Iron Posts of Observation & Paper Mache of Interpretation
On Feb 5, 2005, at 12:47 PM, Tony Smith wrote:
"Jack, you say:"
... The hedgehog is specifically a uniform radial gradient field
between two concentric spherical boundaries.
The gradient field is zero outside the two boundaries. ...
"What I have is one spherical boundary."
OK then it's not a hedgehog. Not the same idea. What I am talking about is very specific in
"Topological Quantum Numbers in Nonrelativistic Physics"
by David Thouless (World Scientific,1998)
See Fig 1 in the Thouless book
Note from Thouless Fig 1 that all the arrows have SAME LENGTH, i.e. uniform radial gradient field a_g that is zero inside the spherical core r = 20 AU our case, and is zero outside the outer sphere. See Section 1.4
The "multi-layered multi-colored" (Frank Wilczek's words) vacuum coherence (local spontaneous broken symmetry order parameter), in this example and at this scale, lives in the space SO(3)/SO(2) equivalent to the sphere S2.
" contained in the space between an inner and outer spherical surface the magnetization might always point outwards [or inwards] from the inner surface, taking up the direction (but keeping constant magnitude) ... no continuous deformation of the magnetization, keeping the magnitude constant, can turn this into a state of uniform magnetization. This is a topological configuration of the magnetization known as a hedgehog." p. 7
Now it is obvious that the NASA Pioneer data is showing the SAME GLOBAL TOPOLOGY with "magnetization" replaced by the gravitational tug a_g ~ -cH(t), H(t) is the Hubble parameter of FLRW cosmological metric showing up on a rather short scale of tens of AUs.
What we obviously seem to have here is an EXPLODING SHELL of EXOTIC VACUUM DARK ZERO POINT ENERGY DENSITY emanating from the center of the Sun whose field distribution is
/\zpf ~ H/cr
between the two spherical boundaries in accord with Einstein's field equation
Guv + /\zpfguv = 0
where /\zpf is a local scalar field related to the vacuum coherence local order parameter by
/\zpf = Lp^-2[1 - Lp^2|Vacuum Coherence|^2]
where I assume the t'Hooft-Susskind "World Hologram" to normalize the Vacuum Coherence "Higgs Field".
"Outside the boundary, gravity is due (a la Segal and generalized MacDowell-Mansouri) to the conformal gauge group Spin(2,4) = SU(2,2)."
I don't know yet what this means. I do not understand the fancy Segal et-al ideas at all. I am pulling a complete blank. I am pulling a Puthoff, i.e. I am just a Yankee metric engineer in the bowels of the Star Ship cranking her up to see why the saucer won't fly! :-)
All I need is Einstein's 1916 GR and spontaneous broken vacuum symmetry of the right kind. I am basically "curve fitting" the data points i.e. plastering the "iron posts of observation" with the "paper mache" of interpretation to paraphrase John Archibald Wheeler.
My "tall ship" is Einstein's "Guv + /\zpfguv = 0" and "the star to steer her by" is P.W. Anderson's "More is different". :-)
"Inside the boundary, the conformal gauge group symmetry is broken, and gravity inside is due (a la MacDowell-Mansouri) to the anti-deSitter (compact version of Poincare) gauge group Spin(2,3) = Sp(2)."
I don't know what you mean by "the conformal gauge group symmetry is broken" - where is your local vacuum order parameter? You must, and so must I of course, show explicitly how to get the SO(3)/SO(2) factor space for the order parameter that the data demands. It's the locality of the vacuum coherence order parameter that explains why spacetime physics is local even though the micro-quantum substratum is nonlocal.
"If you look closely at how the MacDowell-Mansouri mechanism, and its generalization, works then you may see that
my model is to your model
gauge groups are to Einstein-type lagrangians for GR
(conformal (with one setting of your order parameter
anti-deSitter) with the other setting of your order parameter)"
Could be. I simply do not know any of that stuff. It seems to be a lot of excess mathematical baggage not needed. Thing of the algorithmic complexity. My program is a lot shorter than yours!
"It is clear to me that simplicity is in the eye of the beholder,"
No it's not. Think of theory as a computer program. There are objective measures of complexity.
"so that when you say "... my model is a lot simpler than yours ..." I can reply by saying the exact same thing:
"... my model is a lot simpler than yours ..."
Could be, but I do not at all understand the heuristic ideas of your model as yet. I am not saying you are wrong, only that I am completely unfamiliar with the literature you cite and it would take me much too long to try to learn it when I do not seem to need it. I am not doing math for math's sake here. If I could jump up and down and recite a spell to make her fly, I would! :-)
"It only depends on with which formalism (gauge groups or GR lagrangians) you are more familiar and comfortable. Ideally, everybody would be equally familiar with all formalisms."
Theoretical physics today is long on formalism and short on contact with data.
"Since I don't have the time now to write this stuff up in some detailed way that is suited by your taste, and since my web material (written in a way suited to my taste) is available to you if you want to make the effort to understand it (remember, there is no royal road to understanding math and physics), I will end this line of discussion for now."
Maybe so Tony. I am not saying your model is wrong. I do not however, at this time understand any of it! Maybe others will and will be able to explain it like Dyson explained Schwinger - I prefer to be like Feynman in this little drama. But your ideas should be included as we are now going where no string theorist has dared to go! :-)