Time, Space, and Physical Constants as Emergent from an Information-Theoretic Substrate

Abstract

We develop an information-theoretic substrate \(S=(X,\sim,I,T)\) as a working theory of ordered emergence: a state space \(X\), a coarse-graining equivalence \(\sim\), an information measure \(I\), and a transition structure \(T\) that respects preservation bounds \(I(T(x))\ge\rho_T\,I(x)\). In this theory, emergent does not mean only "already present but unrecognized": it means brought forth / produced / created at the coarse or projected level—new effective ontology (a time arrow, spatial metrics, usable constants-as-bounds) that is not identical to micro \(X\). The theory's default ontology treats this creation as brought forth under intentional order: we postulate (Postulate 10.2) an ordered / intentional cause of emergence—a structured, design-like constraint instituting which maps and measures survive—not an optional equal peer of "random law." From \(S\) we expound emergent time (a monotone \(\tau\) on the quotient \(X/\sim\)), emergent space (geometry induced by projections \(P:\mathbb{R}^N\to\mathbb{R}^k\) with singular-value control of \(\rho\)), and bidirectional micro-causality (reversible substrate transitions; thermodynamic arrows only after coarse-graining). We methodically exclude random causality as a sufficient generator of the ordered substrate phenomena explained here, while allowing that ordered coarse-graining may still absorb random micro noise. Non-random structure together with \(\sim\), \(P\), selective \(I\), and ordered \(T\) cancels / suppresses / quenches chaotic alternatives: chaos does not produce the preserved \(\rho\)-geometry or monotone \(\tau\) in this framework. Physical constants \(c\) and \(\hbar\) remain interpretive bounds—not derived predictions. Composition yields \(\rho_{12}\ge\rho_1\rho_2\). Dimensional folding (\(15\mathrm{D}\to7\mathrm{D}\), PCA \(74\to19\), staged folds) is cited as operational \(\rho\)-instances: structured spikes succeed where isotropic/chaos-like regimes fail fidelity—corroboration of the exclusion chain whose residual cause is a creator (§10.6). Zenodo version field 2.0.0; manuscript 2.3.1 (theory edition). New version of doi:10.5281/zenodo.18452947; concept doi:10.5281/zenodo.18452946. Resource type corrected to Preprint.