Introduction: The Most Profound Discovery
In 1964, John Bell proved that no local hidden variable theory can reproduce all quantum predictions. This is "the most profound discovery of science" (Stapp).
Bell Inequalities
For local hidden variables, correlations are bounded:
\[|S| = |E(a,b) - E(a,b') + E(a',b) + E(a',b')| \leq 2\]This is the CHSH inequality (Clauser, Horne, Shimony, Holt).
Quantum Violation
Quantum mechanics predicts:
\[S_{QM} = 2\sqrt{2} \approx 2.83\]This exceeds the classical bound of 2!
Experimental Tests
- 1972: Freedman & Clauser (first test)
- 1982: Aspect experiments (closing loopholes)
- 2015: Loophole-free tests (Delft, Vienna, NIST)
- 2022: Nobel Prize for Bell test experiments
Quantum mechanics wins. Local hidden variables are ruled out.
The Quantum Connection
Bell's theorem tells us nature is fundamentally non-local—not that signals travel faster than light, but that quantum correlations can't be explained by any locally-realistic theory. This is the deepest way quantum mechanics differs from our classical intuitions.