By L. Mason
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Additional resources for Relativity and Electromagnetism [lect notes]
Example text
It therefore follows that the length of a rigid metre-rod moving in the direction of its length with a velocity v is 1 − v 2 c 2 of a metre. The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving, the shorter is the rod. For the velocity v = c we should have 29 1 − v 2 c 2 = 0 , and for still greater velocities the square-root becomes imaginary. From this we conclude that in the theory of relativity the velocity c plays the part of a limiting velocity, which can neither be reached nor exceeded by any real body.
This question leads to a general one. In the discussion of Section VI we have to do with places and times relative both to the train and to the embankment. How are we to find the place and time of an event in relation to the train, when we know the place and time of the event with respect to the railway embankment? Is there a thinkable answer to this question of such a nature that the law of transmission of light in vacuo does not contradict the principle of relativity? In other words: Can we conceive of a relation between place and time of the individual events relative to both referencebodies, such that every ray of light possesses the velocity of 25 transmission c relative to the embankment and relative to the train?
Let M be the mid-point of the distance A —→ B on the travelling train. Just when the flashes 1 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. 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.