why do you put such a simple "norm" on PE?

unforunately, evn though "four-momentum" can
be mathematically conserved, the whole
idea of spacetime is an obfuscation, nothing
but mere phase-space. momentum cannot usefully be thought of,
without the concept of time, and this is clear
from the use of quaternions in SR,
where the "real, scalar" part is time,
clearly completely different from the "pure,
imaginary vector" part of space.

** *Total energy = kinetic energy – sqrt((potential energy)^2

For reference, the Lagrangian under GR is

** *L = sqrt([g]_00 – (ds/dt)^2 / c^2)

This exercise demonstrates how the conservation of four-momentum can
be derived if one is willing to get himself demystified. *If not, the
haunted soul will be trapped in the limbo world of knowing the