| Not knowing the specific state - and being incapable of knowing - is the critical bit. TL;DR: (edit) ignore the rest of this and just go read a lot on Bell's Theorem and the Double Slit Experiment. Both demonstrate concretely the essence of the weirdness. (I'll leave the rest below just to keep me honest about my ignorance.)
it's a provably special state where randomness allows it to have the needed characteristics for the math to work at all. [1] Also disclaimer: I'm not a PhD physicist, just a BS in engineering physics. This is merely how I cope with the idea. Think of it like this: given time, chaotic systems become unpredictable and noisy. An electron whizzing around an atom doesn't need much time before it's state is utterly unpredictable at any measurable level (Heisenberg Uncertainty assures this must happen eventually, and pretty fast it turns out). So what if we isolate that little electron from the outside world? Then even the universe becomes uncertain, and must assume ANY possible state is valid and happening at once, blurring them together based on how likely each is given the last known observation! Otherwise the next observation could be contradictory to expectations, and seg fault the universe (perhaps just locally). This way though, the universe can always say "well I thought it could have been that" and be correct, even if it only thought it really unlikely. But until the universe interacts with the state then, once coherence [2] sets in only probability can hint at what state it is in. Thus it is random in the before-the-fact sense like the probability before rolling a die, as opposed to an after-the-fact sense like a coin that is already flipped yet hidden. And - here's the catch - the math needs to treat it as unknown. To label the parts of an unlabeled system will break the algebra! And if a distribution of states is unknown in a mathematically precise ignorance, this is indistinguishable from true randomness. Such pure conceptual states are rare in our messy universe (at least observationally), but they do exist and can be proven to exist in the same way a one time pad can be proven to be cryptographically secure. Thanks for being my duck, I needed to think about something interesting today! [1] Perhaps the most amazing bit is that if it weren't random, then it would act differently, since the distribution of observations would vary from the expected random field after enough observations. And this has been done! Study the double slit experiment deeply, as it really is a fantastic empirical example of why interfering via observation adjusts our interpretation of the results.
[2]This term is jargon here, like quark colors. It's not coherence like a laser's. |