It seems to me(I am unfamiliar as yet with its use in Maxwell's equations- I think it may be been discovered even then?) that the Lorentz factor is verified by experiment but not "proved" as such.

I am certainly not disputing what has been shown experimentally to be the case but I am wondering if there is another approach that could be taken.

Suppose we have a finite system of particles and a method of making their relative motions asymmetric ,is there a method whereby we can quantify the relative (speed of) motion between any two particles .

(I realize that "particles" is an approximation of how things are but can we follow this admittedly flawed logic ?)

So ,is there a mathematical procedure that ,in a finite system of small objects or particles would allow one to quantify relative motion between any two objects and ,by extension to find a maximum value as a function of the overall number perhaps of the objects?

If this was a theoretical /mathematical possibility then it would satisfy my (mathematical?) curiosity to increase to number of particles without limit and determine what this number would be as it would be another way of evaluating the "maximum speed limit"

Don't get me wrong . If "my" figure differed from c ,I would agree it was probably (very probably ,even certainly) wrong but this is an avenue I am trying to go down but am limited by my lack of mathematical skills.