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The European Physical Journal Special Topics

Bohmian mechanics of the three-slit experiment in the linear potential

Georgi Gary Rozenman, Denys I. Bondar, Wolfgang P. Schleich, Lev Shemer, Ady Arie

Published Dec 1, 2023• 5 citations
Publisher

Abstract

Abstract We report on a three-slit experiment in the presence of a linear potential with surface gravity water waves. For these classical waves, we reconstruct the Bohm trajectories as well as the corresponding quantum potentials.
DOI
10.1140/epjs/s11734-023-01044-8

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Abstract In 1952 David Bohm proposed an interpretation of quantum mechanics, in which the evolution of states results from trajectories governed by classical equations of motion but with an additional potential determined by the wave function. There exist only a few experiments that test this concept and they employed weak measurement of non-classical light. In contrast, we reconstruct the Bohm trajectories in a classical hydrodynamic system of surface gravity water waves, by a direct measurement of the wave packet. Our system is governed by a wave equation that is analogous to the Schrödinger equation which enables us to transfer the Bohm formalism to classical waves. In contrast to a quantum system, we can measure simultaneously their amplitude and phase. In our experiments, we employ three characteristic types of surface gravity water wave packets: two and three Gaussian temporal slits and temporal Airy wave packets. The Bohm trajectories and their energy flows follow the valleys and bounce off the hills in the corresponding quantum potential landscapes.
This thesis deals with the theoretical and experimental details of trying to understand \nand infer the quantum potential from Bohmian mechanics using Bohmian trajectories. In \nthis work, some of the key components of the history of Bohmian mechanics is given, a \ntheoretical explanation of how to measure the Bohmian potential, followed by an overview \nof the experimental apparatus and its components. Some tests of the experimental apparatus \nare then presented followed by a discussion of the results. Lastly, some interesting \nfollow up experiments are de ned and discussed. \n \nBohmian mechanics, while completely agreeing with quantum mechanics could not be \nmore di erent from the standard notions such as the fact that particles retain their classical \nidentity of a point like object that have de nite and causal trajectories. In this realm, rst \ndeveloped by de Broglie, these particles move and are guided by a wave, which turns out \nto be the wave function itself. Typically, the velocity of the particles anywhere in space \nis given by spatial derivatives of the phase of this wave and the energy content of the \nparticles is given by the temporal derivative. The trajectories can bend even when there \nare no outside (classical) forces that are acting on the objects. This is due to the fact that \nthese observations of Bohmian mechanics must conform to the standard measurements in \nquantum mechanics. \n \nOne detail that has gone unmeasured (in the sense of inference) in a laboratory setting, \nis the quantum potential (the mysterious force that moves particle to make sure they \nreproduce the measurements of quantum mechanics). Using the technique of measuring \nthe trajectories of photons, the question was asked, can the quantum potential for single \nphotons in the double slit be inferred? A setup has been built in order to try and answer this \nquestion using a single photon detecting camera and a heralding spontaneous parametric \ndown conversion source. Unfortunately, the quantum potential still goes unmeasured due \nto noise in the camera pictures destroying the integrity of the signal and an interesting \nproblem of trying to stitch together the quantum potential at the varying z-planes.
The causal quantum mechanics (i.e. Bohmian or de Broglie-Bohm or Bohm-de Broglie quantum mechanics) has made possible to calculate the trajectories of electrons in a typical double-slit experiment [C. Philippidis et al., Il Nuovo Cimento, 52 B, 15-28 (1979)]. The trajectories do not correspond to an uniform movement but to an accelerated one. The acceleration is caused by the quantum potential. From the quantum theoretical point of view, there is a probability for the electron to emit photons, with a certain emission power, during its movement from the slits to the screen. We find a quantum general formula for the emission power of photons, valid independently of the interpretation. Then, according to the Copenhagen interpretation, this formula gives a strictly zero value for the emission power because the electron moves as a free particle after it leaves the slit and before reach the screen. Then, there is no emission of photons. In the case of the causal interpretation, the emission power results, for a concrete real experiment, in a very tiny but not a zero value, driven by the square of the quantum potential gradient. We give an idea of the type of spectrum that could be measured. A brief idea of a possible experimental arrangement in order to detect this effect, is given.
Quantum mechanics is often praised as a theory which unifies classical mechanics and classical wave theory. Quanta are said to behave either as particles or waves, depending on the type of experiment they are subjected to. But where in the standard formalism can a pointlike particle structure actually be found? Perhaps only to some degree in the reduction postulate applied to position measurements. In reaction to this unsatisfactory state of affairs, Bohmian mechanics introduces a mathematically precise particle concept into quantum mechanical theory. The fuzzy wave functions are supplemented by sharp particle world-lines. Through this additional structure some quantum phenomena like the double slit experiment have lost their mystery.
Young’s double slit experiments, which represent the mystery of quantum mechanics, have been interpreted by quantum probability waves and by de Broglie-Bohm trajectories/pilot waves. Computer simulations of Bohm’s theory predict that (1) trajectories cannot cross, and (2) there is a triangle-shape area behind the double slit, in which there is no trajectory, i.e., no photons. In this article, we report the observations of novel comprehensive double slit experiments, which show that trajectories exist and cross in the triangular area. We show new phenomena that, in 2D cross double slit experiments and which way 2D cross double slit experiments, photons propagate along trajectories in the far field, and behave as particle and distribute as wave.