Special relativity of two clocks

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Discussion Overview

The discussion revolves around the synchronization of two clocks in different reference frames, specifically addressing the time offset observed in one frame compared to another. Participants explore the factors involved in this offset, including the proper length of the body and the implications of special relativity.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions why the time offset for two synchronized clocks in frame S is given by ##\frac{Lv}{c}## in frame S', suggesting confusion over the absence of a factor of ##\gamma##.
  • Another participant challenges the assumption that a factor of ##\gamma## should be present and prompts a review of how the relation is derived.
  • A participant asserts that the correct time offset should be ##\frac{Lv}{c^2}## instead of ##\frac{Lv}{c}##, noting that the latter is in units of length.
  • One participant references a specific section of a textbook that illustrates the problem with synchronized clocks on a train, indicating that it provides a visual explanation of the factors involved.
  • Another participant acknowledges their earlier mistake in stating the time offset and expresses that they have since resolved their confusion, while also critiquing the clarity of the textbook explanation.

Areas of Agreement / Disagreement

Participants express differing views on the correct formulation of the time offset, with some asserting the presence of a factor of ##c^2## and others questioning the need for a factor of ##\gamma##. The discussion remains unresolved as multiple competing views are presented.

Contextual Notes

There are indications of confusion regarding the derivation of the time offset and the appropriate factors to consider, highlighting potential limitations in the explanations provided in the referenced textbook.

Physgeek64
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Why is it that for two clocks that are synchronised in one frame, S, but not in another, S', is there an offset in the time by a factor of ##\frac{Lv}{c}##, as measured in S'. Where L is the proper length of the body, as measured in S. I'm confused as to why there is not a factor of ##\gamma## here

Many thanks
 
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Why do you think there should be a factor ##\gamma##? Have you looked at how the relation is derived?
 
Physgeek64 said:
Why is it that for two clocks that are synchronised in one frame, S, but not in another, S', is there an offset in the time by a factor of ##\frac{Lv}{c}##, as measured in S'. Where L is the proper length of the body, as measured in S. I'm confused as to why there is not a factor of ##\gamma## here

Many thanks
I'm pretty sure the offset in time is Lv/c2, not Lv/c (since obviously Lv/c is in units of length).

Also section 11.3 of this link has a problem that comes up with your Lv/c involving synchronized clocks on a train. It has a nice picture too showing the distance the photon must travel, which gives those two factors.

http://www.people.fas.harvard.edu/~djmorin/chap11.pdf
 
Battlemage! said:
I'm pretty sure the offset in time is Lv/c2, not Lv/c (since obviously Lv/c is in units of length).

Also section 11.3 of this link has a problem that comes up with your Lv/c involving synchronized clocks on a train. It has a nice picture too showing the distance the photon must travel, which gives those two factors.

http://www.people.fas.harvard.edu/~djmorin/chap11.pdf

How careless of me- I did mean over ##c^2##. Funnily enough, this was the book that caused my confusion. I don't feel like he explains it very well. However, I have since worked it out- so all it good.

Thank you for replying though- it's very appreciated :)
 
Physgeek64 said:
How careless of me- I did mean over ##c^2##. Funnily enough, this was the book that caused my confusion. I don't feel like he explains it very well. However, I have since worked it out- so all it good.

Thank you for replying though- it's very appreciated :)
Haha no it definitely could be clearer, but it does have a good picture I think.
 

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