Overview
Cosmochrony proposes a minimalist ontological starting point: a single relational substrate $\chi$ whose dynamics are intrinsically irreversible. Time is not introduced as an external parameter, but corresponds to a directed relaxation (ordering) structure of $\chi$.
A structural necessity result follows from minimal operational assumptions (ontological uniqueness and effective observability): an injective projection from the relational substrate to spacetime observables cannot support non-trivial holonomy. Emergent gravitational dynamics therefore require non-injective projection.
Bounded relaxation fluxes act as a universal structural constraint. The saturation bound on relaxation gradients selects a unique admissible infrared encoding and excludes pathological configurations in which the projection collapses locally to injectivity.
Within this constrained structure, emergent gravity is not postulated but follows from the combination of non-injective projection and bounded relaxation.
A central distinction is drawn between the fundamental substrate $\chi$ and effective spacetime-level descriptions, collectively denoted $\chi_{\text{eff}}$. These effective descriptors are meaningful only in projectable regimes, where stable geometric and causal notions can be consistently defined.
The projection from $\chi$ to effective observables is generally non-injective: distinct underlying configurations may correspond to operationally indistinguishable spacetime events or measurements. This introduces an intrinsic distinction between what is observable and what is resolvable: some structural degrees of freedom can be physically real while remaining irreconstructible “under the hood” within $\chi_{\text{eff}}$.
Spacetime geometry is treated as an effective encoding of relational connectivity. In admissible regimes, spectral criteria and Laplacian-based reconstruction provide a concrete, operational pathway from relational structure to emergent metric notions, while predicting breakdown outside projectable domains.
Dynamical laws are not postulated at the substrate level, but arise from universal structural constraints on relaxation and projection. In projectable regimes, the effective action admits a Born–Infeld-like form, selected as a canonical encoding of bounded relaxation fluxes and causal saturation. This non-linear encoding is selected by the saturation bound on relaxation gradients, which plays a dual role of ultraviolet completion and infrared uniqueness constraint. This action is not fundamental to $\chi$, but an auxiliary representation valid within effective spacetime descriptions.
The framework further introduces a projective thermodynamics: irreversibility and macroscopic arrows of time are tied not only to relaxation, but also to a projection entropy associated with non-injective identification of underlying states. In this view, effective heating, dissipation, and “thermodynamic” behavior can reflect projection saturation and informational degeneracy, not merely microscopic agitation.
Stable localized configurations of $\chi$ give rise to matter-like excitations, while topological and relaxation constraints underpin effective interactions. In particular, electric charge is interpreted as a chiral–torsional invariant of relaxation fluxes, with admissibility constraints favoring neutral large-scale sectors and pair-creation-like restoration mechanisms in extreme regimes.
Core statements (high level)
- Structural necessity: Non-injective projection is not optional but required under ontological uniqueness and effective observability.
- Bounded relaxation: A universal saturation constraint on relaxation gradients ensures infrared uniqueness and excludes locally injective collapse.
- Single-substrate ontology: one pre-geometric relational entity $\chi$, not a field on spacetime.
- Projection hierarchy: spacetime quantities arise only in projectable regimes via $\chi_{\text{eff}}$.
- Intrinsic irreversibility: time ordering reflects directed relaxation, not an external parameter.
- Non-injectivity: effective observables underdetermine the underlying configuration; observability differs from resolvability.
- Projective thermodynamics: projection entropy and saturation constrain effective macroscopic behavior and arrows of time.
- Derived dynamics: effective laws emerge from bounded relaxation and saturation constraints (Born–Infeld-like encoding).
- Emergent geometry: metric notions arise as an operational encoding of relational connectivity, accessible via spectral reconstruction in admissible regimes.
Articles and technical notes
The Cosmochrony framework is developed across a small set of focused articles addressing distinct structural aspects. Together, they form a coherent pipeline from relational structure to emergent geometry, effective dynamics, and late-time phenomenology.
