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)(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Proof of invariance of dp1*dp2*dp3/E

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