Does the Gravitational Field Follow the Quantum State or Its Expectation Value? A Tunable-Probability Page-Geilker Experiment

Matter-wave interferometry has confirmed the superposition principle for objects as large as fullerenes and, most recently, nanoparticles of thousands of atoms. Because every massive object sources a gravitational field, a long-standing question follows: does the gravitational field of a delocalized quantum system track the realized quantum state, or the probability-weighted expectation value of its mass distribution (semiclassical gravity)? We first revisit a distant-observer thought experiment in which gravitational which-path information appears to threaten complementarity, and summarize its modern resolution, which turns the apparent paradox into an argument for the quantization of the gravitational field. We then propose a variant of the 1981 Page–Geilker experiment that generalizes a protocol of Kent: the position of a macroscopic source mass is controlled by a quantum random trigger whose firing probability p is continuously tunable, a precision gravimeter monitors the local field, and an otherwise identical run with a classical pseudo-random trigger serves as a control. For no-collapse semiclassical gravity we derive, for a repeated protocol with reset, the field offset in intervals without a release and the suppression of the gravimeter step at quantum-triggered releases; both depend on p, whereas every event-sourced theory predicts a p-independent, event-following field, and the control run cancels systematics that scale with the release rate. Order-of-magnitude estimates indicate that a superconducting gravimeter and a 100–1000 kg source can bound the fraction of “counterfactual” mass that gravitates at the 10−3 level as a function of p. We state which hypotheses the experiment can falsify, why decoherence restricts its scope to no-collapse semiclassical theories, and how the design could be migrated to mesoscopic masses, where the question remains open. Version 2 (September 2026) of a manuscript first written in June 2026. 10 pages, 1 table, 44 references. Also submitted to arXiv (quant-ph, cross-list gr-qc).