-
Spectral Reconstruction of Spacetime Geometry
Relational and spectral derivation of effective metric geometry without postulating a background manifold; regime diagnostics via spectral admissibility and breakdown criteria. -
Bell Inequality Violations from Non-Injective Projection
Structural origin of quantum correlations from non-injective effective descriptions, without invoking dynamical nonlocality, retrocausality, or hidden-variable dynamics. -
Born–Infeld Geometry from Bounded Relaxation
Emergence of non-linear Born–Infeld-like encoding and effective spacetime geometry from bounded relational relaxation and flux saturation in projectable regimes. -
Galaxy Rotation Curves and the Hubble Tension
Phenomenological study of late-time gravitational dynamics in low-density environments, linking galaxy rotation curves and the Hubble tension through a common effective saturation mechanism without invoking dark matter particles in this effective regime. -
Charge, Mass, and Inertia as Saturated Responses
Structural and conceptual analysis of mass, electric charge, and inertia as distinct symmetry classes of saturated effective response arising from non-injective relational descriptions, fully consistent with Standard Model phenomenology and without modifying its dynamics. -
The Lamb Shift and the Schwinger Effect
Structural and interpretative analysis of the Lamb shift and Schwinger pair production as consequences of finite spectral resolution and flux saturation arising from non-injective relational descriptions, fully consistent with precision quantum electrodynamics and without introducing a dynamical vacuum. -
A Unified Real-Space Frustration Mechanism for
Superconductivity
Structural analysis of superconductivity as projective phase locking of composite configurations driven by real-space frustration minimization and lattice symmetry constraints, predicting d-wave symmetry in cuprates and extended s± symmetry in nickelates, with explicitly falsifiable scaling, disorder, and pressure signatures. -
Infrared Einstein Response from a Renormalized Spectral Entropy Functional
Spectral-geometry analysis showing that the renormalized metric variation of a minimal elliptic Laplace-type operator yields an infrared-dominant local Einstein tensor term, with explicit quadratic-curvature, non-local, and anomaly contributions, and recovering the Newtonian 1/r profile as the static weak-field limit of the same resolvent-mediated entropy mechanism. -
Local Spectral Thermodynamics and the Einstein Equation as a Spectral Equilibrium Condition
Spectral-geometry analysis in which heat-kernel locality defines a curvature-corrected local spectral multiplier field, the compatibility identity $\delta S_\Pi=\int\beta^{-1}\delta E_\Pi$ emerges in the infrared regime, and Einstein’s equation arises as the constrained extremum condition of the projective entropy functional, with the normalization of $8\pi G$ fixed by geometric and stress-tensor conventions rather than by thermodynamic postulates or horizon assumptions. -
Causal Propagation and Gravitational Waves from Projective Spectral Dynamics
Lorentzian completion of the spectral-entropy framework in which a retarded quadratic kernel is defined via $\mathrm{Re}\,\log\det' D_g$ (or a Schwinger–Keldysh prescription), the infrared spectrum propagates exactly two transverse-traceless tensor modes, and a universal $k^4$ dispersion correction $\omega^2=c^2k^2-\gamma\ell_\chi^2k^4$ emerges from the Seeley–DeWitt hierarchy, yielding observational constraints on the pre-geometric scale $\ell_\chi$ without introducing additional scalar or vector degrees of freedom. -
Topological Invariants of Admissible Configurations:
Charge Quantisation, Absence of Magnetic Monopoles, and Projective Chirality in Cosmochrony
Topological analysis of the admissible projection fibre in which electric charge appears as a $\pi_1$ winding invariant of the U(1) sector, the bounded-flux reduction of the Hopf base yields a canonical admissible model with $\pi_2=0$ and therefore no isolated magnetic monopoles, and parity violation is interpreted as projective chirality, i.e. an orientation dependence of admissibility under non-injective projection, with a clear separation between canonical-model results and the open extension to the full effective configuration space. -
Non-Injectivity as a Structural Necessity
of Genuine Emergence
Structural theorem showing that any genuinely emergent effective description must be non-injective: a fully injective projection implies structural isomorphism and therefore no true emergence, while non-injectivity entails fibre multiplicity, positive projection entropy, and the necessary loss of information underlying gauge structure and effective degrees of freedom.
Quantitative program (selected targets)
Cosmochrony emphasizes falsifiable, quantitative targets. The current program prioritizes extracting effective parameters from structural constraints and comparing them to known scales and anomalies, in domains where the framework yields sharp signatures.
- Spectral invariants: robust eigenvalue hierarchies and spectral-dimension stabilization in admissible regimes.
- Strong-field thresholds: deprojection/saturation signatures near high-curvature regimes affecting effective propagation and observables.
- Cosmology: relaxation-driven effective expansion laws and quantitative comparison to late/early-universe inference (including Hubble-like limits).
- Galactic dynamics: rotation-curve and lensing signatures from relaxation constraints without adding matter components.
- QED-scale tests: bounded-relaxation corrections in regimes analogous to vacuum polarization and pair-creation thresholds.
- Gravitational coupling: Relation between effective gravitational strength and microscopic capacity parameters induced by saturation constraints.
Interactive exploration
Discussion assistants built on the full set of published Cosmochrony articles and documents. They can answer readers’ questions, provide progressive explanations, and clarify both conceptual and technical aspects of the framework.
References
Jérôme Beau. Cosmochrony: A Pre-Geometric Relational Framework for Emergent Physics. Zenodo. DOI: 10.5281/zenodo.17957509