Question

【Special Relativity】

For a clock moving at the velocity v = ˆxv in S, how much change in time does
it read over a lapse of time of "t in S? For an observer at rest in S, when he/she sees
the face of the clock, how fast is the clock ticking in comparison with his/her own
watch? Consider separately the two possibilities: (a) the clock is moving towards the
observer, and (b) the clock is moving away from the observer.

Answer 1

As we know in general that the time dilation is given by

So we have the two cases

1. When moving toward the S then

v is (-v) so we get

Now for the other case

2. Moving away from the S then

v will be now +v so

it will be given by

So we get that the time will remain same for the observer in both of the cases . And that is