That whole thinking - that states are well defined, and can be only either one or the other - that's the classic world approximation, it's not reality. You firmly believe in it because your crucial early years, when you were crawling on the floor at your parents' house, were spent in a classic-world-approximation universe. That's why it's so hard for you (and pretty much everyone else) to let go of it.
The quantum phenomena are the more fundamental reality. This classic universe that you think you understand is just an epiphenomenon. Just foam floating on the ocean.
The fundamental reality of the electron is the wave function. States, and everything else, emerge from it. It's not a corpuscle. It's not a wave. It does not behave like ping-pong balls, or like waves in a pond, although it shares a few characteristics. Fundamentally, it's something different. The only way to know that entirely different thing is via the mathematics of quantum mechanics - and whatever intuition you can derive from it after you do the math.
There is no equivalent for that stuff at the human scale of things.
Very much this. This should be prologue to any introduction QM book/class/whatever.
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Building on this idea, "an electron can be both states at the same time" isn't necessarily the right way to think about it.
I mean, it's sort of right, but relies on an intuitive understand of what the heck that even means. And QM reality is grounded not in our human intuition, but in the math of wave functions. If we associate "state up" with a wave function concentrated one way and "state down" concentrated the other way and "both states" as a mixture, then okay. We give foreign concepts familiar descriptions all the time. (Like, maybe, telling someone that a byte is a letter...it's kind of true, for some concept of letter.)
But the true fundamentals of QM are not particles or waves or discrete states, but wave functions and Hilbert space.
The quantum phenomena are the more fundamental reality. This classic universe that you think you understand is just an epiphenomenon. Just foam floating on the ocean.
The fundamental reality of the electron is the wave function. States, and everything else, emerge from it. It's not a corpuscle. It's not a wave. It does not behave like ping-pong balls, or like waves in a pond, although it shares a few characteristics. Fundamentally, it's something different. The only way to know that entirely different thing is via the mathematics of quantum mechanics - and whatever intuition you can derive from it after you do the math.
There is no equivalent for that stuff at the human scale of things.