Pilot-Wave Physics Across Scales: From Rotating Black Holes to Time Dependent Phases*

Wave–particle duality, a defining feature of quantum mechanics, finds a tangible macroscopic counterpart in pilot-wave hydrodynamics, where millimetric droplets (“walkers”) self-propel across a vertically vibrated fluid bath by coupling to their own wavefields. These systems reproduce many hallmarks of quantum behavior—quantization, tunneling, and interference—from entirely classical dynamics, offering a new experimental window into foundational physics.

Among several new explorations, we focus on a rotating black hole analogue realized via a spinning fluid meniscus. Walkers trapped in this curved hydrodynamic geometry exhibit orbital precession and horizon-like behavior reminiscent of frame-dragging and ergospheres in general relativity. The resulting geodesic-like trajectories show clear analogies to test-particle motion around rotating Kerr black holes. In the weak-field limit, the droplet dynamics converge to predictions from gravitoelectromagnetic theory, suggesting this system as a viable platform for testing classical limits of general relativity.

We modify our experiment in order to consider the behavior of droplets confined to a circular annulus under the influence of a time-dependent central vortex. Under specific temporal modulations of the vortex rotating rate, the system exhibits a nontrivial cubic phase shift in the droplet’s momentum, closely resembling the Kennard cubic phase known from semiclassical Newtonian quantum gravity. This emergent behavior opens a novel route for exploring time-dependent geometric phases and their analogues in both classical and quantum contexts.