The Pilot-Wave Theory, also known as the de Broglie-Bohm theory or the Bohmian mechanics, is an interpretation of quantum mechanics that aims to provide a deterministic explanation for quantum behavior. It introduces the concept of a pilot wave, which guides the behavior of quantum particles.
In the Pilot-Wave Theory, particles are described by their positions and velocities, just like in classical physics, but there is an additional element called the pilot wave. The pilot wave is a wave associated with each particle, which guides its motion. It is influenced by a wave function that obeys the Schrödinger equation, similar to standard quantum mechanics.
According to the theory, when a particle is measured, its position collapses to a definite value, as in standard quantum mechanics. However, unlike in the Copenhagen interpretation, the wave function does not collapse. Instead, it continues to evolve according to the Schrödinger equation. The particle's motion is determined by the interaction between its position and the pilot wave.
The pilot wave carries information about the potential paths the particle can take, and it guides the particle's motion in a way that is consistent with the statistical predictions of quantum mechanics. The particle moves in a manner that is influenced by the overall distribution of the pilot wave, resulting in behavior that exhibits wave-like interference patterns and probabilistic outcomes.
The Pilot-Wave Theory is a non-local theory, meaning that the behavior of a particle is influenced by the positions of other particles instantaneously, regardless of the distance between them. This non-locality is a departure from the local interactions of standard quantum mechanics.
While the Pilot-Wave Theory provides a deterministic explanation for quantum behavior, it is important to note that it introduces additional elements beyond the wave function, such as the pilot wave itself, which makes it more complex than standard quantum mechanics. Furthermore, the theory is not widely accepted and remains a topic of ongoing debate and investigation among physicists.
Overall, the Pilot-Wave Theory offers an alternative interpretation of quantum mechanics by introducing a guiding pilot wave to explain the probabilistic behavior of particles.