Saturday, December 18, 2004

The Universes Next Door
PS The NASA Pioneer 10&!! Anomaly a_g = cH ~ 10^-7 cm/sec^2 directed back to Sun is more evidence for the local macro-quantum Higgs order parameter, this time with S^2 symmetry forming a dark energy hedgehog topological defect starting at 20AU from Sun. ending we do not know where yet. The Galactic Halo holding our solar system in the Galaxy is also a dark energy exotic vacuum blob that is more stable than Vilenken's thin vacuum domain wall.

Preliminaries on the nonlocality of gravity energy from Penrose "Road to Reality".

Note that Shipov's "oriented point" in his torsion theory extension of 1916 GR has a non-trivial topology configuration space with a spinor structure as shown in detail by Roger Penrose.

The Cartan p-form is a "density" unlike the graded Grassmann algebra analog to it. A p-form in a N > p space is a N - p dimensional hyper plane element that is dual to the p mult-vector field. The multi-vector from Grassmannian wedge products is not a "density" for integration.

Think of the multi-vectors like the Bohm hidden variable particle trajectories and the dual p forms as the pilot qubit wave fronts.

The p-form is the intersection of p 1-form covectors (N-1 dim hyperplane elements) Fig 12.10 p.228 Penrose. See Fig 12.7 & 12.8 & 12.9 p. 226 on covectors as generalized contours but with a "twist" obstruction p. 225

The p-form is what we integrate over a p-dim submanifold of the N-dim manifold. The topology is generally mutiply connected with Betti numbers and other global topological measures.

Curvature is a 2-form integrated over 2-dim sub-manifolds of spacetime. Diff(4) is automatic for these global integrals and they are, therefore, independent of the arbitrary choice of overlapping local coordinate patches or charts whose atlas covers the entire manifold. The overlap transition functions between them are precisely Einstein's general coordinate transformations (GCT) and GCT symmetry means completely arbitrary LOCAL choices of coordinate charts exactly like the completely arbitrary choice of phases in SU(n) local gauge theories! There is no rule that we MUST choose the largest possible local charts for example. However, each choice of a local coordinate chart specifies a possible distribution of local observers some (LIF) on intrinsic geodesics of the metric space others (LNIF) not. That is, there is a well conceived physical measurement scheme associated with EVERY GCT subject to local causality light cone constraints and negligible quantum gravity uncertainty in the light cone localizations.

Every GCT transition function is a switch from one configuration of local observers to another all inside a small enough spacetime blob without obstructions from event and particle horizons so that they can all exchange light signals.

"One of the beauties of this ... is that it automatically deals with any changes of variable that we may choose to invoke."

The p-forms are INVARIANT under GCT and so are their GLOBAL INTEGRALS. There is an analog to the Cauchy integral residue theorem sum over poles with the Betti-numbered wormhole handles analogous to the poles in evaluating the integrals. For our problem we are talking about the hologram closed 2-surfaces enclosing volumes.

"The parameters x^u or x^u' could be taken to be one of the coordinates in a coordinate patch in this ambient space, where we are happy to change to a different coordinate when we pass to another coordinate patch." p. 230

"This eliminates the explicit mention of awkward quantities known as 'Jacobians'" p. 235

*None of this point set topology manifold structure closely tied to local causal measurement theory is in Hal Puthoff's too simple PV theory without a consistent measurement theory.

Splitting universes require a non-Hausdorf manifold. Fig 12.5 p. 223

A Hausdorff space forbids the splitting and fusion of alternative world timelines in a PK Dickian multi-verse of parallel universes next door. A non-Hausdorff space means we can pass to a universe next door where Phillip Roth's "The Conspiracy Against America" and P.K. Dick's "The Man in the High Castle" are actual realities down to the last comma!

On Dec 18, 2004, at 3:44 PM, Jack Sarfatti wrote:

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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