This paper proposes two clock-native observables to probe gravity: (1) a sign-locked flux → redshift-drift template, and (2) a general visibility kernel that bounds fluctuations of the lapse (time field) from interferometer data.
The paper provides analysis-ready estimators, null tests, and sensitivity bounds; lab runs are pipeline validations (with software signal injections and strict \(1/r\) scaling), and there are no detection timelines asserted.
Positioning & terminology: “Quantum temporal geometry” here means semiclassical temporal phase fluctuations of the lapse (a constraint-projected metric/stress effect in GR), not a new particle; the work is framed lapse-first with honest gauge notes (shift \(\omega\) carries rotation), and Section 2 → 4 flow: first the classical flux→drift result, then quantum consequences expressed directly as phases/visibilities for clocks.
Why this matters (bounds-first): phrasing GR in lapse-first variables makes many observables directly “clock-native,” which yields clean, sign-definite templates (the flux→drift scales like \(1/r\)) and linear visibility bounds on the two-point function \(C_{\Phi}\) of lapse fluctuations. The contribution is a conservative pipeline for setting limits with current platforms.
| Symbol | Name | Meaning (units) | Typical value/example | Metaphor |
|---|---|---|---|---|
| \(N=e^{\Phi}\) | Lapse | Clock-rate factor; \(d\tau=N\,dt\) (dimensionless) | \(N=1\) at today’s normal clocks | “Gearing” of time |
| \(\Phi\) | Time potential | \(\ln N\) controlling proper-time flow (dimensionless) | \(\Phi=0\) today by convention | “Altitude” of time |
| \(\omega\) | Shift (gravitomagnetic) | Carries rotation/mass-current effects | Nonzero when there’s frame dragging | “River flow” of space |
| \(y=\ln(\nu_\infty/\nu_r)\) | Fractional redshift | Clock frequency ratio (dimensionless) | used in drift template | “Pitch change” of a note |
| \(V\) | Interference visibility | Fringe contrast (dimensionless) | \(V\in[0,1]\) | “Sharpness” of stripes |
If you’re ready, we’ll tackle Step 2 — the Flux → Redshift-Drift law (the paper’s first core observable) next.