagation effects — opacity, differential Faraday rotation, and multiple rotation-measure components — and from line-of-sight gravitational-potential and gauge systematics, at realistically achievable multi-wavelength polarimetry — for concreteness, the band coverage and precision of the existing AT20G 4.8/8.6/20 GHz and simultaneous UBVRI polarimetry, unless a stated, justified alternative capability class is adopted — so that the residual bias in the fitted AA, and hence in Δγp\Delta\gamma_p, is controlled relative to its statistical uncertainty, making polarimetric limits on Δγp\Delta\gamma_p systematics-controlled measurements rather than upper limits; and establish what such a controlled polarimetric test could discriminate among specific metric gravity theories, including general relativity and its alternatives. Concretely, this involves: (a) constructing or ruling out a propagation model incorporating the effects listed above and quantifying the residual bias or degeneracy they induce in AA and in the derived Δγp\Delta\gamma_p; (b) propagating polarization-angle measurement uncertainties, including the case of catalogue angles published without errors; (c) replacing the Keplerian point-mass Laniakea treatment with a line-of-sight potential model whose gauge and model dependence is controlled, or showing why no such treatment can support a quantitative bound; and (d) deriving what polarimetric observables, if any, carry theory-discriminating power beyond a conservative Δγp\Delta\gamma_p bound. Resolving any one of (a)–(d) with a quantitative, falsifiable result counts as partial progress but leaves the overarching objective open; a full resolution requires (a) and (c) jointly together with a quantitative answer to (d), and that answer may be negative: completing (c) via its negative branch, or completing (d) by showing that no polarimetric observable carries theory-discriminating power, counts as a full (negative) resolution of the overarching objective and not partial progress, with (b) supplying the uncertainty treatment on which (a) and (c) depend rather than resolving the task on its own. These four aspects serve the single overarching objective of upgrading the multi-wavelength polarization-angle equivalence-principle test from a systematically vulnerable upper limit to a trustworthy measurement, as explicitly deferred by Yi, Zou, Wei & Zhou (2020).

References

  1. Yi, Shuang-Xi; Zou, Yuan-Chuan; Wei, Jun-Jie; Zhou, Qi-Qi (2020). Constraining Einstein's equivalence principle with multiwavelength polarized astrophysical sources. Monthly Notices of the Royal Astronomical Society, 498, 4295-4302. DOI: 10.1093/mnras/staa2686. https://doi.org/10.1093/mnras/staa2686
  2. Wei, Jun-Jie; Wu, Xue-Feng (2021). Testing fundamental physics with astrophysical transients. Frontiers of Physics, 16, 43500. DOI: 10.1007/s11467-021-1049-x. https://doi.org/10.1007/s11467-021-1049-x
  3. Minazzoli, Olivier; Johnson-McDaniel, Nathan K.; Sakellariadou, Mairi (2019). Shortcomings of Shapiro delay-based tests of the equivalence principle on cosmological scales. Physical Review D, 100, 104047. DOI: 10.1103/PhysRevD.100.104047. https://doi.org/10.1103/PhysRevD.100.104047
  4. Reischke, Robert; Hagstotz, Steffen; Lilow, Robert (2022). Consistent equivalence principle tests with fast radio bursts. Monthly Notices of the Royal Astronomical Society, 512, 285-290. DOI: 10.1093/mnras/stab3571. https://doi.org/10.1093/mnras/stab3571
  5. Reischke, Robert; Hagstotz, Steffen (2023). Consistent constraints on the equivalence principle from localized fast radio bursts. Monthly Notices of the Royal Astronomical Society, 523, 6264-6271. DOI: 10.1093/mnras/stad1866. https://doi.org/10.1093/mnras/stad1866
  6. Li, Chunlong; Zhao, Hongsheng; Cai, Yi-Fu (2021). New test on the Einstein equivalence principle through the photon ring of black holes. Physical Review D, 104, 064027. DOI: 10.1103/PhysRevD.104.064027. https://doi.org/10.1103/PhysRevD.104.064027
  7. Wang, Xian-Liang; Yang, Shu-Cheng; Han, Wen-Biao (2025). Tests of weak equivalence principle and graviton mass with LIGO-Virgo catalog. Communications in Theoretical Physics, 77, 125402. DOI: 10.1088/1572-9494/addfc4. https://doi.org/10.1088/1572-9494/addfc4