Relativity: Formulating dT, v, l Expression

• shyguy79
In summary, the problem is to find an expression linking the change in time (dT) and the particle's velocity (v) with its length (l) at relativistic speeds. The equations for Lorentz factor (γ), time dilation (T), and length contraction (l) are provided. The attempt at a solution involves rearranging the equation for length contraction to solve for √1-(v^2/c^2) and then using it in the equation for time dilation. The problem is still being explored and may need to be discussed in a different forum.
shyguy79

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...

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:

$L_{0}=L\sqrt{1-\frac{v^{2}}{c^{2}}}$

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

$\sqrt{1-\frac{v^{2}}{c^{2}}}=\frac{L_{0}}{L}$

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

$\delta T=\frac{\delta T_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

becomes

$\delta T=\frac{\delta T_{0}L}{L_{0}}$

It's just an idea...

Does anyone have any pointers? Perhaps try this under a different sub-forum maybe?

What is the theory of relativity?

The theory of relativity is a scientific theory proposed by Albert Einstein in 1915, which explains the relationship between space and time and how they are affected by gravity.

What is the equation for the time dilation in special relativity?

The equation for time dilation in special relativity is dT = dT0 / √(1 - v2/c2), where dT is the observed time, dT0 is the proper time, v is the velocity of the object, and c is the speed of light.

How does the length of an object change in special relativity?

In special relativity, the length of an object changes according to the Lorentz contraction formula, l = l0√(1 - v2/c2), where l is the observed length, l0 is the proper length, v is the relative velocity, and c is the speed of light.

What does the equation E=mc2 represent in the theory of relativity?

The equation E=mc2 represents the relationship between energy (E), mass (m), and the speed of light (c). It shows that mass and energy are interchangeable and can be converted into one another.

What is the difference between special relativity and general relativity?

Special relativity deals with the relationship between space and time in the absence of gravity, while general relativity incorporates the effects of gravity on the fabric of space-time. General relativity is considered to be a more comprehensive theory than special relativity.

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