Modification of Aberration due to the Helicity-Rotation Coupling

We review the physical basis for the assumption of locality in relativistic physics and its connection with the aberration of starlight. As a consequence of the hypothesis of locality, the standard relativistic formulas for the Doppler effect and aberration are independent of the polarization of the incident electromagnetic or gravitational radiation. The modification of these formulas due to the helicity-rotation coupling are discussed. In connection with the aberration of polarized radiation, we note that the helicity of radiation incident on a rotating observer couples to its angular velocity of rotation resulting in a slight helicity-dependent modification of the standard aberration formula. We discuss the physical origin of this effect and estimate the magnitude of the helicity aberration.

💡 Research Summary

The paper revisits the hypothesis of locality, which underlies the extension of special relativity to accelerated observers, and examines its limitations for wave phenomena. The locality assumption treats an accelerated observer as instantaneously equivalent to a momentarily comoving inertial frame, allowing point‑by‑point application of Lorentz transformations based solely on the observer’s instantaneous velocity. While this works well for particle‑like measurements, the authors argue that electromagnetic and gravitational waves exhibit intrinsic non‑locality that the hypothesis cannot fully capture.

After a historical overview of stellar aberration—from Rømer’s speed‑of‑light measurement to Bradley’s discovery and the subsequent wave‑theoretic interpretations—the paper introduces the helicity‑rotation coupling. When an observer rotates with angular velocity Ω, the helicity (spin) of an incident circularly polarized photon (or a spin‑2 graviton) couples linearly to Ω. This coupling adds a tiny correction to the standard aberration formula. In the first‑order approximation the observed angle α′ becomes
α′ ≈ α + β sin α ± (Ω/ω) sin α,
where β = v/c is the usual aberration term, ω is the wave’s angular frequency, and the ± sign reflects the helicity.

Quantitative estimates show that for Earth’s rotation (Ω≈7.3×10⁻⁵ rad s⁻¹) and visible light (ω≈3×10¹⁵ rad s⁻¹), the helicity‑rotation term is of order 10⁻²⁰ rad, far below current astronomical measurement precision (≈10⁻⁹ rad). Nonetheless, the effect could become relevant in ultra‑precise laser interferometry or in low‑frequency gravitational‑wave detectors, where ω is much smaller and the ratio Ω/ω can be appreciable.

The authors conclude that the hypothesis of locality provides only a first‑order (ray‑optics) description of wave phenomena. The helicity‑rotation coupling quantifies the next‑order correction, highlighting a subtle but fundamental limitation of the locality assumption. Future high‑precision optical and gravitational‑wave experiments may need to incorporate this correction to achieve their targeted accuracies.