## Saturday, January 01, 2005

Dark Energy from Entropy of World Hologram

On Jan 1, 2005, at 3:05 PM, Jack Sarfatti wrote:

On Dec 31, 2004, at 4:36 PM, Carlos Perelman wrote:

Dear Antonio, Jack, Matti and Tony :

Jack, about the notation. The whole purpose of my paper

Mod. Phys. A vol 17, no. 32 ( 2002 ) 2095-2103

Anti de Siter Gravity from BF-Chern-Simons-Higgs theories

was to show that the MacDowell-Mansouri formulation of gravity

I don't know that work.

can be embedded in a
*more* fundamental Topological BF theory

or that.

... and of course to DERIVE the relationship that

rho (vacuum ) = (L_Planck)^ { -2 } (R_Hubble )^ { -2 } ~ 10^{ - 122 } (Planck mass)^4 .

What is rho? Energy density?

Do you mean

Vacuum Energy Density = hc/Lp^2(c/H)^2 ~ 10^-17x10^66x10^-56 ergs/cc = 10^-7 ergs/cc

Here H = R(t)^-1dR(t)/dt

R dimensionless in usual FRW metric convention.

OK I think I see.

In my theory that seems to fit t'Hooft-Susskind Hologram quite well I get the same number, but with a very different time dependence

I get

Vacuum Energy Density = hc/Lp^4R(t)^2

That is

/\(Sarfatti) = 1/(LpR(t))^2 ~ 10^-56 cm^-2

In contrast

/\(Castro) = (H/c)^2 = (1/c^2R(t)^2)(dR(t)/dt)^2 ~ 10^-56 cm^2

So we are close numerically, but there is an essential difference. I do not use c/H(t) as the cosmic length scale, instead I use LpR(t) (R(t) is a pure number)

My theory says that the t'Hooft-Susskind-Hawking-Bekenstein Hologram Entropy of the Universe is

S(Universe)/kB = R(t)^2 ~ 10^122 BITS (now)

Where

R(t)^2 = [1 - Lp^3|Vacuum Coherence|^2 - 1]^-1

Therefore R(pre -> post inflation vacuum phase transition) ~ 1 BIT at initial singularity where |Vacuum Coherence| = 0.

The mean energy to erase a BIT in the vacuum is ~ hc/LpR(t)

Therefore the vacuum dark energy density is

~ (Entropy of Universe/kB)(hc/LpR(t))(1/LpR(t))^3 = hc/Lp^4(1/R(t))^2

~ 10^-17x10^132x10^-122 = 10^-7 ergs/cc

Furthermore, my model explains why the entropy of the early universe is low from the formation of the vacuum coherence. This explains the Arrow of Time and solves the problem with inflation raised by Roger Penrose.

Vacuum Coherence obeys a GCT covariant Landau-Ginzburg equation depending on metric guv, which, in turn, depends on the Goldstone Phase of the Vacuum Coherence in a nonlinear self-organizing feedback-control loop.

On Dec 31, 2004, at 1:13 PM, Jack Sarfatti wrote:

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

On Jan 1, 2005, at 3:06 PM, Jack Sarfatti wrote:

re: http://www.arXiv.org/abs/gr-qc/0407060

Zielinski has been making over-simplified naive exaggerated unjustified claims about Alex Potorak's theory that need to be checked. Alex presented "Gravity as Nonmetricity" at GR 17. I make a few initial queries. These equations are all from Alex's handout at GR 17.

AFFINE CONNECTION = LEVI-CIVITA CONNECTION + NONMETRICITY + TORSION

You need to specify which connection is used to define the covariant derivative.

Einstein's 1916 GR only used the LEVI-CIVITA CONNECTION, therefore Alex's theory is an extended theory beyond Einstein's and is physically and mathematically not at all equivalent to Einstein's theory.

Alex defines a "gravitational field" as the "nonmetricity of the affine connection". What this really means physically must be spelled out in great detail.

