A Potential Foundation for Emergent Space-Time

TL;DR

This paper derives Minkowski space-time and Lorentz transformations from the causal ordering of events, proposing that space-time mathematics emerges from the consistent quantification by an observer, not as a fundamental physical entity.

Contribution

It provides a novel derivation of space-time geometry from causality without assuming a manifold or constant light speed, suggesting space-time is emergent.

Findings

Minkowski metric derived from causal event ordering

Lorentz transformations obtained without prior assumptions

Space-time mathematics emerges from observer-based event quantification

Abstract

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an observer can consistently quantify events and their relationships to one another. The result is a potential foundation for emergent space-time.