Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof of invariance of dp1*dp2*dp3/E

  1. Oct 31, 2008 #1


    User Avatar

    If we introduce four-dimensional coordinate sistem with component of four-momentum on axis, then dp1*dp2*dp3 can be considered as zeroth component of an element of hypersurface given by p^2=m^2*c^2. Element of this hypersurface is parallel to 4-vector of momentum so we have that dp1*dp2*dp3/E is ration of components of two parallel vectors so it must be invariant under Lorentz transformation. (this proof is from Landau, Lifgarbagez - Fields)
    This proof seems ok but I can't see why I cannot apply it to show (wrongly) that dxdydz/t is invariant.

    Thanks in advance.
  2. jcsd
  3. Oct 31, 2008 #2


    User Avatar
    Science Advisor

    The proof for momentum and energy uses the constraint E^2=p^2+m^2.
  4. Nov 1, 2008 #3


    User Avatar

    Yes, that is equivalent to p^2=m^2*c^2 (p is 4-vector of momentum). So for x, I can watch hypersurface given by equation x^2=c*\tau (x is 4-vector, and \tau proper time). So the rest is same and conclusion is worng (namely that dxdydz/t is invariant)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook