On Tuesday, November 18, 2003, at 06:48 AM, Arkadiusz Jadczyk wrote:
On 17 Nov 2003 at 16:53, Jack Sarfatti wrote:
I am still looking for a good complete pedagogical discussion of this and
what the 4 special conformal generators mean physically. I know what all
the others mean.
The other 4 generators are generators of boosts to "uniformly
accelerated motions". SU(2,2) acts singularly on the Minkowski space.
It acts smoothly, in a non-singular way, on the "compactified
Minkowski space", that is with added "light cone at infinity".
Topology (S^3 x S^2) / Z_2.
ark
Thanks Ark. I will review hyperbolic motion in MTW.
So there is a connection to the equivalence principle.
I still need to read a definitive pedagogical review
of the details and also look again at the Utiyama &
Kibble papers to make sure I remember them correctly.
Since Einstein's gravity field for curved space-time
comes from locally gauging the translation subgroup T4
of the conformal group, and the torsion field, absent
in GR comes from locally gauging the Lorentz subgroup
O(1,3) what new compensating fields do we get from
locally gauging the entire 15 parameter conformal group?
That's the question here.
On 17 Nov 2003 at 19:16, Jack Sarfatti wrote:
If the hyperspace
is globally not oriented like a one-sided Mobius strip or a Klein Bottle
then Trivial(x) locally
unwraps the global twists.
Ark corrected:
"Jack,
Not quite true. Imagine space-time that consists of just one point -
call it x, and let the fiber over it, f(x), is a Klein bottle. The
hyperspace itself is then just the Klein bottle. It is non-oriented.
Yet local trivialization gives you {x} X f(x) - which is the same -
still non-oriented.
What local trivialization does - it allows us to "untwist" twists
along the base, but not along the fibre.
ark"
OK thanks. :-)
Tony Smith wrote:
"Jack, you ask:
'... 4 special conformal generators ...
What do they locally gauge to?
My hunch is /\zpf,u ...'
Yes, I think so too, and have written some stuff about it
on my web page at
http://www.innerx.net/personal/tsmith/coscongraviton.html
The basic reference for that work is a paper by Aldrovandi and Pereira at
http://xxx.lanl.gov/abs/gr-qc/9809061
which describes in some detail how the special conformal group
gives rise to cosmological "constant" type terms.
My contribution, built on their nice math foundation,
is to count degrees of freedom and get a result that
at a critical time in the past the ratio of "matter forms" in
our universe should have been:
67% Dark Energy
27% Dark Matter
6% Ordinary Matter
and if you follow evolution in ways that seem reasonable to me,
you get a present-day content in a range of (depending on whether
Cold Dark Matter is in the form of Primordial Black Holes,
or MOND, or a mixture thereof)"
Remember Tony it is an essential falsifiable precise prediction of my
MACRO-QUANTUM vacuum emergent gravity model that "dark matter" and "dark
energy" are essentially the same exotic vacuum zero point energy density
w = -1 field
/\zpf = (alpha')^-1[(alpha')^3/2|Vacuum Coherence|^1 - 1]
where alpha' = 1/(variable string tension) is a generalized Witten parameter
(h = c = 1 convention that Witten likes to use)
/\zpf > 0 is anti-gravitating "dark energy"
/\zpf < 0 is gravitating "dark matter"
Weak curvature Poisson eq is
Grad^2(Exotic Vacuum Potential) = c^2/\zpf
Large clumps of w = -1 /\zpf < 0 like what keeps galaxies stable mimics
w = 0 CDM like you pointed out in our e-mail discussions.
The same idea works on the micro-scale keeping the spatially extended
electron stable by holding in the self-electric charge and compensating
the "spin" centrifugal inertial force.
Indeed Brian Greene's "vibrating strings of pure energy" in NOVA's "The
Elegant Universe" are in reality these "Type II superconducting" vortex
cores of exotic vacuum where Vacuum Coherence --> 0 with trapped EM flux.
Universal Regge Slopes follow trivially.
Therefore my precise prediction is that no dark matter detector will
click with the right stuff. Only false positives. All dark matter
detectors will remain dark if correctly designed. This is a null
experiment like the Michelson-Morley experiment that was asking the
wrong question. Dark matter, like dark energy is a virtual off mass
shell vacuum effect not real on mass shell particles flying through
space to trigger detector clicks.
If experiment shows otherwise my theory is falsified in the Popper sense.
Tony continued:
"68-75% Dark Energy
28-21% Dark Matter
4% Ordinary Matter
The observed composition by WMAP:
73% Dark Energy
23% Dark Matter
4% Ordinary Matter
is between the 75-21-4 result of assuming Cold Dark Matter is
made up of Primordial Black Holes,"
This I disagree with as given above. A large glob of exotic vacuum with
/\zpf < 0
need not be a black hole with a singularity.
"and to the 71-25-4 result of assuming that Cold Dark Matter is
a (reasonable to me) mixture of Primordial Black Holes and MOND.
Unfortunately from my point of view, I cannot put these results
on the Cornell arXiv because I am blacklisted.
It is especially unfortunate because they indicate that your
model is on the right track (except that I don't like the naive
form of supersymmetry that exists in superstring theory).
Tony"
Also from Tony
"Saul-Paul, you ask about more details on the OD and TD structures,
but I haven't really done much more than I described in my previous
e-mail message. It is pretty clear in my mind, but I haven't written
down details yet (and being blacklisted I am not too enthusiastic about
doing much more writing down of stuff -...
As to supersymmetry, if any reasonably interpreted experimental
results clearly show the existence of one of the naive supersymmetry
partner particles (squarks, winos, etc), then my model is dead
and should be thrown in the trash can.
My model does, as you suggest in a remark about my 27-dim spaces,
have a subtle form of supersymmetry that does appear at very
high energies (when the spacetime goes to 8-dim and the Higgs
stuff is unfrozen and all particles are massless). At that energy
level, there is only one generation of fermions (8 of them)
and all 28 D4 generators are on the same footing.
In my 8-dim Lagrangian,
the gauge boson term has 28 x 1 = 28 degrees of freedom
and
the fermion term also has 8 x 7/2 = 28 degrees of freedom
the factor of 7/2 coming from the effective dimensionality of
fermion particles in 8 dimensional Lagrangians.
Therefore, the boson degrees of freedom exactly cancel
the fermion degrees of freedom at high energies,
and we get to see nice symmetries down here at low energies
due to residual effects of the high-energy subtle supersymmetry.
Tony"
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