posted by Yves
The quantity E^2 − p^2c^2 is an invariant quantity in Special Relativity. This means that it has the
same value in all inertial frames even though E and p have different values in different frames.
1)Show this explicitly by considering the following case: A particle of mass m is moving in the +x direction with speed u and has momentum p and energy E in the frame S. If S' is moving at speed v in the standard
way, determine the momentum p' and energy E' observed in S', and show that
E'^2 − p'^2*c^2 = E^2 - p^2*c^2
I know the formulas are
p = mu/(1-u^2/c^2)^1/2 and
E = mc^2/(1-u^2/c^2)^1/2
but I don't know what to do for frame S'
Any help appreciated