After reading some shaky DK discussions of physics issues, I promised (threatened?) to write introductions to the basics of modern physics, relativity and quantum mechanics. The relativity intro was easy and perhaps not too troubling. Now we get into the strange stuff.
The tradition is to present the development of quantum mechanics quasi-historically. The disadvantage of that approach is that one tries to picture the new phenomena in old frameworks, and these pictures tend to persist. So I'm going to follow a different path. In this introduction, we'll just smash the old framework. In the next installment, we'll look at the weird structure that arises from the ruins.
What do we all believe about the world? Einstein thought it was deterministic, that "God doesn't throw dice", but we won't start with any strong opinion like that. We'll start with something much milder, from a paper by Einstein, Podolsky and Rosen:
If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.
So we aren't insisting that nothing be pure chance, just that things which are fully predictable have some actual physical cause. Furthermore, the cause must be located where the effect occurs, not somewhere else or at some point in the future. Borrowing from our discussion of relativity, that means that the causes can't travel around faster than the speed of light. Otherwise, according to perfectly good points of view, they'd travel backwards in time and lead to all sorts of sci-fi paradoxes.
The assumptions I've just described are called "local realism." In our gut, we all believe them. Now I'll describe how we know they are false.
People's eyes glaze over if we talk about unfamiliar particles. So I'll tell a silly story about people. Its logical structure is absolutely identical to the true story we can tell about some smaller stuff.
Say you notice on a moon (your planet has 6 moons) some guy who every second raises one hand or the other. So far as you can tell, he does it randomly. Is it really random, or does he have some hidden system? Looking directly, there's no way to tell. Fortunately, you have two eyes, and can look through trick binoculars at the moon directly opposite his. (No movies are allowed.) There's another guy there, and he raises the same hand each time. There's no time for signals to get from one guy to the other, so they must have got their patterns coordinated ahead of time. You can predict one based on the other, so they are each determined by some "element of reality." Maybe they both came from earth where they picked up matching instructions. There are 3 pairs of moons, and each pair acts this way whenever you check it. So all the guys have "elements of reality" (memorized lists?) telling them which hand to raise when.
Now let's just look at one moon from each pair. We'll call them A, B, and C. With only two eyes, you can only see two at once. When you look at A and B, you find that 85% of the time, they raise the same hand. So their lists must differ 15% of the time. When you look at B and C, you find the same 15% difference.
What do you expect if you now look at A and C? Maybe those 15%'s that each differed from B were the same, so A and C will always agree. Maybe those 15%'s didn't overlap, so A and C will disagree 30% of the time. Or it could be anywhere in between. Simple.
So now you look at A and C. They differ 50% of the time. Impossible. The A and C lists can't both be almost the same as the B list and yet so different from each other.
So those lists couldn't really exist. Maybe only parts of the lists exist, the parts that have instructions for the moons you're looking at. Maybe somehow these moon-men knew which moon pair you'd look at when. So you try switching around which pair of moons you look at each time. Sometimes you use what feels like "free will" to pick a pair of moons. Sometimes you roll dice. Sometimes you use random number generators in your calculator. None of it makes any difference.
Could there be a complete conspiracy, where your "free will", your dice, your random number generators, etc. were all controlled by the same entity that decided which random-looking lists to hand out to the moon men? Sure, we can't rule that out, but we don't believe it.
So if our story were to be true, we'd have shown that the world cannot be described by ANY non-conspiratorial local-realist picture. Somehow, the world "knows" that those guys on opposite moons must raise the same hand even though it has absolutely nothing in it to set which hand it will be. Of course, this story is nonsense.
Nevertheless, many, many stories with identical logical structure, but involving some small-scale events, are simple experimental results. One of my colleagues has set up a version of this experiment for a routine undergrad lab. Undergrads can show violations of the "Bell Inequalities" (one of which you saw illustrated above), the relations derived in the 1960's by John Bell to describe the limits on the behavior of non-conspiratorial local realism.
Non-conspiratorial local realism is false. So when we start to describe the positive content of quantum mechanics in the next installment and you find yourself saying "Oh, maybe it's like....", stop yourself. Are you likening it to something that obeys local realism? If so, that ain't it.