In [[physics]], a '''hidden-variable theory''' is a [[Determinism|deterministic]] physical model which seeks to explain the probabilistic nature of [[quantum mechanics]] by introducing additional, (possibly inaccessible), variables.
The [[mathematical formulation of quantum indeterminacy|Indeterminacymechanics]] ofassumes that the state of a system previousprior to measurement is assumed to be a part of the [[mathematical formulation of quantum mechanicsindeterminacy|indeterminate]]; moreover,quantitative bounds foron this indeterminacy can beare 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 [[Quantum nonlocality|nonlocal interactions]] be allowed. One notable hidden-variable theory is the [[de Broglie–Bohm theory]].
In their 1935 [[Einstein–Podolsky–Rosen paradox|EPR paper]], [[Albert Einstein]], [[Boris Podolsky]], and [[Nathan Rosen]] in their [[Einstein–Podolsky–Rosen paradox|EPR paper]] argued that [[quantum entanglement]] might indicateimply that quantum mechanics is an incomplete description of reality.<ref name="EPR">{{cite journal |last1=Einstein |first1=A. |last2=Podolsky |first2=B. |last3=Rosen |first3=N. |year=1935 |title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? |journal=[[Physical Review]] |volume=47 |issue=10 |pages=777–780 |bibcode=1935PhRv...47..777E |doi=10.1103/PhysRev.47.777 |doi-access=free}}</ref><ref>{{cite journal |last1=Genovese |first1=M. |date=2005 |title=Research on hidden variable theories: A review of recent progresses |journal=Physics Reports |volume=413 |issue=6 |pages=319–396 |arxiv=quant-ph/0701071v1 |bibcode=2005PhR...413..319G |doi=10.1016/j.physrep.2005.03.003 |s2cid=14833712 |quote=The debate whether Quantum Mechanics is a complete theory and probabilities have a non-epistemic character (i.e. nature is intrinsically probabilistic) or whether it is a statistical approximation of a deterministic theory and probabilities are due to our ignorance of some parameters (i.e. they are epistemic) dates to the beginning of the theory itself}}</ref> [[John Stewart Bell]] in 1964, in his [[Bell's theorem|eponymous theorem]] proved that correlations between particles under any [[Local hidden-variable theory|local hidden variable theory]] must obey certain constraints. Subsequently, [[Bell test]] experiments have demonstrated broad violation of these constraints, ruling out such theories.<ref name=":0">{{cite news |last=Markoff |first=Jack |date=21 October 2015 |title=Sorry, Einstein. Quantum Study Suggests 'Spooky Action' Is Real. |work=[[New York Times]] |url=https://www.nytimes.com/2015/10/22/science/quantum-theory-experiment-said-to-prove-spooky-interactions.html |accessdate=21 October 2015}}</ref> Bell's theorem, however, does not rule out the possibility of nonlocal theories or [[superdeterminism]]; these therefore cannot be falsified by Bell tests.
