A sophisticated layperson friend of mine asked me a question which
I had to confess had never really occurred to me before. I told
him I'd consult a prestigious panel of friends. So here goes:
Why should the Pauli principle *not* be considered itself to be
the equivalent of a "fifth force"?
Most sources explain the origin of degeneracy pressure along
something like these lines: Fermions cannot occupy the same
quantum state. Thus, as the spatial extent of their wavefunctions
become more and more similar, they are forced to occupy higher
energy levels. This is equivalent to the effects of a repulsive
force.
Fair enough, but the effect is at least *seemingly* independent of
whether or not the particles interact in any other way--i.e., via
the strong, electroweak, or gravitational mechanisms. Now it is
true that all fermions *do* interact by at least one of these
mechanisms, but *is* this a requirement for fermions? If so, why
exactly? And if not, how would we explain the existence of
degeneracy pressure in the case of two noninteracting fermions?