Click here to flash read.
Without the mass-energy equivalence available on Minkowski spacetime
$\mathbb{M}$, it is not possible on 4-dimensional non-relativistic
Galilei/Newton spacetime $\mathbb{G}$ to combine 3-momentum and total
mass-energy in a single tensor object. However, given a fiducial frame, it is
possible to combine 3-momentum and kinetic energy into a linear form (particle)
or $(1,1)$ tensor (continuum) in a manner that exhibits increased unity of
classical mechanics on flat relativistic and non-relativistic spacetimes
$\mathbb{M}$ and $\mathbb{G}$. As on $\mathbb{M}$, for a material continuum on
$\mathbb{G}$, the First Law of Thermodynamics can be considered a consequence
of a unified dynamical law for energy-momentum rather than an independent
postulate.
No creative common's license