In 1916 GR the LEVI-CIVITA CONNECTION "gravitational field" (LC) =/= 0 only in Local Non-Inertial Frames (LNIF) and certain combinations of components of it are the INERTIAL FORCES. The Einstein equivalence principle EEP asserts that (LC) = 0 in any Local Inertial Frame (LIF). The LOCAL TETRAD eu^a MAP

guv(LNIF) = eu^anab(LIF)ev^b

is between COINCIDENT LIFs and LNIFs at same event P. nab is the constant Minkowski metric. Therefore, at the extremum of the point test particle dynamical action

guv(P),w = 0

, = ordinary partial derivative

gab(P'|LIF) ~ nab(LIF) + (1/2)gab(P|LIF),c,d(P'-P)^c(P'-P)^d + ...

This is the EEP Ansatz! Note that the second order terms in the Taylor series contain the tidal stretch-squeeze curvature information in the relative coordinates of an extended test particle in the LIF whose center of mass moves on a timelike geodesic extremum in the curved spacetime. There are NO INERTIAL FORCES in LIF's including the REST LIF of a test particle whose center of mass is on a geodesic where "weight" vanishes.

In contrast

guv(P'|LNIF)

~ guv(P|LNIF) + guv(P|LNIF),w(P'-P)^w + (1/2)guv(P|LNIF),w,l(P'-P)^w(P'-P)^l

Similarly one can Taylor expand the Jacobian matrices at P' of the GCTs connecting coincident LNIF's in overlapping coordinate charts x^u & x^u' in same neighborhood of the common physical event P.

Alex's nonmetricity theory, like Gennady Shipov's torsion theory is what Einstein would call attempts at a unified geometrodynamic theory. The physical motivation of Alex's theory is not clear to me at present time from his paper. He does claim that in nonertial frames:

"Inertial forces play the role of a gauge field whose potential is the affine connection". He also claims to have a local pure gravity energy density and a cosmological constant in terms of the affine connection that includes both torsion and nonmetricity fields defined, not with respect to the 1916 Levi-Civita connection, but with respect to the affine connection in a self-consistent way. However, the physics of all this remains obscure.

Nonmetricity in the sense of the smaller 4D (LC) connection is expected from extra space dimensions of Kaluza-Klein "hyperspace". Torsion comes from locally gauging the 6 Lorentz space-time rotations beyond 1916 GR, which is merely the local gauging of the 4 translations generated from 4-momentum. One can also locally gauge the 4 conformal boosts to uniform proper accelerated hyperbolic motion and the 1 dilation.

Relation to the metric engineering of Warp, Wormhole & WMD AKA W^3:

In 1916 GR, with only the (LC) connection, in 4D with zero torsion and zero nonmetricity. The 2 Bianchi identities give vanishing GCT covariant divergences

Guv(vacuum)^;v = 0

This means that the pure vacuum stress-energy current densities are locally conserved all by themselves and, therefore, in the presence of matter

Tuv(matter)^;v = 0

Metric engineering practical warp drive stargate time travel is impossible to achieve under these tight restrictions. The alleged "fact" of "alien" UFOs suggests that such restrictions are not absolute. We cannot ignore such "data".

In contrast when we add exotic vacuum dark zero point energy corrections, and ignore Tuv(matter) as a good approximation we get for the exotic vacuum

Guv + /\zpfguv = 0

where

Guv(exotic dark energy zpf vacuum)^;v + /\zpf^,vguv = 0

using only the (LC) connection. Using the AFFINE CONNECTION will obviously give more torsion field and nonmetricity field correction terms. I ignore those here. We are no longer constrained by the enormous spacetime stiffness factor c^4/G = string tension = 10^19Gev/per 10^-33 cm since we do not try to tweak the Tuv(matter) term the way Hal Puthoff and Eric Davis propose to do in their entirely, in my opinion, dead end impractical strategy for metric engineering W^3 as we see in the UFO phenomenon.

