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The second great quantum experiment

The Bell test.

The double-slit experiment is famous because it's weird. The Bell test is consequential because it's the formal proof that quantum mechanics cannot be replaced by any theory of pre-existing hidden properties. The 2022 Nobel Prize was awarded for finally confirming this experimentally without loopholes.

The question being asked

When you measure an entangled pair of particles, you find their outcomes are correlated. Why? Two possibilities:

  1. Local hidden variables — each particle leaves the source carrying a hidden "cheat sheet" that determines what answer it will give to any measurement question, just like a deck of cards split into two piles. Boring, classical, intuitive.
  2. Quantum nonlocality — the particles share an entangled state that has no definite answers until measured, and measuring one instantly determines what the other will produce. Weird, but what quantum mechanics says.

In 1964, John Bell showed these two pictures make different statistical predictions for a particular measurement protocol. You can test which is true experimentally.

The CHSH inequality

The clearest form is by Clauser-Horne-Shimony-Holt (CHSH). Alice picks one of two measurement angles, a or a'. Bob picks b or b'. Each gets an outcome of +1 or −1. Run this many times and compute the correlation E(setting_A, setting_B) — the average product of their outcomes.

Now combine four of these into one number:

S = E(a, b) − E(a, b') + E(a', b) + E(a', b')

Bell's result: any local hidden-variable theory must give |S| ≤ 2. No matter how clever the hidden cheat sheet, you can't exceed it.

Quantum mechanics, on an entangled singlet state and the right angle choices, predicts |S| up to 2√2 ≈ 2.828 — the Tsirelson bound. The gap from 2 to 2√2 is the empirical fingerprint of quantum reality.

Try it yourself

Hit Start stream below. The widget creates entangled pairs and routes them to Alice and Bob, who randomly choose between angle pairs (a / a') and (b / b'). Watch S climb past 2 and approach 2.828 as the trial count grows. Then slide the angles around — for most settings, S stays inside the classical box.

entangled source|Ψ⁻⟩ = (|01⟩ − |10⟩)/√2ALICEdetectora = 0° / a' = 90°BOBdetectorb = 45° / b' = 135°
CHSH = E(a,b) − E(a,b') + E(a',b) + E(a',b')S = —
−2√2−2 (classical)0+2 (classical)+2√2

Fire some photon pairs to start computing the CHSH correlation.

Alice angles

Bob angles

Fire entangled pairs

E(a, b) — 0°,45°

—(0)

E(a, b') — 0°,135°

—(0)

E(a', b) — 90°,45°

—(0)

E(a', b') — 90°,135°

—(0)

What you're seeing: An entangled photon pair is created in the middle. Alice and Bob each measure one photon at a randomly chosen polarizer angle. The product of their two ±1 outcomes is averaged across many trials to compute the correlation E. CHSH (S) combines four correlation measurements. Any theory where each photon has a pre-existing answer to the question "what would you do at angle X?" must satisfy |S| ≤ 2. Quantum mechanics violates this, up to 2√2. The 1982 Aspect experiment, refined by Hensen (2015) and three 2022 Nobel-winning teams, confirmed the violation experimentally — proving the universe really is nonlocal.

Why this is the most consequential experiment in modern physics

Bell's theorem doesn't just say "quantum mechanics is right." It says any future theory that replaces quantum mechanics must also be nonlocal. Einstein's "spooky action at a distance" isn't an artifact of incomplete theory; it's a property of the universe.

Specifically: there is no way to explain entangled measurement outcomes using only what the particles carry with them when they leave the source. Information about Alice's measurement somehow affects Bob's outcome despite no signal having time to travel between them — this has been verified at distances up to 1,200 km (China's Micius satellite, 2017).

The 2022 Nobel Prize

John Clauser, Alain Aspect, and Anton Zeilinger won the 2022 Nobel Prize for closing the various "loopholes" in earlier Bell tests:

  • Clauser (1972) — first experimental test. Showed violation but with detection-efficiency and locality loopholes still open.
  • Aspect (1982) — switched the measurement angles after the photons were already in flight. Closed the locality loophole if you assume the switches were truly random.
  • Hensen et al. (2015), Giustina (2015), Shalm (2015) — "loophole-free" Bell tests. Closed both detection and locality loopholes simultaneously, using entangled electrons in nitrogen-vacancy diamond centers and entangled photons. The verdict: |S| > 2, no escape.
  • Zeilinger — built the experimental quantum-teleportation and entanglement-distribution toolkit that underpins quantum networking today.

By 2022 the conclusion was unambiguous: local hidden-variable theories are dead. The universe really is nonlocal.

Why investors should care

Three direct commercial implications:

  • Quantum key distribution (QKD) — BB84 and E91 use the impossibility of undetected eavesdropping that Bell's theorem implies. Every commercial QKD product ultimately depends on Bell nonlocality.
  • Device-independent QKD goes one step further — security is guaranteed by Bell-inequality violation, without trusting the hardware. This is the long-term direction for satellite QKD (Micius, EuroQCI).
  • Quantum networking uses entanglement distribution as its core protocol. The viability of a quantum internet (DOE testbeds, EuroQCI) rests on the same physics that Aspect and Zeilinger validated.

Now you've seen the two big quantum experiments. For the rest of the toolkit, head to the primer. For the next interactive demo: double-slit. Or jump to landmark papers to read the originals.