# Did the Feynman heuristic of “simple effects have simple causes” fail for spin statistics?

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.

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For those who wanted to have a link to Feynman's Dirac lecture. youtu.be/cKzzG5DS6V8 – gns-ank Mar 24 '13 at 22:00
A playlist with all parts of Feynman's Dirac lecture is here: youtu.be/cKzzG5DS6V8?list=PLC3D8F5EA631EBA02 – gns-ank Mar 24 '13 at 22:12
@gns-ank, thanks, I didn't know it was available online! – Terry Bollinger Mar 24 '13 at 22:48
Honestly, your question is not clear for me, "why whole-spin particles always seems to be bosons", do you mean why Bosons behaves like Bosons? or why there is two types of fundamental particles? or how spin affects there behavior? – TMS Mar 24 '13 at 22:59
Hi @TMS: That would be "why are the two always correlated?" Bosons, with wavefunctions that are symmetric under exchange, always seem to have whole-unit spin; while fermions, with wavefunctions that are anti-symmetric under exchange, always seem to have spins that are offset by one half of a spin unit. It's that correlation that's a bit tough to explain in a simple way. I think it would also be fair to say that since there is no simple explanation even for what spin is at the level of an electron, which is after all a point-like particle, it's even tougher to explain its impact. – Terry Bollinger Mar 25 '13 at 3:47

+1 for a really nice pair of belt videos, despite my very sincere "please no!" plea on that point :). "Exchanging buckles twice = 720$^{\circ}$" is going to confuse folks who see only a 360$^{\circ}$ rotation, but Feynman and others do explain why that is. Spin 1 becomes "no belts, just buckles", which alas is not mentioned in the description. The shared underlying math is correctly noted. But alas: I'm guessing that most folks who see even a good video like that will go away wondering why belts are "just like spin 1/2" (spinors) and buckles "just like spin 1". So: Good Feynman capture. – Terry Bollinger Mar 28 '13 at 18:18