## Sunday, November 6, 2011

### Greek Trinity II

After the destruction of the pagan temples, a more unified Church succeeded in quelling Neoplatonic thought, for a while. In Europe, a notable Renaissance Neoplatonist was Giordano Bruno, burned at the stake in 1600. The charges against him spoke to the Neoplatonic elements of his cosmology, with its plurality of worlds of the mind, and so called erroneous opinions about the Trinity. At his sentencing, Bruno said,
Perhaps you, my judges, pronounce this sentence against me with greater fear than I receive it.
As the modern Theosophists say,
Modern science and philosophy are said to have been born in this century. Any one, however, who is acquainted with the scientific and philosophical concepts of the ancient Greeks will discover that these "modern" ideas are but warmed-over dishes covered, in most cases, with a thick sauce of crass materialism.
Thus many a modern scientist has failed to understand Bruno's words, and Galileo's relatively unthreatening views. Bruno's infinite aether was not pre-ordained by an external observer, but was the substance of which the mind created matter, and the logos was the Word of the Trinity.

1. Once upon a time, I often said that the 19th century American philosopher C. S. Peirce was the founder of Category Theory, with his work on diagrammatic logic. But Bruno himself deserves this honour. And if Bruno, then we must respect the long murky chain of history, backwards to ancient times.

2. Bruno may have only been an intermediary.
The Wikipedia entry on Ramon Llull says:
"... Around 1275, Llull designed a method, which he first published in full in his Ars generalis ultima or Ars magna ("The Ultimate General Art", published in 1305) ... It is believed that Llull's inspiration for the Ars magna came from observing Arab astrologers use a device called a zairja. ...
Llull also invented numerous 'machines' for the purpose.
One method is now called the Lullian Circle, each of which consisted of two or more paper discs inscribed with alphabetical letters or symbols that referred to lists of attributes. The discs could be rotated individually to generate a large number of combinations of ideas. ... These combinations were said to show all possible truth about the subject of the circle. Llull based this on the notion that there were a limited number of basic, undeniable truths in all fields of knowledge, and that we could understand everything about these fields of knowledge by studying combinations of these elemental truths.
...
The idea was developed further by Giordano Bruno in the 16th century, and by Gottfried Leibniz in the 17th century for investigations into the philosophy of science. Leibniz gave Llull's idea the name ars combinatoria, by which it is now often known. Some computer scientists have adopted Llull as a sort of founding father, claiming that his system of logic was the beginning of information science. ...".

Tony

PS - As I have said on my web site,
I think that it goes back even further to ancient African IFA divination.

PPS - On another matter, the 3x3 Kobayahsi-Maskawa matrix:
If Electroweak Symmetry Breaking and Mass Generation occurs around 300 GeV or so
then
quarks etc should be massless at higher energies
and
the LHC should be able to do experiments at those higher energies at which quarks should be massless
so
the LHC should be able to measure Massless Realm Kobayashi-Maskawa matrix parameters.

It will be interesting to see whether the Massless Realm K-M parameters are the same as or different from the K-M parameters we measure in the low-energy Massive Realm.

Since my model calculations of K-M parameters are based on fermion mass ratios
my calculation method is not applicable to the Massless Realm.

Therefore, I am very interested in alternative fundamental ways to calculate K-M parameters,
and your work on circulants (such as vixra 1008.0015) seems an interesting approach.
What ideas do you have for fundamental derivation of the parameters you use in section 4 of that paper ?

Have you presented ideas for calculations of Massless Realm phenomena that might be experimentally testable to LHC people ?

3. Interesting, Tony. Of course, in those centuries (1200-1600) there would have been many European and Eastern scholars with access to ancient works that have since been lost. We have the Vedas, and so on, but just imagine what was in all those destroyed libraries!

Re the CKM: as my blog shows, I have been struggling with these parameters for some years now. First, since the continuum fields are constructed from categorical algebra, we need to find the right 'series' of discrete data from the motivic point of view. This would probably be incredibly easy for a good mathematician, which is why it is so frustrating thinking about it on my own.

4. Re massless quarks: we could take a punt and use (1) the tribimaximal form for neutrino mixing (probably broken by $\theta_{13}$) along with (2) a quark lepton complementarity ansatz to reduce the three quark parameters to a two parameter form. But which one? Using $(-0.231,24)$ we obtain an almost-CKM form with a zero entry in place of the smallest entry, like for the TBM matrix.

