A concept in an alternative explanation of
quantum mechanics. It was first put forward by Prince
Louis de Broglie, under what name I don't know, in the early years of the theory, but withdrawn after
Pauli pointed out that it had to involve weird
non-local effects.
David Bohm proposed it again in 1952, as a result of working on the Einstein-Podolsky-Rosen paradox. He was willing to accept non-locality, and built up a new theory of QM on the idea that a particle was indeed a classical particle, with a determinate position and velocity, evolving in a deterministic way: that is, he said the Heisenberg uncertainty principle was not fundamental but merely a consequence of our ignorance of certain hidden variables. The hidden part, responsible for the quantum (non-classical) effects, is carried by the pilot wave that accompanies each particle. Bohm called what it carried the quantum potential.
This traverses the universe non-locally, i.e. in effect acts simultaneously everywhere, and interacts with all other particles' pilot waves, guiding the particle as thought guides a dancer (as he once put it), and producing the quantum effects we observe. Its ability to influence does not diminish with distance, because it does not operate in the ordinary dimensionality of spacetime: rather it brings the whole universe together in what Bohm called the implicate order. He believed it was akin to mind.
Few scientists believe in Bohm's theory, and as physics the pilot wave is quite as complicated and counter-intuitive as anything it is meant to account for.