Came across the following interesting problem :(adsbygoogle = window.adsbygoogle || []).push({});

Two explosions take place at the same place in a rest frame with a time separation of 10 s in that frame. A) Find the time between explosions, as measured in a frame moving with a speed 0.9 c with respect to the rest frame according to classical physics.

B) Find the time between explosions, as measured in the frame moving with a speed 0.9 c with respect to the rest frame according to the special theory of relativity.

Here I wish to discuss the solution for A).

Time gap between explosions as measured in the moving frame can be found applying Galilean Transformation i.e. t' = t. Thus, the time gap as measured from moving frame = 10 sec.

The above explanation is most obvious. However, came across the following counter view point :

Classical (or Galilean) transformation is based upon every day observations/experiences where in the velocities encountered are negligible as compared to the velocity of light (v << c). As such an event taking place in a stationary reference frame S appears to take place at the same instant in another moving reference frame S' with velocity v<<c. Hence, t' = t provided v<<c (this assumption is implied even if not stated).

Further, the Lorentz Transformations t' = (t - vx/c^2)/ \/(1 - v^2/c^2) reduces to Galilean transformation t' = t for v << c. Problem is, in the given problem v is not very very less than c. Hence, strictly speaking t' = t does not apply. To an observer in frame S' the events will not appear to occure at the same instant as in frame S even from the classical point of view. The classical treatment of the problem should be similar to that of the Doppler effect of sound where the source of sound is stationary and the listener is moving away with a constant velocity.

Any comments/views?

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# Time gap between explosions in moving frame of reference

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