The Configurable Universe: Constants as Chamber Invariants

Abstract

The fundamental constants of nature are usually treated as free parameters: numbers that could have been anything, were set somehow, and are found by observation. We argue for an alternative reading. The constants are structural invariants of a chamber within a configuration-space construction, in the same sense that the dimension of a vector space is an invariant of the space’s structure rather than a parameter of it. We call this the configurable-universe view. In this picture the framework does not require a physically realized multiverse: there is one configuration space, one chamber, no probability distribution over alternative universes; and the constants are determined by the chamber’s structure rather than by anthropic selection or accident. The view is concretely realized by Twistor Configuration Geometry (TCG) [Zhang FPA, Zhang Review], in which nine numerical relations among fundamental constants admit a coordinated reading as invariants of a stratified space

where $\mathcal{K}_{r}(I)$ is the chamberwise Fulton–MacPherson / Axelrod–Singer compactification of $r$ labeled points on an oriented interval. We articulate the configurable-universe thesis, distinguish it from anthropic and landscape responses to the fine-tuning problem, locate it relative to existing relational programs (Penrose, Smolin, Rovelli), state its empirical content (no tunable knobs, no temporal variation in fundamental constants, presence of structural relations among observables), and offer a critical self-assessment of the position’s bite versus its risk of being a relabeling exercise. The configurable universe is offered as a research program, not a settled theory; its strongest empirical evidence is the existence of non-random algebraic patterns among nine measured dimensionless relations across electromagnetic, weak, lepton, hadronic, gravitational, and cosmological sectors, which a free-parameter ontology does not predict.

v2 update (2026-05-07)

The active TCG/FPA postulate ledger is refreshed from the v1 listing P0–P6 to P0–P4, P5’, P6, reflecting the closure of the original P5 ($\mu_{\rm contact} \simeq M_Z$) on three foundational obstructions reported in Paper #13 (Electroweak Boundary, DOI:10.5281/zenodo.20075926) and its replacement by the dimensionless weak-sector boundary condition P5’: $g_{2,W}^2 = 4/(3\pi)$. §4.3, §4.4, and Table 1 are correspondingly recategorized: the weak-sector identification (O9) elevated from phenomenological to postulate-level (P5’); the strong-coupling identification (O4) demoted to phenomenological SM scale assignment $\mu = M_Z$ for $\alpha_s$. §6.5 and §7.4 now reference the multi-relation look-elsewhere audit performed in Paper #6 v2 (DOI:10.5281/zenodo.20062462), with $K_{\rm eff}$ at three formal grammar levels and an $N_{\rm eff} \sim 5$–$6$ independence reduction; the look-elsewhere problem is now quantitatively bounded rather than merely qualitatively flagged. The philosophical content is unchanged.

DOI

https://doi.org/10.5281/zenodo.20077307