Lorentz from Galilei, deductively

TL;DR

This paper demonstrates that Newtonian mechanics inherently contains signs of Lorentz invariance, suggesting special relativity could have been deduced from Newtonian principles without prior experimental indications.

Contribution

It reveals that Newtonian mechanics is more Lorentz-invariant than previously recognized and derives universal velocity-dependent corrections to long-range interactions.

Findings

Newtonian mechanics shows subtle Lorentz invariance signs

Derived universal velocity-dependent interaction corrections

Potential implications for post-Newtonian expansion in GR

Abstract

I argue that in the Lagrangian formulation of standard, Galilei-invariant Newtonian mechanics there are subtle but concrete signs of {\em Lorentz} invariance. In fact, in a specific sense made explicit in the paper, Newtonian mechanics is more Lorentz-invariant than Galilei-invariant. So, special relativity could have been discovered deductively, before there were any indications---such as Maxwell's equations---that Galilei relativity had to be modified. To make this anti-historical exercise less academic, I derive certain velocity-dependent corrections to long-range interactions between spinless point particles. Such corrections are universal; in particular, they do not depend on the spin of the field mediating such interactions or on how strongly coupled such a field is. I discuss potential applications to the post-Newtonian expansion of general relativity.