[snip]
But consider the limitation described in physics by the "Pauli exclusion
principle", or, better yet, the "principle of parity". These are both
statements of limitation. In both cases, all one has to do to disprove
the limitation is to find a single example for which the limitation does
not apply. And, as I am sure Glenn is aware, the principle of parity WAS
successfully overthrown. <<
There is a difference between the Pauli exclusion principle and the Partiy
principle. The exclusion prinicple follows mathematically from the fact that
electrons must be described by what are called anti-symmetric wave functions.
Mathematically, this is
(let Y be the Psi normally used. Ascii has no greek characters)
Thus, Y is the wave function for a particular electron. When dealing with 2
electrons, Y(1) and Y(2) they are superposed by the equation
Y[total]= {1/sqrt(2)}[Y(1)Y(2)-Y(2)Y(1)] = 0
This is the superposition of two waves governed by antisymmetric wave
functions.
Symmetric wave functions are superposed by the equation
Y[total]={1/sqrt(2)}{Y(1)Y(2)+Y(2)Y(1)} which is not zero everywhere.
Thus the antisymmetric wave function gives no electron if they occupy the
same state ie. Y(1)=Y(2) whereas the symmetric function allows multiple
states. (see Resnick and Eisberg, Quantum PHysics, 1986), p. 305)
The parity principle was not so well founded in theory as is the exclusion
principle (Stan Zygmunt you might want to comment here :-) ). Parity was
always observed to be conserved in electromagnetic and Strong force reactions
and so it was assumed to be conserved in weak interactions. It turned out it
wasn't. If I have mis-stated this last part, some better physicist can
correct me.(see ibid p. 654)
Thus, the parity situation really was in the nature of proving a negative. If
every interaction I observe agrees with parity, that does not prove that
there are NO exceptions. But in the case of the electron, and the exclusion
principle, if I prove that the antisymmetric wave function applies to the
electron, then the exclusion principle is a consequence of that proof. The
situations are different I believe.
One of the best evidences that electrons MUST obey the antisymmetric wave
functions is the consequences if they didn't. If they were symmetric waves
all electrons would be gathered into the lowest energy shell around each
nucleus regardless of the atomic number. All elements would be like noble
gases and would form no molecules. Because of this, life would not exist if
electron waves were symmetric.
One final housekeeping chore - Stephen Jones asked about speciation above the
species level. Try triticale. It is a polyploid cross between Triticum
(wheat) and Secale (rye) and it produces a new genus Triticale See J.H.
Hulse and D. Spurgeon, Triticale. Scientific American, August 1974. At least
at one time, teosinte was a different genus from corn but after it was found
to have made corn by means of polyploidy, some have re classified it into the
same genus as corn.
glenn