We were already having fun with that one over in the omnibus Aviation thread. See here & subsequent:
Funny enough, in a sense the hoverover / caption is sorta true.
From one POV typical 24-hour time designations (“military time” to Americans) are all assumed to be AM. If “everything is AM” means that “1100” is 11 hours after midnight, then it would also mean that “1300” is 13 hours after midnight. Which it really is. Hmmm.
That’ll never happen on a real computer, though, since the constant is so high that you couldn’t actually build that much memory with all the matter in the universe.
Interestingly, “Sun Tea” isn’t even on the graph (my mother made it fairly often so it occurred to me immediately). Although mentioned on explainxkcd as something British likely wouldn’t even think of due to not enough sun. So I guess that would make it eldritch horror tea by British standards.
If a fermion has no electric or strong force charge, then exclusion can’t be an indirect manifestation of those forces (do neutrinos have a “weak” charge?).
What looks like a “Pauli exclusion principle force” is always a manifestation of some force or another, but it can be different forces in different situations. Two fermions can’t occupy exactly the same state, but what constitutes a “state”? It’s always a manifestation of some potential or other, and that potential is a result of one or more forces.
What would happen if you could assemble a ball of neutrinos whose gravity would exceed the limits of the exclusion between them? Presumably the energy potential would induce some sort of transformation that would remove the fermion limit, but what exactly? In stars the transformation is to convert electrons and protons into neutrons which can pack much more tightly before wavefunction overlap becomes an issue; but presumably that mechanism wouldn’t be available in the case of neutrinos.
The potential in that case would be due to a combination of the weak force and gravity. As the gravitational forces increased, the neutrinos would get closer together, which would change the weak potential, which would enable them to get closer together. I don’t know enough about the weak interaction to say if there would be some stable bound state, but regardless of whether there is or not, at some point you’d eventually overcome that and collapse into a black hole.
It’s a question that is way beyond my education, but I would suppose that since neutrinos have such a tiny rest mass even a moderate increase in energy levels would accelerate them to near light-speed, making gravitational confinement difficult at best. A “neutrino ball” if it is possible at all would probably have to hover on the very knife edge of collapsing into a black hole.
So I gather that a lot hinges on the exact definition in physics of a “force”. I would have classically defined a force as that which can accelerate a mass; does this mean that Pauli repulsion can prevent the compaction of fermions but cannot actually accelerate them?