Is there any general significance to calculated quantities that depend purely on general powers of the velocity of a particle/system/etc? The first power being momentum and the second being kinetic energy.
I know that in relativistic mechanics the momentum and energy become quantities that must actually be expressed in infinite orders of velocity since energy and momentum are functions that can be expressed as power series of velocity. So, if there is any significance to the momentum and energy being to first and second order in Newtonian mechanics respectively, why do they go to functions of infinite order when special relativistic effects become a concern.
Or am I making connections that lead nowhere?
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