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Can someone put entanglement in laymens terms? I understand that photon spin affects an entangled photon across any distance, what I don't understand is how spin works, does a photon only have "spin after its measured", and if so, doesn't this have massive communication applications? I haven't taken physics yet, so keep that in mind.

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I will give you an everyday example of entanglement. Suppose that you knew a pair of twins , Paul and James, and you were told how lucky they were because each had become a director of a bank, one in Philadelphia and the other in New York. If you meet Paul in the bank in Philadelphia you immediately know that James has the post in New York.

With photons and other elementary particles and quantum mechanical systems, there exists a mathematical function ( analogous to the knowledge of who Paul and who James is) , when one measures a part of the system, inevitably, due to the mathematics, you know what the rest of the system is.

In case of photon spin, take a pi0 meson which decays into two photons. If one measures the spin of one of the photons to be +1, one immediately knows that the other that left unmeasured has a spin of -1, because of the functional dependence due to the decay , no matter how far away it has gone.

Basically, the state of photon 2 depends (is entangled) with what is going on with photon 1, even if they are far apart. The photons are entangled , tied up to each other, due to the mathematical function that connects them and the nature of a measurement.

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I want to add to the (otherwise excellent) answer of anna v. Because from that answer it sounds like it's not such a big deal, right? The photons could have been sent out as (photon 1: +1, photon 2: -1) or as (photon 1: -1, photon 2: +1), so if you measure one you'll obviously know the other immediately.

The crazy thing about it is that until we measure one of the photons, we are neither in the one case nor in the other. This can be experimentally confirmed, but it's probably difficult to understand if you haven't taken physics yet. The keyword here is Bell inequalities.

Maybe you can get some kind of intuitive grasp if you know that this property "spin" can be measured along different directions. And once you have measured the spin of one of the photons in some direction, the spin of the other one will be aligned along the direction the first one was measured in, and exactly opposite.

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A photon always has spin. The question is how much of that spin is projected along a certain axis (usually the convention is to choose the z axis, but this is arbitrary and we could choose any axis.)

The entanglement part is sort of like this:

Suppose you have 2 photons that are really far apart, and they are in a state that is explained by a function that says $ \psi = (up,down) + (down,up) $. Let (up,down) mean that the first photon is up, and the second photon is down. Let (down,up) mean that the first photon is down and the second photon is up.

When you measure a photon, the system "collapses" (although, the wave function collapse isn't as mystic nowadays as it was 50 years ago) to either (up,down) or (down,up).

So suppose that the photons were $ {really} $ far apart. If you made a measurement on photon 1 and the wavefunction "collapsed" to (up,down) then you know right away that the second photon is down, even when they are lightyears and lightyears away.

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In quantum mechanics a system can be described as an abstract state containing all information we can possibly have about it. We use this information to predict the outcomes of measurements made on that system, but this prediction is intrinsically probabilistic.

Two systems are entangled when we find a correlation between the outcomes of measurements on both systems that is not explainable in terms of classical states. By this I mean that the correlation does not arise from structural or dynamical relationships between the systems that we could understand and model, instead it is there because somehow, and this is very clear in the mathematical framework, although hard to make sense of, both systems are actually one indivisible entity: they are described by the same quantum state, in a superposition of possible configurations, so that it is not possible to, well, "disentangle" them.

What is weird here is that the systems may be spatially separated so that measurements can be made while there is no causal connection between the systems: what happens to one system as we measure it is not able to have an effect to the way the other one is being measured. So the entanglement correlation is non-local, and acausal. It is just there.

It is a correlation between probabilistic distributions, observable at posteriori, which cannot be interpreted as a relationship from cause to effect. And thus, no, it does not lend to any communication application. It is best understood (in my opinion) as a sort of underlying nonlocal symmetry of the physical world.

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