A Pre-Metric Relational Framework for the Emergence of Physical Structure

Abstract

This technical note develops a pre-metric relational framework for the emergence of measurable physical structure and the conditional reconstruction of Lorentzian geometry. The proposal distinguishes the emergence of causal order from the emergence of metric scale: asymmetric effective reachability is treated as a possible antecedent of causal precedence, while a stabilised relational measure is introduced as a candidate antecedent of continuum volume. The central reconstruction target is the transition from a stabilised relational structure (X,≺,μR) to a Lorentzian manifold (M,gμν), under explicit assumptions of causal regularity, continuum emergence and convergence of the relational measure. The framework is constrained throughout by a non-retroprojection principle: no physical concept is introduced before the structural conditions required for its meaning have emerged. The note is complementary to Why 3+1 Dimensions? A Pre-Metric Relational Reconstruction of Space, Time and Causal Structure and forms part of the broader theoretical programme developed in Before the Origin — From Pre-Reality to a Readable Cosmos.