Say we're measuring spins of entangled particles with random entangled spins.

So the real problem isn't that "when one is up, then the other will magically be up too." That could be accomplished with local hidden variables (e.g. shared seeds on a PRNG, or your examples).

The real problem is that when you measure A in the "up" direction, and then B in the "10 degrees east of up" direction, then B seems to know that you measured A in the "up" direction.

That is to say: B's probability distribution as a function of the direction its being measured is correlated to the direction that A is measured. There's no way to construct an "A-independent" probability distribution of B's results for arbitrary directions. The probabilities won't sum to 1 and still match experimental results.

It's unfortunate that "A up" therefore "B up" is a degenerate case of this reality where classicality actually works, because it leads to confusion.

(Also the reason you can't use this magic to communicate FTL is that you can only ask one yes/no question of each particle, and because B's probability distribution is distorted in a symmetric way based upon A's measurement, you're still going to get a 50/50 response for yes/no questions asked of random entangled particles)

Feel free to comment, as I paste this on every misunderstanding of Bell's Theorem here, and I edit to make more clear each time.

What if I have a million A/B pairs, measured in parallel. Each bit is 100 A measurements, 1 for up and 0 for down. Why is this not FTL communication of 10k bits?

Because you can't use it to pass information to someone listening to only a single end of the pair. You have to measure both particles to detect the correlation, or else all you're getting is random noise.

Imagine I'm flashing a light at you on and off, randomly. Some of the flashes aren't random and contain a message. To read the message, or even detect its existence, you have to know which flashes were random, and this is what observing both particles in an entangled pair allows us to do. There is no signal with only a single particle.

It's FTL communication of 10k random bits, whatever that gets you besides a great symmetric encryption key to share between you and the other end.

I also went through a phase where quantum entanglement seemed mundane and easily explained. However, I realized that this was merely because I was taking the analogies too literally.

The key difference between a bag of coins and a microscopic quantum system is that the contents of the bag before being observed is unknown, whereas the quantum state is actually indeterminate. By observing one entangled particle, you force the other to also take on a definite state. Read up on Bell's inequality for the experimental justification of this idea.

In the lab

http://arxiv.org/abs/1511.03189

You didn't even give a decent troll argument against entanglement. What you should've said is that: "I have two bags of coins, one full of silver and one full of copper. I have no idea which is which. I put one bag across town, hidden under a rock. I open up the other bag at home, it's all copper. Thus I know the other bag is all silver. So amazing." In your scenario, you made an observation of what was inside the bags, which is not allowed. It's still a troll argument though, because entanglement is arcane as heck!

To stretch your analogy to breaking point, the explanation that makes the most (least?) sense to me that I've read is thus: First, imagine all the coins have no mass. And a mischevious quantum cat either puts all the copper and sliver coins in the same bag leaving the other empty, or puts all the copper coins in one bag and the silver in the other.

Not knowing which placement has been done, you put one bag in your freezer, and drive across town with the other bag.

Then you ask yourself the question, or perform an experiment to tell you, "Which bag did the cat put all the coins in?", at which point you open the bag and find it full of coins or empty, determining the state of the bag you have, and the state of the bag in your freezer at home.

No problem, huh?

Except, if you'd asked a different question, or performed a different experiment, to tell you "Which bag contains all the copper coins, and which contains the silver coins?" - you would have still got a valid response, and found the bag either full of copper or silver coins, again determining the state of the other bag at home.

That's the nature of entanglement. Without knowing the state, the nature of the question you ask of one particle will determine what sort of answer you get, in a way that instantaneously affects the bag at home too. i.e. someone opening your freezer just after you ask your question will see the other bag in a consistent state with the bag you have.

That's why it's so gorram weird.

Read up on it more, if you care:

http://physics.stackexchange.com/questions/3158/why-is-quant...

http://physics.stackexchange.com/questions/126622/quantum-en...

The choice between locality and realism can be easily summed up as thus:

  Either you believe the state exists but is unknown, and 
  cannot be known until measured,

  or, you believe that you know the state does not exist,
  and materializes upon measurement.

But what these two concepts drive at, is whether or not a single meaningful, distinctive, isolated history determined the current state of the universe, and whether or not there is only one deterministic way to arrive at the present moment.

If you're satisfied that their might be multiple past states which could all produce the same result, determining the current state, then you can safely ignore these semantic debates, about whether there is a concrete-but-unknown value, or whether the present value remains uninitialized and undefined.

crontumCombudor's Dictionary. Science, noun. "A semantic debate."

If you could put the bag into the all-silver state after leaving it across town by taking all the silver coins out of another bag, that would be a big deal.

So magnetize a sample of iron as a permanent magnet, cut the sample in half, send the second half to the moon, and re-polarize first half here on earth, and show me that it's lunar partner has spontaneously re-magnetized itself in agreement with its earthbound phantom amputated Siamese twin. And then back again, ad infinitum.

Is this all a round about way of saying you don't believe in quantum entanglement? Because that would be simpler and I wouldn't bother arguing.

What do you mean by that?

(Obviously you don't mean necessarily literally on paper)

Do you claim that the predictions that are made about what is observed are false, or that the interpretation is wrong, or?

Surely you don't mean that by interpreting it in a particular way, it causes different things to happen, so I can't think of anything other than those two.

I think he means that the "entanglement" as understood by general public, i.e. as "I do something to particle A, and suddenly particle B changes" is an invalid way of reading the math; you didn't do anything to B, you merely figured out, by interacting with A, in which world you're in.

You see, this is the thing that kills me when thinking about the quantum world. The Many Worlds interpretation is so clean and obvious, except for one thing - it requires creating a new universe for each quantum entanglement event. Gah!

Of course that does make me think about forking processes and copy-on-write, and the idea that our reality is just a simulation in a computer and that maybe creating new universes is not as expensive as we might at first think...

I'm starting to think about this along the "zero-worlds interpretation" - i.e. there is only one world, but it's not based on discrete particles with states, but on probability distributions. We perceive the world as if it was already mostly simple, but it's because we too are entangled with stuff. There are no many worlds of particles, because particles are not the building blocks of a world. If you look at it from the hypothetical computer simulating us, it's kind of like storing the set of all natural numbers - you can store slices of it in lists (and then quantum entanglement under MWI works by figuring out in which list you are) vs. storing a generator function.

I admit I'm still in the process of learning and figuring this stuff out.

I believe this is the Bertlmann's socks argument. If you care to dig into this a bit deeper you might just have a braingasm.