Wednesday, January 04, 2006

Beyond Reductionism

On Jan 4, 2006, at 6:30 PM, Gary S. Bekkum wrote:
Dan has been big on Laughlin for a while.

If so, Dan should not downgrade physics!

Laughlin (Stanford) wrote:

"I have no idea whether the properties of the universe as we know it are fundamental or emergent,"

But I do have the idea! That's the whole point here!

Somewhat over simplified

e = 1 + Lp"d(Goldstone Vacuum Phase)" = LINE TETRAD = 1 + B

ds^2 = e(Flat)e = (1 + B)(Flat)(1 + B) is Einstein's 1915 NONLINEAR theory of gravity.

Note the B^2 nonlinearity

When the PLANCK COSMIC LANDSCAPE vacuum manifold is S2 rather than the above S1, then

B is not closed.


dB =/= 0 is the CURVED AREA 2-FORM

d^2B = 0 is the CURVED VOLUME 3-FORM

it is locally zero, but nonlocally non-zero in the DeRham Integral from the Higgs Field Goldstone Phase Singularities AKA topological defects.

This is the generalized NONLOCAL Bohm-Aharonov Effect (B-A).

Ordinary EM B-A is "Flux without flux" i.e. "Area without area" i.e. A is 1-form & B = dA is 2-form, but dA = 0 where the electrons are on the closed loop, nevertheless the dA =/= 0 far away inside the coil shifts the positions of the electrons on the screen. This is a string defect topology where the superconducting ground state manifold is S1.

For geometrodynamics we UP THE ANTE A NOTCH to S2


i.e. Hawking-Bekenstein entropy of black holes + 't Hooft-Susskind World Holography

"but I believe the mere possibility of the latter must give string theorists pause for it would imply that more than one set of microscopic equations is consistent with experiment—so that we are blind to the microscopic equations until better experi ments are designed—and also that the true nature of these equations is irrelevant to our world. So the challenge to conventional thinking about the universe posed by these small-science discoveries is actually troubling and very deep."

On Jan 4, 2006, at 2:07 PM, Jack Sarfatti wrote:

The electroweak-Higgs field density is 10^40 joules/cc ~ 6 10^58 ev/cc

The electron mass is ~ 5x10^5 ev

(2x10^-18cm)^3 ~ 10^-53cm^3

Therefore, the electro-weak coherence length in the sense of the local nonlinear Landau-Ginzburg equation is ~ 2x10^-18cm

i.e. the point defect S2 core for leptons and quarks is a sphere ~ 2x10^-18 cm.

This means that the electro-weak Higgs field drops from its constant
value to zero inside each lepton and quark in a tiny sphere of ~
2x10^-18 cm.

On Jan 4, 2006, at 8:58 AM,

Correction of sign

/\zpf = (Quantum of Area)^-1(|Higgs Field|^2 - 1)

because a topological defect is where

|Higgs Field| -> 0

Goldstone Phases undefined (phase singularity)

In order that the defect be STABLE the zero point pressure must be POSITIVE, i.e.

/\zpf < 0

This is a kind of WIMP, i.e. a self-sustaining GLOB of dark matter.

The 10^-33 cm Planck-scale vacuum manifold G/H ~ S2 fiber also means that the non-bounding closed spacelike 2D surfaces in ordinary 3 + 1 space-time contain all the geometrodynamical degrees of freedom of the interior that contains the point defect phase singularity (Quantized World Hologram).

The t-Hooft-Susskind CONJECTURE is PROVED and Einstein's GR emerges from it.

On Jan 3, 2006, at 7:18 PM, Jack Sarfatti wrote:

On Jan 3, 2006, at 5:50 PM, Gary S. Bekkum wrote:


"Cern's chief theorist Professor John Ellis even thinks finding the Higgs could shed light on another great mystery in physics: dark energy.

Dark discovery

In 1998, two teams studying supernovae showed that this dark energy is accelerating the expansion of the Universe. Subsequent work revealed that dark energy may make up about 70% of the Universe, but the best theories could not explain it.

According to John Ellis, however, the Higgs field is the perfect candidate for the source of dark energy."

