Cosmological Constant from Susskind's Hologram (Sign typo correction)
From: Jack Sarfatti (sarfatti_at_pacbell.net)
Date: 12/31/04
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Date: Fri, 31 Dec 2004 21:22:47 GMT
Sorry, I forgot to update the sign correction in older stuff below -
here corrected.
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Note when Vacuum Coherence = 0 PRE-INFLATION
R(Initial Singularity) = 1
i.e. 1 Bit thinking of universe as cosmic computer with David
Finkelstein's chronons 10^-44 sec of erasures - resetting the register
so to speak.
As the large-scale Vacuum Coherence limits to
|Vacuum Coherence|^2 -> 1/Lp^3
R(t) -> infinity
Vacuum Coherence can exceed this limit on smaller non-cosmological scales.
On Dec 31, 2004, at 12:43 PM, Jack Sarfatti wrote:
Inflation demands total stuff is at critical density for flat 3D space,
i.e. k = 0 in large-scale FRW metric
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum
coherence) = 1
Omega(on-mass-shell matter) ~ 1/R(t)^3, i.e. w = 0 in R(t)^-3(1 + w)
for v/c << 1
Omega(on-mass-shell radiation) ~ 1/R(t)^4, i.e. w = +1/3
with Omega(random zpf) + Omega(vacuum coherence) ~ 1/R(t)^0 independent
of R(t) since w = -1 for both random "normal fluid" zpf and condensate
(vacuum coherence)
/\ is from random zpf causing both dark energy (negative pressure) and
dark matter (positive pressure) exotic vacuum phases.
Clumps of w = -1 positive pressure, possibly like the Galactic Halo
mimic w = 0 dark matter in their gravity lensing. Positive and negative
pressure exotic vacua can each either universally attract or repel
depending on their detailed distribution relative to the test particle.
However localized negative pressure exotic vacuum clumps anti-gravitate
for test particles outside their domain of support. Similarly, localized
positive pressure clumps gravitate for test particles outside their
support. The effective gravity strength G* of clumps of exotic vacuum
regions can be larger than Newton's G.
Guv + /\zpfguv = 0
is the zero torsion field GR Poisson equation for exotic vacua.
In the Newtonian weak-field slow-speed limit, neglecting gravimagnetism,
this is
Grad^2(Potential Energy per unit test mass of exotic vacuum field) ~
c^2/\zpf
Susskind's World Hologram Conjecture requires
Einstein's cosmological constant /\ ~ [LpR(t)]^-2
With critical energy density hc/Lp^4R(t)^2 = (mpc^2/Lp^3)R(t)^-2
Therefore Omega(/\) is independent of R(t) consistent with w = -1
Lorentz covariance and EEP of GR. Similarly for Omega(Vacuum Coherence),
which is my new term.
OK trash what I wrote late last night on this when I was very tired. I
woke up fresh with a start with the correct way to think about the
problem - after taking a 600 mg ibuprofen for shoulder ache from over
exercise at the health club.
Here is how Lenny Susskind's world hologram really does work and how it
explains the dark energy!
1. Trash H. We don't need it.
2. The FRW space expansion factor R(t) is dimensionless. Everything is
in units of Lp.
3. The Susskind-Hawking-Bekenstein-t'Hooft hologram entropy of the
Universe is simply
S/kB = (1/4)R(t)^2
I have written this before of course.
R(now) = 10^61
This is a nice formula because it also explains the Arrow of Time since
the entropy of the universe is 0 at the initial singularity here, i.e.
R(initial singularity) = 0 or, if you prefer Finkelstein's chronons it
is 1-bit at t = 0.
4. OK roughly model everything as photons.
The photon thermal distribution is
hf/(e^hf/kBT - 1) + hf/2
But the dark energy is, to first approximation virtual photons hf/2
whose mean value is hc/LpR(t).
5. Therefore we need virtual energy hf/2 to "erase" each bit every time
the cosmic quantum computer clears its register to step forward another
chronon to compute the history of the universe
Therefore, the dark energy density the vacuum fabric of curved spacetime
needs to compute itself is
(R(t)^2/4)(hc/LpR(t))(1/Lp^3R(t))^3 = (hc/Lp^4)1/4R(t)^2 = (hc/4Lp^2)/\
Einstein's cosmological constant /\ = 1/Lp^2R(t)^2 = 10^-56 cm^-2 NOW
hc/Lp^2 = c^4/G
6. So this says that Einstein's cosmological constant /\ is getting
smaller as the Universe expands. On the other hand, w = pressure/(energy
density) = -1 for random micro-quantum zero point energy.
The energy density of cosmic stuff scales as R(t)^-3(1 + w)
For example w = 0 for ordinary matter so that Omega(matter) ~ R(t)^-3
w = +1/3 for cosmic black body real photons so that Omega(CMB) ~ R(t)^-4
w = -1 for RANDOM micro-quantum vacuum zero point fluctuations (from
covariance) so that
Omega(ZPF) ~ R(t)^-0 = constant.
7. However in my macro-quantum theory of the world hologram
/\ = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
Equating this with the world hologram formula in the large-scale FRW
metric limit
1/Lp^2R(t)^2 = (1/Lp^2)[1 - Lp^3|Vacuum Coherence|^2]
1/R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]
R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2]^-1
Where from inflation
Omega(random ZPF) + Omega(matter) + Omega(radiation) + Omega(vacuum
coherence) = 1
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