Doppler Effect
The Doppler effect is the change in the observed frequency of a wave caused by relative motion between its source and its observer: a source approaching the observer delivers its wave crests more often and the frequency rises; a receding source delivers them less often and the frequency falls.
The standard account
Christian Doppler set out the principle in 1842 in Über das farbige Licht der Doppelsterne, arguing that the colours of binary stars should be affected by their motion. Christophorus Buys Ballot tested it acoustically in 1845 by having trumpeters play a held note on an open railway carriage while musicians on the platform judged the pitch, and Hippolyte Fizeau independently applied the idea to the spectral lines of light in 1848.
For waves in a medium — sound in air, for instance — the classical result is not symmetric between source and observer. Motion of the source changes the wavelength emitted into the medium; motion of the observer changes the rate at which crests are encountered. The two give different formulas, and in principle the difference lets one determine motion with respect to the medium itself.
For light, special relativity gives a different treatment. With no medium and no preferred frame, only the relative velocity can appear, and the longitudinal formula acquires a factor √((1−β)⁄(1+β)) with β = v⁄c. The characteristic prediction is the transverse Doppler shift: a source moving purely across the line of sight, with no radial velocity at all, should still be seen redshifted by the time-dilation factor 1⁄γ. Herbert Ives and G. R. Stilwell reported detection of the second-order shift in 1938 using canal rays, and that experiment is generally taken as the key confirmation. The effect underlies Doppler radar, Doppler ultrasound, laser cooling, radial-velocity planet detection and stellar spectroscopy.
The cosmological redshift deserves a note here, because it is routinely described in popular accounts as a Doppler shift and is not one in the standard theory. In mainstream cosmology it is attributed to the expansion of space during the light's transit, not to a velocity through space, and the two give different formulas at large z.
On this wiki
Because the Doppler effect is the one place where wave theory makes an explicit, testable statement about relative versus absolute motion, it is a recurring battleground in the literature collected here, and the arguments run in two directions.
Doppler as a replacement for special relativity. Neil E Munch argued across a series of papers that the relativistic and classical Doppler treatments are more sensitive to their starting assumptions than is usually admitted, and that the classical account is preferable. With Francisco J. Müller he compared the two in Discussion of Relativistic and Non-relativistic Theories of the Doppler Effect (1997), concluding that a transient asymmetric effect persists which favours the classical formula and is in principle demonstrable. He pressed the case further in Critical Flaws in Special Relativity and Its Possible Replacement by Doppler Concepts (2002) and applied Doppler's original 1842 conception — light speed constant relative to a medium — to superluminal astronomical sources in Possible Doppler Results from Stellar Emitters Traveling at Super-Luminal Speeds (2004), where he derives the counter-intuitive result that an approaching superluminal emitter would appear redshifted, and suggests this as an additional source of the large redshifts seen in astronomy.
The transverse shift and time dilation. Hartwig Wolfgang Thim reported a null result in Absence of the Relativistic Transverse Doppler Shift at Microwave Frequencies (2003): a 33 GHz signal received by rotating antennas showed no frequency shift, with an apparatus he states was sensitive well below the predicted value of (v⁄c)² ≈ 5 × 10⁻¹⁴. His conclusion is that either time dilation does not exist or it depends on absolute rather than relative velocity. This stands against the Ives–Stilwell result and its many successors, and readers should weigh the two directly; the experiments are not of the same design and the discrepancy has not been resolved in the mainstream literature, which does not accept the null result.
Doppler and the Michelson–Morley null result. Paul Wesley argued that the Michelson–Morley outcome is itself explicable as a classical Doppler effect, in Michelson-Morley Null Result for Sound of Light: A Classical Doppler Effect (2005) and in the related Michelson-Morley Result Proves Special Relativity Wrong and Evidence for Newtonian Absolute Space and Time. Curtis E Renshaw takes the opposite view of the evidence in The Experiment of Fizeau as a Test of Relativistic Simultaneity (2008), arguing that the Fizeau experiment amounts to a successful test of relativistic simultaneity — a reminder that contributors here are not of one mind.
Doppler and cosmology. Richard A Waldron, in An Infinite Non-Expanding Universe in Dynamic Equilibrium (1991), takes it as a constraint on any ballistic model of light that large redshifts cannot be Doppler shifts, so a non-Doppler mechanism is required. That is the point of entry to the largest body of work here on the subject: see Redshift, Tired Light and Intrinsic redshift for the alternative mechanisms, and Big Bang for what follows if the redshift is not a velocity effect.
Further material is indexed under Category:Relativity, Category:Light and Category:Emission Theory.
Open questions
Nothing about the classical Doppler effect is in dispute. What is genuinely at issue is narrower and worth stating precisely: whether the second-order (transverse) shift observed in the mainstream experiments demonstrates time dilation as a relative-velocity effect, or is instead consistent with an absolute-motion interpretation in which the shift depends on velocity relative to a preferred frame. The two accounts agree on most experiments and are hard to separate, which is why the rotating-antenna and one-way-speed measurements described above keep being attempted.