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The Einstein quotes are rather apt. There was a famous disagreement between some well known physicists about what quantum entanglement meant for the principle of locality. The argument that you explain above is the same as that used by some of the brightest minds in physics in the 1930s, including Einstein: http://en.wikipedia.org/wiki/Bohr-Einstein_debates#The_argum...

It was a hotly debated topic for several decades. Until 1964 we weren't even sure we could ever resolve it, then a fellow named John Bell published a testable theorem showing a divergence between quantum mechanics and the classical explanation you have above (http://en.wikipedia.org/wiki/Bell's_theorem). In 1972, the first successful experiment of this theorem was performed, and incredibly, it showed entanglement is in fact more complicated than can be explained with classical mechanics http://en.wikipedia.org/wiki/Bell_test_experiments. The experiments have been repeated and refined over the years and little by little, the once common theory of local variables is now almost completely dead.

Notice that I say 'I shoot' above, so the moment you start to look at correlations, I start to decide into which pockets I shoot. ( For example determined by the results of an EPR experiment.) However, my rant is not so much about details of entanglement as it is about science journalism, after I have read the entire article, I still have no idea what the paper is about.

You are misunderstanding the physics. Suppose A and B are two quantum entities that result from a collision. They are entangled and moving away from each other. The math very clearly says that a modification of A's state will alter B's state after the time of collision. In fact, it must do so, since A and B do not have separate states. Their states are the same one little chunk of math.

This even works if the states are known! This is how quantum cryptography works. You put two particles into Bell state with each other, give one to someone else, and then decide later what message you want to send.

I recommend learning the math. It is pretty simple if you already have linear algebra.

Well, what I am saying is, that the state of two entangled photons (with polarization +,-) is

    s_e= a |+-> + b |-+>

and not

    s_n= a |+-> + b |-+> + c |--> + d |++>

as is the case for two arbitrary photons. ( See also my post script to the original post.)

I don't know why you think that?

a|+-> + b|-+> is a very special-case entanglement. Yes, you'll see that one mentioned in Wikipedia (and quantum cryptography and etc) because it's very simple.

The general form for the states of two photons is exactly as you have listed for s_n. For some coefficient values of a, b, c, d, the photons are "entangled", for some, they are not "entangled". How do you know which is which? It is whether you can factor the polynomial into two separate expressions of the form (x|+> + y|->). If you can do this, the photons are not entangled; if you cannot do it, they are entangled.

Since most sets of (a, b, c, d) represent unfactorable expressions, you would expect almost any expression chosen at random to represent an entangled pair. Clean un-entanglement is the rare exception.

Clean un-entanglement is the rare exception.

This is true only for pure-state entanglement (which itself is a rare exception ;-).

If that's all there was to entanglement, we would just use the term "ignorance of the actual state". The issue with entanglement is that the system will show properties of being in _both states at once_, which is distinct from being in one unknown state, which is your analogy. There's really no classical analogy that I know of that correctly fits entanglement in QM.

The most-cited analogy would be Shrodinger's Cat: http://en.wikipedia.org/wiki/Schr%C3%B6dinger's_cat

Entanglement arises from the mix of mutual exclusive states and superposition. Superposition of two states is what is missing in the classical world.

I would call being in both states at once a quantum phenomenon, which has not much to do with entanglement.

I think you're misrepresenting this. In your example, the colour of both balls is fixed the whole time. In entanglement, it isn't fixed the whole time. It's not fixed until observed. We take them a light-year apart, and they don't have any value. When we look, one will be "up" and one will be "down," but until we look, it's not decided.

Then we look at one, and it is decided. If someone a second later looks at the other one, a light year away, it will be the opposite state. That has also been decided. Us looking at something over here caused a decision about what state something is in to be made over there, a light-year away. How did us doing something here affect a decision a light-year away? Two seconds ago the state of that particle a light year away was undecided; the "universe" had not given it a value. Then we did something here, and that particle a light year away had its value fixed. It did not have that value the whole time while we were moving the particles apart, but now it does.

I don't think that I am misrepresenting this, however I should perhaps have made clearer what I mean by classical vs. quantum. So I take the view, that entanglement can be traced back to the smaller than naively expected state space, which is something that can be constructed in classical physics. If you then quantize such a system, then the system would be in a superposition of the classical states.

The problem of local realism then arises from this smaller state space and the collapse of the wave function during the measurement.

So are you saying it is, or is not, odd that a decision made here can affect something a light year away? If you don't find that odd that's great for you; you obviously have a far more intuitive understanding of the universe than most people.

Assuming that it actually effects a particle at a distance, it is odd. But I simply see it as a oddity of the collapse of the wave function, which is no more surprising than finding just one photon in a double slit experiment even when the detectors are space like separated.

If that's all it was, it wouldn't be so mysterious. It's been shown that the billiard ball can be either red or white up until the point you check it, and that the other ball will spontaneously resolve.

That's based off what I know, though, I may be wrong.

Yep, Bell's Theorem [1] states that it's more than just a question of not knowing which is which ahead of time.

[1] http://en.wikipedia.org/wiki/Bell%27s_theorem