The aberration of starlight is generally accepted as constituting a direct, observational evidence for the validity of the Lorentz transformation formulae. Usually, the line of arguing is as follows:
If the rest frame of the star is the unprimed system and the rest frame of the observer the primed system and both move relative to each other with velocity v in the direction of their x-axes, then the corresponding Lorentz- transformation is (c= speed of light):
x'=γ(x-vt)
y'=y
z'=z
t'=γ(t-vx/c2) ,
with
γ= 1/√[1-(v/c)2] .
At t=t'=0 the origin of the two systems shall coincide and at this moment a light signal be emitted from the star along the z- axis. According to the above formulae this yields the following trajectory in the observer's frame:
x'=-γvt
z'=z=ct
t'=γt
or
x'=-vt'
z'=ct'/γ .
Thus, the light ray appears to be rotated compared to the unprimed frame by the well known 'tilt angle' α with
tanα= (-x')/z' =γv/c .
However, as an isotropically emitting body, the star obviously also sends a light ray along the coordinates
x=vt
y=0
z=ct/γ ,
which, as one easily finds by inserting these values into the original equations, is observed in the primed system as travelling along the z'- axis.
The star is therefore observed exactly at the same apparent point where the light was emitted (the original and all other rays would miss the observer (located on the z'-axis) altogether). As the only consequence of the Lorentz transformation, the star appears to be rotated by the angle α; one would need in fact an additional Lorentz- transformation at the observer in order to have an aberration effect.
However, even a rotation of the star should not occur if the speed of light is truly independent of any motion of source or observer (see my page
Speed of Light).