A recent article claims to measure the speed of quantum particles in the classically forbidden regime where the energy of the particles is lower than the local potential, and further claims that the results of this experiment challenge Bohmian mechanics. But this interpretation of the experiment is incorrect (and dubious even in the context of ordinary quantum mechanics). A proper analysis of the system from a pilot-wave perspective shows that it predicts the same distribution of particle positions (and so the same experimental results) as ordinary quantum theory. The speed measured by the experiment in this regime is fictitious.
A recent article claims to measure the speed of quantum particles in the classically forbidden regime where the energy of the particles is lower than the local potential, and further claims that the results of this experiment challenge Bohmian mechanics. But this interpretation of the experiment is incorrect (and dubious even in the context of ordinary quantum mechanics). A proper analysis of the system from a pilot-wave perspective shows that it predicts the same distribution of particle positions (and so the same experimental results) as ordinary quantum theory. The speed measured by the experiment in this regime is fictitious.
Recently, Sharoglazova et al. [Nature 643, 67 (2025)] proposed a procedure for determining the speed of a quantum particle in the classically forbidden region of a potential step, and implemented it in a beautiful experiment. The inferred speeds disagree significantly with the Bohmian velocities, which the authors presented as an experimental challenge to Bohmian mechanics. This is puzzling because the speeds are inferred from particle populations in coupled waveguides for which Bohmian mechanics and standard quantum mechanics make identical predictions. We resolve the puzzle by a detailed theoretical analysis of the experimental setup. We show that the speed inference rests on an assumption that fails in the relevant (evanescent) regime according to both Bohmian mechanics and standard quantum mechanics -- namely that the inter-waveguide tunneling time is set by the transverse coupling and is not affected by entanglement with the longitudinal degree of freedom. We also consider a second speed estimate suggested by Sharoglazova et al., which is based on the Büttiker dwell time formula for particles in the forbidden region. We show that the authors applied the formula incorrectly, and that a correct application yields exact agreement with the predictions of Bohmian mechanics. Our analysis includes explicit calculations of Bohmian trajectories, dwell times, and longitudinal speeds in the two-dimensional waveguide model of the experiment.
The recent paper by Sharoglazova et al. reports an energy-dependent parameter ν extracted from the spatial distribution of photons in a coupled-waveguide experiment. The authors interpret ν as the speed of quantum particles, even in the classically forbidden regime, and claim that its finite value contradicts the Bohmian mechanics prediction of zero particle velocity. This challenge arises from a fundamental misunderstanding of the operational meaning of v within the Bohmian ontological framework. We demonstrate that v quantifies the spatial gradient of the wavefunctions amplitude, a geometric property of the guiding field, not the kinematical velocity of point-like particles. The experiment therefore does not challenge but rather illustrates the clean ontological separation between the wave and particle aspects inherent to Bohmian mechanics.
We reanalyze a recent experiment by Sharoglazova et al. [Nature (London) 643, 67 (2025)] highlighting the role of the transient regime. We prove that in the evanescent state of the stationary regime their experimental data can be interpreted in terms of Bohmian quantum mechanics. At the same time, Bohm's quantum potential can be reinterpreted as a kinetic-energy term in the framework of Nelson's stochastic quantum mechanics, with a hidden-variable, nonclassical speed fitting the experimental data as well. The experiment can be interpreted as well within orthodox quantum mechanics and is therefore not conclusive in selecting or challenging any framework.
In quantum mechanics, regions of negative local kinetic energy can manifest. This occurs when the wave function's amplitude undergoes significant decay, typically associated with quantum tunneling. Here, we investigate the particles motion in a system of two coupled waveguide potentials, where the population transfer between the waveguides effectively acts as a clock, allowing particle speeds along the waveguide axis to be determined [1]. We implement this idea for photons in optical microcavity, using a novel nanostructuring method [2] to create waveguides. By applying this scheme to evanescent phenomena at a reflective potential step, we determine an energy-speed relationship for classically forbidden motion, which shows speed increase as energy decreases. Our findings contribute to the ongoing tunneling time debate, and separately, can be viewed as a test of Bohmian trajectories in quantum mechanics. [1] Klaers, J., Sharoglazova, V., & Toebes, C. (2023). Physical Review A, 107(5), 052201. [2] Vretenar, M., Puplauskis, M., Klaers, J.. Adv. Optical Mater. 2023, 2202820.
Abstract Classical mechanics characterizes the kinetic energy of a particle, the energy it holds due to its motion, as consistently positive. By contrast, quantum mechanics describes the motion of particles using wave functions, in which regions of negative local kinetic energy can emerge 1 . This phenomenon occurs when the amplitude of the wave function experiences notable decay, typically associated with quantum tunnelling. Here, we investigate the quantum mechanical motion of particles in a system of two coupled waveguides, in which the population transfer between the waveguides acts as a clock, allowing particle speeds along the waveguide axis to be determined. By applying this scheme to exponentially decaying quantum states at a reflective potential step, we determine an energy–speed relationship for particles with negative local kinetic energy. We find that the smaller the energy of the particles—in other words, the more negative the local kinetic energy—the higher the measured speed inside the potential step. Our findings contribute to the ongoing tunnelling time debate 2–6 and can be viewed as a test of Bohmian trajectories in quantum mechanics 7–9 . Regarding the latter, we find that the measured energy–speed relationship does not align with the particle dynamics postulated by the guiding equation in Bohmian mechanics.
In our work [Sharoglazova et al., Nature 643, 67-72 (2025)], we reported the first measurement of the speed of tunnelling particles by comparing two orthogonal motions in a coupled-waveguide system. Here we respond to objections raised in comments, referee reports, preprints, and articles. In particular, we distinguish two questions that are often conflated: whether Bohmian mechanics reproduces the measured density, and whether the standard guiding equation assigns the correct state of motion to the particles. The first point follows under the usual quantum equilibrium assumptions. By contrast, identifying the guiding velocity with particle motion is an additional physical postulate, since the standard guiding equation does not follow from the Schrödinger equation alone. We argue that, in the evanescent regime, the state of motion assigned by the standard guiding equation is in disagreement with the speed following from our experiments. To make the distinction explicit, we also present a bidirectional Bohmian model that reproduces the same stationary density while assigning finite speeds compatible with the speed inferred in the evanescent regime.