Relativity: Formulating dT, v, l Expression

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Homework Help Overview

The discussion revolves around formulating an expression that connects the change in time (dT), the velocity (v) of a particle, and its length (l) at relativistic speeds, specifically within the context of relativity.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to clarify the relationship between dT, v, and l, with some questioning the need for additional variables such as dl or dv. Others are exploring the implications of Lorentz Length Contraction and suggesting potential rearrangements of equations to connect these variables.

Discussion Status

The discussion is ongoing, with participants sharing ideas and seeking clarification. Some have proposed rearranging existing equations to explore connections between the variables, while others are looking for guidance on how to approach the problem further.

Contextual Notes

There appears to be some uncertainty regarding the specific variables needed in the formulation, as well as the appropriate context for the discussion, with suggestions to possibly explore it in a different sub-forum.

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Homework Statement


Formulate an expression linking the change in time (dT) and the particle's velocity (v) with it's length (l) occurring at relativistic speeds

Homework Equations


γ = 1/√1-(v^2/c^2)
T = γT
l = γl

The Attempt at a Solution


Not really sure what it's after...
 
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You have "dT" but no other "d". You must have either "dl" or "dv". Which is it?
 
I think it implies dL
 
Just been looking at this question again and knowing that provided that v is a constant in the Lorentz Length Contraction:

[itex]L_{0}=L\sqrt{1-\frac{v^{2}}{c^{2}}}[/itex]

Then shouldn't we be able to rearrange this for [itex]\sqrt{1-\frac{v^{2}}{c^{2}}}[/itex] to make

[itex]\sqrt{1-\frac{v^{2}}{c^{2}}}=\frac{L_{0}}{L}[/itex]

and then feed this into the equation for Δt perhaps? So that

[itex]\delta T=\frac{\delta T_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/itex]

becomes

[itex]\delta T=\frac{\delta T_{0}L}{L_{0}}[/itex]

It's just an idea...
 
Does anyone have any pointers? Perhaps try this under a different sub-forum maybe?
 

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