I'll use your comment to correct myself, I meant to write "qubit" heh. Thanks yes, after posting my comment, I was researching qubits and Hilbert spaces and stumbled onto ergodic processes, where the properties of a process can be inferred from random sampling:
https://en.wikipedia.org/wiki/Ergodic_process
I believe that combining it with the Born rule (which gives the probability that a measurement of a quantum system will yield a given result) might lead to Gleason’s theorem:
https://en.wikipedia.org/wiki/Born_rule
https://en.wikipedia.org/wiki/Gleason%27s_theorem
This is all so far outside of my wheelhouse though that I'm almost certainly not really saying anything.
Which is the fundamental issue I take with quantum mechanics. It introduces too much new terminology for simple concepts because experts appreciate the short notation to be productive, as you said. I've been programming for three decades but would never try to explain it in Lisp. I'd start with Javascript, but demonstrate where each conceptual flaw occurred so that the student derives much of Lisp before I get to it.
The heart of my cognitive dissonance is: I need to know what separates theory from quantum systems in real life. If we know what we're trying to do, then we should be able to build it in a simulator and just pause it periodically and examine the state.
Is the limit of that the speed of our computers? Is it that quantum mechanics plays out at the speed of light? Is it that entangled particles are really connected regardless of distance, because without hidden variables they have to be, so can't be simulated?
So far the best I can do is, imagine we're breaking N bit cryptography. We have one key, and know a mathematical relationship to the key we're trying to find, but the search space is huge. Maybe every time we sample, some percentage of the qubits reveal something, but we don't know which ones. Maybe we sample more, and see that certain ones tend to stay the same. Maybe when we get down to a tractable number of qubits remaining (like 32), we just brute force search the remaining bits classically by iterating over the (2^32) permutations?
Apparently there's just no path in layman's terms to get from my improper description to what really happens. Which isn't true in computer science. If I understand a topic, it's borderline trivial to explain with metaphors.
Ok I think after writing this out, I'm looking for an open source implementation of quantum mechanics that doesn't use established terminology. Maybe it looks like a wiki with every use case and bit of errata answered. So like, everywhere that complex numbers appear, we could just use independent vectors and formulas to get the angle and magnitude. Same for matrices, forget about eigenvectors, just explain it in a way that people understand, like center of mass or the direction with the least rotational inertia. No integrals, just summation and approximation. Yes, we'd lose the abstractions that let us find new associations, but after we have working mental models, I think we'd grasp them automatically by our curiosity. Instead of hitting this woo woo wall that makes it impossible to talk about with enthusiasts like me!