Hints at a relationship between friction and relativistic physics

TL;DR

This paper reveals a mathematical analogy between frictional mass loss in mechanics and relativistic mass increase, suggesting that relativistic structures could have been discovered through classical friction studies before 1905.

Contribution

It demonstrates that treating bodies losing mass due to friction as variable mass systems yields a relationship similar to relativistic mass formulas, indicating a possible pre-1905 discovery of relativistic mathematics.

Findings

Relativistic mass formula analogous to frictional mass loss

A new reference frame transformation with relativistic features

Application to cosmological problems

Abstract

In applied mechanics Reye's law (1860) establishes, via energy arguments, that the mass of the debris produced by dry friction in the contact of rigid bodies is proportional to the work done by friction forces. This result has long been used for the determination of the distribution of pressure in the contact of rigid bodies, and hence for the design of brakes. In this work I show that, when bodies losing mass due to friction are treated, as they should, as variable mass systems, a relationship analogous to the relativistic mass formula is recovered. This result suggests that mathematical structures typical of relativistic physics could have been discovered prior to 1905, without making any reference to electromagnetism, group theory or the speed of light. Also this result could point to the existence of a physical theory depending on two constants, the speed of light (Reye's constant) and a universal frictional deceleration with respect to an absolute frame. The limit of the theory for vanishing friction would give Special Relativity, as the absolute frame would become unobservable, while the limit for the speed of light going to infinity would lead to Aristotelian mechanics, i.e. a classical mechanics type theory presenting universal friction. Finally, I present a reference frame transformation that displays these features and I apply the theory to some open cosmological problems.