Velocity expressed as difference...

[Endy0816]

Just curious what the time dilation and length contraction equations would look like in a system based on:

 

v = c - v_Normal

 

for finding velocity.

 

I was thinking along the lines of how we convert to Kelvins. Wondering how things would look if we did something similar with velocity.

 

[pzkpfw]

But what's V_Normal?

That implies there's some absolute velocity that other velocities can be compared to. There is no such thing.

[timo]

[math] \gamma = \left( 1 - \frac{v_{\rm normal}^2}{c^2} \right)^{-1/2} = \left( 1 - \frac{(c - v_{\rm new})^2}{c^2} \right)^{-1/2} = \left( 1 - \frac{c^2 -2 c v_{\rm new} + v_{\rm new}^2}{c^2} \right)^{-1/2} = \left( 2 \frac{v_{\rm new}}{c} - \frac{ v_{\rm new}^2}{c^2} \right)^{-1/2}[/math]

There is no real reason to do the conversion akin to Celsius->Kelvin, since the zero of our "normal" velocity measurement already correspond to "absolute zero". A more common conversion is to set the maximum to 1 (100%), i.e. [math]v_{\rm new} = v_{\rm normal}/c[/math]. Then, [math] \gamma = \left( 1 - v_{\rm new}^2 \right)^{-1/2}[/math], which in fact makes the time dilatation factor look simpler.

Edited February 17, 2016 by timo

[Endy0816]

I meant normal only in how we normally measure. Start at zero and count up. This would reverse things. Start you at the value of c and decrease as you went faster.

 

Think that is what I am looking for Timo. I'll take a look at it. Many thanks.

Edited February 17, 2016 by Endy0816