It recently came to my attention that there exists two "kinds" of Lorentz invariants: the covariant and the noncovariant ones.(adsbygoogle = window.adsbygoogle || []).push({});

The covariant ones would be Lorentz scalars e.g. fully contracted Lorentz tensors. If one applies the Lorentz transformation to a covariant Lorentz scalar, one would find it is invariant in form and in numerical value.

On the other hand, quantities like EV (volume times energy) are certainly not Lorentz scalars and they are most certainly not form invariant under Lorentz transformations (energy goes to energy and momentum, volume goes to volume and time), yet they appear to be numerically identical in all Lorentz frames. One can show this by noticing that the volume gets contracted: V = V_0/gamma, while the energy is related to the mass by E = gamma * m. (c=1) Therefore EV=mV_0 which is obviously the same number in every Lorentz frame.

I'm still not quite sure what to make of these quantities. None of the standard textbooks explicitly deals with it. Any thoughts?

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# Covariant and noncovariant Lorentz invariants

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