the Theory of Relativity
Ardeshir Mehta, N.D.
December 9, 2001
in his book Relativity:
The Special and General Theory (1920):
|IX. The Relativity
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.
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
B on the travelling train. Just when the flashes of lightning
occur, this point M' naturally coincides with the point
but it moves towards the right in the diagram with the velocity
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
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
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!
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