CHAPTER 1The puzzle

In which Einstein discovers something about quantum mechanics that he cannot bring himself to accept, and a quiet Northern Irish physicist, thirty years later, finds a way to ask the universe directly.

§1.1Einstein in 1935

Picture Albert Einstein in 1935. He is fifty-six years old, living in Princeton, having fled Germany two years earlier. He has spent the last decade in a slow-motion argument with the founders of quantum mechanics — Niels Bohr in particular — about whether their new theory is the whole truth about reality, or only a piece of it.

Einstein's worry isn't that quantum mechanics gets the wrong answers. It gets the right answers. The problem is what those answers mean. In the standard textbook reading, quantum mechanics gives only probabilities for individual events. Toss a quantum coin and the theory does not tell you an underlying mechanism that fixes the result in advance — not the way an ordinary coin toss is fixed by the throw, the air, and the table. There is, the theory seems to say, simply no fact of the matter until you look.

Einstein famously refused this. "God does not play dice," he is supposed to have said. He believed, deeply, that the randomness was a sign of missing knowledge, not fundamental indeterminacy. There must be some deeper layer underneath that quantum mechanics hadn't yet figured out — like how thermodynamics looks random until you discover atoms, and then suddenly the randomness is just unknown atomic positions. He wanted physics to find the atoms underneath the dice.

And so, with two collaborators — Boris Podolsky and Nathan Rosen — he wrote a four-page paper in 1935 that was supposed to settle the matter. It described a thought experiment so cleverly constructed that any honest reading of it seemed to force the conclusion that quantum mechanics had to be incomplete. The paper was titled "Can quantum-mechanical description of physical reality be considered complete?" The answer, the authors insisted, was: no.

The thought experiment goes something like this. Take two particles. Let them be created together in such a way that their properties are linked — when you measure one, you can predict, with certainty, what you'd find if you measured the other. Now let them fly apart. Far apart. Half a galaxy apart, if you like. Wait until they're separated by a distance light couldn't cross in any reasonable time.

Now measure one. Whatever you find, you instantly know what the other would do. But — Einstein insisted — nothing physical can be travelling between them at this point; they're too far apart. Therefore the answer about the second particle must have already existed, predetermined, before you looked. The information was in the second particle all along; quantum mechanics just hadn't told you it was there. Therefore quantum mechanics is incomplete.

This argument was so elegant, and Einstein so famous, that it stopped the conversation cold. Bohr eventually replied with something nobody quite understood. The paper sat there for thirty years, a kind of philosophical embarrassment that working physicists mostly chose to ignore. There seemed to be no way to test whether Einstein was right or wrong. It was just an argument about words.

§1.2Thirty years later, Bell

Enter John Stewart Bell. Born in Belfast in 1928, son of a horse trader, the only one of four siblings to attend university. By the early sixties Bell had become a quiet but respected theoretical physicist at CERN — the European particle-physics laboratory in Geneva. He was on sabbatical in 1963–64, spending time at SLAC in California, Brandeis, and the University of Wisconsin. Among his hobbies, in his off-hours, was thinking about whether Einstein had been right.

Bell's contribution, when it came, was so simple that several physicists later said they could have done it themselves had they only thought to try. He noticed something Einstein and everyone else had missed: the question wasn't whether the second particle's answer was predetermined. The question was whether any local theory in which the answers were predetermined could match all the predictions of quantum mechanics, across every measurement you might choose.

That's a much sharper question. It turns out — as Bell proved in the next six pages — that the answer is no. There exist specific experiments where any local "predetermined-answers" theory must give one set of statistics, and quantum mechanics must give a different set. So the universe itself can settle the dispute. You just have to do the experiment.

The rest of this book walks you through Bell's argument. We're going to set up the experiment Bell described, see what quantum mechanics predicts will happen, see what any "Einstein-style" theory must predict, and watch the two predictions come apart. By the end you'll understand what was actually proved, and what wasn't.

§1.3Two boxes, two dials

Here's the setup. There's a small device in the middle of a long room. Every few seconds, when we press a button, it spits out two tiny particles in opposite directions — one to the left, one to the right. Don't worry about what the particles "are." For our purposes, they're just objects with one important property: they were born together and they "remember" each other.

