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Derivation of relativistic momentum

  1. Jul 1, 2014 #1
    Hi all,
    Is it possible to derive the equation p = ymv, and hence based on this, kinetic energy formula, without referring to 4-vectors or 2-dimensional collisions, that is derive it in one dimension?
    I tried this website/pdf but the mathematics is beyond my understanding. So could some one either explain the pdf, or derive the equation themselves?
    Here is the link:
  2. jcsd
  3. Jul 1, 2014 #2

    Simon Bridge

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    ... yes - sort of.

    You start by showing that p=mv is not conserved in all reference frames.

    Note: in 1D, the 4-vector just has a zero in each of the unused positions.
  4. Jul 1, 2014 #3


    Staff: Mentor

    Since the derivation in the paper you linked to looks valid, I would say yes. :wink:

    Can you be a bit more specific about what in the pdf you are unable to understand?
  5. Jul 2, 2014 #4
    i don't get the mathematical processes from equation 3.6 and 3.7.
  6. Jul 2, 2014 #5
    Hi albertrichardf,

    In addition to the paper you referred to, Louis De Broglie derived that (and other formulas expressed in 3-vectors) using Hamilton-Jacobi mathematics. It's possible to go still further and derive the relativistic energy equation and all of its variations.
  7. Jul 2, 2014 #6


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    It's just a taylor series.

    Basically the idea is that you can approximate a function near a point by a straight line

    If you have f(x) and you want to approximate it near some value "a", the first 2 terms of the series are

    f(a) + (df/dx)*(x-a)

    see http://en.wikipedia.org/wiki/Taylor_series
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