People travelling
in this train will with a vantage view the train as a rigid
reference-body (co-ordinate system); they regard all events in
Fig. 01: file fig01.gif
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 be 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 arrow B of the embankment. But the events
A and B also correspond to positions A and B on the train. Let M1 be
the mid-point of the distance A arrow B on the travelling train. Just
when the flashes (as judged from the embankment) of lightning occur,
this point M1 naturally coincides with the point M but it moves
towards the right in the diagram with the velocity v of the train.
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