/\zpf ~ 1/r^2 = 1/NLp^2
required by world hologram
This explains exactly why the dark energy is small on large scale need to allow the universe to exist.
The amount of dark energy in a quantum cell of space is
(hc/Lp^2)(1/NLp^2)(Lp^2/3N^1/3Lp^1/3)^3 = hc/Lp
is a scale-invariant!
On Jul 10, 2007, at 8:01 AM, Jack Sarfatti wrote:
This will go into next major revision of my archive paper
VOLUME WITHOUT VOLUME!
OK here is exactly how the world hologram projector works!
r ~ N^1/2 Lp required from world hologram postulate
(simple white noise Brownian motion)
&r ~ N^1/6 Lp = quantum metric fluctuation required from world hologram postulate consistent with Heisenberg uncertainty & miniblackhole formation
"fermionic" anti-correlated "pink noise" Brownian motion
r/&r ~ N^1/2/N^1/6 = N^(3/6-1/6) = N^2/6 = N^1/3
Consistent with Euclidean intuition!
That is, the world lattice is wavelet, i.e. resolution-dependent. The quantum "cell" adjusts so that it appears the Volume ~ N (size of quantum cell of 3D space)
It's like in relativity where space and time distort to keep ds^2 invariant, here the size of the quantum gravity fluctuation in the cell of 3D spacelike slices distorts to preserve the "illusion" of a 3Dim space geometry
Volume without volume!
&r is a kind of coherence length for the THREE vacuum ODLRO Higgs fields in "3D" projection with TWO independent Goldstone phases of the world hologram. Kleinert's world crystal lattice is a lattice of point monopole nodes in the Higgs fields, i.e. Goldstone phase singularities analogous to Abrikosov's vortex string lattice in Type II superconductors where there are only TWO real Higgs fields with ONE Goldstone phase.
On Jul 9, 2007, at 9:28 PM, Jack Sarfatti wrote:
Surreal Night Thoughts of a Beyond The Fringe Theoretical Physicist
This explains &l > (Lp^2L)^1/3
&l is the quantum uncertainty in measuring length l
from Heisenberg uncertainty + black hole formation and how it connects to the world hologram as anti-correlated fractal deviation from Brownian motion with fractal parameter 1/3.
This motivates my choice for dimensionless spin 1 tetrad coupling (Lp^2/\zpf)^1/3.
"world hologram" is that the geometrodynamic field is a "surface field" - volume is a projection from its surrounding surface.
In my emergence theory this is reflected in the closed 2-form dTheta/\dPhi, where Theta & Phi are the two effective Goldstone phases of the world hologram from three real vacuum ODLRO Higgs fields whose nodes locate point geometrodynamic "monopole" defects.
This picture is the 3D projection down from a 9D hyperspace.
dTheta/\dPhi is a "area" operator.
Since it is closed, i.e. d^2 = 0, the volume operator = d(Area) is identically zero!
Integrating the area operator over a boundary-less closed non-bounding surface enclosing N point defects - each "hedgehogs" gives a non-vanishing "Wrapping Integer" N.
This integral of dTheta/\dPhi ~ NLp^2.
If we had a Gauss law it's as if there is an interior integral of the vanishing volume operator.
NLp^2 = 4pir^2
r ~ N^1/2Lp
This is an "ordinary Brownian motion"
V ~ N^3/2Lp^3
&r = (Lp^2r)^1/3 ~ N^1/6Lp
for the quantum fluctuation in r.
When N^1/2Lp = 10^28 cm
N^1/2 = 10^61
N = 10^122
122/6 ~ 20
&r ~ 10^-13 cm