Past exam of the mathematics course of the University of Cambridge 2024 iii Paper 325 3 c Solution 2026-09-28
Yes in both directions. The Page–Geilker experiment tests whether a classical gravitational field is sourced by the expectation value of macroscopically superposed matter configurations. The Colella–Overhauser–Werner experiment uses the Earth's effectively classical field as an external potential and therefore does not distinguish an expectation-value semiclassical source law from a quantized gravitational field.
Conversely, the Colella–Overhauser–Werner experiment directly observes coherent matter-wave interference and a gravitationally generated relative phase in a neutron wavefunction. Page and Geilker did not maintain and recombine coherent branches of the macroscopic source, and their torsion-balance measurement was not an interference experiment. Thus their experiment did not test the neutron gravitational phase effect. The experiments probe opposite sides of the coupling: quantum matter responding coherently to gravity, and gravity responding to branch-dependent quantum matter.