New generalized uncertainty principle with parameter adaptability for the minimum length

TL;DR

This paper proposes a new generalized uncertainty principle that maintains a fixed minimum length regardless of parameter sign, resolving previous contradictions in quantum gravity models.

Contribution

It introduces a unified GUP formulation that ensures a consistent minimum length, independent of the parameter being positive or negative.

Findings

Unified GUP with fixed minimum length

Resolves contradiction between negative parameter scenarios and quantum gravity

Provides a model-independent feature of minimum length

Abstract

There have been many papers suggesting that the parameter of the generalized uncertainty principle should be negative rather than positive in some specific scenarios, and the negative parameter can remove the minimum length. However, the minimum length is a model-independent feature of quantum gravity and it should not be affected by the specific scenarios. In order to solve this contradiction, we derive a new generalized uncertainty principle to reflect a fixed and unified minimum length in both cases of positive and negative parameters.