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Special relativity question

  1. Sep 8, 2007 #1
    1. The problem statement, all variables and given/known data
    I am trying to solve produce an equation and the last step requires that

    [tex] \frac{ \partial {m \mathbf{v}}}{\partial {s} } = \frac{ \partial { \mathbf{p}}}{c \partial {t} } [/tex]

    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. jcsd
  3. Sep 10, 2007 #2
    Well, why haven't you tried to write ds in terms of dt? This gives

    [tex]ds = \sqrt{(c\,dt)^2-x^2} = \sqrt{c^2-v^2}\,dt[/tex]

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