Temporal Information Dynamics in the Scalar Temporal Field Ontology: Part III – Temporal Channel Theory and Information Transport

Temporal Information Dynamics (TID) — Part III extends the Scalar Temporal Field Ontology (STFO) into a full theory of information transport governed by the scalar temporal field τ(xμ)\tau(x^\mu)τ(xμ). While Parts I–II introduced temporal-depth complexity, loop-protected information, disformal cryptographic hardness, and geometric information flow, this Part III installment derives the complete temporal-channel structure encoded in ∇μτ\nabla_\mu \tau∇μτ and its fluctuations. Key contributions of this work include: • Covariant Temporal Information Current:A geometric information current Iμ=I(x)∇μτXI^\mu = \mathcal{I}(x) \frac{\nabla^\mu \tau}{\sqrt{X}}Iμ=I(x)X∇μτ is derived directly from the STFO field equations, with a conservation law emerging in the shift-symmetric regime. • Temporal Flux Tensor and Transport Law:A full transport tensor Ξμν=uμuν+cτ2hμν\Xi_{\mu\nu} = u_\mu u_\nu + c_\tau^2 h_{\mu\nu}Ξμν=uμuν+cτ2hμν governs anisotropic information propagation, where cτc_\taucτ is the effective propagation speed obtained from the STFO Lagrangian. • Noise Kernels from Temporal Fluctuations:The δτ propagator generates a physically derived noise spectrum, enabling quantitative predictions for distortions, channel bias, and stability. • Temporal Channel Capacity:A closed-form capacity expression is derived, Cτ=ατ∣∇τ∣1+σδτ2,C_\tau = \frac{\alpha_\tau |\nabla\tau|} {\sqrt{1 + \sigma_{\delta\tau}^2}},Cτ=1+σδτ2ατ∣∇τ∣, giving the first information-theoretic bound rooted in a physical ontology of time. • Causal and Disformal Bounds:Information flow is constrained by the disformal metric and the geometry of temporal depth, yielding directional dependence and anisotropy testable in laboratory systems. • Experimental Predictions:Interferometric phase asymmetry, atomic-clock drift, and NMR echo modulation scale directly with ∣∇τ∣|\nabla \tau|∣∇τ∣, providing measurable channels for falsifying the theory. This paper completes the core of Pillar VII of the Scalar Temporal Field Ontology, establishing a physically grounded, covariant, and testable theory of information flow and channel structure derived entirely from the dynamics of a scalar field of time. Author: Cale Scott HoweProgram: Scalar Temporal Field Ontology (STFO)Contact: [email protected]