Double-slit experiment with single wave-driven particles and its relation to quantum mechanics

Abstract

In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.

Simulations of pilot-wave dynamics in a simple harmonic potential

“…While claims of single-particle diffraction and interference [6] have been contested [7], tunneling [8,9], orbital quantization in both a rotating frame [10][11][12] and harmonic potential [13,14], and wavelike statistics in confined geometries [15][16][17][18] are all robust quantumlike phenomena. This hydrodynamic pilot-wave system and its relation to realist quantum theories, specifically, de Broglie's double-solution pilot-wave theory [19] and its modern extensions [20], were recently reviewed by Bush [21,22].…”

Scattering theory of walking droplets in the presence of obstacles

“…[10][11][12][13][14] involving various degrees of sophistication in the theoretical modelling. The straight-line motion of a droplet on a free surface can be well described by an empirical ansatz which was proposed in [6], see also [7], and essentially confirmed later in [10] from a more fundamental perspective, see also [15] for a stability analysis.…”

Darwinian Evolution and Quantum Evolution are Complementary: A Perspective

“…Abdurakhimov et al have recently shown an overlap between the quantum and the classical world when studying the interactions of light (electromagnetic fields) and matter (electrons) [1]. Rabi splitting of eigenfrequencies of the coupled motion is observed both in the cavity reflection spectrum and ac current of the electrons, the latter probed by measuring their bolometric photoresponse.…”

“…This was clearly demonstrated in the double slit experiment whereby light was shown to exist as both a wave and a particle, assuming either property depending on whether it is measured. As such, when observed, light will unfold as a particle and when not observed it will act as a wave function [1,5,6]. This was the basis of one the most famous debates between two of the greatest minds in the history, Einstein and Bohr [7].…”

“…At that level, quantum particles can be anywhere in space until they are "observed" or measured. Quantum particles exhibit wave-particle duality that could be affected by whether there is a conscious observer or not [1][2][3][4], such that there is no independent observer because the presence of the observer can exert an effect on the experiment, "or at least apparently so". Thus, it seems that absolute reality is "merely an illusion albeit a persistent one", as described by Einstein himself, and could only exist if there is an observer, and thus we refer to the term common reality "as observed by humans" when describing reality.…”