Einsteinís "Train" Thought-Experiment 
Contradicts the Theory of Relativity


Ardeshir Mehta, N.D.



December 9, 2001

Einstein writes in his book Relativity: The Special and General Theory (1920):

IX. The Relativity of Simultaneity 

We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. 1. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises: 

Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative. 

FIG. 1 

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A --> B of the embankment. 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 --> B on the travelling train. Just when the flashes 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. We thus arrive at the important result: 

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). 

What?!? In reality the observer on the train "is hastening towards the beam of light"? But didnít we hear Einstein say just a few moments earlier that according to the Principle of Relativity, it should be impossible to tell whether a person or an object is in reality moving or not?!?

So which is it to be, Mister Genius? Is the guy on the train moving in reality, or is he moving only relative to the embankment?

If the former, the Theory of Relativity stands refuted, because according to it there can be no such thing as movement in reality.

And if the latter, then the above argument of Einsteinís about the relativity of simultaneity stands refuted, because there is no movement of the guy in the train in reality, and he can only be moving relative to the embankment, and to the people on it. So even if to them it appears that he does not see the flashes simultaneously, to him, since in his frame ó i.e., relative to himself, and of course to the train as well ó heís not going anywhere, it should appear that the flashes are seen simultaneously!

Any comments? e-mail me.