In a cyclotron, the time to make it all the way around is Different

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    Cyclotron Time
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Discussion Overview

The discussion revolves around the application of the formula t = gamma * t' in the context of a cyclotron, particularly focusing on whether this formula can be used for circular paths and how it relates to time dilation effects in special relativity.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the relevance of applying the formula t = gamma * t' to a circular path.
  • Another participant asserts that the formula is significant for GPS location, mentioning an additional term related to centripetal acceleration that depends on the observer's location.
  • A different participant challenges the notion of gravitational time dilation in the context of centrifugal acceleration, labeling it as "hogwash."
  • One participant confirms that the formula can be applied in this scenario, stating that in special relativity, only the instantaneous speed matters, which remains constant in circular motion. They suggest that integration along the circular path could serve as a proof.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the formula in this context, with some supporting its use while others question its relevance and introduce alternative considerations. The discussion remains unresolved regarding the validity of the claims made.

Contextual Notes

There are unresolved assumptions regarding the relationship between time dilation effects and centripetal acceleration, as well as the definitions of terms used in the discussion.

physics user1
Can I apply the formula t= gamma * t' if the path is Circular?
 
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Why would you want to do that ?
 
That formula is important for GPS location. But there is another term, due to the centripetal acceleration, that also depends on the observer's location.
 
Meir Achuz said:
That formula is important for GPS location. But there is another term, due to the centripetal acceleration, that also depends on the observer's location.
Are you trying to talk about gravitational time dilation in the context of a centrifugal acceleration field? Sounds like hogwash.
 
Cozma Alex said:
Can I apply the formula t= gamma * t' if the path is Circular?
Yes. In special relativity the only thing that matters is the instantaneous speed, and that's constant here.

You can prove it by integrating the interval along the circular path of you want.
 
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