IndisputableMonolith.QFT.DynamicCasimirRecognition
Formalizes the dynamic Casimir effect in RS QFT: a time-dependent boundary modulation drives a photon-production functional that vanishes for static walls and is strictly positive under nonzero drive. Phi-locked schedules and a DynamicCasimirCert package the RS constraints on top of the static Casimir phi-correction layer. QFT and Casimir specialists would cite it when connecting moving-mirror photon creation to the phi ladder. The module is mostly definitions plus elementary vanishing and positivity lemmas.
claimA time-dependent boundary modulation $\delta a(t)$ induces a photon-production functional $\mathcal{F}[\delta a]$. Static boundaries give $\mathcal{F}=0$; nonzero modulation gives $\mathcal{F}>0$. Phi-locked dynamic schedules and a Dynamic Casimir certificate encode the RS constraints relative to the corrected pressure $P_{\mathrm{RS}}(a)=P_{\mathrm{Casimir}}(a)(1+\delta\varphi)$.
background
The upstream Casimir phi-corrections module supplies the RS layer $P_{\mathrm{RS}}(a)=P_{\mathrm{Casimir}}(a),(1+\delta\varphi)$ and algebraic sanity facts, leaving material response as hypotheses until a Lifshitz/dispersive boundary module exists.
Dynamic Casimir physics concerns photon creation from vacuum when a cavity boundary moves. This module lifts that setting into RS by treating a time-dependent boundary modulation as the drive, defining a photon-production functional of that drive, and recording the elementary static-vanishing and nonzero-positivity facts.
Phi-locked dynamic schedules restrict the modulation to the discrete self-similar timing forced by the golden ratio fixed point in the RS forcing chain. A certificate object packages the schedule and functional positivity for downstream use.
proof idea
Definition-heavy module, not a single deep theorem. Boundary modulation and the photon-production functional are introduced as data. The static-boundary lemma is the direct evaluation that a time-independent drive yields zero production. The nonzero-modulation lemma is a positivity statement for the functional under a nontrivial drive. Phi-locked schedules and the DynamicCasimirCert are packaging definitions that sit on the imported Casimir phi-correction layer; no heavy analytic estimates appear here.
why it matters in Recognition Science
Places the dynamic Casimir effect inside the RS QFT stack, above the static phi-corrected Casimir pressure. It is the natural bridge from equilibrium Casimir pressure corrections to nonequilibrium photon creation under moving boundaries, with schedules constrained by the same phi self-similarity that forces the eight-tick octave and related discrete structure elsewhere in the framework.
No downstream consumers are wired yet in the graph, so the module is a leaf that future moving-mirror or cavity-QED certificates can import. It does not yet close material-response or dispersive-boundary hypotheses left open upstream.
scope and limits
- Does not derive a full Lifshitz or dispersive moving-mirror spectrum.
- Does not compute numerical photon yields or mode-resolved spectra.
- Does not discharge material-response hypotheses left open in CasimirPhiCorrections.
- Does not claim experimental bounds; only formal vanishing and positivity structure.
- Does not connect yet to charged-sector or non-Abelian QFT modules.