Doubly Special Relativity with a minimum speed and the Uncertainty Principle

TL;DR

This paper proposes a new symmetry in space-time involving an invariant minimum speed, which could underpin the uncertainty principle by introducing a fundamental low-energy limit connected to a preferred frame.

Contribution

It introduces a novel invariant minimum speed in space-time, breaking Lorentz symmetry and linking it to the origin of quantum uncertainty.

Findings

A minimum speed $V$ acts as a fundamental limit in space-time.

The invariant minimum speed leads to a new symmetry principle at low energies.

The approach offers a potential foundation for the uncertainty principle.

Abstract

The present work aims to search for an implementation of a new symmetry in the space-time by introducing the idea of an invariant minimum speed scale ($V$). Such a lowest limit $V$, being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the space-time at the subatomic level for very low energies close to the background frame ($v\approx V$), providing a fundamental understanding for the uncertainty principle, i.e., the uncertainty relations should emerge from the space-time with an invariant minimum speed.