Length contraction and time dilation in relativity

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Homework Help Overview

The discussion revolves around a problem in special relativity, specifically addressing length contraction and time dilation as they pertain to an elementary particle's lifetime as observed in different frames of reference. The original poster attempts to determine the proper lifetime of a particle that travels a specified distance at a significant fraction of the speed of light before decaying.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore different methods to calculate the proper lifetime of the particle, questioning the consistency of results obtained through various approaches. Some participants express confusion over the interpretation of distances in different frames and the implications of length contraction.

Discussion Status

The discussion is active, with participants providing insights and clarifications regarding the calculations and underlying concepts. There is recognition of potential misconceptions about how distances are perceived in different frames, and some participants suggest revisiting the algebraic relationships to clarify discrepancies.

Contextual Notes

Participants note that the problem involves specific values and equations from special relativity, including the Lorentz factor, and highlight the importance of understanding which frame is considered at rest versus which is moving. There is mention of potential rounding errors and the need for careful analysis when applying the equations.

  • #31
Orodruin said:
Alternatively, imagine that the rod is at rest in the particle rest frame and that in the lab frame the other end of the rod passes the position where the particle eventually will decay at the same time as the particle is created. Since the rod is length contracted, it will indeed be longer in the particle's rest frame. However, in the particle's rest frame, the particle creation is not simultaneous to the event that the other end of the rod passes the position in the lab frame where the particle will eventually decay. Therefore the length of the rod divided by the velocity of the lab frame will not give the correct time.I am going to stop you right there because this is a fundamental misunderstanding of relativity. There is no way you can identify a particular frame as a "moving" frame. All movement is relative, in classical mechanics as well as in special relativity. Relative to the lab frame, the particle is moving. Relative to the particle's rest frame, the lab is moving.
I'm very very very confused, but yes I understand that all movement is relative. That was a poor choice of words on my part.
 

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