Technical Appendix: Noise Budget and Detection Feasibility for the SWYGERT AO 167X Laser

Technical Appendix: Noise Budget and Detection Feasibility for the SWYGERT AO 167X Laser

DOI (to be assigned)

February 26, 2026

John Swygert

Abstract

This technical appendix presents the noise budget, strain-amplitude model, and detection feasibility analysis for the SWYGERT AO 167X tabletop laser system. The device is designed to drive a microscopic cavity volume across the substrate disequilibrium threshold Γ = 167 within the TSTOEAO framework. TSTOEAO predicts a narrowband strain tone at f* ≈ 0.83 GHz with amplitude h_min ≈ 1.7 × 10^{-23}. The coupling mechanism is specific to TSTOEAO and differs from standard general-relativity quadrupole radiation. This appendix provides an order-of-magnitude feasibility assessment using demonstrated interferometric and cryogenic techniques.

1. System Parameters

  • Cavity length: 15–50 cm (tunable)

  • Pump: 1030 nm, 50–500 fs, 0.1–10 PW

  • Mode waist w₀ ≈ λ/167

  • Peak focal intensity: 10^{22}–10^{24} W/cm² (exceeds Γ = 167)

2. Strain-Amplitude Model

Within TSTOEAO, when the focal energy density exceeds the universal disequilibrium threshold Γ = 167, the substrate is predicted to respond with an equilibrium-correction cascade. Within this framework, excess disequilibrium energy density is assumed to couple to an effective metric perturbation proportional to the local disequilibrium energy density under resonant confinement. The effective strain amplitude is modeled as

h_min = (2π G / c⁴) × (ΔE / V) × Q_cavity × (λ / 2π)

where
 • ΔE / V = excess energy density above Γ = 167
 • Q_cavity = cavity quality factor (∼10^6–10^7 for this design)
 • λ = reduced wavelength corresponding to f* ≈ 0.83 GHz

This expression is a TSTOEAO-specific coupling ansatz linking substrate disequilibrium energy density to effective strain via resonant amplification. It is not derived from standard GR quadrupole emission. Substitution of representative design parameters yields an estimated h_min(f*) ≈ 1.7 × 10^{-23}. The predicted tone is narrowband (Δf/f < 10^{-3}) and phase-coherent with the pump pulse. Dimensional analysis confirms consistency with dimensionless strain.

3. Noise Budget (0.83 GHz Band)

  • Quantum shot noise: ∼10^{-23} / √Hz with squeezed-light readout (10 dB demonstrated in LIGO prototypes in the audio band; GHz implementation requires bandwidth adaptation)

  • Thermal noise (cryogenic sapphire mirrors at 4 K): < 5 × 10^{-24} / √Hz

  • Seismic / acoustic: suppressed below 10^{-24} / √Hz with standard isolation

  • Radiation pressure: negligible at this frequency

  • Order-of-magnitude integrated noise floor (1 μs equivalent bandwidth): < 5 × 10^{-24}

4. Detection Considerations

Order-of-magnitude SNR estimates indicate detectability in principle. Realized SNR will depend on achieved squeezing bandwidth, photodetector and electronics noise at 0.83 GHz, and cavity coupling efficiency. A conservative design target is SNR ≥ 5.

Detection may employ dual Michelson or Fabry-Pérot readout with squeezed-light injection and cryogenic mirrors. While such components are demonstrated in LIGO-class facilities, GHz readout requires dedicated implementation and bandwidth optimization.

5. GR Comparison and Falsification

Under standard GR quadrupole radiation assumptions, tabletop sources yield h(f*) ≪ 10^{-30}. Observation of a persistent narrowband tone near the predicted amplitude would therefore constitute a falsifiable deviation from GR expectations and support for the TSTOEAO-specific coupling mechanism.

Conclusion

The 167X system is presented as a testable TSTOEAO prediction accompanied by an order-of-magnitude feasibility analysis. The strain amplitude is modeled from the Γ threshold and cavity parameters within the TSTOEAO framework. The noise assessment suggests potential detectability with adapted GHz interferometric implementation. This appendix defines the experimental criteria required for empirical validation.

References

  1. Swygert, J. S. (2025). The SWYGERT AO LASER 167X: Tabletop Probe of Substrate Equilibrium Threshold.


  1. Swygert, J. S. (2026). Equilibrium Substrate Echoes in Gravitational Wave Signals.



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