Pilot wave theory, also known as de Broglie-Bohm theory or Bohmian mechanics, is an alternative interpretation of quantum mechanics. According to this theory, particles possess both a particle-like nature and are guided by a pilot wave that determines their motion.
In pilot wave theory, the pilot wave is a real, physical wave that propagates through space and interacts with the particles. The pilot wave influences the motion of the particles and guides them along specific trajectories. These trajectories are deterministic and well-defined, in contrast to the probabilistic nature of standard quantum mechanics.
In this interpretation, the pilot wave carries the quantum information associated with the particles. The particles themselves are still considered to be localized entities with definite positions. The coherent waves associated with the particles are not necessarily "instantly infinite" but rather represent the superposition of all possible states of the system.
It's important to note that pilot wave theory is just one of the interpretations of quantum mechanics and is not widely accepted as the mainstream interpretation. The standard formulation of quantum mechanics, known as the Copenhagen interpretation, does not involve explicit pilot waves and focuses on the mathematical description of wave functions and their probabilistic interpretation.