Hidden variable
| Scientific Theory | |
|---|---|
| Name | Hidden variables |
| Type | Class of interpretations of quantum mechanics |
| Author(s) | Albert Einstein, Louis de Broglie, David Bohm, John Stewart Bell and others |
| Keywords | hidden variables, determinism, realism, von Neumann proof, Bell's theorem, non-locality |
A hidden-variable theory is any account of quantum mechanics in which the statistical predictions of the standard formalism arise from underlying properties of physical systems that the formalism does not describe. On such a view a quantum system possesses definite characteristics at all times, and observed randomness reflects incomplete knowledge rather than genuine indeterminism in nature.
The position is most famously associated with Albert Einstein, who held that quantum mechanics, though correct as far as it goes, is an incomplete description — the argument of the 1935 Einstein–Podolsky–Rosen paper. It stands directly opposed to the Copenhagen orthodoxy, on which the wave function is a complete description and unmeasured properties simply do not exist.
The impossibility proof and its collapse
From 1932 the question was widely regarded as closed by John von Neumann's proof that no hidden-variable theory could reproduce quantum mechanics. For three decades the proof was cited to dismiss the entire programme without examination.
It does not establish what was claimed. Its argument rests on an assumption that no reasonable hidden-variable theory need satisfy — that the average of a sum of observables equals the sum of their averages, even for quantities that cannot be measured together. The philosopher Grete Hermann identified this defect in 1935 and was ignored. It was rediscovered and made widely known only in the 1960s by John Stewart Bell, who judged the proof "not just flawed, it's silly."
Meanwhile David Bohm had in 1952 constructed an explicit working hidden-variable theory, demonstrating by direct example that the supposedly impossible was possible. See De Broglie–Bohm theory.
Local and non-local varieties
The decisive constraint came from Bell's 1964 theorem, which showed that no local hidden-variable theory — one in which distant systems cannot influence one another faster than light — can reproduce all quantum correlations. Experiments have since favoured the quantum predictions.
This result is often reported as having eliminated hidden variables altogether. It did not. What it eliminates is the local variety. Non-local hidden-variable theories, of which the de Broglie–Bohm theory is the leading example, are entirely consistent with Bell's theorem and with experiment. The proper conclusion is that if hidden variables exist, they are non-local — and, as Bell emphasised, that nature itself is non-local.
On this wiki
The critical literature catalogued here examines these questions closely, including Measurement Theory via Hidden Variables Not Subject to Bell's Theorem, Nonlocal Theories Satisfying Bell's Inequality, Significant Facts Revealed by the EPR Paradox and Bell's Theorem and Demystifying the EPR Paradox. Further material is indexed under Category:Quantum Theory.