Necessity Recursion and a Pre-Registered φ-Attractor Prediction for Proper-Time Superposition in Optical Ion Clocks

Abby Davis

Published May 10, 2026• 0 citations

Abstract

On 20 April 2026, Sorci, Foo, Leibfried, Sanner, and Pikovski (Phys. Rev. Lett.) proposed that next-generation optical ion clocks with squeezed-state preparation can probe whether proper time exists in quantum superposition — a single clock ticking faster and slower at once. Their work establishes the protocol; the laboratory measurement is forthcoming. That prospective window permits a genuine pre-registered prediction. Fibonacci Causal Loop Theory (FCLT) holds that any stable system governed by depth-2 necessity recursion, S(n)=S(n−1)+S(n−2), is driven to the golden ratio φ=(1+√5)/2 — the unique algebraically forced attractor of its characteristic equation x²−x−1=0. We advance the hypothesis that proper-time superposition is such a system, the two temporal branches playing the role of the two prior states, so that the ratio of fast- to slow-ticking amplitudes approaches φ upon decoherence. From this we obtain one parameter-free, falsifiable prediction — t₊/t₋ → φ ≈ 1.61803, with δ = |R−φ|/φ and falsification at δ > 0.10 — logged under Protocol V3.1 prior to experimental resolution. We claim no confirmation: the prediction is offered as not-yet-tested, to be adjudicated by the Stevens/NIST program. A second, independent signature (φ-structured fringe spacing in the squeezed regime) provides an internal consistency check.

DOI: 10.5281/zenodo.20111776

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