Scientific theory
In 1905, Albert Einstein published the principle of special relativity, which soon became a theory. Special relativity predicted the alignment of the Newtonian principle of Galilean invariance, also termed "Galilean relativity", with the electromagnetic field. By omitting from special relativity the luminiferous aether, Einstein stated that time dilation and length contraction measured in an object in relative motion is inertial—that is, the object exhibits constant velocity, which is speed with direction, when measured by its observer. He thereby duplicated the Lorentz transformation and the Lorentz contraction that had been hypothesized to resolve experimental riddles and inserted into electrodynamic theory as dynamical consequences of the aether's properties. An elegant theory, special relativity yielded its own consequences, such as the equivalence of mass and energy transforming into one another and the resolution of the paradox that an excitation of the electromagnetic field could be viewed in one reference frame as electricity, but in another as magnetism.
Stellar aberration (derivation from Lorentz transformation)
In the year 1926 the astrophysicist Robert Emden published the article "Aberration und Relativitätstheorie" in the journal "Naturwissenschaften". In this article he states that the direction of a light ray isn't influenced by the motion of the star or by the motion of Earth. At that time, the opponents of the special theory of relativity reasoned that the theory must be flawed, because it would state that the stellar aberration would depend on the relative velocity of the star — which would be in contradiction to observation — and R. Emden's article explains that the special theory of relativity does not predict this. Today, the special theory of relativity isn't contested anymore but there are still articles that suggest that the aberration would depend on the relative velocity of the star.