It all began in October 1927, at the Fifth Solvay Congress in Brussels. It was Louis de Broglie’s first congress, and he had been “full of pleasure and curiosity” at the prospect of meeting Einstein, his teenage idol. Now 35, de Broglie happily reported: “I was particularly struck by his mild and thoughtful expression, by his general kindness, by his simplicity, and by his friendliness.”

Back in 1905, Einstein had helped pioneer quantum theory with his revolutionary discovery that light has the characteristics of both a wave and a particle. Niels Bohr later explained this as “complementarity”: depending on how you observe light, you will see either wave or particle behaviour. As for de Broglie, he had taken Einstein’s idea into even stranger territory in his 1924 PhD thesis: if light waves could behave like particles, then perhaps particles of matter could also behave like waves! After all, Einstein had shown that energy and matter were interchangeable, via *E* = *mc*^{2 >. }

Einstein was the first to publicly support de Broglie’s bold hypothesis. By 1926, Erwin Schrödinger had developed a mathematical formula to describe such “matter waves”, which he pictured as some kind of rippling sea of smeared-out particles. But Max Born showed that Schrödinger’s waves are, in effect, “waves of probability”. They encode the statistical likelihood that a particle will show up at a given place and time based on the behaviour of many such particles in repeated experiments. When the particle is observed, something strange appears to happen. The wave-function “collapses” to a single point, allowing us to see the particle at a particular position.

Born’s probability wave also fitted neatly with Werner Heisenberg’s recently proposed “uncertainty principle”. Heisenberg had concluded that in the quantum world it is not possible to obtain exact information about both the position and the momentum of a particle at the same time. He imagined the very act of measuring a quantum particle’s position, say by shining a light on it, gave it a *jolt* that changed its momentum, so the two could never be precisely measured at once.

When the world’s leading physicists gathered in Brussels in 1927, this was the strange state of quantum physics.

The official photograph of the participants shows 28 besuited, sober-looking men, and one equally serious woman, Marie Curie. But fellow physicist Paul Ehrenfest’s private photo of intellectual adversaries Bohr and Einstein captures the spirit of the conference: Bohr looks intensely thoughtful, hand on his chin, while Einstein is leaning back looking relaxed and dreamy. This gentle, contemplative picture belies the depth of the famous clash between these two intellectual titans – a clash that hinged on the extraordinary concept of quantum entanglement.

At the congress, Bohr presented his view of quantum mechanics for the first time. Dubbed the Copenhagen interpretation, in honour of Bohr’s home city, it combined his own idea of particle-wave complementarity with Born’s probability waves and Heisenberg’s uncertainty principle.

Most of the attendees readily accepted this view, but Einstein was perturbed. It was one thing for groups of particles to be ruled by chance; indeed Einstein had explained the jittery motion of pollen in apparently still water (dubbed Brownian motion) by invoking the random group behaviour of water molecules. Individual molecules, though, would still be ruled by Newton’s laws of motion; their exact movements could *in principle* be calculated.

By contrast, the Copenhagen theory held that subatomic particles were ruled by chance.

Einstein began his attack in the time-honoured tradition of *reductio ad absurdum* – arguing that the logical extension of quantum theory would lead to an absurd outcome.

After several sleepless nights, Bohr found a flaw in Einstein’s logic. Einstein did not retreat: he was sure he could convince Bohr of the absurdity of this strange new theory. Their debate flowed over into the Sixth Solvay Congress in 1930, and on until Einstein felt he finally had the pieces in place to checkmate Bohr at the seventh congress in 1933. Two weeks before that, however, Nazi persecution forced Einstein to flee

to the United States. The planned checkmate would have to wait.

When it came, it was deceptively simple. In 1935 at Princeton, Einstein and two collaborators, Boris Podolsky and Nathan Rosen, published what became known as the Einstein-Podolsky-Rosen paradox, or EPR for short. Podolsky wrote up the thought experiment in a mathematical form, but let me illustrate it with jellybeans.

Suppose you have a red and a green jellybean in a box. The box seals off the jellybeans from all others: technically speaking, the pair form an “isolated system”, and they are “entangled” in the sense that the colour of one jellybean gives information about the other. You can see this by asking a friend to close her eyes and pick a jellybean at random. If she picks red, you know the remaining sweet is green.

This is key to EPR: by knowing the colour of your friend’s jellybean, you can know the colour of your own without “disturbing” it by looking at it. But in trying to bypass the supposed observer-effect in this way, EPR had also inadvertently uncovered the strange idea of “entanglement”. The term was coined by Schrödinger after he read the EPR paper .

So now apply this technique to two electrons. Instead of a colour, each one has an intrinsic property called “spin”. Imagine something like the spin axis of a gyroscope. If two electrons are prepared together in the lab so that they have zero total spin, then the principle of conservation of angular momentum means that if one of the electrons has its spin axis up, the other electron’s axis must be down. The electrons are entangled, just as the jellybeans were.

