# Speed of light in aether

I've been recently reading about the famous Michelson-Morley experimental attempt to detect the Earth motion with respect to the aether. According to Wikipedia, Michelson initially made a mistake calculating the time that the light takes to propagate in the transverse direction(perpendicular to the Earth velocity). In his calculation he assumed that the transverse travel time $T_t=2cL_t$, where $L_t$ is the length of the transverse channel. In this case, the speed of light in the aether frame is $\sqrt{c^2+v^2_{Earth}}$, since Michelson did not know about the relativity theory yet.Later, it was corrected by Lorenz, who said that the speed of light in the transverse direction must be $c_t=\sqrt{c^2-v_{Earth}^2}$, thus in the aether frame the speed of light remains $c$.

What was Lorenz' motivation to think that the speed of light is always $c$ in the aether frame? Is it because they believed at the time that Maxwell's equations give the speed of light in aether? And how did they know that the light must acquire the longitudinal component $v_{Earth}$? Maybe when the light is radiated it does not have the longitudinal component in the aether frame.

• Lorentz and Einstein eventually came to terms on the subject of aether, the conclusion of which was not that a medium did not exist (Einstein openly acknowledged that his theory of relativity still depended on one), merely that the overall nature of this medium is such as to make absolute motion relative to space itself simply undetectable by any means (and therefore meaningless). Motion can only be detected relative to other objects (or a system of objects) in space. – Steve Feb 28 '18 at 23:08
• I do not understand the question. The whole point of introducing ether was that its frame of reference was attached to the absolute space, and $c$ was defined as the absolute speed of light. How the light is radiated is described by Maxwell's equations (which were supposed to hold in the absolute frame), there was no "maybe". – Conifold Mar 1 '18 at 4:48