On Sep 13, 2007, at 5:26 PM, Jack Sarfatti wrote:
Our early universe has low entropy compared to present universe. Sir Roger Penrose says this is a big problem for inflation theory - it's the Arrow of Time problem - why irreversible aging is in same sense as expansion of 3D space with dark energy speeding up of that cosmic expansion.
Our past universe post-inflation is not de Sitter. Our future universe is de Sitter with
/\ ~ 1/NLp^2
N ~ 10^122 Bekenstein bits.
This gives the actually observed large-scale dark energy density
10^-29 grams/cc ~ (10^-2cm)^-4 ~ hc/NLp^4
note that NLp^4 = (Geometric mean of smallest Planck scale with largest future Omega deSitter horizon scale)^4
i.e. 10^-2 cm ~ (10^-33 cm 10^28 cm)^1/2
this is precisely what we expect from the retro-causal world hologram in which 3D space at our moments of perception of our entire pocket universe on the landscape is simply a hologram image of the future 2D deSitter horizon.
World hologram says that N area bits on the surrounding horizon are 1-1 with N interior "volume without volume" BITs.
i.e. &L ~ N^-1/6 Lp
L ~ N^1/2Lp
L^3 ~ N^3/2Lp^3
&L^3 ~ N^1/2Lp^3
L^3/&L^3 = N^3/2/N^1/2 = N
where &L^3 = volume-without-volume of quantum gravity foam bubble. Exactly N bubbles for N area quanta - 1-1. This is the fundamental physical meaning of the "world hologram".
In this case the horizon is not a closed spacelike surrounding 2D surface on a 3D spacelike slice of spacetime, but is the 2D de Sitter horizon of our future light cone of our detectors. That is, all the converging blue-shifted advanced null signals on our telescopes and other advanced signals back to the moment of inflation. The future dark energy created de Sitter horizon is the world hologram. See figure 19 (i) p. 130 "causal diamond" of Hawking & Ellis "The large-scale Structure of space-time" for a Penrose diagram picture of what I am talking about. I mean the upper half of (i).
This solves Penrose's problem with inflation since retro-causal measurement lowers the entropy of the past object (Alpha inflation) being measured and raises the entropy of the future measuring apparatus (G. Moddell, AAAS USD Retrocausality Workshop, June 2006) - Omega (far future de Sitter horizon) - Alpha (inflation phase transition) form a globally consistent Novikov loop of self-creation.
On Sep 13, 2007, at 4:41 PM, Jack Sarfatti wrote:
PS Also Paul what you have been looking for is natural in this tetrad substratum. It is not natural on the metric tensor/Levi-Civita connection level because of bilinear tetrad cross terms.
Complete Einstein-Cartan tetrad is
e^a = I^a + B^a
Where B^a is the intrinsic curvature tetrad field - without committing to my specific hologram model where
B^a --> N^-1/3A^a
N = (Closed Surrounding Horizon 2D Surface)/4Lp^2 Bekenstein's formula
No perturbation theory on background dependent Minkowski spacetime is implied here. That's a Red Herring. My model is background-independent in Lee Smolin's sense.
Nothing I say demands B^a << I^a as in perturbation theory.
I^a has all the inertial force effects of non-geodesic frames in Minkowski spacetime.
T^a(Minkowski) = dI^a + w^abcI^b/\I^c = 0 zero torsion 2-form in Minkowski spacetime
R^a^b(Minkowski) = d(w^a^bcI^c) + w^ac'cI^c'/\w^b^cc"I^c" = 0 zero curvature 2-form in Minkowski spacetime
However, cross terms I^a with A^b occur in the general case mixing inertial with intrinsic effects.
On Sep 13, 2007, at 4:21 PM, Jack Sarfatti wrote:
On Sep 13, 2007, at 12:12 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
The A^a q-number part is still emergent, it's just that it is the residual q-number random zero point part.
OK, but then how can you say that this part is equivalent to a quantized Yang-Mills field of the kind considered
by t'Hooft, for purposes of renormalization?
Because it has a very similar formal structure to the internal symmetry Yang-Mills quantum field operators.
Positive frequency part creates a q-number A^a quantum out of the coherent c-number A^a condensate. Negative frequency part puts a quantum back into the c-number condensate etc. 2 independent polarizations if massless etc.
Let's just look at the intrinsic q-part, there is a natural "Yang-Mills" field 2-form
F^a = dA^a + w^ac'cA^c'/\A^c
With Lagrangian density 0-form ~ *[(1/4)*F^a/\Fa]
Note that A^a = A^a(condensate c-number) + A^a(q-number)
so that the bare Hamiltonian from the Lagrangian has quartic terms. Thus is same formal structure as in Yang-Mills.
Think of sound waves in a crystal. Sound, like gravity and torsion, is an emergent collective phenomenon out of the individual lattice atoms right? You can have "classical" "condensate" sound waves (many phonons in same momentum state - I mean narrow wave packet), but also you can detect "particle" like phonon quantum effects in the fluctuations - but the phonon itself is a collective object out of the atomic substratum.
And these phonon quantum effects can be treated as manifestations of an "emergent" quantized field?
Is that what you mean?
Yes. Sound is an emergent collective phenomenon. At low intensities you get quantum fluctuations - phonon analog to quantum optics effects Poisson noise, sub-Poisson et-al. Sound has both classical wavelike properties and quantized particle phonon properties for different kinds of experiments. I am saying that both intrinsic tetrad curvature ~ A^a and intrinsic torsion ~ w^a^bcA^c are both collective emergent both c-number and q-number like sound is. Sakharov basically had this idea in 1967 though not as detailed.
Note I suppress the possible model-dependent "hologram" N^-1/3 coupling factors and pure Minkowski I^a terms in the above rough heuristics,