Hidden Variable Theories

Hidden variable theories are interpretations of quantum mechanics that explain the apparent randomness of quantum measurement outcomes by positing underlying deterministic variables that are not accessible to current experiment. If such variables exist and are in principle knowable, the probabilistic predictions of quantum mechanics are an expression of ignorance — exactly as Laplace's Demon required of classical probability — rather than an irreducible feature of nature.

The most developed hidden variable theory is de Broglie-Bohm theory (Bohmian mechanics), which adds a pilot wave guiding particle trajectories deterministically beneath the quantum-mechanical wavefunction. It reproduces all predictions of standard quantum mechanics exactly while maintaining that particles have definite positions at all times. The appearance of randomness is due to our ignorance of exact initial conditions — a classical epistemic limit, not an ontological one.

Bell's Theorem (1964) placed severe constraints on hidden variable theories: any local hidden variable theory — one where the hidden variables cannot transmit information faster than light — produces predictions that violate the observed correlations in entangled systems. Experimental tests have consistently confirmed quantum mechanics and refuted local hidden variables. Non-local hidden variable theories (like Bohmian mechanics) remain viable but require nonlocal influences that are, by construction, undetectable in practice.

The hidden variable program is the closest modern physics has come to rehabilitating the Laplacean vision: a world with a complete description, underneath which probability is merely what we see when we look without sufficient resolution. Whether this rehabilitation is successful depends on questions — about nonlocality, ontological parsimony, and the role of the observer — that remain live.