2020/10/09 by Nicolis, Alberto
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #History and Philosophy of Physics (physics.hist-ph)
paper · doi:10.48550/arxiv.2010.04743
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.