Researchers first measured the Bohm orbits and the quantum potential in a classical system

In doing so, the researchers confirmed scientific phenomena that had so far only been predicted theoretically

Researchers from Tel Aviv University and universities in the United States and Germany, were able to measure for the first time Bohm trajectories and the quantum potential in a classical system, phenomena that until now had been theoretically predicted and only partially measured. The scientific discovery was made possible as part of a study that examined the dynamics of propagation of packets of surface gravity waves on the surface of water, by measuring them along an 18 meter long water wave pool. These waves fulfill the fundamental equation of quantum theory, the Schrödinger equation, and therefore make it possible to measure wave phenomena known from quantum theory in a classical system.

The team of researchers includes Georgi Geri Rosenman, Ph.D from the School of Physics at Tel Aviv University, Prof. Dennis Bonder from Tulane University in the USA, Prof. Wolfgang Schleich from Ulm University in Germany, Prof. Lev Shemer from the School of Mechanical Engineering at Tel Aviv University and Prof. Adi Aryeh from the School of Electrical Engineering and The Marco and Lucy Shaul Nano-Photonics Chair. The study was recently published in the prestigious journal Physica Scripta.

Figure 1 - Upper part: Schematic description of the experimental system for measuring surface gravity waves on the surface of water and extracting Bohm orbits and the quantum potential. Bottom: (a) Front view of the pool where the waves are generated. (b) The computer-controlled wave generators. (c) Sensors that measure water level.
Figure 1 - Upper part: Schematic description of the experimental system for measuring surface gravity waves on the surface of water and extracting Bohm orbits and the quantum potential. Bottom: (a) Front view of the pool where the waves are generated. (b) The computer-controlled wave generators. (c) Sensors that measure water level.

making waves

De Broglie-Bohm theory, also known as Bohemian mechanics, describes the evolution of the wave function of a quantum particle in space and time by a series of defined trajectories (called Bohm trajectories) in which the particle moves in one of them. These trajectories are determined by an equation of motion that depends on the initial wave function. Reasonably, one can define a quantum potential that defines the evolution of the wave function. The theory is named after Louis de Broglie (1892–1987) and David Bohm (1917–1992) and was proposed by them to explain the phenomena measured in quantum physics.

Figure 1 - Right: experimental measurements of the two-crack experiment and measured Boehm trajectories (black bars). The realization of the cracks is done in the time domain, by creating two pulses of surface gravity waves, at times (t=-4, +4 sec). You can see the development of the Boehm trajectories along the wave pool (X axis). There are areas that no route crosses, and the wave strength measured in them will be zero. The reason for this is that a destructive conflict is created in these areas. In contrast, there are areas where there is a high density of Boehm orbits, and where the wave power is maximum (as a result of constructive interference). Figure 2 - Left: shows the quantum potential. The wave moves only in the 'valleys' (meaning areas where the potential is low) and does not reach the 'mountains' (meaning areas where the potential is high).
Figure 1 - Right: experimental measurements of the two-crack experiment and measured Boehm trajectories (black bars). The realization of the cracks is done in the time domain, by creating two pulses of surface gravity waves, at times (t=-4, +4 sec). You can see the development of the Boehm trajectories along the wave pool (X axis). There are areas that no route crosses, and the wave strength measured in them will be zero. The reason for this is that a destructive conflict is created in these areas. In contrast, there are areas where there is a high density of Boehm orbits, and where the wave power is maximum (as a result of constructive interference). Figure 2 - left: shows the quantum potential. The wave moves only in the 'valleys' (meaning areas where the potential is low) and does not reach the 'mountains' (meaning areas where the potential is high).

A new window for understanding the dynamics of waves

While the de Broglie-Bohm theory was developed for the description of a quantum system, the experiment carried out deals with a classical system of surface gravity waves on the surface of water, but those that satisfy the Schrödinger equation. Thus, the research team recognized that de Broglie-Bohm theory could be applied to experimentally examine Bohm orbits and the quantum potential, but in a large device that can be seen with the eye. In the experiment, surface gravity waves are produced in an 18-meter-long pool, which behave similarly to tiny material waves in the quantum world, and thus the researchers were able to measure in a macroscopic system phenomena that were originally predicted for quantum systems.

In particular, the experiment can be seen as a complete reconstruction of the Bohm trajectories of the famous experiment of bypassing a wave packet through two slits. The realization of the cracks was done in the time domain by exciting two pulses of surface gravity waves at the entrance plane of the wave pool, after which the evolution of the wave function along the pool was measured, from which the Bohm trajectories and the quantum potential were determined. The experimental system was also used to measure other wave packets such as a wave packet created by the bypass of three cracks, and a wave packet whose shape is an Airy function. Beyond confirming Bohm's theory for quantum waves and Bohm orbits, these experiments open a new window towards understanding the dynamics of various types of classical waves, including electromagnetic waves, plasma, acoustic and more. Bohm trajectories make it possible to illustrate visually how these waves develop in space and time and give an intuitive understanding of the phenomena of constructive and destructive conflict of these waves.

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