Dimensional Reduction in Quantum Gravity

TL;DR

This paper suggests that at the Planck scale, quantum gravity effectively reduces to a two-dimensional description, imposing strong constraints on model building and explaining the difficulty in formulating consistent quantum black hole models.

Contribution

It proposes a dimensional reduction at the Planck scale based on unitarity and entropy considerations, impacting quantum gravity model development.

Findings

Quantum gravity exhibits effective 2D behavior at the Planck scale.

Dimensional reduction constrains the construction of quantum gravity models.

No fully consistent quantum black hole models have been achieved due to these constraints.

Abstract

The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time. This observation, deduced from not much more than unitarity, entropy and counting arguments, implies severe restrictions on possible models of quantum gravity. Using cellular automata as an example it is argued that this dimensional reduction implies more constraints than the freedom we have in constructing models. This is the main reason why so-far no completely consistent mathematical models of quantum black holes have been found. Essay dedicated to Abdus Salam.