A revision of the Generalized Uncertainty Principle

TL;DR

This paper revises the Generalized Uncertainty Principle by challenging the conventional assumption that its leading correction is proportional to the gravitational constant, proposing instead that it may be proportional to the first power of the Planck length, implying less suppressed departures from standard quantum mechanics.

Contribution

It introduces a revised perspective on the leading order correction to the Generalized Uncertainty Principle, suggesting it may be proportional to the Planck length rather than the gravitational constant.

Findings

Leading order correction may be proportional to the Planck length

Departures from quantum mechanics could be less suppressed

Challenges standard assumptions in quantum gravity theories

Abstract

The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant $G_N = L_{Pl}^2$. On the other hand, the emerging picture suggests a set of departures from the standard theory which demand a revision of all the arguments used to deduce heuristically the new rule. In particular, one can now argue that the leading order correction to the Heisenberg Uncertainty Principle is proportional to the first power of the Planck length $L_{Pl}$. If so, the departures from ordinary quantum mechanics would be much less suppressed than what is commonly thought.