Minimum Length - Maximum Velocity

TL;DR

This paper explores a framework combining minimum length in space-time with reference frame invariance, linking it to doubly special relativity and predicting relationships between minimum lengths and ultra-relativistic particle velocities.

Contribution

It introduces a novel formalism connecting minimum length hypotheses with reference frame transformations and doubly special relativity, providing new insights into ultra-relativistic particle behavior.

Findings

Predicted ratio between minimum lengths in space and time.

Connected minimum length properties with velocity-energy relations.

Utilized OPERA results to estimate minimum length ratios.

Abstract

We study a framework where the hypothesis of a minimum length in space-time is complemented with the notion of reference frame invariance. It turns out natural to interpret the action of the obtained reference frame transformations in the context of doubly special relativity. As a consequence of this formalism we find interesting connections between the minimum length properties and the modified velocity-energy relation for ultra-relativistic particles. For example we can predict the ratio between the minimum lengths in space and time using the results from OPERA about superluminal neutrinos.