I have to say right off the bat, I'm a little frustrated that there seem to be very contradictory answers about this, at least to a layman like me. If two particles are entangled and you separate them by some huge distance, and you measure one of the spins, you know the other particle must be spinning the opposite direction.
The usual analogies I hear are things like, well if you have a blue and red marble, you scramble them in a bag and then take one blindly, and give the other to your friend, if you look at your marble and see blue, you know your friend must have red.
To me this sounds like "boringly classical pre-determination." Like this whole spooky action at a distance is really just "the spins were already opposite to begin with and we just separated them," as if we had a machine that spat out pairs of opposite-colored marbles and now we're surprised that they're always opposites regardless of how far apart we are when we see them.
At the same time people say it's not like that either (Bell's inequalities). In quantum mechanics the state of something is in this weird superposition where it's not known for sure — it's sort of everything at the same time and it only takes on a particular state according to a probability distribution. So the two particle spins are unknown and yet somehow when you observe one, it "communicates" to the other (regardless of distance) what its state is so it "knows" to become to opposite.
But apparently it's not that either and there's no communication actually taking place or information passing from one to the other, and this is what really gets my goat. The usual response is that we cannot choose what the state is or input any kind of information that can come out the other end.
I feel this answer is a bit of a cop-out because it doesn't address the confusion, just sort of attacks low-hanging fruit over some semantic difference in the word "communication" even though what is really being asked is the sort of cause-effect relationship going on. I am fine with the idea that we can't directly input what we want or use it to communicate. But how is it not a form of "the particle is communicating something" or "causing" or "influencing" something to happen in the other?
Normally this discussion goes nowhere and someone inevitably says "Well you just have to learn quantum mechanics." I always find this answer deeply unsatisfying. It feels like the other person is giving up on you and can't be bothered to explain it.
So… what's going on? I'm not stupid but I'm also frustrated that these two interpretations both seem to be wrong and yet no one can actually seem to address the core point of confusion despite Googling this question across blogs, news articles, Reddit, Physics forums, Quora, etc.
It's always the same back-and-forth. "There's no communication… but it's not like the states were known to begin with either." How on earth is there a third possibility to this?
Best Answer
In short:
That said, you're certainly correct in one respect: there's a lot of very poor descriptions of what entanglement is and how it works in the popular-science press. In particular, these two paragraphs do a very good job of summing up a very common misconception that arises from poorly-written material:
Your interpretation of that description is indeed correct. However, quantum-mechanical entanglement goes much further than that property, and this is exactly the content of Bell's theorem.
To be more precise, Bell's theorem is a description of systems that use "boringly classical pre-determination" (known in the technical lingo as Hidden-Variable Theories) to produce correlated outcomes, and it makes quantitative statements about which kinds and what amounts of correlations you can expect from such a system.
Bell's bigger argument then goes on to construct quantum-mechanical states that break those bounds, and which therefore (provably) cannot be explained with "boringly classical pre-determination" at all. And, when we talk about Bell-test experiments, we refer to experiments that implement those states and show that you do indeed get more correlations than classical pre-determination can produce.
This does raise the question about how your initial model,
fails to describe the quantum systems at play. The answer is that this classical model is unable to describe superposition states between the blue-marble and red-marble states of each bag, and for the quantum-mechanical description to work at a level where it can exceed the classical bounds on correlations, it needs to be able to measure on the superposition state $$ |\text{blue marble}⟩ + |\text{red marble}⟩ $$ and to distinguish it from the 'conjugate' superposition state $$ |\text{blue marble}⟩ - |\text{red marble}⟩, $$ where that $-$ sign is a truly new, fully quantum-mechanical ontological feature that doesn't exist in classical mechanics.
OK, so it's not classical pre-determination. But is it faster-than-light communication, then?
Well... also no, this time because of another theorem of quantum mechanics - the No-Communication Theorem. This theorem states that, if you have any arbitrary entangled states linking two parties, and you allow them to perform any arbitrary physical operation on them, it is provably impossible to transmit a message in any way other than classical communication.
But that's at the level of the (ostensibly human) operators of the experiment, though. Do the particles themselves communicate?
And the answer here is that yes, it's not inconceivable that they do. More to the point, it is a consistent interpretation of quantum mechanics to suppose that there is a hidden-variable theory that underpins QM. Since Bell's theorem rules out hidden-variable theories which are 'local' and 'realist', the price for doing so is that those variables need to be 'non-local', which basically means that changes in those variables can propagate at FTL speeds.
However, the price for that is that the No-Communication Theorem requires that, to be consistent with QM, such a hidden-variable theory needs to somehow make that FTL communication completely inaccessible above the quantum-mechanical layer of the description. And that then means that, when you build those theories, they come out looking extremely contrived and artificial.
And here is where it gets subjective: most working quantum mechanicists are extremely uncomfortable with those theories as models of what reality is "really like". There are very good reasons to be uncomfortable with them, but $-$ as in all things where the interpretations of quantum mechanics are concerned $-$ this is ultimately a subjective thing.
Now as for the bulk of the text that you've written $-$
Your observation is correct: this is indeed unsatisfying. But the hard truth is that, while it would be wonderful to know what's "really going on" between two entangled particles, we simply don't know. There's a broad array of proposals of how one should understand this, but they all have serious drawbacks and for each of them there's multiple reasons to think that it's completely bonkers.
We do know a lot about entanglement:
But as to what's "really going on", we just don't know.
Judging from your text, it sounds like you already have a pretty decent understanding of the epistemology around entanglement, and that you've reached the kind of grounded frustration at the weirdness of the theory that's widely shared among working physicists. We know it's weird. We agree that it ultimately makes very little sense. We absolutely would like a better answer. We are actively searching for better answers, and we are making decent progress $-$ we are indeed advancing the state of the theory, bit by bit, and we're getting better and better at examining single quantum systems in ways that allow us to test QM in finer and finer ways. But we've yet to find that better answer.