Yes, that is how it is in my theory where the nonrandom coherent vacuum Higgs fields (more than one) are sources and sinks of random zero point energy density ~ /\zpf (in geometrodynamic units of curvature i.e. 1/Area).

My ANSATZ is that only the locally "wood" random ZPF bends space time because the non random condensate Higgs field is the "marble" geometrodynamic field that is being bent!

/\zpf = (Quantum of Area)^-1[1 - |Higgs Field|^2]

Where the "Higgs field" is normalized to be a pure number.

/\zpf > 0 is repulsive virtual "dark energy" with positive zero point energy density, assuming w = - 1.

/\zpf < 0 is attractive virtual "dark matter" with negative zero point energy density, assuming w = - 1.

In the Newtonian static limit of general relativity Einstein's exotic vacuum field equation

Guv + /\zpfguv = 0

reduces to the Poisson equation for Vzpf the gravity potential energy per unit test mass m directly induced by zero point energy density ~ /\zpf.

Laplacian Vzpf = c^2/\zpf

Note, for a spherically symmetric uniform zero point energy density 3D harmonic oscillator potential

Vzpf = -(1/2)c^2/\zpfr^2

for test particle mass m

Fzpf/m = - dVzpf/dr = +c^2/\zpfr

This is a radial universal attractive confinement force for /\zpf < 0.
It is repulsive for /\zpf > 0

Laplacian of Vzpf = -c^2d^2V/dr^2 = -c^2/\zpf

Where the sign convention is that a positive source term is an attractive field.

If the Higgs field has n real components Hi, then

|Higgs Field|^2 = Sum of Hi^2, i = 1 to n

The number of Goldstone phases that defines the vacuum manifold "landscape" G(unordered)/H(ordered) as the unit sphere S^n-1 for fixed |Higgs Field| magnitude with n - 1 Goldstone phases.

n = 2 has 1 Goldstone phase

n = 3 has 2 Goldstone phases

n = 4 has 3 Goldstone phases ...

Note when n = 1, then we have S^0 i.e. +1 and -1 with discrete Goldstone phases 0 and pi.

The smooth curved space-time tetrad field in local frame invariant form is a Cartan 1-form B ~ d(Goldstone Phase)

d = exterior derivative

Lp^2 = hG/c^3

for n = 2 with only one Goldstone phase theta

B = Lpd(theta)

dB = Lpd^2(theta) = 0 locally

However, for a closed loop surrounding the string vortex defect where Higgs --> 0 and Goldstone phase is undefined

Line integral of B around the closed (non-bounding cycle) loop = Lp integer

integer = winding number

because first homotopy group ~ integers

It's AS IF "Stokes theorem" there is a "flux" "dB" through the loop.

This is the Bohm-Aharonov effect of "flux without flux" like Wheeler's "mass without mass" and "charge without charge"

Next n = 3 with Goldstone phases theta, phi

B/Lp = [(dtheta)(phi) - (theta)(dphi)]

note the - sign. If it were + what I want will not work.

dB/Lp = 2(dtheta)/\(dphi) =/= 0

d^2B = 0

This gives trivially for

A = dB/Lp^2 = Geometrodynamics Area Flux Density

1. Bekenstein-Hawking S ~ Area/Lp^2

2. 't-Hooft/Susskind hologram

i.e. Volume without volume since, for a non-bounding 2-cycle surrounding at least one "monopole" point defect, the non-trivial second homotopy

Closed Surface Integral of A ~ Lp^2(integer)

integer = sphere wrapping number i.e. 2D winding number from non- trivial 2nd homotopy group for stable defects.

Then use the singular AS IF Gauss theorem i.e.

dA is locally zero but not globally zero.

dA is the "Volume without volume" 3-form.

"The Higgs mechanism fills all of space with a field. Unlike the gravitational field, which is strong around the Sun and the centre of the galaxy, the Higgs field would have essentially the same value everywhere," he explains.

'It would give you dark energy, in the sense that dark energy is energy density in empty space a long way away from any matter.'

There's just a small problem with the idea, says John Ellis: it gives 120 orders of magnitude too much dark energy.

If we find the Higgs, it would corroborate this whole theory that there's this Higgs field sitting throughout the Universe providing dark energy. Then we can get on to the next question which is why it has the value it does."

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