Modification of Aberration due to the Helicity-Rotation Coupling

TL;DR

This work investigates how the locality assumption in relativity underpins standard aberration formulas and extends the framework to include helicity-rotation coupling for polarized radiation. It derives a Doppler-like frequency shift $\omega' = \gamma(\omega - M\Omega)$ with $M=L+S$, and a helicity-dependent aberration correction $\mathcal{A}_{\pm}^s \approx \mathcal{A}\left(1\mp s\hat{\mathbf{k}}\cdot\mathbf{\Omega}/\omega\right)$, showing that polarization and spin contribute to observed aberration. The main conclusion is that the helicity aberration is suppressed by the small factor $\Omega/\omega$ and is thus currently undetectable, but it provides a fundamental signature of spin-rotation coupling and motivates nonlocal theories of accelerated observers. These results bridge classical wave descriptions with relativistic kinematics and have implications for precision Doppler tracking and polarized radiation handling in rotating frames.

Abstract

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.

Figures (1)

• Figure 1: Schematic illustration of the aberration angle $\mathcal{A} = \alpha' - \alpha$. The observer moves along the horizontal axis with speed $v$. The solid and dashed lines indicate the directions of incidence of light in the background and moving inertial frames, respectively.