Gravity from a Modified Commutator

TL;DR

This paper proposes a modified position-momentum commutator that captures key features of gravity, such as holography and dimensional reduction, by linking quantum mechanics with gravitational phenomena.

Contribution

It introduces a simple, dimensionally consistent commutator model that qualitatively reproduces gravity's IR/UV correspondence and holographic behavior.

Findings

Commutator exhibits IR/UV correspondence.

Demonstrates dimensional reduction in quantum states.

Suggests potential for quantitative gravity modeling.

Abstract

We show that a suitably chosen position-momentum commutator can elegantly describe many features of gravity, including the IR/UV correspondence and dimensional reduction (`holography'). Using the most simplistic example based on dimensional analysis of black holes, we construct a commutator which qualitatively exhibits these novel properties of gravity. Dimensional reduction occurs because the quanta size grow quickly with momenta, and thus cannot be "packed together" as densely as naively expected. We conjecture that a more precise form of this commutator should be able to quantitatively reproduce all of these features.