Does Special Relativity Apply to a Moving Clock?

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Discussion Overview

The discussion revolves around the application of Special Relativity (SR) to a moving clock, particularly in the context of different reference frames. Participants explore the implications of time dilation for a clock moving at speed u in the S frame, and whether SR principles apply when considering another frame S' moving at speed v relative to S.

Discussion Character

  • Debate/contested
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant asserts that a moving clock runs slow, questioning whether SR applies to a clock moving with speed u in the S frame or only when considering another reference frame S' moving in the x'-direction.
  • Another participant argues that all clocks run slow in their respective frames, emphasizing the importance of the chosen frame for analysis.
  • A participant presents a mathematical query regarding the elapsed time for the moving clock in the S frame, suggesting that time dilation may or may not apply depending on the context of the question.
  • Some participants express confusion about the relevance of the S' frame, suggesting it may be unnecessary for the question posed.
  • A later reply indicates that the question was part of a quiz, proposing a specific formula for time dilation in the S frame.
  • Another participant reminds that homework questions should be posted in a designated forum with an attempt at a solution.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of the S' frame in the discussion. There are differing views on how to approach the problem and whether time dilation applies in the context presented.

Contextual Notes

The discussion includes assumptions about the relevance of different reference frames and the application of time dilation, which remain unresolved. The mathematical steps and transformations involved are not fully detailed.

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

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