How could you even know this when you didn't even know what gauge invarience was until I explained it to you? It is the description in layman terms that I have just regurgitated to you. Your jumping to conclusions.Layman, you're constructing your own meaning for a term that already has a well established meaning that you don't understand.
Don't do that. It's counterproductive to communication.
The locations of the beams of light are not in the same locations in each frame. It shows that the locations of the beams are at different locations at the same time intervals in both frames. It is just an overlay of the Lorentz Transformations and a Minkowski Diagram, I don't think that would prove a violation of simultaneity, only that the Lorentz Transformation and a Minkowski Diagram do not agree on the locations of the beams at the same time intervals.Good, so we've established that there's no problem in the train observer's frame, and no problem in the platform observer's frame.
All experiments carried out by each observer happen as expected, with light always moving at c.
Now:
The blue flashes are like the Michelson-Morley experiment.
The yellow and red flashes are Einstein's thought experiment.
Can you see that there is no conflict between the two?