Lorentz from Galilei, deductively

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.

10 pages

References in corpus (4)

• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Effective field theory calculation of second post-Newtonian binary dynamics
• Static two-body potential at fifth post-Newtonian order
• Effective field theory for gravitational radiation in scalar-tensor gravity