1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Momentum for my exam tomorrow

  1. Apr 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Let P be the 4 momentum
    u be the 4 velocity
    a) Evaluate the Lorentz invariant [itex]P^2[/itex]
    b)Differentiate [itex]P^2=P_{\mu}P_{\mu}[/itex] and show that

    2. The attempt at a solution

    The first part yields an answer of [tex]E^2 -p^2 c^2=m^2 c^4[/tex]

    Now for part b. Does the P^2 have anything to do with the equality that needs to be proven? Do i need to differentiate P^2 with respect to time? Do i hav to differentiate
    [tex]E^2 -p^2 c^2=m^2 c^4[/tex] with respect to time?

    Please help!

  2. jcsd
  3. Apr 15, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, differentiate with respect to time. The derivative of P^2 obviously gives zero since m^2 c^4 is constant.

    Now, write P^2 = E^2 - p dot p c^2

    (my small p is the three momentum and dot is the dot product

    so d/dt(P^2) = 2 E dE/dt - 2 c^2 p dot dp/dt

    This must be zero. Now write E= gamma mc^2 and p = gamma m u where u is the ordinary three velocity
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Momentum for my exam tomorrow