Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique

TL;DR

This paper develops a master equation for fermions and bosons within a modified special relativity framework with two invariant scales, introducing new variables to incorporate linearity and locality, and discusses the quantum-gravitational nature of spacetime in this context.

Contribution

It introduces a formal master equation for SR2, incorporating conjugate variables to address non-linearity and non-locality, and explores the implications for spacetime and particle properties.

Findings

Master equation for fermions and bosons in SR2

Introduction of conjugate variables (chi^0, chi)

Spacetime in SR2 has an intrinsic quantum-gravitational character

Abstract

We present a Master equation for description of fermions and bosons for special relativities with two invariant scales, SR2, (c and lambda_P). We introduce canonically-conjugate variables (chi^0, chi) to (epsilon, pi) of Judes-Visser. Together, they bring in a formal element of linearity and locality in an otherwise non-linear and non-local theory. Special relativities with two invariant scales provide all corrections, say, to the standard model of the high energy physics, in terms of one fundamental constant, lambda_P. It is emphasized that spacetime of special relativities with two invariant scales carries an intrinsic quantum-gravitational character. In an addenda, we also comment on the physical importance of a phase factor that the whole literature on the subject has missed and present a brief critique of SR2. In addition, we remark that the most natural and physically viable SR2 shall require momentum-space and spacetime to be non-commutative with the non-commutativity determined by the spin content and C, P, and T properties of the examined representation space. Therefore, in a physically successful SR2, the notion of spacetime is expected to be deeply intertwined with specific properties of the test particle.