Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy

TL;DR

This paper introduces a new generalized uncertainty principle that predicts a maximum observable momentum without a minimal length, aligning with quantum gravity theories, and explores its implications on quantum mechanics and black hole thermodynamics.

Contribution

It proposes an exact GUP with a maximal momentum and no minimal length, extending previous models and analyzing its physical consequences.

Findings

Maximal observable momentum is incorporated into the GUP.

The model aligns with string theory and quantum gravity predictions.

Implications on quantum mechanics and black hole thermodynamics are explored.

Abstract

We present a novel generalization of the Heisenberg uncertainty principle which introduces the existence of a maximal observable momentum and at the same time does not entail a minimal indeterminacy in position. The above result is an exact generalized uncertainty principle (GUP), valid at all energy scales. For small values of the deformation parameter $\beta$, our ansatz is consistent with the usual expression for GUP borrowed from string theory, doubly special relativity and other quantum gravity candidates that provide $\beta$ with a negative sign. As a preliminary analysis, we study the implications of this new model on some quantum mechanical applications and on the black hole thermodynamics.