Hidden-variable theory

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${\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }$ Schrödinger equation
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In physics, a hidden-variable theory is a deterministic physical model which seeks to explain the probabilistic nature of quantum mechanics by introducing additional (possibly inaccessible) variables.

Indeterminacy of the state of a system previous to measurement is assumed to be a part of the mathematical formulation of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle. Most hidden-variable theories are attempts to avoid this indeterminacy, but possibly at the expense of requiring that nonlocal interactions be allowed. One notable hidden-variable theory is the de Broglie–Bohm theory.

In 1935, Albert Einstein, Boris Podolsky, and Nathan Rosen in their EPR paper argued that quantum entanglement might indicate quantum mechanics is an incomplete description of reality.^[1][2] John Stewart Bell in 1964, in his eponymous theorem proved that correlations between particles under any local hidden variable theory must obey certain constraints. Subsequently, Bell test experiments have demonstrated broad violation of these constraints, ruling out such theories.^[3] Bell's theorem, however, does not rule out the possibility of nonlocal theories or superdeterminism; these therefore cannot be falsified by Bell tests.