Plain English: This section nails down that the paper isn’t adding a new field. In ADM language the lapse \(N=e^{\Phi}\) and the shift \(\omega\) are Lagrange multipliers enforcing constraints; only the two transverse–traceless (TT) tensor modes propagate. The correlator \(C_\Phi\) that enters visibility is not a new scalar degree of freedom — it’s the constraint-projected, gauge-fixed imprint of linearized metric/stress fluctuations on an observer’s clock. All the signatures here are just GR rewritten in “clock-native” variables, which makes them easier to compute and test.
Registered analysis & nulls recapped (how you keep yourself honest): Pre-register band, vetoes, stacking, and pass/fail rules (flux channel: sign + strict \(1/r\); visibility channel: a preset threshold). Then follow the exact steps: whiten \(\dot y\) by measured \(S_y(f)\); build \(s(t)=\int L\,dt\) so \(s(f)=L(f)/(i2\pi f)\); estimate \(\lambda\) with GLS; quote the variance. Run nulls: shuttered source, cold dump, time slides, off-band. Outcome: either \(\lambda=G/(c^4 r)\) within errors, or you publish an upper limit; for visibilities, report bounds on \(S_\Phi(\Omega)\) (both Markovian and filter-weighted).
Implementation warning (one last time): Controlled-flux lab runs validate pipelines only; EM/thermal near-field couplings swamp gravity, and \(\delta\Phi\) is not a propagating scalar (the “effective action” is a noise-kernel model).
| Symbol | Name | Meaning (units) | Typical value/example | Metaphor |
|---|---|---|---|---|
| \(N=e^{\Phi}\) | Lapse | Proper-time scale factor \(d\tau=N\,dt\) (–) | \(N\!\approx\!1\) in weak fields | “Time gear ratio” |
| \(\omega\) | Shift | Gravitomagnetic potential (flows/rotation) | Nonzero for frame dragging | “River current of space” |
| TT | Tensor modes | The two propagating GW polarizations | Only waves that travel in vacuum | “Two violin strings of gravity” |
| \(C_\Phi\) | Lapse correlator | \(\langle\delta\Phi(t)\delta\Phi(t')\rangle\) (–) | Enters visibility kernel | “Echo of time ripples” |
| \(\lambda\) | Flux→drift gain | Predicted \(G/(c^4 r)\) (s²·kg\(^{-1}\)·m\(^{-1}\)) | Tested via GLS & \(1/r\) | “Gear from flux to drift” |