Quantum entanglement

A non-physicist friend expressed deep puzzlement about measurements at opposite ends of the Universe being somehow linked. Here I describe what I take to be the current state of theoretical and experimental knowledge about the “spooky action at a distance” that bothered Einstein and many other people.

The aspect of quantum mechanics that is pretty widely known and accepted is that small objects (atoms, electrons, nuclei, molecules) have “quantized” properties and that when you go to measure one of these quantized properties you can get various results with various probabilities. For example, an electron can have spin “up” or “down” (counterclockwise or clockwise rotation as seen from above; the Earth as seen from above the North Pole rotates counterclockwise, and we say its spin is up if we take North as “up”). The Earth, being a large classical object, can have any amount of spin (the rate of rotation, currently one rotation per 24 hours). The electron on the other hand always has the same amount of spin, which can be either up or down.

Pass an electron into an apparatus that can measure its spin, and you always always find the same amount of spin, and for electrons not specially prepared you find the spin to be “up” 50% of the time and “down” 50% of the time. (It is possible to build a source of “polarized” electrons which, when passed into the apparatus, always measure “up”, but the typical situation is that you have unpolarized electrons, with 50/50 up/down measures.) It is a fundamental discovery that with a beam of unpolarized electrons it is literally impossible – not just hard, but impossible – to predict whether the spin of any particular electron when measured will be up or down. All you can say is that there is a 50% probability of its spin being up. It’s also possible to prepare a beam of partially polarized electrons, where for example you know that there is a 70% probability of measuring an electron’s spin to be up, but that’s all you know and all you can know.

So much for a review of the probabilistic nature of measuring a quantized property such as spin for a single tiny object. Next for the aspect of quantum mechanics that is less widely appreciated, which has to do with measures on one of a group of tiny objects. A simple case is two electrons that are in a “two-particle state”, where one can speak of a quantized property of the combined two-particle system. For example, in principle it would be possible to prepare a two-electron state with total spin (“angular momentum”) zero, meaning that electron #1 could be up, and electron #2 would be down, or vice versa. As a matter of fact, it was only in the last few decades that experimental physicists learned how to prepare such multiparticle states and make measurements on them, and it is these experiments, together with superb theoretical analyses, that have clarified the issues that worried Einstein. (Actually, most experiments have involved photons rather than electrons, but I’ve chosen the two-electron system as being more concrete in being able to make analogies to the spinning Earth.)

Suppose Carl prepares a zero-spin electron pair and gives one electron to Alice and the other to Bob (Alice and Bob are in fact names used in the scientific literature to help the reader keep straight the two observers.) Alice and Bob keep their electrons in special carrying cases carefully designed not to alter the state of their electron. They get in two warp-speed spaceships and travel to opposite ends of our galaxy or, if one prefers, to opposite ends of the Universe (if the Universe has ends). Many years later, Alice measures the state of her electron and finds that its spin is up (there’s an arrow pointing up on her carrying case indicating what will be called “up”, and a similar arrow pointing up on Bob’s carrying case). If Bob measures his electron, he will definitely find its spin to be down.

One might reasonably interpret these observations something like this: Carl happened to give Alice an “up” electron and (necessarily) gave Bob a “down” electron. There was a 50/50 chance of giving Alice an up electron, and this time Carl happened to give her an up electron. Then of course no matter how long Alice waits before measuring her electron, she’s going to find that it is “up”, and no matter how long he waits Bob is going to find that his electron is “down”. Yes, there are probabilities involved, because neither Carl nor Alice knows the spin of the electron until Alice makes her measurement, but the electron obviously “had” an up spin all the time.

The amazing truth about the Universe is that this reasonable, common-sense view has been shown to be false! The world doesn’t actually work this way!

Thanks to major theoretical and experimental work over the last few decades, we know for certain that until Alice makes her measurement, her electron remains in a special quantum-mechanical state which is referred to as a “superposition of states” – that her electron is simultaneously in a state of spin up AND a state of spin down. This idea is very hard to accept. Einstein never did accept it. In a famous paper in the 1930s, he and a couple of colleagues proposed experiments of this kind and, because quantum mechanics predicts that the state of Alice’s electron will remain in a suspended animation of superposed states, concluded that quantum mechanics must be wrong or at least incomplete. It took several decades of hard work before experimental physicists were able to carry out ingenious experiments of this kind and were able to prove conclusively that, despite the implausibility of the predictions of quantum mechanics, quantum mechanics correctly describes the way the world works.

I find it both ironic and funny that Einstein’s qualms led him to propose experiments for which he quite reasonably expected quantum mechanics to be shown to be wrong or incomplete, only for it to turn out that these experiments show that the “unreasonable” description of nature provided by quantum mechanics is in fact correct. These aspects of quantum entanglement aren’t mere scientific curiosities. They lie at the heart of work being done to implement quantum computing and quantum encryption.

What about relativity, and that nothing can travel faster than light? Not a problem, actually. The key point is that Alice cannot send any useful information to Bob. She cannot control whether her measurement of her electron will be up or down. Once she makes her “up” measurement, she knows that Bob will get a “down” measurement, but so what? And all Bob knows when he makes his down measurement is that Alice will make an up measurement. To send a message, Alice would have to choose to make her electron be up or down, as a signal to Bob, but the act of forcing her electron into an up or down state destroys the two-electron “entangled” state.

I recommend a delightful popular science book on this, from which I learned a lot, “The Dance of the Photons” by Anton Zeilinger. Zeilinger heads a powerful experimental quantum mechanics group in Vienna that has made stunning advances in our understanding of the nature of reality in the context of quantum mechanics. In this book he makes the ideas come alive. The book includes detailed discussions of Bell’s inequalities and much else (Bell was a theoretical physicist whose analyses stimulated experimentalists to design and carry out the key experiments in recent decades).

It seems highly likely that Zeilinger will get the Nobel Prize for the work he and his group have done. A charming feature of the book is that Zeilinger is very generous in giving credit to many others working in this fascinating field. Incidentally, there is some movement in the physics community to bring contemporary quantum mechanics into the physics major’s curriculum, which in the past has been dominated by stuff from the 1920s.

Bruce Sherwood

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