New publication
V. Sharoglazova, M. Puplauskis, C. Mattschas, C. Toebes, and J. Klaers, “Energy-speed relationship of quantum particles challenges Bohmian mechanics”, Nature 643, 67 (2025). link
In this study, we investigate the motion of particles associated with evanescent wave functions, which arise when quantum particles are reflected at a potential step. To this end, we confine the particles to one-dimensional waveguides and couple two such waveguides in a controlled manner by placing them parallel to each other at a small distance. The coupling between the waveguides provides a temporal reference for the particles’ motion. By comparing the motion of particles within a single waveguide to the tunneling-induced hopping between the waveguides, we can draw conclusions about the speed at which the particles move. This approach sheds light on tunneling dynamics and can be interpreted as a test of Bohmian mechanics, where particle velocities play a central role.
The outcome of our experiment is striking: particles appear to move where, they should be at rest. Contrary to the prediction of the Bohmian guiding equation, our experimental observations indicate that particles in evanescent quantum states are not stationary—they move with a well-defined speed. This measured speed supports the core idea behind the de Broglie relation: that motion and wavelength are fundamentally linked—but with a twist. For evanescent wave functions, we find that a modified de Broglie-type relation, λ = ℏ / mv, holds, where λ is the decay length and v denotes the non-directional particle speed measured in our experiment. Our results therefore suggest that both phase gradients and amplitude gradients play complementary roles in encoding motion within a quantum mechanical wave function. This stands in contrast to the Bohmian guiding equation, which attributes motion exclusively to phase gradients. In other words, our findings challenge whether the ontology implied by Bohmian trajectories is realised in nature.