Saturday, December 18, 2004

The Multiverse is a Hologram

t'Hooft and Susskind building on Bekenstein and Hawking conjectured that the dimensionless information content in a volume of space is the area of its boundary divided by 4Planck area. Whether those are c-bits or qubits is left unclear.

In Cartan's forms, which are automatically Diff(4) invariant, and which permit integrals on curved manifolds, circumventing some of the gravity nonlocality problem, the Levi-Civita connection field is a 1-form and the curvature is a 2-form.

Einstein's field equation, including the dark energy local field correction, is

Guv + /\zpfguv = 8pi(G/c^4)Tuv

The dimensions of the "marble" geometrodynamic LHS are 1/Area consistent with the Cartan curvature 2-form with INVARIANT Hodge DeRham integrals over 2D coform AREAS. This is automatically HOLOGRAPHIC since VOLUMES are replaced by AREAS!

This is because 8pi(G/c^4) has dimension [Length/Energy] = (String Tension)^-1.

Note that non-Perturbative background-independent Quantum Loop Gravity also rests fundamentally on the quantum area operator as does my own macro-quantum coherent "More is Different" emergence derivation of Einstein's local GR from the rigid Goldstone phase of the Higgs Vacuum Order Parameter in the Inflationary Phase Transition of the Big Bang from the unstable flat false micro-quantum vacuum to the stable curved macro-quantum coherent holographic vacuum with lower zero point energy density (small Cosmological Constant) and lower entropy (smaller phase space volume).

That is, Cartan's tetrads eu^a come from the Bohm elasticity giant pilot wave constraint

eu^a,a = Kronecker Deltau^a,a + (Area Quantum)(Goldstone Phase),u

,a is ordinary partial derivative

When the "rigid" Goldstone Phase = 0

eu^a = Kronecker Deltau^a

guv(Curved LNIF) = eu^a(Minkowski)abev^b = (Minkowski)uv = PRE-INFLATION FALSE VACUUM

in that limit.

In general

guv(LNIF) = [Minkowski (LIF)]uv + (1/2)(Eu,v + Ev,u)

Eu = (Quantum of Area)(Goldstone Phase),u

This is not perturbation theory and guv is a dynamical field.

Note also that the Vilenken unstable flat DARK ENERGY vacuum domain wall solution is a finite spacetime blob "Lorentzian instanton" inside of which there is zero conformal curvature with a non-trivial {LC} connection field. Hovering LNIF observers at a fixed distance z from the wall (x-y plane) must fire their rocket motors away from the wall that is effectively an anti-gravity field in Newton's sense. Timelike LIF geodesics appear as hyperbolic "constant accelerating" Rindler motion to these stationary hovering non-geodesic LNIF observers using non-gravity force (ejected propellant) to keep off the geodesics that recede from the wall in the wall's brief violent history.

This is "Curvature without curvature" a nonlocal GR analog to the Bohm-Aharonov effect of "Magnetism without magnetism". The gravity energy is also nonlocal and this is another example of the disembodied footprint of micro-quantum nonlocality in the local macro-quantum Einstein field equations. There is no such thing as the "classical world" there is only the "macro-quantum world" created in the More is different Inflationary Big Bang.

The conformally curved vacuum region outside the finite spacetime blob of the Vilenken-Taub Curvature without curvature solution is like the magnetic flux inside the long thin solenoid in the Bohm-Aharonov electron beam experiment. The need for LNIF non-geodesic observers to fire their rockets away from the wall to stay at a fixed distance z from the wall is like the fringe shift in the Bohm-Aharonov experiment. However, here EVERY POINT in the BLOB is like the coming together of the two paths for the alternative histories of the electron in the Bohm-Aharonov analog. This is familiar in GR where the universe recedes equally from every vantage point with no preferred "center" like an infinite homogeneous rubber sheet stretching isotropically from every point.

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