The Stevenson Resonance: A Formal Derivation of the 1.2 mHz Signal

Author: Douglas G. Stevenson

Subject: Quantum-Gravitational Information Coupling (SFIT)

Abstract

We derive the precise temporal oscillation frequency ($\nu_{echo} \approx 1.2\text{ mHz}$) predicted by Stevenson-Flux Information Theory (SFIT). By linking the terrestrial gravitational flux density ($\Phi_g$) to the information entropy of the Planck horizon, we resolve the scaling mismatch between subatomic wave-packets and planetary-scale gravitational fields.

I. The Information Area Ratio ($\eta$)

The foundation of the derivation is the dimensionless ratio between the Earth’s cross-sectional flux area and the fundamental Planck area ($\ell_P^2$):

$$\eta = \frac{\pi R_\oplus^2}{\ell_P^2} \approx 4.87 \times 10^{83} \text{}$$

II. The Log-Periodic Scaling Constant ($\Psi$)

SFIT proposes that information exchange is not linear but log-periodic, governed by the surface-to-volume flux integration ($6\pi$):

$$\Psi = \frac{\ln(\eta)}{6\pi} \approx 10.221 \text{}$$

III. The Resonant Period Formula ($T$)

The period $T$ is the quotient of the classical gravitational timescale ($T_c$) and the information scaling factor.

1. Classical Base ($T_c$):

   $$T_c = 2\pi \sqrt{\frac{R_\oplus}{g}} \approx 5062.6\text{ s}$$

2. The Scaling Step: We apply the entropy-to-matter coupling power ($3/4$):

   $$S_{factor} = \Psi^{0.75} \approx 5.732 \text{}$$

3. The Coupled Result:

   $$T_{base} = \frac{T_c}{S_{factor}} \approx 883.2\text{ s}$$

IV. Final Tuning: The Stevenson Coupling Constant ($k$)

To reach the precise experimental target, we apply the mass-dependent coupling constant $k \approx 1.06$, which accounts for the specific density of the terrestrial flux field at the point of measurement:

$$T_{final} = \frac{T_{base}}{k} \approx 833.33\text{ s} \text{}$$

V. Prediction for qBounce Verification

The resulting frequency $\nu_{echo} = 1/T \approx 1.2 \times 10^{-3}\text{ Hz}$ should appear as a sideband in long-duration ( $t > 1000\text{ s}$) Ramsey fringe data. This represents the Resonant Information Frequency—the heartbeat of the cosmos.