Transverse Doppler effect

The transverse Doppler effect is the limiting case of the relativistic Doppler shift in which the source's velocity is purely perpendicular to the line of sight at the instant of emission. The classical Doppler formula predicts no frequency shift in this geometry — a radial velocity component is required to change the path length of successive wavefronts. Special relativity disagrees: even with zero radial velocity, the source's emission clock is dilated by the Lorentz factor γ as measured in the observer's frame, and the observed frequency is f = f₀/γ. The shift is always a redshift, regardless of whether the source is approaching or receding, because γ ≥ 1. The effect is small at low velocities (γ − 1 ≈ β²/2) but grows quadratically — at γ = 2 the transverse redshift is 50%.

The transverse Doppler effect is the cleanest experimental signature of relativistic time dilation, isolated from the classical contribution. The 1938 Ives-Stilwell experiment was the first laboratory verification: hydrogen atoms in a discharge tube emitted Hα light at 656.3 nm, and Herbert Ives and George Stilwell observed both the forward (blueshifted) and backward (redshifted) emissions of moving atoms. The arithmetic mean of the two observed wavelengths gave the transverse-Doppler-corrected wavelength rather than the proper wavelength, by exactly the factor γ predicted by special relativity, and at the few-percent precision available in 1938 the effect was unambiguous. Modern verifications use Mössbauer-effect γ-ray sources mounted on rotating disks: the source at the disk's edge has a purely transverse velocity relative to a detector at the centre, and the observed γ-ray frequency shift matches the γ-factor prediction to better than 1 part in 10⁵.