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Note: An axiomatic derivation of the Doppler Factor for relativistic speeds

The relativistic Doppler effect, generalized by replacing the square root by an arbitrary positive exponent, gives a condition which is equivalent to each of two compelling invariance properties involving the relativistic addition of velocities. We prove these facts under regularity and other reasonable background conditions. Accordingly, these two invariance properties are inconsistent with the Lorentz-FitzGerald Contraction. A relativistic Doppler effect arises when a source of light and an observer of that source are in relative motion with respect to each other. When the source and the observer are moving toward each other at a speed v, the wavelength perceived by the observer decreases as a function of v according the special relativity formula