That is a trivial fact, the wave function of a system completely describes the state of the system and that of course includes the angular momentum. But the wave function has nothing to do with a physical wave with physical properties, it is a pretty abstract construction and the physical properties are essentially encoded in the base vectors of the Hilbert space. I only skimmed the paper but I didn't come across something that plausibly argued that the wave function is the fundamental physical entity.
Not meaning to argue that the wave function is a physical entity but rather that particles aren't required to "exist" as a physical entity to explain experimental data.
I would say nothing is required to exists. Just take the idea that our universe may be a simulation, then nothing in the universe is real. It could then be that the real universe out there is similar to ours or we could be the Game of Life of the real universe which could be totally incomprehensible to us with concepts that aren't even imaginable in our little world. Or take Last Thursdayism, the idea that the universe somehow came into existence last Thursday with fake memories of the past in our all heads and so on. Or Solipsism. There is no way you could ever find out that something like that was true or not.
We just have to make some assumptions about the nature of the universe and accept them as axioms, otherwise you can not even start to draw conclusions. Some assumptions may look more reasonable then others but I guess that is more or less an illusion, last Thursdayism looks only unreasonable because you have already rejected the idea and accepted some other assumptions.
So what is real? Particles? Fields? Wave functions? We pretty surly don't know. Some will say the fields are the real things because they give us virtual particles and that matches experiments, others will say that fields are not real because they have gauge symmetries - gauge redundancies - and how can something that is underdefined be real? It seems certainly possible that we will be able to rule one or another view out in the future because they can not accommodate some new discovery but we are probably not yet there and there is definitely no consensus.
Not to forget that there are quite a couple of new directions in the last years and decades, like space and time emerging from entanglement, the holographic principle, gravity as an entropic force and what not. There is probably a good chance that some or all our fundamental concepts of physics as of today will not survive the next century, millennium or million years. I mean they will still exist as useful approximations but no longer been seen as fundamental.
I'm not in disagreement. I certainly could have been more careful with my original wording.
I had a gut reaction to the original commenter's statement that angular momentum was a "physical reality at the subatomic level" and should have been more direct in my response.
