Relativity of Simultaneity: Train-Platform Experiment

[Mohammed_I]

I am going to talk about the famous train-platform experiment where two lightnings strike both ends of the platform and the observer on the platform is in the midpoint of the two events.

From the frame of reference of the platform, the light from event A (the one the train is moving towards) reaches the observer on the train first. And then the light from both A and B reach the observer on the platform at the same time. And finally the light from event B reaches the observer on the train.

Now if we want to explain what happened from the reference frame of the observer on the train, we could come up with 3 scenarios.

First, we could assume that classical mechanics works for high speeds and say that relative to the observer on the train, the light moving towards him is moving faster than the light following him. This will be consistent with the first observation (The light from event A will reach first, then both lights will reach the other observer at the same time. And then the light from event B will reach this observer) But of course the problem with this scenario is that it assumes that light doesn't move at the same speed for all frames of references which follows that it assumes there is an absolute frame of reference in which light moves in any two opposite directions with the same speed.

Second, we can explain it the same way it was explained by Einstein and say that from the frame of reference of the observer on the train event A happened before event B.

My question is, why did we assume in the first place that simultaneity is in fact what is relative here, why don't we say that relative to the observer on the train both events happened on the same time but the distance between the observer and event A is smaller than the distance between the observer and event B. This assumption will also be consistent with the observation from the frame of reference of the platform, because relative to the observer on the train, the platform is moving backwards in a way that on the spacetime diagram it will intersect with the intersection of the light cones of the two events.

What I am saying here suggests that for a frame of reference moving with a uniform velocity relative to another frame of reference, distances in front of the moving frame of reference will be shorter than in the other frame of reference and distances behind it will be longer but simultaneity remains absolute.

I just want to know why that is considered wrong?

BTW, I know that relative to the observer on the platform the observer on the train is at the midpoint between the two events at the time the two events happen. I am just saying that that doesn't necessary mean that the observer on the train also sees himself at the midpoint of the two events at this particular moment.

 

[Janus]

Consider that the train is long enough so that, at the time of the strikes, part of the train is next to the point of the strike, so that each strike leaves a char mark on the train.
The train is made of cars of equal length.

So let's say, that at the moment of the strikes according to the embankment observer, there are 201 cars between the points of the strikes . If we number the car at one strike as car one, and the car at the other strike as car 201, then car 101 is adjacent to the embankment observer at the time of the strikes. Since the train observer in adjacent to the embankment observer at this same moment, then the train observer is sitting in car 101.

The train observer will also see the lightning make char marks on cars 1 and 201, and considering that he is sitting in car 101, he will, by his reckoning note that he is an equal distance from the char marks and that the lightning strikes took place an equal distance from himself.

 

[Mohammed_I]

Thank you Janus, but I don't think that actually works because this model doesn't suggest that the train is symmetric relative to the observer on the platform.

But when trying to explain two beams of light on a moving object moving in opposite directions towards two mirrors it doesn't work.

Sorry for taking too long to reply, it took me some time to think things through and then I got caught up with some stuff. Thank you again.