Does Special Relativity Apply to a Moving Clock?

In summary, the conversation discusses the application of Special Relativity to a moving clock in different reference frames. The question asks how much time has elapsed for a clock moving with speed u in the x-direction in the S frame, relative to the S frame. It also mentions the use of the S' frame, but it is ultimately determined that it is not necessary for solving the problem. The solution is that the moving clock's time is dilated within the S frame by ((1-(u/c)^2)^(-1/2).
  • #1
Kunhee
51
2
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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  • #2
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'.
 
  • #3
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?
 
  • #4
This question seems rather confused. Notably, as written, S' is unused in the question. Is it a homework question?
 
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  • #5
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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  • #6
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).
 
  • #7
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.
 

Related to Does Special Relativity Apply to a Moving Clock?

1. What is special relativity and how does it apply to a moving clock?

Special relativity is a theory proposed by Albert Einstein that explains the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion and that the speed of light is constant, regardless of the observer's frame of reference. This means that the rate at which time passes for an object depends on its relative motion to an observer, including the movement of a clock.

2. Can special relativity affect the accuracy of a moving clock?

Yes, special relativity can affect the accuracy of a moving clock. According to the theory, as an object moves faster, time passes more slowly for it compared to a stationary observer. This means that a clock moving at a high speed will appear to run slower to an observer, affecting its accuracy.

3. What is the equation for time dilation in special relativity?

The equation for time dilation in special relativity is t' = t / √(1 - v^2/c^2), where t' is the time measured by an observer in motion, t is the time measured by a stationary observer, v is the relative velocity between the two observers, and c is the speed of light. This equation shows that as the relative velocity increases, the time measured by the moving observer decreases.

4. Does special relativity only apply to clocks moving at high speeds?

No, special relativity applies to all objects in motion, regardless of their speed. However, the effects of time dilation are only noticeable at extremely high speeds, such as near the speed of light. For everyday objects and speeds, the differences in time are too small to be observed.

5. How does special relativity affect GPS systems?

GPS systems rely on precise time measurements to determine location. Due to the effects of special relativity, the satellites in the GPS network experience time dilation, causing their clocks to run slower than clocks on Earth. Without taking this into account, GPS systems would be significantly less accurate. Scientists have to use corrections and adjustments to account for this time dilation and ensure the accuracy of GPS technology.

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