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Surely fault about relativistic momentum

  1. Feb 26, 2009 #1
    Dear Friends

    Two identical particles are running, in opposite directions, along the x axis of a reference frame having the origin coinciding with their barycentre; they hits frontally and glue together.

    Their speeds are ("b" for before collision, "a" for after) :

    V1b = u
    V2b = -u
    Va = 0

    Let's watch the event from a reference frame moving toward right at speed u.

    Relativistic speed composition gives:

    V1b' = 0
    V2b' = - 2u / ( 1 + u^2/c^2)
    Va' = -u

    This way the relativistic momentum is not conserved:

    m ( 0 )+ m ( - 2u / ( 1 + u^2/c^2) ) != 2m ( -u )

    Obviously, I'm wrong but really can't see what is going the bad way.
    Please, can you give any hints ?

    Best regards!!

    Barbara Da Vinci
  2. jcsd
  3. Feb 26, 2009 #2


    User Avatar
    Science Advisor

    Relativistic momentum is not equal to mv, it's equal to [tex]mv\gamma[/tex], i.e. [tex]\frac{mv}{\sqrt{1 - v^2/c^2}}[/tex]
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