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Up to now our considerations have been referred to a particular

body of reference, which we have styled a "railway embankment."

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 a vantage view 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:

image001

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.