| hidden variables | |
|---|---|
| Name | Hidden-variable theories |
| Caption | Schematic of hidden-variable models positing extra parameters underlying quantum states |
| Field | Quantum mechanics |
| Introduced | Early 20th century |
| Notable figures | Albert Einstein, Erwin Schrödinger, David Bohm, John Stewart Bell, Niels Bohr |
| Notable works | Einstein–Podolsky–Rosen (1935), Bohm (1952), Bell (1964) |
hidden variables
Hidden variables are hypothetical, unobserved parameters introduced to account for the apparent indeterminism of Quantum mechanics by restoring underlying determinism or objective states. Debates over hidden-variable models have shaped foundational research, experimental tests, and interpretations of quantum phenomena such as entanglement, nonlocality and measurement. The question of whether quantum randomness reflects ignorance about additional variables or is irreducibly fundamental remains central to the philosophy and physics of the quantum domain.
Hidden-variable proposals aim to supplement the wavefunction or quantum state with extra degrees of freedom that determine measurement outcomes. Motivations include restoring realism, preserving causal determinism associated with classical physics, and providing clear accounts of the measurement problem. Proponents argue that hidden variables can yield clearer ontology and avoid concepts like the collapse of the wavefunction; critics contend that such models must confront empirical constraints, notably those arising from Bell's theorem and Kochen–Specker-type contextuality.
Discussion of hidden variables predates formal quantum theory debates: Albert Einstein and colleagues formulated the Einstein–Podolsky–Rosen (1935) argument to claim quantum mechanics is incomplete and might require additional variables. Louis de Broglie initially proposed pilot-wave ideas in the 1920s, but the Copenhagen interpretation advocated by Niels Bohr dominated. Interest revived when David Bohm published a detailed deterministic model in 1952, now called Bohmian mechanics, that reconstructed quantum predictions using particle positions guided by a wave. The modern rigorous critique culminated in John Stewart Bell's 1964 paper proving constraints on local hidden-variable models, prompting experimental tests by groups including Alain Aspect and later laboratories such as Anton Zeilinger's and NIST groups.
Hidden-variable theories are classified by properties such as determinism, locality, and contextuality. Major classes include: - Deterministic nonlocal theories: exemplified by Bohmian mechanics, where hidden positions evolve under a guiding equation and nonlocal correlations arise explicitly. - Stochastic or indeterministic models: e.g., stochastic mechanics variants that add random hidden processes while seeking to reproduce quantum statistics. - Local hidden-variable models: those that attempt to preserve relativistic locality; largely constrained or ruled out by Bell's theorem and empirical tests. - Contextual hidden-variable models: accept that measurement outcomes depend on the measurement context, in line with results from the Kochen–Specker theorem.
Each approach handles observables, symmetry, and relativistic compatibility differently; efforts to reconcile hidden variables with quantum field theory and special relativity remain active topics.
Bell's theorem proves that no local hidden-variable theory can reproduce all quantum predictions for entangled systems. Bell derived inequalities (e.g., CHSH inequality) that local realistic models must satisfy. Empirical violations of Bell inequalities, first observed in experiments by Alain Aspect (1982) and subsequently in increasingly loophole-free demonstrations by teams including Anton Zeilinger, Ronald Hanson and the Delft University of Technology group (2015), favor quantum mechanics and nonlocal correlations over local realism. These experiments address loopholes such as detection efficiency and locality; while they disfavor local hidden variables, they do not rule out all hidden-variable frameworks (notably nonlocal or contextual models).
Beyond Bell, no-go theorems like Kochen–Specker theorem demonstrate that noncontextual hidden-variable assignments to quantum observables are impossible in Hilbert spaces of dimension three or higher. The theorem and subsequent refinements show that assuming value definiteness independent of measurement context conflicts with quantum structure. Other results—such as Gleason's theorem—constrain the types of probability measures compatible with quantum projections, further limiting hidden-variable reconstructions. Contextuality has been formalized as a resource in quantum information and linked to computational advantages in quantum computing.
Hidden-variable research has influenced major interpretational debates. Bohmian mechanics offers a deterministic ontology with clear particle trajectories, while remaining explicitly nonlocal. Other interpretations, such as the Many-worlds interpretation, avoid hidden variables by embracing branching wavefunctions. The viability of hidden variables touches on broader themes: the nature of causality, the status of probability in physics, and the compatibility of quantum theory with relativity. Philosophers and physicists (e.g., Howard Wiseman, Tim Maudlin) continue to analyze whether hidden-variable approaches provide superior explanatory power or merely shift conceptual difficulties.
Contemporary work explores relativistic and field-theoretic extensions of hidden-variable models, reconstructions of quantum theory from operational principles, and experimental tests probing finer aspects of contextuality and nonlocality. Research groups at institutions like Perimeter Institute, CERN, University of Oxford and Massachusetts Institute of Technology investigate foundations, while quantum information labs (e.g., QuTech, IBM Research) employ contextuality and entanglement as resources. Applied outcomes include device-independent quantum cryptography, where Bell-inequality violations certify randomness and security without trusting devices—an area linking foundational no-go results to practical quantum technologies.
Category:Quantum mechanics Category:Philosophy of physics