A pilot wave is a concept associated with the de Broglie-Bohm interpretation of quantum mechanics. According to this interpretation, particles have both a wavefunction and a "pilot wave" that guides their motion. The pilot wave determines the trajectory of a particle, while the wavefunction describes the probability distribution of the particle's position.
In the de Broglie-Bohm interpretation, a particle's trajectory is determined by the interaction between its pilot wave and the surrounding quantum field. The pilot wave guides the particle's motion along a well-defined path, which is often referred to as a "single path" or "hidden trajectory." This trajectory is not subject to the probabilistic nature of the wavefunction, and thus the particle's position is considered to be localized along this path.
Decoherence, on the other hand, is a process by which a quantum system interacts with its environment, leading to the loss of coherence and the appearance of classical behavior. When a particle undergoes decoherence, its wavefunction interacts with the environment and becomes entangled with it, effectively "collapsing" the superposition of states into a specific state. As a result, the particle becomes localized in a particular position or state, and the other possible paths or states are no longer observed.
In the de Broglie-Bohm interpretation, the pilot wave determines a single path for the particle, but this does not mean that all possible paths are resolved into a single path. The other paths or possibilities still exist in a sense, but they do not manifest in the observed behavior of the particle. The pilot wave guides the particle along a specific trajectory, leading to a localized outcome, while the other possibilities remain unobservable.
It's important to note that the de Broglie-Bohm interpretation is just one among several interpretations of quantum mechanics, and there are other interpretations that offer different explanations and perspectives on the behavior of particles and wavefunctions. The choice of interpretation is still a matter of scientific debate and philosophical consideration.