11 Dynamic Casimir Effect: Post-Threshold Nonlinearity of Wall Speed Versus Pair Yield

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and keeps the structure fixed. For general readers: the Dynamic Casimir Effect (DCE) refers to photon-pair creation when a boundary condition changes rapidly enough—by moving a mirror in effect or modulating circuit parameters—so that vacuum fluctuations are converted into real quanta.

I. One-Sentence Goal

Measure how photon-pair yield changes with effective wall speed across multiple “engineered boundary” platforms (superconducting transmission lines/cavities, opto-/micro-electro-mechanical mirrors, and rapidly tuned refractive media). Under blinding and cross-platform replication, look for: a clear threshold turn-on, a convex post-threshold nonlinearity (yield rises faster than linearly with wall speed), and a normalized, platform-agnostic curve shape that is insensitive to carrier frequency and device geometry. Seek conjugate-frequency correlations and zero-lag co-occurrence as pair signatures. Success supports engineered-vacuum participation and a shared path contribution in Energy Filament Theory (EFT); failure or explanations by thermal noise, amplifier leakage, or pump crosstalk count against it.

II. What to Measure

• Threshold and curve shape: Describe the yield–speed curve with plain terms—flat baseline at low speed, a distinct knee (threshold), then a convex rise post threshold (“accelerating uplift”), instead of formulas.
• Pairwise linkage and spectral pairing: In conjugate bands that satisfy energy balance, test for simultaneous appearance and a zero-lag peak; check whether the ranking of conjugate-band correlation strengths is stable.
• Normalization invariance: After rescaling by effective wall speed and a normalized yield (text normalization that accounts for cavity loss, noise floor, and coupling), test whether curves from differing carriers, geometries, and platforms overlap within uncertainty.
• Environment/impedance modulation: Compare high-impedance/high-Q/strong-coupling with low-impedance/low-Q/weak-coupling settings; verify that threshold location and post-threshold slope shift in the pre-registered direction.
• Pump–signal isolation: Vary pump power/frequency/phase and confirm that yield and conjugate correlations do not track proxy indicators of pump leakage (for example, mirror-image lines of the pump).

III. How to Do It

1. Platforms and boundary implementations:
   • Superconducting microwaves: transmission lines/cavities with Superconducting Quantum Interference Device (SQUID) arrays, fast-tuned capacitors/inductors.
   • Optical/near-infrared: rapid cavity-length modulation, piezo/micro-electro-mechanical mirrors, or fast-tuned intracavity refractive media.
   • Radio/terahertz: varactor-diode arrays and sub-wavelength metasurfaces.
   • Pre-define a text formula for effective wall speed (modulation depth × modulation frequency × geometry factor) and for recording yield and correlation (event rates/correlation-peak grades as text intervals).
2. Acquisition and blinding workflow:
   • Dual-channel readout: route conjugate bands to independent chains (independent local oscillators or clocks; electrical/optical isolation).
   • Multi-pump program: scan multiple pump frequencies/phases/pulse shapes, including far-off-resonance and near-resonance sets.
   • Pre-registered grading: assign strong/medium/weak and rising/flat/saturating grades to wall speed, yield, correlation peaks, noise floor, and coupling.
   • Independent pipelines:
     1. The count-and-spectrum team reports yield–speed curve grades and conjugate-band orderings.
     2. The correlation team reports zero-lag versus side-lobe contrasts and cross-band correlation grades.
     3. Teams share only wall-speed settings and pump labels, not numerical outputs.
   • Arbitration: A third party aligns thresholds, post-threshold shapes, normalized overlaps, and conjugate-band consistency, stratified by platform/device/institution.

IV. Positive/Negative Controls and Removal of Artifacts

1. Positive controls:
   • Yield–speed curves show a clear threshold plus convex post-threshold rise.
   • Zero-lag co-occurrence peaks appear in conjugate bands and increase monotonically with wall speed.
   • After normalization, curves from different carriers/geometries/platforms overlap within uncertainty; threshold and slope shift predictably with impedance/Q/coupling.
2. Negative controls:
   • With pump off or at far-off-resonance, yield collapses to the noise floor, and conjugate correlations vanish.
   • With injected pump leakage or local-oscillator crosstalk, correlation peaks track instrument state and do not replicate across platforms.
   • Heating/noise injections that mimic rising yield but fail to produce conjugate correlations indicate a thermal-noise impostor.

V. Systematics and Safeguards (Three Items)

• Pump leakage and parasitic mixing: can fake thresholds and correlations. Safeguard: dual isolation between cavity/line and readout, anti-phase/out-of-phase pump cancellation tests, and deliberate-leakage injections that should break the conjugate correlation pattern.
• Gain drift and noise-floor wander: can distort curve shape. Safeguard: bracket runs with thermal/noise calibrations, regress gains over time, and report a separate grade for noise-floor changes versus wall speed.
• Heating and nonlinear losses: high pump power can create false thresholds. Safeguard: real-time temperature/loss monitoring, short-duty pulses, and power-doubling versus slope tests to separate thermal effects from genuine thresholds.

VI. Execution and Transparency

Pre-register effective-speed definitions, yield/correlation grading rules, positive/negative controls, exclusion criteria, and statistics. Keep hold-out devices/bands per platform for final confirmation. Exchange raw data across institutions for independent reprocessing and repeat across seasons and configurations. Publicly release text grading tables for speed–yield/correlation, pump and isolation configurations, noise/temperature logs, and key intermediate artifacts. This chapter forms a closed loop with the chapters on quantum-tunneling pore statistics and zero-lag correlations, cavity quantum electrodynamics (“engineered vacuum”), and steady-state Schwinger-limit crossings; cross-references are required.

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more platform classes and two or more institutions, observe a stable threshold and convex post-threshold rise.
   • Conjugate-band zero-lag peaks grow monotonically with wall speed and do not flip or rescale with carrier frequency or geometry.
   • After normalization by effective wall speed, yield curves overlap across platforms and tune as predicted with impedance/Q/coupling.
   • In negative controls, signals vanish or collapse, resisting reproduction by leakage or thermal noise.
2. Refutation (fails):
   • No clear threshold, or no consistent convex rise after threshold.
   • Conjugate correlations track instrument/pump states, flip/rescale with carrier frequency, or persist under pump-off/leakage/heating controls.
   • Normalized curves fail to overlap across platforms, or apparent signals appear only in one pipeline or device.