Bell Tests

One-Sentence Significance

Bell tests compare measured correlations with inequalities obeyed by local hidden-variable models and violated by quantum mechanics.

What Was Measured

Bell experiments measure correlations between outcomes at separated stations for different measurement settings. In the CHSH scenario, the combination

$$S = E(a,b) + E(a,b') + E(a',b) - E(a',b')$$

obeys

$$\lvert S\rvert\le2$$

for local hidden-variable models satisfying the CHSH assumptions. Quantum mechanics can reach

$$\lvert S\rvert=2\sqrt2$$

for suitable ideal states and measurements.

What It Showed

Experiments have observed Bell-inequality violations, ruling out broad classes of local hidden-variable explanations under the tested assumptions. They are not merely demonstrations that entanglement exists; they test a sharper constraint on correlations.

Historically important steps include early photon-correlation tests, Aspect’s time-varying analyzer experiments, and later experiments designed to close major locality and detection loopholes.

What It Did Not Show By Itself

Bell violation does not enable controllable faster-than-light signaling. It also does not remove every possible interpretive loophole or assumption. The theorem and experiments rely on assumptions such as setting independence, locality conditions, statistical analysis, and faithful implementation of the measurement scenario.

The careful statement is stronger and cleaner than the slogan: nature violates Bell inequalities under conditions that are incompatible with the tested local hidden-variable models.

Modern Interpretation

Bell tests are central to quantum foundations and quantum information. They motivate device-independent protocols, randomness certification, and entanglement certification under specified trust assumptions.

The reference home for the named experiment is the glossary card; the theorem and inequality have separate theorem/result cards.

Canonical Links

• Bell Test Experiments Glossary Entry
• Bell Theorem
• CHSH Inequality
• Entanglement in Foundations
• Bell States

Common Myths

• Bell tests prove faster-than-light communication.
• Bell tests are just ordinary entanglement demonstrations.
• A Bell inequality violation is assumption-free.
• Every entangled state violates CHSH.
• “Local realism” is a precise single assumption. The actual assumptions must be stated.

Quick Check

Why does Bell violation not allow superluminal messaging?

Solution

The violation appears in joint correlations after data from both stations are compared. Each local marginal distribution remains uncontrollable by the remote setting, so no usable message is sent faster than light.

References

• J. S. Bell, “On the Einstein Podolsky Rosen Paradox,” Physics 1, 195-200, 1964.
• J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Physical Review Letters 23, 880-884, 1969.
• S. J. Freedman and J. F. Clauser, “Experimental Test of Local Hidden-Variable Theories,” Physical Review Letters 28, 938-941, 1972.
• A. Aspect, J. Dalibard, and G. Roger, “Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers,” Physical Review Letters 49, 1804-1807, 1982.
• B. Hensen et al., “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682-686, 2015.