# Quantum Gravity Spacetime: Universe vs. Multiverse

## TL;DR

This paper explores how quantum gravity theories must account for uncertainty principles and proposes a new way to determine valid spacetime models.

## Contribution

The paper introduces a quantum covariance criterion to select physically admissible spacetimes in quantum gravity theories.

## Key findings

- Current quantum gravity theories like string theory fail to meet the quantum covariance criterion.
- Theories using a universe representation satisfy the Heisenberg Generalized Uncertainty Principle and the quantum covariance criterion.

## Abstract

Starting from the realization that the theory of quantum gravity (QG) cannot be deterministic due to its intrinsic quantum nature, the requirement is posed that QG should fulfill a suitable Heisenberg Generalized Uncertainty Principle (GUP) to be expressed as a local relationship determined from first principles and expressed in covariant 4-tensor form. We prove that such a principle places also a physical realizability condition denoted as “quantum covariance criterion”, which provides a possible selection rule for physically-admissible spacetimes. Such a requirement is not met by most of current QG theories (e.g., string theory, Geometrodynamics, loop quantum gravity, GUP and minimum-length-theories), which are based on the so-called multiverse representation of space-time in which the variational tensor field coincides with the spacetime metric tensor. However, an alternative is provided by theories characterized by a universe representation, namely in which the variational tensor field differs from the unique “background” metric tensor. It is shown that the latter theories satisfy the said Heisenberg GUP and also fulfill the aforementioned physical realizability condition.