General-relativistic particle trajectories via quantum mechanical weak values and the Schwarzschild-Alcubierre spacetime

We show that the average trajectories of relativistic quantum particles in Schwarzschild spacetime, obtained via quantum mechanical weak measurements of momentum and energy, are equivalent to the predicted flow lines of probability current in curved spacetime quantum theory. We subsequently demonstrate that these trajectories correspond exactly to classical null geodesics in a hybrid Schwarzschild-Alcubierre spacetime. This threefold equivalence demonstrates how quantum theory in curved spacetime can be formulated via operationally defined measurements, and that such a theory may be interpreted deterministically, in the spirit of hidden-variable models such as Bohmian mechanics, through the novel connection to an underlying ``guiding metric.''