What is Bell’s theorem?

September 12, 2025

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Bell’s theorem is a fundamental result in quantum mechanics that demonstrates the incompatibility between the predictions of quantum mechanics and classical local realism.

Concept

Local realism: The idea that:
1. Locality – Information cannot travel faster than the speed of light.
2. Realism – Physical properties exist before they are measured.
Quantum mechanics predicts correlations between entangled particles that cannot be explained by any local hidden variable theory.

Bell’s Inequality

John Bell formulated mathematical inequalities (Bell inequalities) that any local realistic theory must satisfy.
Experiments with entangled particles show violations of Bell inequalities, confirming that:
- Either locality or realism (or both) must be abandoned.
- Quantum entanglement produces correlations stronger than classical physics allows.

Implications

Non-locality: Quantum entangled particles can exhibit correlations instantaneously across distance, even if separated.
Quantum Foundations: Confirms that quantum mechanics is inherently probabilistic, not deterministic.
Quantum Technologies: Underpins quantum cryptography, teleportation, and other entanglement-based protocols.

Example (Conceptual)

Two entangled particles are sent to Alice and Bob.
They measure spin in different directions.
The measurement outcomes are correlated in a way that violates classical expectations, matching quantum predictions.

✅ Summary:
Bell’s theorem proves that no theory based on local hidden variables can reproduce all the predictions of quantum mechanics. It confirms the strange, non-local correlations of entanglement that are central to modern quantum technologies.