Transverse Doppler Effect
Also known as: Second-Order Doppler Shift · Time-Dilation Redshift
Even when a source flies straight ACROSS your line of sight — with zero radial velocity — you still see it redshifted, purely because its clock is time-dilated. There is no classical counterpart; this shift is relativity, naked.
A source orbits/crosses the observer's sightline; at closest approach (transverse) the observed frequency dips to f_src/gamma, shown by a color-shifting marker.
Equivalent forms
A pure, first-principles manifestation of time dilation with no wavefront-bunching admixture — the cleanest optical test of the gamma factor.
Dimensional analysis
Einstein predicted the transverse shift in 1907 as a direct consequence of time dilation; Ives and Stilwell measured it in 1938 (ironically while trying to disprove relativity).
- Precision tests of special relativity in ion storage rings
- Corrections to atomic-clock frequencies for moving ions
- Second-order Doppler broadening in spectroscopy
- A transverse-moving source is NOT unshifted — the classical prediction of zero shift is wrong
- The sign depends on whether 'transverse' refers to emission or reception geometry
- This is not caused by any radial velocity component; it is pure time dilation
Limiting cases
What if…
You get the general relativistic Doppler formula; the transverse case is the special angle where the first-order term vanishes.
Then aberration flips the geometry and you get a BLUESHIFT by gamma instead — geometry matters.
Source crossing at 0.6c
- fsrc:
- 500000000000000
- beta:
- 0.6