Enlarged Bound on the Measurability of Distances and Quantum $\kappa$-Poincar\`e Group

TL;DR

This paper explores how quantum mechanics and general relativity impose fundamental limits on distance measurements, linking these bounds to structures in the quantum $$-Poincare9 group, thus providing a new perspective on measurability constraints.

Contribution

It reveals that the quantum -Poincare9 group's structures naturally lead to bounds on distance measurability when quantum and gravitational effects are considered.

Findings

Identifies a fundamental bound on distance measurements due to quantum and gravitational effects.

Connects the measurability bound to the mathematical structures of the quantum -Poincare9 group.

Provides a new theoretical insight into the limits of measurement precision in quantum gravity contexts.

Abstract

When quantum mechanical and general relativistic effects are taken into account in the analysis of distance measurements, one finds a measurability bound. I observe that some of the structures that have been encountered in the literature on the Quantum $\kappa$-Poincar\`e Group naturally lead to this bound.