Destructuring Physics: A functional derivation of spacetime

TL;DR

This paper advocates for a minimalistic, function-based formulation of spacetime in physics, simplifying its mathematical structure while retaining core physical properties, building on previous research in topology and causality.

Contribution

It introduces a novel, abstract notion of spacetime as a family of functions over an arbitrary set, reducing complexity and unifying various concepts in a minimal framework.

Findings

Spacetime can be represented as a family of functions on an arbitrary set.

The minimalistic approach preserves fundamental physical properties.

Unifies causality and topology through simple mathematical structures.

Abstract

I propose that Physics should be formulated using minimal mathematical structure, beginning with its foundational arena: spacetime. This paper opens with a concise overview of several research directions explored in previous work. Among these are the proposal to represent spacetime at the quantum scale using (measure) closed ordered spaces; the unification of causality and topology through quasi-uniformities; the concept of the product trick to unify causality and metricity; the introduction of upper semi-continuous (stable) Lorentzian distances; the representation of spacetime via steep time functions; and the formulation of the Lorentzian distance formula. Subsequently, the properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime can be introduced in a general and minimalistic way as nothing more than a family of functions defined over an arbitrary set. This abstraction removes unnecessary mathematical complexity, reducing spacetime to its essential elements while preserving its most fundamental physical properties.