Motivated by a recent prediction [Commun. Phys. 6, 195 (2023).] that time-of-flight experiments with ultracold atoms could test different interpretations of quantum mechanics, this work investigates the arrival times predicted by the stochastic interpretation, whereby quantum particles follow definite but nondeterministic and nondifferentiable trajectories. The distribution of arrival times is obtained from a Fokker-Planck equation and confirmed by direct simulation of trajectories. It is found to be, in general, different from the distribution predicted by the Bohmian interpretation, in which quantum particles follow definite deterministic and differentiable trajectories. This result suggests that trajectory-based interpretations of quantum mechanics could be experimentally discriminated.
Motivated by a recent prediction [Commun. Phys. 6, 195 (2023).] that time-of-flight experiments with ultracold atoms could test different interpretations of quantum mechanics, this work investigates the arrival times predicted by the stochastic interpretation, whereby quantum particles follow definite but nondeterministic and nondifferentiable trajectories. The distribution of arrival times is obtained from a Fokker-Planck equation and confirmed by direct simulation of trajectories. It is found to be, in general, different from the distribution predicted by the Bohmian interpretation, in which quantum particles follow definite deterministic and differentiable trajectories. This result suggests that trajectory-based interpretations of quantum mechanics could be experimentally discriminated.
It is well known that orthodox quantum mechanics does not make unambiguous predictions for the statistics in arrival time (or time-of-flight) experiments. Bohmian mechanics (or de Broglie--Bohm theory) offers a distinct conceptual advantage in this regard, owing to the well-defined concepts of point particles and trajectories embedded in this theory. We revisit a recently proposed experiment [S. Das and D. D\"urr, Sci. Rep. 9, 2242 (2019)], the numerical analysis of which revealed a striking spin dependence in the (Bohmian) time-of-arrival distributions of a spin-1/2 particle. We present here a mathematically tractable variant of the same experiment, where the predicted effects can be established rigorously. We also obtain some results that can be compared with experiment.
We propose an experimental time-of-flight test of the photon "trajectory" predictions of the Bohmian version of quantum mechanics. The photon trajectories in free space, as predicted by Bohmian mechanics, deviate from expected straight-line paths, bending and turning corners in the presence of quantum interference. We propose an experiment using two such corner-turns that should, in principle, allow these hypothetical Bohmian photons to arrive at a timing detector earlier than conventional photons traveling on the straight-line paths predicted by standard quantum mechanics.
The question of how to interpret and compute arrival-time distributions in quantum mechanics remains unsettled, reflecting the longstanding tension between treating time as a quantum observable or as a classical parameter. While recent studies have primarily contrasted arrival-time predictions across different interpretations of quantum mechanics, here we investigate this ambiguity within the standard quantum-mechanical framework itself. Moreover, most previous studies have focused on the single-particle case in the far-field regime, where these distinct approaches yield very similar arrival-time distributions and a semi-classical analysis typically suffices. Recent advances in atom-optics technologies now make it possible to experimentally investigate arrival-time distributions for entangled multi-particle systems in the near-field regime, where a deeper analysis beyond semi-classical approximations is required. Even in the far-field regime, due to quantum non-locality, the semi-classical approximation cannot generally hold in multi-particle systems. Therefore, in this work, two fundamental approaches to the arrival-time problem---namely, the time-parameter and time-operator approaches---are extended to multi-particle systems. Using these extensions, we propose a feasible two-particle arrival-time experiment and numerically evaluate the corresponding joint distributions. Our results reveal regimes in which the two approaches yield inequivalent predictions, highlighting conditions under which experiments could shed new light on distinguishing between competing accounts of time in quantum mechanics. Our findings also provide important insights for the development of quantum technologies that use entanglement in the time domain, including non-local temporal interferometry, temporal ghost imaging, and temporal state tomography in multi-particle systems.
It is notorious that quantum mechanics cannot predict well-defined values for all physical quantities. Less well-known, however, is the fact that quantum mechanics is unable to furnish -- without additional assumptions -- probabilistic predictions even in emblematic scenarios such as the double-slit experiment. In contrast, trajectory-equipped theories naturally have more predictive power. This work formalizes the aforementioned assertions and illustrates them through three case studies: (i) free particle, (ii) free fall under a uniform gravitational field, and (iii) the double-slit experiment. Specifically, we introduce a prescription for constructing an arrival-time probability distribution within generic trajectory-equipped theories and then derive a conditional probability distribution that is unreachable by quantum mechanics. Our results can, in principle, be tested experimentally, thereby assessing the validity of trajectory-based determinism without the need for experiments involving the direct measurement of arrival time.
The arrival time statistics of spin-1/2 particles governed by Pauli's equation, and defined by their Bohmian trajectories, show unexpected and very well articulated features. Comparison with other proposed statistics of arrival times that arise from either the usual (convective) quantum flux or from semiclassical considerations suggest testing the notable deviations in an arrival time experiment, thereby probing the predictive power of Bohmian trajectories. The suggested experiment, including the preparation of the wave functions, could be done with present-day experimental technology.
Abstract How to compute the probability distribution of a detection time, i.e., of the time which a detector registers as the arrival time of a quantum particle, is a long-debated problem. In this regard, Bohmian mechanics provides in a straightforward way the distribution of the time at which the particle actually does arrive at a given surface in 3-space in the absence of detectors. However, as we discuss here, since the presence of detectors can change the evolution of the wave function and thus the particle trajectories, it cannot be taken for granted that the arrival time of the Bohmian trajectories in the absence of detectors agrees with the one in the presence of detectors, and even less with the detection time. In particular, we explain why certain distributions that Das and Dürr (Sci. Rep. 9: 2242, 2019) presented as the distribution of the detection time in a case with spin, based on assuming that all three times mentioned coincide, are actually not what Bohmian mechanics predicts.