One prospective definition of 'intuitive' is something which makes sense to us without much or any thought, as in the pieces just fit together. Quantum mechanics does not fit such a definition. That a square peg won't fit in a round hole seems fairly intuitive. That matter operates in a fundamentally probabilistic manner at the quantum level clashes with our notion that matter is either there or it is not, which is exactly what we observe in our everyday experience at the human scale. I'd venture that what we find intuitive is related somehow to the challenges our forbears faced in their evolutionary environment, noting that our ancestors did not face tests of their abilities to comprehend quantum mechanics in their struggle to survive and reproduce.This is why I belong to the "shut up and calculate" school. If quantum mechanics can't be pleasant, then it might as well be useful. In my view, one problem with making QM intuitive, is that we don't even know what "intuitive" should look like. And I think the remarkable progress made in the past century may owe itself to setting that question aside.
Coming from the perspective of a philosopher, I'm not sure how to wrap my head around many aspects of the atomic and subatomic realm. If empty space is not actually empty, then it prompts questions about basic logic regarding the difference between something and nothing.
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