Of all the laws of physics, the Pauli Exclusion Principle
seems the most like a fiat. Two
innocent fermions would like to snuggle together in the same quantum state,
just like their buddies the bosons do (technically, it’s called “bundling”),
when in pops Professor Pauli and says (for reasons best known to himself): “NEINNN! Es ist streng verboten
!!”
Initially, the Heisenberg Uncertainty Principle feels
something like this: like the
children in the Märchen who are warned never to go too near a certain spot in
the forest, or a certain room in the castle (or a certain tree in the Garden,
if memory serves), physicists are warned not to inquire too nicely into both the location and the momentum of a particle, nor any other pair of conjugate
quantities. But it turns out
that the principle need not be stipulated,
but can be derived, in various
ways. Thus Feynman, in QED
(p. 56), claims that the principle falls out of his favorite technique of
adding-up little arrows -- “There
is no need for an uncertainty principle!”
And Stein & Skakarchi (Fourier Analysis, p. 160) show that it
follows from that fact that, if a given function is ‘bunched’, then its Fourier
transform cannot be: in which case
the mysterious Principle turns out to be a simple truth of mathematics, and not
a peculiarity of physics.
*
My mind was brought back to these reflections while
reviewing my distressingly slender résumé so far: which, despite my world-celebrated discovery of the Higgs
Boson (documented here), would scarcely suffice for a Nobel Prize in
Physics, or even a Mitch ‘n’ Gladys Memorial Prize in Some Kind of
Science. Accordingly, we
feel the need to beef it up a bit, with the following finding, arrived at
entirely independently of Pauli, when my brother and I were respectively five
and seven years old:
The Metapenguin Exclusion
Principle ®
My brother and I developed this in what we may call (in
retrospect, though at the time we did not call it anything at all) the “Voice
Game”: which consisted in this.
~
There were precisely three available voice-registers: Normal, Low, and Squeaky. Only one of us could be in any
given register at one time. What
you actually said, in this register, was up to you; in practice, we didn’t say much beyond “*I* have the lo-o-ow voice.” -- “And I-yee have the squeeeaky
voice!”
In principle we
would transition at random among the registers, in accordance with the
statistics of Weak Decay. But
there was a symmetry-breaking consideration: Naturally, any kid would want the
Squeaky voice. I remember one time
when my brother was occupying it, and I tried to entice him out of it by
saying, in a hearty TV-commercial voice, as though it were the best thing in
the world: “*I* have thee Norrrmal
voice.” Hoping thereby to
entice him to a Lyman transition from Squeaky to Low, his hope being thus to
entice me to a Balmer transition up
to Squeaky, whereupon he could grab
Normal -- only to find that it wasn’t as much fun as it was cracked up to be.
Such was the Voice Game.
~
From this, the fermionic version associated with Pauli follows easily as a special case. We leave this as an exercise for the
reader.
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