Misinference of interaction-free measurement from a classical system

Abstract

Interaction-free measurement is thought to allow for quantum particles to detect objects along paths they never traveled. As such, it represents one of the most beguiling of quantum phenomena. Here, we present a classical analog of interaction-free measurement using the hydrodynamic pilot-wave system, in which a droplet self-propels across a vibrating fluid surface, guided by a wave of its own making. We argue that existing rationalizations of interaction-free quantum measurement in terms of particles being guided by wave forms allow for a classical description manifest in our hydrodynamic system, wherein the measurement is decidedly not interaction-free.

Figures (3)

• Figure 1: A schematic of the Elitzur-Vaidman bomb experiment. A particle emitted from a source $S$ passes through a beam-splitter $B_1$, at which point its associated wave (a wave function elitzur_quantum_1993 or a pilot-wave hardy_existence_1992) is split in two. The wave is then recombined at a beam-splitter $B_2$, and the particle continues toward the detectors. In the absence of a bomb, the particle will be detected at $D_1$$100\%$ of the time, while in its presence, the particle will be detected at $D_2$$25\%$ of the time. A detection event at $D_2$ indicates the presence of a live bomb along a path the particle never took. Red and blue dashed lines indicate possible paths taken by a particle emitted from $S$ in the absence and presence of the bomb, respectively.
• Figure 2: Surreal trajectories in quantum mechanics and pilot-wave hydrodynamics frumkin_real_2022: (a) A variant of the interferometer setup considered by Englert, Scully, Süssman, and Walther (ESSW) Englert1993. An incoming wave packet is split by a beam splitter $B$ and reflected by the mirrors $M_1$ and $M_2$. The wave packets interfere in the region $I$ and then move towards the detectors $D_1$ and $D_2$. The blue path represents the particle trajectory anticipated by ESSW, while the red path is that predicted by Bohmian mechanics, the so-called "surreal trajectory". The red dot represents the one-bit, which-way detector employed in the weak-measurement experiments of Mahler et al. mahler_experimental_2016. (b) In the associated hydrodynamic analog frumkin_real_2022, droplets reflect off submerged barriers, indicated in white. When the setup is symmetric, the droplet enters the right or left channel with equal probability and is then reflected off the associated barrier. Its subsequent deflection away from the system centerline results in a real surreal trajectory. Twenty such trajectories are shown. (c) When one of the barriers is removed, the symmetry of the system is broken. The walking droplet is then reflected away from the remaining barrier, resulting in the trajectory that one might expect.
• Figure 3: Interaction-free measurement in pilot-wave hydrodynamics: (a) A schematic illustration of the topography used in the experiment. The upper half of the left barrier (orange) plays the role of a "bomb". (b) In a symmetric setup, the droplet enters the right or left channel with equal probability. If the droplet goes to the left channel, it detonates the "bomb", and if it goes to the right, it is deflected away from the system centerline, resulting in a “surreal” trajectory frumkin_real_2022. Thus, the droplet will always be detected on the right side of the setup. Twenty such trajectories are shown. (c) If the "bomb" is removed, the symmetry of the system is broken, the droplet's pilot-wave does not interact with the bomb, and "surreal" trajectories are suppressed. Thus, the droplet will always be detected on the left side of the setup. If the bomb is present $50\%$ of the time, there is $25\%$ chance of the droplet being detected on the right, and so the bomb on the left. The scale bar represents the Faraday wavelength $\lambda_{F}=4.84$ mm