The wave-like properties of all fermions can be explained with any variant of the many-worlds interpretation (MWI) that you prefer.

Essentially in MWI each neutron in each universe is a point (actually three because of the quarks), but that point is not in the same place in all universes. The "closer" a parallel universe is, the closer the neutrons are to each other spatially. The universes aren't discrete, they form a continuum that is locally smooth, forming a differentiable manifold.

It's the distribution across the parallel universes that's continuous and wave-like, not the individual neutrons! The wave mechanics of QM is simply a description of the cross-universe distribution of neutrons interacting with the cross-universe distribution of other particles.

This was not the initial mental model developed in the early days of quantum mechanics. The founders of the theory flatly rejected MWI based on largely religious objections. It's absurd if you think about it, but the weird and complex mathematics of QM is simply a product of these people pretending parallel worlds don't exist.

It's a way of pretending functions can have multiple values in one place without actually admitting that this requires additional dimensions, otherwise they're not mathematical functions!

They also like to pretend that scalars have probability distributions... except sometimes when interacting with other probability distributions that magically stop being distributed at the same time.

In computer terms: This is like someone pretending that arrays are passed into a function using a CPU register that can have many values at the same time. It's just absurd.

Note that MWI as originally formulated by Everett does not work this way. Eg quoting from the Discussion section of his thesis:

> [I]t seems to us to be much easier to understand particle aspects from a wave picture (concentrated wave packets) than it is to understand wave aspects (diffraction, interference, etc.) from a particle picture.

or

> This view [ie Everett's view, as described in the thesis] also corresponds most closely with that held by Schrödinger.

The main point of MWI is not to go back to a more classical picture of point particles, but to remove wave-function collapse and Heisenberg cut from the description.

Quantum Mechanics is actually incredibly conservative, with theoreticians simply refusing to abandon notions shown to be incompatible with reality for over a century now.

Same with Spin. Okay, so particles aren't literally spinning spheres. We get it. Stop pretending they are and then Spin won't be so mysterious any more!

It’s just an evocative name?

Okay then, if it's impossible, don't print what it isn't. Put down in writing what it is. That is all.

However, unlike the operators for the usual sense of angular momentum, there are additional solutions that appear, which have the half-integer spins.

And, in a sense the spin contributes to the angular momentum.

I don’t see a problem with saying “it is in some ways kind of like if it were spinning, but it isn’t quite the same. Here is the math to describe it, and how that math is like and how it is unlike something spinning.” . It seems better than just saying “here is the math which describes it”.

I don’t think your classical CPU analogy is really applicable here.

The wave function is exactly that, many values describing the probability of the particle in space. The act of measurement is what sets the value of the wave function. Take the classic electron diffraction experiment. It’s not the measurement that defines the wave-like property there.

Take tunneling through a potential barrier, why can the particle tunnel? Tunneling is a consequence of the wave function defining the probability of particle in all space.