Illustrated Physics
physics, drawn
Concept

Transverse doppler — where it appears

The frequency shift seen at right angles to a source's motion, which is time dilation alone and has no classical counterpart. It is second order in the speed, so it was not measurable until a moving hydrogen beam was compared with a stationary one in 1938.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Three answers where sound has two, and one where it has none. The factor by which an approaching source's frequency is raised, against its speed as a fraction of the wave speed. For sound it matters which of the two is moving: a moving source gives 1/(1 − β) and a moving observer gives 1 + β, and at 0.5 of the wave speed those are 2.000 and 1.500. For light there is one answer, 1.732 — the geometric mean of the other two, exactly — because there is no medium to be moving with respect to. The fourth curve is the transverse shift, which happens at closest approach when the distance is not changing at all: 0.866, and nothing classical predicts it.

The shift that survives at right angles

For sound it matters which of the two is moving, and the two answers differ. For light there is one answer — their geometric mean — and a term with no classical counterpart at all: a source going past at closest approach, with its distance not changing, is still shifted.

relativity · Doppler Where the light that was sideways ends up. The direction a photon is seen to travel in the laboratory, against the direction it was emitted in the frame of the source, for a source moving at 0.5c, 0.9c, 0.99c. The straight diagonal is what would happen if a boost only changed frequencies; every curve lies well below it, which is aberration. The number that matters is where the emitted right angle lands, because half of everything emitted is on that side of it: 60.0° at 0.5c, 25.8° at 0.9c, 8.1° at 0.99c. The usual shorthand for that angle is 1/γ, which gives 49.6°, 25.0°, 8.1° — good to a few per cent only once the source is genuinely relativistic, and wrong by 17% at 0.5c. Nothing is emitted differently in any of these cases: the source is radiating exactly as it always did, and it is the map from its angles to ours that has changed.

The sky that crowds into a cone

A boost does not only shift frequencies. It remaps directions, so half of everything a fast traveller can see is squeezed into a forward cone of half-angle about 1/γ — and because brightness carries four powers of the Doppler factor, what lies ahead is overwhelming and what lies behind has effectively gone.

relativity · Doppler

Named alongside it

The objects these essays reach for when they reach for this one.

The Lorentz factorReference framesRelativistic beamingRelativistic dopplerAberrationDipole radiationDopplerEnergy fluxIntensityLight coneSynchrotron radiationTime dilation

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