Someone here recently noted that "The spin-statistics thing isn't a problem, it is a theorem (a demonstrably valid proposition), and it shouldn't be addressed, it should be understood and celebrated."
"Spin statistics" is of course the shorthand way of referencing a most curious fact about the universe, which is this: If a particle of any type has a "spin" measured in whole units of quantized angular momentum, it will be a boson, a group that includes energy-like force particles such as photons. However, if its spin is (rather strangely) off-set by half a unit, it will instead be a fermion, which includes the particles that occupy space and that make up most ordinary matter.
The rule is very simple. The explanation of it is arguably a bit more complicated.
I find it fascinating that Nobel Laureate Richard Feynman worried over this simple theorem for decades, yet he never seemed to find an explanation for it that truly satisfied him. It was not a lack of mathematical explanations, I should note. It was because Feynman deeply believed in a rather simple search heuristic: very simple relationships should in general also have simple, easily-conveyed explanations.
Alas, Feynman's last attempt to explain spin statistics, in his Dirac Lecture, always seemed to me one of his least clear bits of exposition ever. I am fairly confident Feynman would have assessed his Lecture that way himself, as he tended to be quite brutal in self-critiques on anything related to clarity of explanation.
(I think there is an interesting family insight in that observation, incidentally: Richard Feynman's scientifically inclined father always hoped that his son, who had received the education he was never able to have, would someday explain all those little physics mysteries to him. The young Richard took that duty very seriously, and never really abandoned it, even towards the end of his own life.)
So, my question and challenge: How is everyone doing on Feynman's spin-statistics challenge these days?
Do you, fair reader, have in your hands some truly simple explanation for why whole-spin particles always seems to be bosons, and ones with half-spin offsets always seem to be fermions?
I am not asking for twisty belts and wine glasses (please, no!), nor am I asking for something math free... though I do think anyone trying to answer this question should first look at how Feynman handled even complex numbers in his book QED. What I am asking for is insight, the kind of explanation that makes the reader stop and think wow, of course that's it, why didn't I see it what way before?
So, anyone? I probably will not put an explicit bonus on this one, but if someone can provide an explanation that knocks everyone's +1 socks off, I guarantee I'll contribute at least a couple of hundred points to that overall consensus.