BUT, since the TBM is definitely associated to mass for charged leptons, via the Koide rule, and all $3 \times 3$ qutrit operators are closely related to mass, I would guess that massless mixing has to be the identity matrix. Could the LHC see something closer to the identity? That would be my bet.

5. As to "... the massless mixing has to be the identity matrix ..."

you have there a very interesting and important idea
(you should put it on vixra to establish credit).

It makes physical sense:

The massive Z0 and massless photon will in the Massless Realm
become massless W0 plus the massless high-energy QED gauge boson
and
the Weinberg angle will not be relevant in the Massless Realm.

if all fermions are massless
there is no energy to be gained in any decay chain
like
tauon to muon to electron
or
tau-neutrino to mu-neutrino to electron neutrino
or
Tquark to charm to up (by W0)
or
Bquark to strange to down (by W0)
or
Tquark to strange to up (by W+/-)
or
Bquark to charm to down (by W+/-)

so

any lepton or quark fermion will just stay as it is
until it has interactions that bring its energy down
below the ElectroWeak Mass Generation threshold.

Maybe experiments in the Massless Realm will not show
anything that distinguishes the second and third generation fermions
from the first generation (mass having gone away)
and
so theoretical physics models will only need to have
one fermion generation at high energies (Massless Realm).

As to why nothing like the Massless Realm has yet been seen at the LHC,
note that
the LHC beams have only been operating at 7 Tev for protons
and
protons are not elementary particles but are complicated
bags of quarks and gluons.

If the ElectroWeak transition to the Massless Realm takes place
at 300 GeV (about as low as you could go)
the 3 valence gluons would carry 1 TeV
and
since gluons (and maybe virtual sea quarks) might carry the remaining 6 TeV
(in Lagrangian QCD most of the proton mass is gluon binding energy)
it may be that the LHC has yet to reach the Massless Realm.

If the ILC collides electrons at 500 GeV to 1 TeV
it might be that the ILC would not see much Massless Realm phenomena
(especially if each electron is seen as one valence electron
plus a cloud of virtual electron-positron pairs and photons
among whom the total energy must be divided).

If the CLIC collides electrons up to 5 TeV
then it might be a good bet to see some Massless Realm phenomena.

It would be interesting to estimate what effect Massless Realm phenomena
might have on muons in a Muon Collider.

Tony

6. Interesting thoughts, Tony. I think the appearance of quark gluon plasma physics at CMS, for instance, is already one hint that the LHC could see a shift in the mixing. But without a detailed analysis of the parameter shifts, it is really anyone's guess what will happen, at this point.

7. Alternatively, Tony, putting all CKM entries to $ud$ suggests the democratic mixing matrix, of all equal amplitudes. This too is a kind of identity, which is the natural (infinite product) limit of any complex magic mixing matrix.

8. The democratic mixing matrix for the Massless Realm is a nice idea.

In Z. Phys. C - Particles and Fields 45, 39-41 (1989) Koide said: "...
the mass matrix of the type ... 1/3 x m x

1 1 1
1 1 1
1 1 1

... has name... "democratic" family mixing ...
the ... democratic ... mass matrix can be diagonalized
by the transformation matrix ...

1/sqrt(2) -1/sqrt(2) 0

1/sqrt(6) 1/sqrt(6) -2/sqrt(6)

1/sqrt(3) 1/sqrt(3) 1/sqrt(3)

as

0 0 0
0 0 0
0 0 m

...".

Up in the Massless Realm you might just say that there is no mass matrix,
just a democratic mixing matrix of the form
1/3 x

1 1 1
1 1 1
1 1 1

with no complex stuff and no CP violation in the Massless Realm.

When go down to our Massive Realm by ElectroWeak Symmetry Breaking
then
you might as a first approximation use m = 1
so that all the mass first goes to the third generation as

0 0 0
0 0 0
0 0 1

which is physically like the Higgs being a T-Tbar quark condensate.

The subsequent distribution of mass down to the other quarks
might be determined by octonion combinatoric symmetries
with the third generation quarks being triples of octonions,
the second generation being pairs,
and the first being single octonion basis elements.

Koide applied something like the above reasoning to
get a lepton mixing matrix (which does not have the color force
so the combinatorics would differ from the quark case).

Tony

9. Great, Tony. Well, we shall soon know if your T-Tbar condensate is relevant for LHC observations. Personally, I still favour the full Massive realm for all LHC phenomenology. Either way though, it's you and I against everyone else, it seems!