Natural extension of the Generalised Uncertainty Principle

TL;DR

This paper proposes an extended generalized uncertainty principle (GUP) linked to the cosmological constant, suggesting a minimum observable momentum and advancing the understanding of quantum spacetime in de Sitter space.

Contribution

It introduces a novel extension of the GUP that incorporates the cosmological constant, implying a minimum momentum and enriching quantum spacetime models.

Findings

Extended GUP implies a minimum observable momentum.

Connects the cosmological constant to quantum measurement limits.

Provides a new perspective on quantum spacetime in de Sitter space.

Abstract

We discuss a gedanken experiment for the simultaneous measurement of the position and momentum of a particle in de Sitter spacetime. We propose an extension of the so-called generalized uncertainty principle (GUP) which implies the existence of a minimum observable momentum. The new GUP is directly connected to the nonzero cosmological constant, which becomes a necessary ingredient for a more complete picture of the quantum spacetime.