We develop a theoretical framework for coherent Dynamic Casimir Effect (DCE) photon production in a toroidal array of micro-electromechanical Casimir cavities and derive, in closed form, the master equation that links the array's coherent quantum-vacuum output to the induced linearized spacetime strain. The central result, hᵢj (r, t) = G · η² N² · ℏ A Ω⁷ δd² Tcoh R² / (6π c¹⁰ r), connects the engineered hardware parameters (cavity count N, angular drive frequency Ω, fractional boundary displacement δd, plate area A, toroidal major radius R, coherence time Tcoh, and phase-locking fidelity η) to the radiated quadrupole strain at observer distance r. The equation arises from combining the Moore–Fulling–Davies–Dodonov formalism for single-cavity DCE, the Dicke theorem for coherent N² enhancement in phase-locked emitter arrays, and the linearized Einstein field equations in the retarded gauge. For a representative hardware configuration (N = 5×10⁶, Ω = 2π·32. 768 MHz, δd = 1 nm, A = 10⁻⁸ m², R = 0. 50 m) the equation predicts a coherent DCE photon flux of 2. 4×10⁻¹⁵ ph/s and a radiated strain of 5. 1×10⁻⁸⁶. The dominant engineering dependence is the seventh power of the drive frequency. Re-scaling to the GHz band accessible with FBAR technology, combined with nanopatterning to 10⁸ cavities on a 300 mm wafer, raises the coherent photon flux to approximately 5×10⁻⁴ ph/s at 5 GHz drive and 8×10⁻³ ph/s at 10 GHz drive — within the sensitivity envelope of commercial superconducting nanowire single-photon detectors at signal-to-noise ratios of ≈ 4. 7σ (5 GHz) and ≈ 75σ (10 GHz) over a 10⁵ s (≈28 h) integration. The induced metric strain remains 36–63 orders of magnitude below the sensitivity of present and near-term high-frequency gravitational-wave detectors; the equation therefore constitutes an effective no-go result for laboratory gravitational-wave emission from coherent quantum-vacuum sources of the class considered. The observable coherent DCE photon flux nonetheless provides a direct and falsifiable experimental validation path for the underlying formalism. All numerical claims are reproduced independently at 50-digit precision.
Edgar Manzella (Sat,) studied this question.