Replacing the Notion of Spacetime Distance by the Notion of Correlation

TL;DR

This paper proposes replacing the traditional notion of spacetime distance with correlation strength, suggesting a fundamental information-theoretic structure that underpins quantum fields and spacetime geometry as an approximation.

Contribution

It introduces a novel framework where correlations, rather than spacetime distances, form the primary structure, potentially redefining the foundation of quantum field theory and spacetime geometry.

Findings

Correlation strength increases as spacetime distance decreases.

Standard quantum field correlators can be approximated from the correlation-based structure.

Spacetime and fields are emergent, approximate descriptions of an underlying correlation-based framework.

Abstract

Spacetime is conventionally viewed as a stage on which actors, in the form of fields, move. Here, we explore what may lie beyond this picture. The starting point is the observation that quantum fluctuations of fields are the more strongly correlated the shorter their spacetime distance. As a consequence, the notion of spacetime distance, including the metric as its infinitesimal version, can be replaced by the notion of correlation strength. This suggests a new picture in which abstract (2-point and multi-point) correlators are the primary structure. In general, these abstract correlators can only be described as information theoretic structures and, in principle, they need not bear any relationship to quantum fields or spacetimes. These correlators may allow approximations, however, so that, in certain regimes, they can be mathematically approximately represented as the 2-point and multi-point functions of quantum fields living on a spacetime. In this way, the standard picture of a curved spacetime with fields whose correlators arise from Feynman rules would merely be a convenient approximate picture, while the underlying picture is that of a spacetime-less and field-less information-theoretic structure of abstract correlations.