Non-embeddable relational configurations

TL;DR

This paper explores non-embeddable relational configurations in physics, proposing the 2 instant relation as a model to understand situations where spacetime descriptions fail, highlighting the limitations of individualist approaches.

Contribution

It introduces the 2 instant relation (2IR) as a relational configuration space and analyzes its properties, illustrating non-embeddable configurations in physical systems.

Findings

Identifies conditions under which relational configurations are non-embeddable.

Shows that embeddable configurations correspond to particle worldlines in spacetime.

Highlights potential links between non-embeddability and breakdowns in spacetime descriptions.

Abstract

Relational configurations are defined by the relationships between systems. Individualist configurations are defined by the properties of individual systems. Non-embeddable relational configurations are those for which there is no equivalent individualist description. We suggest that situations in physics where a spacetime description breaks down may be the result of trying to use individualist configurations to model non-embeddible relational configurations. We propose a particular example of a relational configuration space, the 2 instant relation (2IR), whose embeddible configurations describe particle worldlines in a background spacetime. We investigate the properties of these configurations.