>Mathematical models such as quantum mechanics and general relativity work, extraordinarily well. But they aren’t real in the same sense that neutrons and neurons are real Why not? When you really get down to it, aren't both neutrons and neurons ultimately also models? When most people think of a neutron, they think of a classical particle, yet we know experimentally that there is no such thing.
Yeah the author is assuming that "neutrons" have definite boundaries and are unambiguously distinguishable from the soup they inhabit. This is not the case. This is a simple example of how hard quantum mechanics is to think about.
Waves -- even in classical mechanics -- are not "countable", and are best represented in physical models with a continuum, such as field of real numbers.
They're fundamentally different. Quantum Mechanics glosses over this difference because when it was developed, this was too hard to deal with.
A lot of people who briefly studied QM at an undergraduate level assume that it "keeps going" and is applicable to all small-scale processes. In reality, it is not applicable to a wide range of phenomena, including explaining why particles come in countable units.
Similarly, the "infinite size" of electron clouds or the probability distributions of particles such as neutrons are a mathematical shortcut that was explicitly called out as such in the first QM papers. After a century, people just forgot and assumed that QM has a direct correspondence to reality, when it is a simplified abstraction designed to be analytically tractable.
Lastly, many people think that QM predicts that EM waves come in "countable" units called photons. This isn't true in general, and again, was called out as a simplification for the treatment of the emission and absorption of EM waves by atomic matter specifically. Atoms have electron orbitals that can take on only specific values, hence they can only absorb or emit EM waves with specific values. This is not a property shared with free particles or other fields that interact electromagnetically.
QM pedagogy needs to be rethought from the ground up, because nobody seems to be learning QM, but instead they're internalising a limited model they don't actually understand.