That doesn't means what you think that means.It was gauge invarient.
Right, the measured change was essentially zero.This was done in order to determine if there was a difference in the travel time of the beams of light in relation to the motions of the Earth. There was no difference in travel times due to different relations relative to the motions of the Earth. You could not rotate a MME in order to determine your direction of motion or relative motions to the beams of light.
The train thought experiment in Einstein's book did not disagree with the result of the MME.I thought we where talking about the TE published in Einsteins book, that did not agree with the results of the MME as it was expected.
They are different scenarios.
SR agrees with the result of the MME, and agrees with Einstein's train thought experiment.I have read a lot of layman books on theoretical physics, and I don't really know any that describe SR in this fashion. They always describe light behaving in the same way as the MME. It is really just reading the same book over and over again, when it comes to this topic.
This is all based on thinking that the speed of light is the same in all reference frames.This is all based on thinking that the beams of light would arrive at different times.
Look at the spacetime diagrams.
The blue flashes show the MME.
The red and yellow flashes show the train thought experiment.