At each end of the room there's a measurement box. Inside each box is a piece of equipment with two parts:

• A dial the scientist can turn to any angle they like — 0°, 17°, 90°, anything. They can change it before each particle arrives.
• A light that flashes either ▲ or ▼ when the particle is measured.

That's all that comes out: a single up-or-down flash, once per particle. No degrees, no continuous reading. One bit of information, per box, per particle.

Two scientists run two such boxes — let's call them Alice on one side of the lab, Bob on the other. They press the source button. A pair of particles flies out: Alice's goes left, Bob's goes right. Both boxes flash. Alice writes down what her dial was set to and which way her light flashed; Bob does the same on his side. They press the button again. And again. Thousands of times. Then they meet in the middle and lay their notebooks side by side.

§1.4The pattern in the data

Here's the first thing they notice: each notebook, taken alone, looks completely random. About half the flashes are ▲, about half are ▼. There is no detectable pattern in either set of results, no matter what dial setting was used. If you handed Alice's notebook to a stranger, they'd see what looks like a sequence of fair coin flips.

The pattern only appears when you compare the two notebooks side by side, trial by trial.

Start with the easiest case: the trials where Alice and Bob happened to set their dials to the same angle. Maybe they both, by coincidence, picked 30°. Look at every trial where this happened. What do you find?

Their lights flashed oppositely on every single one. Every time Alice's box went ▲, Bob's went ▼. Every time hers went ▼, his went ▲. Not "usually." Always. The pairing is perfect. Across thousands of same-dial trials, the lights are exactly anti-correlated.

That alone might not seem so strange — we'll see in the next chapter that there's a very natural sealed-envelope explanation for it. The strange part is what happens when Alice and Bob's dials don't match. As the angle between their two dials grows, the perfect anti-correlation breaks down — but it breaks down in a very specific, very smooth way.

Three things to notice about this curve. First, it isn't an artefact — it's exactly what quantum mechanics predicts, in a formula so simple we don't need to write it down: at angle θ, the lights match a fraction sin²(θ/2) of the time. Don't worry about the formula; just note that the values 0%, 50%, 100% at angles 0°, 90°, 180° fall right out of it.

Second, when this experiment has actually been performed in real laboratories — first by Stuart Freedman and John Clauser in 1972, then with progressively tighter controls by Alain Aspect, Anton Zeilinger, and many others over the following fifty years — the curve is exactly what experimenters find. There is no doubt that this is what the universe does.

Third, the shape of the curve seems innocent enough. A smooth arc. What could possibly be controversial about a smooth arc? And yet that smooth arc is the entire engine of the next two chapters. Bell's accomplishment was to show that this specific shape, more than any "straight line" or other equally smooth alternative, is impossible to produce by any sealed-envelope theory.

§1.5Why this bothered Einstein so much

Let's circle back to Einstein and the 1935 paper. Why should he have cared about this shape, this curve, these flashes? What was he actually worried about?

Take a single trial. Suppose Alice sets her dial to 30° and her light flashes ▲. Because of the same-dial result we just saw, we know with certainty that if Bob's dial were also at 30°, his light would have flashed ▼. So before Bob even checks his result, before any signal could possibly have travelled between the two boxes, the answer to "what would Bob get at 30°?" is fixed.

So how does Bob's particle know? Two stories:

1. The boring story. Bob's particle was carrying its answer all along, like a sealed envelope it had with it from the moment it left the source. Alice's measurement just reveals which envelope she got; Bob's particle has the matching one. Nothing actually crosses the gap between them. The "instant correlation" is just the mundane fact that the two envelopes were prepared together at a common origin.
2. The spooky story. When Alice measures her particle, something — some signal, some influence, some metaphysical hand — reaches across to Bob's particle and tells it what to do. Faster than light, if necessary. Spooky.

Einstein was sure the boring story had to be right. The spooky story would violate everything he believed about how the universe is allowed to work. Of course there are envelopes. The job of physics, he thought, was to figure out what's written on them. Quantum mechanics, by refusing to even discuss the envelopes, was just being incomplete.

And for thirty years it really did look like there was no way to tell the boring story from the spooky one. Both predicted the same outcomes for any single particle. Both could be made to fit any single measurement. The dispute looked, for all the world, like an argument about preferences rather than physics.

Then John Bell, in 1964, found a measurement that the boring story cannot account for. The next two chapters are the proof.