Special Relativity in Reduced Power Algebras

TL;DR

This paper extends the Lorentz transformations of Special Relativity to reduced power algebras, offering new perspectives on infinities and fundamental constants in physics by incorporating infinitesimal and infinite scalars.

Contribution

It introduces a reformulation of Special Relativity using reduced power algebras, broadening the mathematical framework of the theory.

Findings

Lorentz transformations are extended to reduced power algebras.

Infinities in physics are addressed through infinitesimal and infinite scalars.

New insights into fundamental constants like c and h are proposed.

Abstract

Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are re-formulated using scalars in {\it reduced power algebras}, [2-9], instead of the usual real or complex scalars. Here, the Lorentz coordinate transformations, fundamental in Special Relativity, are extended to versions of Special Relativity that are similarly re-formulated in terms of scalars in reduced power algebras, instead of the usual real or complex scalars. The interest in such re-formulations of basic theories of Physics are due to a number of important reasons, [2-11]. Suffice to mention two of them : the difficult problem of so called "infinities in Physics" falls easily aside due to the presence of infinitesimal and infinitely large scalars in such reduced power algebras, and the issue of fundamental constants in physics, like Planck's $h$, or the velocity of light $c$, comes under a new focus which offers rather surprising alternatives.