# Special relativity question

1. Sep 8, 2007

### ehrenfest

1. The problem statement, all variables and given/known data
I am trying to solve produce an equation and the last step requires that

$$\frac{ \partial {m \mathbf{v}}}{\partial {s} } = \frac{ \partial { \mathbf{p}}}{c \partial {t} }$$

where ds is the infinitesimal Lorentz invariant length, v is velocity, and p is momentum

The problem is that I do not know how to justify this last step.

2. Relevant equations

3. The attempt at a solution

I tried rewriting ds in terms of tau, but then it seemed that this proper time to be equal to non-proper time which is not true.

2. Sep 10, 2007

### Irid

Well, why haven't you tried to write ds in terms of dt? This gives

$$ds = \sqrt{(c\,dt)^2-x^2} = \sqrt{c^2-v^2}\,dt$$

Plug this in and you have a very easy differential equation to integrate,