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I'm a high school student, just learned relativity.

I understand that observed time is different between two different inertial reference frames. I vaguely understand that time is different in two different non-inertial reference frames. Now consider the following:

A watchmaker makes a watch at reference frame A, with the time of the clock corresponding to the time at reference frame A. They then give the watch to another person at reference frame B. (moving relative to frame A at velocity v)

Does the watch track time correctly for the person at B?

Also, if the systems are non-inertial frames, would the results change?

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The clock, in its own reference frame, will continue to run at its natural rate. One way of viewing this problem, which answers both your original question about the clock and your secondary question on about the non-inertial frame, is that the clock's frame of reference is non-inertial. It must accelerate to go from the hand of the clockmaker in frame A to the hand of the buyer in frame B. While it is accelerating, both the clockmaker and the buyer will agree that the clock is running at a non-constant rate while a third observer accelerating with the clock itself continues to see it run just as accurately as when it left the hand of the clockmaker.

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  • $\begingroup$ To check that I have understood correctly: a. To the clock bearer, regardless of their acceleration, also regardless of their change of acceleration, the clock will turn at a constant rate. b. This is true if a clock is defined as "a device that measures the flow of time" My final question is, would there be a way to determine if two different measurements of 1 second within two different accelerating frames is identical? i.e., Is the definition of time only definable within one frame? $\endgroup$ – Sooyoung Cheong Sep 16 '18 at 14:21
  • $\begingroup$ If your buyer in frame B went for a while then decided to reverse course and return the clock to the clockmaker, you'd basically have the "twin paradox". That's been done experimentally with atomic clocks flying on aircraft and it works out as expected. Each clock runs "properly" as viewed by a person sitting next to it the whole way, but when they are brought back together, on clock is behind the other. This is not a question of the unit of measurement - in this case second and which is defined by an atomic process. The definition of the second is good in either frame. $\endgroup$ – Brick Sep 16 '18 at 14:28
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Yes watch will measure correct time for B if it was correct for A . As remember watch is not time means time is a physical quantity which we measure upto our limits using a clock if we go by a speed all things / instruments slow down all phenomena slows down so watch will also start ticking slow / fast acc. to reference frame of B.

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  • $\begingroup$ Would a watch depending on the local acceleration for timekeeping (e.g. pendulum clocks) be changed? $\endgroup$ – Sooyoung Cheong Sep 16 '18 at 14:06
  • $\begingroup$ If gravity of both places are different than pendulum clock will not show correct time not show to relativistic effects not but due to gravity its formula is {2π√(l/g)} $\endgroup$ – Harsh jain Sep 16 '18 at 14:15

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