How Can Two Clocks Be Synchronized if One is Accelerated?

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SUMMARY

The discussion centers on the synchronization of two clocks when one clock is accelerated. The participant initially referenced the time dilation formula, t' = t / (1 - v²/c²), and questioned its applicability to varying speeds. It was concluded that the Lorentz transformation, which underpins this formula, is only valid for constant velocities, thus invalidating the initial assumption regarding time dilation in accelerated frames.

PREREQUISITES
  • Understanding of special relativity principles
  • Familiarity with Lorentz transformations
  • Knowledge of time dilation concepts
  • Basic calculus for integrating functions
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  • Study the implications of acceleration on time dilation in special relativity
  • Learn about general relativity and its treatment of accelerated frames
  • Explore advanced topics in Lorentz transformations
  • Investigate the mathematical integration of variable speeds in relativistic contexts
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Students of physics, particularly those studying special and general relativity, as well as educators and researchers interested in the nuances of time dilation and clock synchronization in accelerated frames.

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Homework Statement


Hi, I have an exercise where we are supposed to find a condition for which two clocks are synchronise if one clock is accelerated.

Homework Equations


The time dilation in an inertial frame moving with velocity v is well known. t'=\frac{t}{1-\frac{v^2}{c^2}}

The Attempt at a Solution


My question is whether this formula can be generalized for time varying speeds such that the time passed in the accelerated frame is given by: t'=\int_0^t \frac{1}{1-\frac{v(\tau)^2}{c^2}}d\tau
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
No problem. I found out that the Lorentz transformation is only valid for constant speeds. So what I thought is wrong. thanks anyway
 

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