I Assumption in the derivation of the Lorentz transformation

[swampwiz]

Actually, I don't think the aether theory was considered to imply anisotropy. It was considered to be a physically preferred 'frame' in the same way as air on earth. What its frame was would be considered an accident of initial condition (in modern parlance, a symmetry breaking in the origin of the universe). But there would be no difference between moving left, right, north, south etc. relative to the aether, nor would homogeneity be violated - different positions in the aether would be equivalent.

So you're saying that the idea is that the æther existed, just that no one really knew where the origin or how the axes were oriented?

 

[PAllen]

So you're saying that the idea is that the æther existed, just that no one really knew where the origin or how the axes were oriented?

No, that's the Lorentz aeither theory. The one before the Michelson Morley experiment, there was the expectation that there would be anisotropy in observed two way speed of light, but this was not considered fundamental, any more than such an observation for sound in air along two directions on a platform moving in air would.

 

[vanhees71]

Well, there was another episode around the Michelson-Morley (MM) experiment in the early 1920ies. Dayton and Miller repeated the MM experiment in 1925 at Mount Wilson with the result of having seen an "aether wind". The rationale behind this was the idea that the null result of the MM is not because of relativity but because
there is an "aether drag" close to the Earth becoming weaker higher up. Of course most of the physicists where very skeptical because of all the confirmations of special (and also some of general) relativity, but there were also some prominent proponents of the aether hypothesis. Thus the measurements where repeated again, some financed by the "Notgemeinschaft der Deutschen Wissenschaft", which shows how important the issue has been considered in those days, with the result that the Dayton and Miller experiment must have been flawed somehow, because indeed the original null result by MM has been confirmed.

 

[Vanadium 50]

Dayton and Miller

One person. Dayton is hist first name. Not as confusing as Hanbury-Brown. But close.

The real reason this never went anywhere is that they were neither confirmed nor "prefirmed". (Past experiments disagreed) At the time, statistics was still being developed, and it wasn't really appreciated that millions of data point was only part of the story.

Tom Roberts re-analyzed the Miller experiment from a modern perspective here: https://arxiv.org/abs/physics/0608238 I dislike re-analysis papers in general, but this one is very good.