So I went through a couple of different books on special relativity ( including Einstein's own book) and I just can't seem to accept relativity of simultaneity as a real thing. I'll explain my confusion and hope that people here will help me to understand.
So in Einstein's train thought experiment, the observer on the railway line reference frame sees the two lightning strikes ( occurring at say A and B) as simultaneous because light from A and B reach him at M at same time ( M is the midpoint of AB) But in the train frame Einstein says
But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A ~T B on the travelling train. Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M' in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated.
Now in reality (considered with reference to the railway embankment) he 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"
So my question is this: just because we see the two events ( by way of receiving light) at two different times because we purposely moved towards one light ray, it shouldn't mean the two events didn't occur simultaneously. It's just that we see it Happen before the other because we moved to receive one light signal earlier but the two events still occurred simultaneously. Please tell where am I misunderstanding. Edit: the possible duplicates are no where near my question. I know that speed of light is constant. Please try and understand my question better.. what I am asking is this thought experiment by Einstein gives the impression that we consider things to be simultaneously if we see ( receive light) from them at same time, but happening and perceiving are two different things. The light strikes could have happened simultaneously but I only moved toward one light signal and hence received it before the other.