Pilot Wave Theory

Pilot wave theory — also called de Broglie–Bohm theory or Bohmian mechanics — is an interpretation of quantum mechanics that restores classical determinism by positing that particles have definite positions at all times, guided by a real wave (the pilot wave) obeying the Schrödinger equation.

In Bohmian mechanics, the apparent randomness of quantum measurement is not fundamental. It arises from ignorance about the exact initial position of the particle — a genuinely classical notion of probability-as-ignorance rather than probability-as-irreducibility. The demon, in principle, survives: if you knew the exact initial positions of all particles and the initial wave function, you could predict all future positions exactly.

The theory reproduces all predictions of standard quantum mechanics. Its cost is nonlocality: the pilot wave is instantaneously sensitive to the configuration of the entire universe, including distant entangled particles. This nonlocality is required by Bell's theorem, which proves that no local hidden variable theory can reproduce quantum correlations. Pilot wave theory is nonlocal, and openly so.

The question pilot wave theory raises is whether the demon's program survives by going nonlocal — whether a determinism that requires instantaneous access to the entire state of the universe is actually determinism, or merely a more elaborate form of the same problem. A demon that needs to know everything before knowing anything has not escaped Laplace's original challenge; it has only renamed it.