I try to understand Einstein's Relativity: The Special and the General Theory, chapter IX., "The Relativity of Simultaneity". Here's an online version: http://www.bartleby.com/173/9.html.
|----M'----v->
####-----A--------M--------B-----####
Einstein considers two lightning strokes happening at two points A and B along a railway embankment. At this moment, two observers M and M' meet each other at the mid-point between A and B. M resides on the embankment, M' is riding on the train moving with velocity v towards B.
Then, paragraph 3 reads:
"... he [the observer at M'] is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."
As far as I understood SR until now, this is actually the non-relativistic point of view. Bearing relativity in mind, the moving observer M' should experience both light beams from A and from B approaching with light speed as well, the beam from B being blue-shifted and the one from A red-shifted. In respect to M' they have different energies, but they should arrive at the same time.
The longer I think about it, the more I doubt whether Einstein found a very fortunate thought experiment here. What do you think about it, could that be true?
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