The Pilot wave theory, also known as the de Broglie-Bohm Wave theory, or the causal interpretation, was one of the many interpretations of quantum mechanics in its early stages of conception and development. It was initially proposed by Louis de Broglie in his 1927 paper "Wave Mechanics and the Atomic Structure of Matter and Radiation", although this had been done only for a single particle. This theory was later developed by David Bohm. The theory suggests that all particles in motion are actually borne on a wave-like motion, similar to how an object moves on a tide. In this theory, it is the evolution of the carrier wave that is given by the Schrödinger equation. It is a deterministic theory and is entirely nonlocal.
Contents
- Fluidic analogs to quantum mechanical experiments
- Quantized orbits
- Quantum tunneling
- Single slit and double slit diffraction
- Zeeman effect
- References
It is an example of a hidden variable theory, and all non-relativistic quantum mechanics can be accounted for in this theory. The theory was abandoned by de Broglie in 1932, and it gave way to the Copenhagen interpretation. The Copenhagen interpretation does not use the concept of the carrier wave or that a particle moves in definite paths until measurement is made. The Copenhagen Interpretation has stood the test of time as the widely accepted interpretation of Quantum Theory since then.
Fluidic analogs to quantum mechanical experiments
An experiment conducted by Yves Couder and Emmanuel Fort, physicists at the Université Paris Diderot in 2006, involved millimeter scale fluid droplets. The droplets bounced up and down on a vibrated fluid bath. The experiment has revived the debate on the correct interpretation and formalism of quantum mechanics. Moreover, it is now considered that more experiments similar to Couder's can actually shed some light on the peculiar results of the Quantum theory.
Couder's Experiment involves an oil-filled tray placed on a vibrating surface. The intensity is such that it is just below the intensity required for the formation of Faraday's Waves on the surface. On dropping a drop of the same fluid on the surface, the presence of an air film between the surface and the drop does not allow the two to coalesce. Thus, the droplet bounces on the surface, rather than simply losing its shape upon impact. This bouncing drop produces waves on the surface and these waves cause the droplet to move along the surface. This system was used to reproduce one of the most famous experiments in quantum mechanics, the double-slit experiment. Another analog was developed by a team of MIT researchers of a classic quantum experiment that involves confining electrons in a circular "corral" by a ring of ions. Instead of electrons, bouncing drops were used. Interestingly, the results in both the cases were similar to the quantum mechanical results. (Quantum Mechanical in Fluidic Macroscopic Experiments)
Quantized orbits
In case of 2 walking droplets on a surface that is vibrating, the droplets were found to orbit each other just as it happens in case of quantized orbits. The drops maintained discrete values of distance between each other and were held in stable configuration.
Quantum tunneling
The probability of a drop to cross a barrier in its path was seen to decrease exponentially as the barrier width increased. This is similar to a particle undergoing quantum tunneling.
Single-slit and double-slit diffraction
The single and double-slit diffraction experiment by Couder and Fort showed that these walking droplets exhibited wave-like interference patterns when passing through single or double slits. This is similar to particles like the electron that are seen to behave like waves as well as particles at the microscopic scale.
Zeeman effect
In an external magnetic field, the energy levels of an atom split up depending on the direction of the angular momentum of the spinning electron. This is known as the Zeeman effect. To create an analogy to an external magnetic field, the bath is rotated. The walkers then either rotate with the bath or against it, just like the case of the atom.