Experiments with the transverse Doppler effect have demonstrated that the wavelength of light increases with the speed of the source relative to the observer. The relativity principle implies that such a change cannot be detected by in situ measurements and this prediction has been verified by wavelength determinations carried out with a cavity resonator over an extended period of time during which the orbital speed of the Earth changes significantly. On this basis it can be concluded that the dimensions of the cavity resonator increase in direct proportion to the Doppler wavelength, and thus that isotropic length expansion occurs with relativistic time dilation, not the anisotropic Fitzgerald-Lorentz length contraction predicted by the special theory of relativity. The failure of the Lorentz space-time transformation to anticipate the length expansion effect is discussed and an alternative set of equations is introduced to eliminate the experimental contradiction in the existing theory.