The idea of practical metric engineering the fabric of spacetime for W^3 is that /\zpf depends on the VACUUM COHERENCE, which can be controlled with small power requirements on board the "Unconventional Flying Object" (Paul Hill) by Josephson-Berry phase coupling not unlike Ray Chiao's intriguing idea for the macro-quantum gravimagnetic-electromagnetic superconducting high-efficiency transducers applied to the non-propagating virtual near fields of gravity and electromagnetism.

On the physical meaning of gauge transformation and general coordinate transformations.

All connection field are also Cartan 1-forms in addition to the their metrical structure.

R. Kiehn points out that for any p-form there are three qualitatively different contributions (similarly for dual co-form manifolds for Hodge-DeRham integrals in curved spacetime and beyond) where

Integral of dp-form on p+1 co-form = Integral of p-form on boundary of p+1 co-form

d^2 = 0

d = Cartan exterior derivative

Boundary & dual to d

&^2 = 0

Boundary of a boundary = 0

Exact form f means

f = dg

Closed form means

df = 0

All exact forms are closed, but not all closed forms are exact.

Quotient space of closed forms mod exact forms = HOMOLOGY

Closed co-forms have &f* = 0, exact p co-forms are boundaries of p+1 co-forms.

Quotient space of nonbounding closed p co-forms mod bounding p co-forms is the co-Homology whose dimension is the Betti number of p-dim wormholes.

A traversable wormhole stargate is in a p = 3 co-form needing dark energy to sustain it for practical time travel "teleportation" "Beam me up Scotty!" Making Star Trek Real.

General p-form

= Trivial Gauge Exact p-form

+ Bohm-Aharonov-Josephson-Berry Nonlocal Wilson Phase Factor closed not-exact p-form

+ LOCAL non-closed p-form

The first term, i.e. trivial gauge exact p-forms are simply the CONTINGENT CHOICE of a local coordinate chart in the neighborhood of physical event E. This contingent choice has direct operational physical meaning and is not simply a formal virtual choice. In the case of Einstein's general relativity this choice specifies the set of generically local noninertial detectors MEASURING event E. In the case of say U(1) EM one can imagine a similar choice in the extra Kaluza-Klein space dimension, or, alternatively, setting an absolute phase on a one-handed clock in internal fiber bundle S1 circle space.

The second term is the non-local global topology term from, for example, non-vanishing Betti numbers of multiple-connectivity in the p-dim slice of the n-dim manifold. This seems to give the Vilenken-Taub curvature-without-curvature for a thin unstable wall of dark energy where the third local "curl" term above vanishes for p = 1 but, nevertheless, non-inertial observers must fire rocket motors with jets pointing away from the wall to hover motionless at fixed distance from the thin wall of dark energy that is antigravitating. That is we have a "gravitational" (LC) =/= 0 field even though the local covariant curl of (LC) (AKA curvature-with-curvature) vanishes! This reminds us of the Bohm-Aharonov effect.

For example an electron beam takes both paths where curl A = 0, but A =/= 0 and there is a shift in the position of the fringes proportional to the quantized flux of magnetic curlA threading the two paths even though no curl A ever touches the electrons. A is like the (LC) connection "universal g-force" and curlA is like the local tidal stretch-squeeze curvature. The Bohm-Aharonov effect is "magnetism without magnetism", the Vilenken-Taub effect (1983) is "curvature without curvature".

Choosing the local gauge in this case is selecting HOVERING NONINERTIAL OBSERVERS who must use non-gravity forces to keep off the timelike geodesics in the vacuum. This is very direct local meaning of the connection field in GR where each contingent choice of local coordinate chart has direct physical visualization. How to visualize the locality of the connection A field in electromagnetism is not so obvious until we focus on the test charge where the canonical momentum is

p = mv - (e/c)A

In that case we can associate A with a pseudo-Galilean transformation

v -> v' = v - (e/mc)A

mv = kinetic momentum

(e/c)A = electromagnetic field momentum of the virtual photon cloud of the test charge

This only really begins to make sense quantum mechanically where

mv = (h/i)d/dx on the qubit Bohm pilot wave of the test charge.