Hidden-variable theory

In physics, hidden-variable theories are proposals to provide explanations of quantum mechanical phenomena through the introduction of (possibly unobservable) hypothetical entities. The existence of fundamental indeterminacy for some measurements is assumed as 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 quantum indeterminacy, but possibly at the expense of requiring the existence of nonlocal interactions. Albert Einstein objected to aspects of quantum mechanics, and famously declared "I am convinced God does not play dice". Einstein, Podolsky, and Rosen argued while assuming local causality that quantum mechanics is an incomplete description of reality. Bell's theorem and the related Bell test experiments have subsequently ruled out nearly all local hidden variable theories, with the exception of the superdeterminism loophole which cannot be closed by Bell test experiments. One notable non-local hidden-variable theory is the De Broglie–Bohm theory. Per its mathematical formulation, quantum mechanics is non-deterministic, meaning that it generally does not predict the outcome of any measurement with certainty. Instead, it indicates what the probabilities of the outcomes are, with the indeterminism of observable quantities constrained by the uncertainty principle. The question arises whether there might be some deeper reality hidden beneath quantum mechanics, to be described by a more fundamental theory that can always predict the outcome of each measurement with certainty: if the exact properties of every subatomic particle were known, the entire system could be modeled exactly using deterministic physics similar to classical physics. In other words, it is conceivable that quantum mechanics is an incomplete description of nature.