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Quantum entanglement is very misunderstood. Partly because commentators often use inaccurate phrases like "this particle over here can affect that particle over there instantaneously", implying faster-than-light communication. Quantum mechanics (of which entanglement is a natural and necessary part) says no such thing. Nothing affects anything else. Nothing travels faster than light. Nonetheless, Einstein was right when he said it is "spooky".

Quantum mechanics is a piece of mathematics that describes the behaviour of systems remarkably well. At its heart, a system is described by a complex function, the so-called wave function (the word "wave" is somewhat an historical misnomer). The wave function contains imaginary numbers. It is not real. It cannot be observed. But you can calculate what it is for a system. This imaginary entity occupies all of space, and you can calculate how it evolves over time. What it represents is probability. If you know the wave function at any moment you can use it to tell the probability of measuring some property that you can observe - like the position of a particle or its momentum or spin.

How does the mathematics work then? Well, the wave function is constructed from a set of underlying "pure" states. For example, an isolated electron can only have its spin 100% up or 100% down. Don't worry about what up or down mean. The important point is that these might be considered "pure" states. The actual wave function at a point in time is constructed as a sum (superposition) of these possible states. You might deduce it is 20% up plus 80% down. Or 50% up and 50% down. What it means is that if you measure the spin you can use those numbers to predict the likelihood of seeing up or down in your experiment. Once you measure it you know whether it is up or down. You have "selected" one of the pure states through a measurement.

That might just sound like mathematical cookery. You might figure in reality it was up or down all along. You just didn’t know which. Well, the mathematics, borne from experiment, really does imply that the system can only be described as a mixture of states until you make a measurement. The outcomes of certain experiments would be different if this were not the case. Read up on Bell Inequalities for details. You may also ask, what about other measurables like position? Following the same logic, the state of the system must be a sum of all possible positions and not necessarily up/down-ness. And that is true. You can build the same complex state function as the sum of the pure states of any observable. Think about that. It means if you select a pure spin state via a measurement then the representation using pure position states must now be different. Measuring spin will change what will happen if you now measure position! Starting to sound a bit spooky?

Now, in reality, everything is entangled with everything else. Entanglement happens whenever things interact (exchange conserved quantities such as energy, momentum, charge, spin). Interactions happen all the time. In fact, the trick to doing quantum experiments is to isolate (unentangle) 1 particle and then entangle it with only 1 other. This has to be done with great care. Let's suppose you managed to create 2 entangled electrons through some interaction. Spin conservation may mean they must have opposite spin. If 1 is spin up, the other must be spin down, and vice versa. These up/down and down/up configurations are now the pure states. The actual state (according to quantum mechanics) is a sum of these two. It may be 50% up/down plus 50% down/up. Just as with the single electron case, if you make a measurement, 1 of these 2 pure states is "selected". You either select up/down or down/up. I.e. if you measure the first electron and the spin is up, you know you've selected the up/down pure state. The other electron must therefore be down. That is all quantum mechanics says. No more, no less. Also, as with the single particle case, you can do some freaky experiments with it. Read up on the delayed choice quantum eraser as an example.

The reason Einstein thought it is spooky is that the fabric of our Universe seems to be a thing that is spread out over all space (and time) and is some blend of all the possible alternate realities we might get from a measurement. If we make a measure then 1 of these blended realities is "selected". That selection occurs over all space instantaneously. Certainly spooky to me. It sounds like some signal is propagated instantaneously from the place where the measurement happened. But quantum mechanics says no such thing. It simply says a pure state (that itself occupies all space) is selected.

What people find wholly unsatisfying is that quantum mechanics says absolutely nothing about what that reality actually is or how the state selection happens. Quantum mechanics is silent on this. The maths works but what it means is not understood by anybody. This is the so-called "measurement problem", or the "interpretation problem", in quantum mechanics.

Notations;

Rob Williams

PhD in Physics, Keele University (Graduated 1990)

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