I Does Special Relativity Apply to a Moving Clock?

[Kunhee]

A Moving Clock runs slow.

But,

If time t has elapsed in the S frame, does SR apply to a clock moving with speed u in the x-direction in the S frame, relative to the S frame?

Or does SR apply only when the clock is in another reference frame S' moving in the x'-prime direction, given that it's also relative to the S frame?

 

[Ibix]

All things are in all frames. The question is, which frame are you using to describe what's going on? If you use S then all clocks described as moving in S run slow compared to clocks described as stationary in S. If you are using S' then all clocks described as moving in S' run slow compared to clocks described as stationary in S'.

 

[Kunhee]

S' is moving with speed v relative to S. (x' direction)
And a clock is moving with speed u in the S frame. (x-direction).

If time t elapsed in the S frame, how much time elapsed for the moving clock in the S frame?

t' = t / y
or
is it just t?

The question didn't specify anything other than the above.

If we are looking for the time elapsed for the clock from the S' frame,
then we can use time dilation after doing velocity transformation.
But since we are looking for the time time elapsed for the clock
from the S frame wherein the clock is moving, does time dilation
still apply although the velocity transformation does not?

 

[Ibix]

This question seems rather confused. Notably, as written, S' is unused in the question. Is it a homework question?

 

[Dale]

As written the S' frame is a distraction. It is not used for anything and is just included to make sure that you understand what can be ignored. So mentally delete any reference to S' and re read the question. Do you know how to handle it now?

 

[Kunhee]

Thanks for the responses. It was a quiz question for a Sp. Relativity class.
I guess the answer is simply that the moving clock's time is dilated within the S frame by ((1-(u/c)^2)^(-1/2).

 

[DrClaude]

Thanks for the responses. It was a quiz question for a Sp. Relativity class.

All such questions must be posted in a homework forum with your own attempt at a solution.