With jellybeans, the colour of your friend’s chosen sweet is fixed, whether or not she actually observes it. With electrons, by contrast, until your friend makes her observation, quantum theory simply says there is a 50% chance its spin is up, and 50% it is down.

The EPR attempt to strike at the heart of quantum theory now goes like this. Perhaps the spin of your friend’s electron was in fact determined before she picked it out. However, like a watermark that can’t be detected until a special light is shone on it, the spin state is only revealed when she looks at it. Quantum spin, then, involves a “hidden variable”, yet to be described by quantum theory. Alternatively, if quantum mechanics is correct and complete, then the theory defies common sense – because as soon as your friend checks the spin of her electron, your electron appears to respond *instantly*, because if hers is “up” then yours will be “down”.

This is because the correlation between the two spins was built into the experiment when the electrons were first entangled, just as putting the two jellybeans in a box ensures the colour of your jellybean will be “opposite” that of your friend’s. The implications are profound. Even if your friend moved to the other side of the galaxy, your electron would “know” that it must manifest the opposite spin in the instant she makes her observation.

Of course, instant action violated Einstein’s theory of relativity: nothing can travel faster than the speed of light. Hence Einstein dubbed this absurd proposition “spooky action at a distance”.

But there was more. Spin is not the only property your friend could have chosen to observe. What EPR showed, then, is that the physical nature of your electron seems to have no identity of its own. Rather, it depends on how your friend chooses to observe her electron. As Einstein put it: “Do you really believe the Moon is there only when you look at it?” The EPR paper concluded: “No reasonable definition of reality could be expected to permit this.” Ergo, the authors believed, quantum theory had some serious problems.

Bohr was stumped by EPR. He ditched the idea that the act of measurement jolted the state of the particle. (Indeed, later experiments would show that uncertainty is not solely the result of an interfering observer; it is an inherent characteristic of particles.)

But he did not abandon the uncertainty at the heart of quantum mechanics. Instead of trying to wrestle with the real world implications, he concluded that we can only speak of what we observe – at the beginning of the experiment and the end when your friend’s electron is definitely “up”, say. We cannot speak about what happens in between.

Einstein and Bohr continued to debate the issue for the rest of their lives. What they really disagreed about was the nature of reality. Bohr believed that nature was fundamentally random. Einstein did not. “God does not play dice with the universe,” he declared.

Nevertheless, Einstein knew that quantum theory accurately described the results of real as opposed to thought experiments. So most physicists considered that Bohr had won. They focused on applying quantum theory, and questions about the EPR paradox and entanglement became a niche interest.

In 1950, Chien-Shiung Wu and Irving Shaknov found oddly linked behaviour in pairs of photons. They didn’t know it at the time but it was the first real-world observation of quantum entanglement.

Later, David Bohm realised Wu and Shaknov’s discovery was an opportunity to take entanglement out of the realm of thought experiments and into the lab. Following Bohm, in 1964 John Bell translated the two EPR alternatives into a mathematical relationship that could be tested. But it was left to other experimenters – most famously Alain Aspect in 1981 – to carry out the tests.

Einstein’s hopes of finding hidden variables that would take the uncertainty out of quantum theory were dashed. There seemed no escaping the bizarre consequences of EPR and the reality of entanglement.

But does this also mean “spooky action at a distance” is real? Entanglement in electrons has been demonstrated at distances of a kilometre or two. But so far that’s too short a distance to know if faster-than-light interactions between them were involved. Things may soon become clearer: at the time of writing, Chinese scientists have just announced the successful transmission of entangled photons from an orbiting satellite over distances of more than 1,200 km.

On the other hand, some physicists have recently taken up Einstein’s side of the argument. For instance, in 2016 Bengt Nordén, of Chalmers University in Sweden, published a paper entitled, “Quantum entanglement: facts and fiction – how wrong was Einstein after all?” Against Bohr’s better judgement, such physicists are once again asking about the meaning of reality, and wondering what is causing the weird phenomenon of entanglement.

Some even suggest that something like a “wormhole” – a tunnel in spacetime between two widely separated black holes, a consequence of general relativity theory first deduced by Einstein and Rosen – may be the mechanism underlying entanglement. The mythical faster-than-light tachyon is another possible contender.

But nearly everyone agrees that whatever is going on between entangled particles, experimenters can only communicate their observations of entangled particles at light speed or less.

Entanglement is no longer a philosophical curio: not only are physicists using it to encrypt information and relying on it to underpin the design of tomorrow’s quantum computers, they are once again grappling with the hard questions about the nature of reality that entanglement raises.

Ninety years after the Fifth Solvay Congress, Einstein’s thought experiments continue to drive science onwards.