A single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties

TL;DR

This paper proposes a single-world interpretation of quantum mechanics based on fundamental measurement uncertainties from quantum gravity, resolving issues with superpositions and global protocols, and aligning with a consistent universe model.

Contribution

It introduces a novel approach incorporating quantum-gravity-induced measurement errors to define events, supporting a single-world view compatible with quantum theory and gravity.

Findings

Global protocols cannot distinguish superpositions under measurement uncertainties.

Predictions align with definite outcomes when considering fundamental measurement errors.

Supports a consistent single-world interpretation compatible with quantum gravity.

Abstract

Within ordinary ---unitary--- quantum mechanics there exist global protocols that allow to verify that no definite event ---an outcome to which a probability can be associated--- occurs. Instead, states that start in a coherent superposition over possible outcomes always remain as a superposition. We show that, when taking into account fundamental errors in measuring length and time intervals, that have been put forward as a consequence of a conjunction of quantum mechanical and general relativity arguments, there are instances in which such global protocols no longer allow to distinguish whether the state is in a superposition or not. All predictions become identical as if one of the outcomes occurs, with probability determined by the state. We use this as a criteria to define events, as put forward in the Montevideo Interpretation of Quantum Mechanics. We analyze in detail the occurrence of events in the paradigmatic case of a particle in a superposition of two different locations. We argue that our approach provides a consistent (C) single-world (S) picture of the universe, thus allowing an economical way out of the limitations imposed by a recent theorem by Frauchiger and Renner showing that having a self-consistent single-world description of the universe is incompatible with quantum theory. In fact, the main observation of this paper may be stated as follows: If quantum mechanics is extended to include gravitational effects to a QG theory, then QG, S, and C are satisfied.