Sunday, July 7, 2013

Frontiers of Pataphysics

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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