Testable scenario for Relativity with minimum-length

TL;DR

This paper introduces a class of space-times with observer-independent velocity and length scales, modifying Lorentz contraction to accommodate a minimum length, and demonstrates this consistency in a specific relativistic framework.

Contribution

It proposes a new class of space-times with invariant length and velocity scales, extending relativity to include a minimum length consistent across all inertial frames.

Findings

Lengths larger than the minimum are preserved across all inertial frames.

The modified Lorentz contraction accommodates a minimum length in relativistic transformations.

The framework is consistent at leading order in the minimum length.

Abstract

I propose a general class of space-times whose structure is governed by observer-independent scales of both velocity ($c$) and length (Planck length), and I observe that these space-times can naturally host a modification of FitzGerald-Lorentz contraction such that lengths which in their inertial rest frame are bigger than a "minimum length" are also bigger than the minimum length in all other inertial frames. With an analysis in leading order in the minimum length, I show that this is the case in a specific illustrative example of postulates for Relativity with velocity and length observer-independent scales.