Phase Change in Light: A & B Signal Reflections

[Nugatory]

When the observer in the middle of a moving train disagrees with the observer on the platform, on the simultaneity of two lightening strikes hitting the front and back of the train, it is because, as Einstein said, it takes longer for the light from the back of the train, than the light at the front of the train to reach the observer on the moving train if we choose to analyze the situation using coordinates in which the platform is at rest

The bolded addition is necessary, but even with that addition you are misunderstanding Einstein's position. Yes, it "it takes longer for the light from the back of the train, than the light at the front of the train to reach the observer on the moving train" when using the platform frame, and Einstein did correctly rely on that fact, but that's not Einstein's insight here.

Einstein's insight is that the most reasonable ("only sensible" would not be excessive hyperbole here) definition of "time a flash of light was emitted" is to subtract the light travel time from the arrival time to get the emission time, and that when using that most reasonable definition observers in relative motion to one another will not agree on the simultaneity of events.

The problem with describing the thought experiment as you have is that you have inadvertently privileged the platform observer - the "takes longer" explanation loses the equally reasonable analysis that says both light signals covered the same distance but were emitted at different times.

 

[jedishrfu]

With @Nugatory excellent comment, I think this is a good time to close this thread.

Thank you all for participating here.

Jedi