## Wednesday, January 05, 2005

Corrections to World Hologram & Einstein's Vacuum Dark Energy

1. The entropy of universe from World Hologram as

S(Universe)/kB ~ R(t)^2

has nice feature that it solves Roger Penrose's problem with inflation of why early universe has low entropy, i.e. why Arrow of Time is in direction of accelerated expansion of space since

R(initial singularity) ~ 0 << R(today) ~ 10^61

However, George Chapline Jr objects to the whole Bekenstein-Hawking entropy ~ surface idea that is the basis of the t'Hooft-Susskind hologram. I sit on the fence on that for the moment.

However, I retract my hologram model where

/\ = (LpR(t))^-2

because it violates w = -1 for zero point energy.

That is the energy density of any "stuff" both real and virtual obeys

energy density ~ R(t)^-3(1 + w)

w = 0 for v/c << 1 real matter

w = +1/3 for radiation (real photons)

w = -1 for RANDOM INCOHERENT virtual quanta of all kinds

The energy density for ordinary matter ~ 1/R(t)^3 and ~ 1/R(t)^4 for radiation. But the dark energy density must be truly constant i.e. independent of R(t).

In my theory, Einstein's Cosmological Constant is

/\ = Lp^-2(1 - Lp^n|Vacuum Coherence|^2) ~ 10^-56 cm^-2

n is either 2 or 3 depending if you believe t'Hooft-Susskind hologram or not.

The formula must be more like what Carlos Perelman is saying

/\ = (H/c)^2

Where H is some truly constant asymptotic value of H = R(t)^-1dR(t)/dt

So that the future of our Universe is quasi-inflationary

R(t) ~ e^Ht

In that case.

OR alternatively we do not use H but introduce another contingent CONSTANT parameter /\ in the sense of the WEP and the infinity of parallel material IT worlds as explained by Max Tegmark on his website.

On Jan 5, 2005, at 4:05 AM, Carlos Perelman wrote:

Dear Christian, Brian, Jack and Tony :

I recall that Christian ( Beck ) wrote a very nice paper about vacuum fluctuations related also to
Brian's ( Josephson ) work. In any case, let me tell Christian ( since he does not know ) about the origins of the Geometric mean relationship among the vacuum energy density
involving the upper and lower scales that is also related to the *neutrino* mass :

rho = ( L_Planck )^{ -2 } ( R_Hubble )^{ -2 } =

( L_Planck )^{ -4 } ( L_Planck / R_Hubble )^{ 2 } ~

10^{ - 122 } (M_Planck )^4 = ( neutrino mass )^4 = agrees with Observations !

The neutrino mass you get from the above relationship is about 10^{ - 3 } electron volts = okay

Christian can see the *derivation* from first principles of
such geometric mean relationship described above in my paper :

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

Anti de Sitter Gravity from ( topological ) BF-Chern-Simons-Higgs Theories

In page 2098 I provide the derivation of such geometric mean relation from scratch.

The throat size of Anti de Sitter also coincides with the throat size of de Sitter space and one can take the future horizon scale of the FRW metric ( Jack's model ) to coincide with the de Sitter throat size.

Anyway, I will not bore you anymore with these messages. It is very curious these results.

Happy New year

Carlos Castro Perelman