Hidden-variable theory
Hidden-variable theory is the idea that quantum randomness comes from unknown, hidden properties of particles. If those hidden variables were known, the behavior of particles would be fully predictable and deterministic.
In standard quantum mechanics, the state of a system before a measurement is not definite. The wave function tells us probabilities of different outcomes (this is the Born interpretation). Some scientists hoped hidden variables would restore definite properties, even if we can’t measure them yet. But doing so often means accepting nonlocal effects: things far apart could influence each other instantly.
A famous challenge to hidden variables comes from the EPR argument (Einstein, Podolsky, and Rosen). They suggested quantum theory might be incomplete and that hidden properties could exist. Bohr disagreed, saying what we can know depends on how we measure, and that quantum predictions are about what happens in experiments, not about hidden realities.
John Bell, in 1964, showed a crucial point: if hidden variables are local (no instantaneous influence at a distance), then certain correlations between entangled particles must satisfy specific inequalities. Experiments testing Bell inequalities, many conducted over the past few decades, have repeatedly violated these inequalities. The results strongly support quantum mechanics and rule out local hidden-variable theories. They do not, however, completely rule out nonlocal hidden-variable theories—that is, theories where distant things can influence each other directly.
One well-known nonlocal hidden-variable theory is the de Broglie–Bohm theory (also called pilot-wave theory). In this view, particles have definite positions, but their motion is guided by a quantum wave that can act instantly across space. This nonlocal guiding wave can reproduce quantum predictions. Bohmian ideas are attractive to some because they keep a clear picture of particles with real properties, but they are controversial because of their strong nonlocality and because the guiding wave lives in a high-dimensional space rather than ordinary three-dimensional space.
There are other related limits on hidden-variable ideas too. The Kochen–Specker theorem shows that you cannot assign fixed values to all quantum observables in a way that’s independent of how you measure them. Experiments testing quantum contextuality have further constrained what hidden-variable theories can look like.
Some researchers have explored possible loopholes or alternative viewpoints. For example, superdeterminism asks us to consider whether the choices about how to measure are themselves determined in advance in a way that could mimic quantum predictions. Others point to many-worlds-type ideas as a way to explain quantum outcomes without hidden variables for a single world.
What does this all mean today? Local hidden-variable theories are strongly disfavored by experiments that test Bell inequalities. Nonlocal hidden-variable theories like Bohm’s remain possible interpretations, but they come with trade-offs and are not universally accepted. The mainstream view is that quantum mechanics, as it is practiced, provides the correct predictions for experiments; hidden-variable ideas are mainly of philosophical interest—offering different ways to think about what quantum phenomena mean.
This page was last edited on 2 February 2026, at 14:37 (CET).