Leptons vs Optimality vs Quarks vs Universe

>>From Osher Doctorow mdoctorow@xxxxxxxxxxx

COPYRIGHT NOTICE
Leptons vs Optimality vs Quarks vs Universe
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005

Take a look at "Quark-Lepton complementarity: a review," H.Minakata,
Tokyo Metropolitan U., hep-ph/0505252 v1 31 May 2005, and also look at
my recent thread on optimality and suboptimality here in sci.physics.

The relationships between quarks and leptons is a mixed one, in which
some things correspond and some don't. The most interesting
relationship is the closeness to the equation:

1) A_S + A_C = pi/4

where A_S is the solar angle, A_C is the Cabibbo angle, and to a good
approximation this holds but not exactly - almost as though probability
were at work, for example.

PI optimality vs suboptimality in general give a mixed picture of
probable causation, so let's start by looking at the "very early"
universe for some clues in regard to these.

The universe arguably "should have been unified and uniform" at or near
the "beginning", which would essentially have meant optimal probable
causation in which the order of events and processes is irrelevant or
interchangeable with probability 1 ("almost or exact certainty"). For
an n-event case, this means:

2) P(A1<-->A2<-->...<-->An) = 1

But the symbol <-->, which here means "mutually cause/influence", is an
intersection of two one-sided causations/influences --> and <--. The
opposite extreme in a sense, of "total non-uniformity or
non-unification" but with high (suboptimal) probable causation, for n
events would arguably be represented in PI by:

3) P(A1-->A2-->...-->An) = 1

If (3) had been the guiding principle of the universe, Shrodinger's cat
or in fact anybody's cat might rule the world in the sense that when
you interchange the order of positional (spatial) events with cats you
seem to often get quite different or confused responses. Of course, to
some degree this holds with people. For example, if somebody comes to
dinner and asks for desert before everything else, there may be
considerable confusion among the other people at dinner.

In combinatorics as a branch of mathematics, ordered vs unordered are
respectively called permutations vs combinations, and for finite
numbers of events or objects there are quite interesting equations in
various scenarios. Combinatorics is generally introduced in
mathematical probability-statistics courses, after which it may or may
not go off on its own in a separate field called combinatorics to
distinguish it from probability-statistics.

If the universe today were unordered everwhere in the above sense, we
could possibly conclude that the universe has an "unordered" principle.
Since the universe has both ordered and unordered aspects, both
permutations and combinations, we could arguably extrapolate to the
early universe and claim that a mixture of ordering and unordering
prevailed then, and that would give us some lepton-quark
correspondences like the pi/4 one above and some non-correspondences
indicated. Conveniently, the lepton-quark differentiation goes way
back to very early after the Big Bang.

Osher Doctorow

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