Summary of Vacuum Coherence Theory

On Jan 6, 2005, at 1:17 AM, Carlos Perelman wrote:

Dear Jack :

Okay, so everything is fine then with setting the infrared scale to be given by the *throat* size of the
hyperboloid (that describes de Sitter, Anti de Sitter space), which is a *constant* parameter.


OK good. It must be *constant*; because w = -1 demands it.

Okay, we agree then on this.

Yes, we agree. I will cite you on that on any publication. It's important that w = -1 severely constrains the possible choices in the model. Do you know if that point is mentioned explicitly in the literature? I don't know this field that well, but Lenny Susskind definitely writes a lot about the (anti) de Sitter space in context of his hologram idea. George Chapline Jr does not like that approach for some reason - he does not like Bekenstein black hole thermodynamics. George is concerned with 3rd law of thermo I think and the fact that condensates (both real and virtual) have zero entropy. Of course I use that to explain why early universe has small entropy.

We can still use hologram idea from Bekenstein -> Hawking -> t'Hooft-Susskind

Entropy of Universe/kB ~ R(t)^2 BITS

to explain the Arrow of Time problem in inflationary cosmology defined by Roger Penrose in "Fashion, Faith & Fantasy" GR 17 Dublin, 2005

However, independent of that

Einstein's Cosmological Constant /\ is CONTINGENT in sense of WEP Anthropic Landscape Darwinism with an infinity of "Level 1" (Max Tegmark) Hubble parallel "material" (Wheeler's "IT") universes in hyperspace as given by chaotic inflation.

/\ = (Constant Throat Size)^-2 = 10^-56 cm^-2

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

In my Vacuum Coherence Theory

/\ = Lp^-2(1 - Lp^n|Vacuum Coherence|^2)

n = 2 for World Hologram Paradigm, where Vacuum Coherence (Macro-Quantum Tsunami) is normalized as [length]^-n/2

At large scale FLRW homogeneous isotropic scale 10^2 -> 10^4 Megaparsecs |Vacuum Coherence| = constant independent of R(t) where

energy density of "stuff" real and virtual ~ R(t)^-3(1 + w)

w = 0 for cold matter

w = + 1/3 for real photons

w = -1 for random incoherent micro-quantum zero point energy vacuum fluctuations of all fields that can be quantized.

w = -1 demands that /\ = constant independent of R(t) on large-scale (not on small scale)

guv CANNOT be quantized because it is an emergent ODLRO "superfluid" field (Sakharov). However, it does have a "normal fluid" residue that huv that can be quantized, i.e. perturbation theory on the dynamical emergent c-number curved background guv. It's like BCS theory in the Gorkov formalism (Nambu-Jona Lasino).

Local ODLRO parameter Vacuum Coherence = |Higgs Amplitude|e^i(Goldstone Phase)

(suppress internal indices like in Yang-Mills type theories e.g. NASA space-probe gravity anomaly UNIFORM radial

a_g = - cH toward Sun suggests S2 space for Vacuum Coherence with hedgehog point topological defect starting 20AU from Sun.

All of this is scale-dependent like ZOOM IN-OUT wavelet transforms (renormalization group flows to fixed points, emergence of symmetries in low energy effective field theories such as here for Einstein's ODLRO 1916 GR)

Completing Andrei Sakharov's 1967 idea with PW Anderson's 1967 "More is different" emergent complexity thesis for ODLRO spontaneous broken ground state symmetries with emergent quasi-particles and collective mode excitations of the effective fields at the new levels of spontaneous self-organization:

guv(LNIF) = (Minkowski)uv + Lp^2(Goldstone Phase)(,u,v)

Pre-inflationary unstable vacuum is zero lepto-quark rest mass conformal vacuum of Penrose's twistors with no gravity at all.

Local Goldstone Phase transformations (transition functions for overlapping local coordinate charts) -> Diff(4) tensor GCTs.

Goldstone Phase(x^u) -> Goldstone Phase(x^u') = Goldstone Phase(x^u') + Chi(x^u,x^u')

GCT Jacobian Matrix

Xu'^u = Chi(x^u,x^u'),u,u' transition function for overlapping local coordinate charts

gu'v'(LNIF') = Xu'^uXv'^vguv(LNIF)

Note 16 second order ordinary partial derivatives of RIGID Goldstone Phase

64 third-order partial derivatives for connection Cartan 1-forms

256 fourth-order partial derivatives for curvature Cartan 2-forms

In general mixed partials need not commute (anholonomy).

Note that Wigner quantum limit of measuring space time with clocks of mass m + condition that no black hole forms in the measurement demands that the quantum gravity uncertainty &l in measurement of distance l is

&l > (Lp^2l)^1/3

If l = throat size ~ 10^28 cm = /\^-1/2

&l = (10^-66 10^28)^1/3 ~ 10^38/3 ~ 10^-13 cm ~ 1 fermi where hadron physics and classical electron radius e^2/mc^2 is.

Universal Regge Slope ~ (1/1Gev)^2 ~ (&l)^2 _ (1 fermi)^2 "quantum of area", i.e. Witten's "alpha'" for hadronic strings not superstrings. (My 1973 paper in "Collective Phenomena").

On Jan 6, 2005, at 1:17 AM, Carlos Perelman wrote:

Dear Jack :

Okay, so everything is fine then with setting the infrared scale to be given by the *throat* size of the
hyperboloid (that describes de Sitter, Anti de Sitter space), which is a *constant* parameter.


OK good. It must be *constant*; because w = -1 demands it.

Okay, we agree then on this.

I can send you a copy of my Mod. Phys. Letts A paper if you wish ?

Yes. You have it in pdf? Just e-mail it. :-)

Stay in touch

Carlos