alt Hacker NewsSo many entry-level explanations of quantum mechanics start with classical physics, waves, particles, the double-slit experiment, etc. and then jump straight to infinite-dimensional Hilbert spaces. In my opinion, there's way too much conceptual baggage that comes with these concepts [0].
As a non-physicist, QM only clicked for me when I learned the linear algebra of one- and two-qubit systems and observables on those systems [1]. The math is accessible at a pre-calculus level, and the most "counter-intuitive" aspects of QM (interference, the uncertainty principle, entanglement) make perfect sense in this framework. I think it's the best starting point for understanding what QM really says.
[0] That's not to say they aren't important historically or for a complete understanding of QM. I'm talking about conceptual understanding for someone, especially an amateur, encountering QM for the first time.
[1] Chapter 2 of Nielsen and Chuang is what did it for me. It's heavygoing if you've never seen linear algebra before, but I don't know of a clearer explanation of the postulates of quantum mechanics.
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Do you have any recommended resources that you used to help learn the linear algebra?
It makes sense in the framework but the framework makes no sense. The model contradicts regular intuition.
Agreed.
Quantum Processes, Systems, & Information by Benjamin Schumacher and Michael Westmoreland is another good treatment along those lines.
Mike and Ike is almost always my standard recommendation.
The math is one thing, but I find the idea that the fundamental pieces of reality aren’t particles a little unsettling.
The classic double-slit experiment is kinda bizarre when one considers the “single electron” case.