Shipov's remarks are in quotes.

On Nov 6, 2005, at 2:45 PM, Jack Sarfatti wrote:

Yes, Gennady I simply made a typo saying "R" when I should have said "W"
that I did not see until you pointed out the objection of the 3rd
derivative. Thanks! The basic idea I had is still correct, but here is
how I should have said it

Locally gauge T4 to get Diff(4) with B as the compensating 1-form field.

e = 1 + B

De = 0

implies

dB + W/\(1 + B) = 0

R = DW is the curvature 2-form

DR = 0 is Bianchi identity

D*W = *J(source)

is Einstein's eq.

D*J(source) = 0

is local conservation of current.

OK I will rewrite it all to fix that.

:-)


Gennady et-al

It's all really very simple. The whole thing i.e.

EM Gauge theory of U(1)

Yang-Mills Gauge theory of SU(2), SU(3) ...

1915 GR of T4 -- Diff(4)

Torsion theory of O(1,3) to ?

For c-number fields where the Diff(4) invariant Cartan notation is to
Schouten notation like Feynman diagrams is to Schwinger notation.

You can do instantly in Cartan notation what it takes much longer to do
in the old notations. And Cartan's invariant notation is much more
heuristic so one can see what's really going on physically much easier
and not get lost in arcane inefficient notational issues of the formal
mathematicians.

Rovelli's home page is here http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html

You can download is free book there. His Ch 2 contains most of the basic
equations I cite below except for

e = 1 + B

B = Lp'd'(Goldstone Phase of U(1)SU(2) --3--U(1))

which is my original equation.

1915 General Relativity in a Nutshell for Dummies ;-)
Jack wrote:
Gennady

You are asking me questions that do not apply in the new formalism.

All I need are the curvature and torsion 2-forms. They can always be
mapped into your formalism via tetrad maps. I don't care about the
details of the older tensor component formalism you use from Schouten -
takes a lot of formal work. What I got is compact simple like the
Feynman diagrams.
On Nov 5, 2005, at 6:23 AM, Gennady Shipov wrote:

Jack!

"The Feynman diagrams it are only "lines" and "points" behind which
quite certain analytical expression stand."


Of course.

"Precisely behind external differential forms quite certain geometrical
expression, wich you name old geometry, stand."

Of course. I have given the forms. They are very simple. For 1915 GR to
keep it simple.

e = 1 + B is Einstein-Cartan tetrad

B is from local gauging of T4 for some matter source field to Diff(4)
only 4 parameters here NOT 6.

ZERO TORSION (see Rovelli) here in this 1915 limit is

De = 0

D = d + W/\

W is the SPIN-CONNECTION 1-form

dB + W/\(1 + B) = 0

so that B determines W

Curvature 2-form is simply

R = DW = dW + W/\W

where

W/\W means Wa^c/\Wc^b

Bianchi identity is

DR = 0

Einstein's field equation is

D*W(Geometry) = *J(Matter)

Geometry = "Marble"

Matter = "Wood"

D*J(Matter) = 0

is local covariant conservation of stress-energy source current.

That's all there is to 1915 GR! That's literally

IT FROM BIT

in my equation

B = Lp'd'(Goldstone Phase)

B = IT

Goldstone Phase = BIT

World Hologram comes from this as well very simply with ~ Lp^2 per BIT
on the "boundary screen" on the causal horizon of expanding accelerating
3-space of our "local" past-light cone universe. All we need is ONE
geometrodynamic monopole point defect per universe in the local vacuum
coherence to get the Bekenstein-Hawking quantization in second homotopy
group = Z quantized wrapping numbers.

That is, the quantized wrapping numbers of the second homotopy group are
simply the Hawking-Bekenstein BITS on the World Hologram SCREEN from
single-valuedness of the local vacuum coherence order parameter.

It's simply the space-time T4 "Maxwell" theory LOCALLY GAUGED in
complete analogy to the locally gauged internal U(1) theory, i.e.,

Locally gauge U(1) for a source field like the electron, A is the
UNCHARGED Abelian compensating potential

F = dA

dF = 0

d*F = *J(source fields)

d*J = 0

is all of Maxwell's c-number field theory.

Similarly for Yang-Mills

Locally gauge SU(2) , SU(3) etc. get B a 1-form with 2 tangent fiber
indices like W spin connection in GR

D = d + B/\

F = DB

DF = 0

D*F = *J(source fields)

D*J = 0

is all of c-number Yang-Mills theory where now B carries the same
charges as the source fields.

Again for comparison

1915 GR is a bit indirect

B now is from locally gauging T4 to get FOUR tetrad fields

e = 1 + B 1-form

actually this is

e^a = 1^a + B^a

a = 0,1,2,3

D = d + W/\

De = 0 implies dB + W/\(1 + B) = 0

R = DW

DR = 0

D*W = *J(sources)

D*J = 0 is local covariant conservation of source currents.

Add TORSION from locally gauging O(1,3) that is not locally gauged in
1915 GR

We now have a new connection

W + S i.e. Wa^b + Sa^b

S is the TORSION connection 1-form from local gauging of O(1,3)

W is the SPIN connection 1-form

Note that B from local gauging of T4 is

B = Lp'd'(Goldstone Phase)

where 'd' is made from the P^a Lie algebra of T4 in sense of

B^a = Lp(Goldstone Phase)^,a

,a is ordinary partial derivative

but the physics is in the SINGULAR GAUGE TRANSFORMATIONS from
NON-TRIVIAL HOMOTOPY of the DEGENERATE VACUUM COHERENT LOCAL ORDER
PARAMETER MANIFOLD G/H from the STANDARD MODEL's

G = U(1)hyperchargeSU(2)weak --3 adjoint irrep of SU(2) -- H = U(1)em

Degenerate Vacuum Manifold is G/H = U(1)hypercharge SU(2)weak/U(1)em = S2

i.e. Cosets of ORDERED U(1)em normal subgroup H in UNORDERED
U(1)hyperchargeSU(2)weak

Homotopy2(S2) = Z = WRAPPING NUMBERS

+1 & - 1 are the HEDGEHOGS

i.e. massive W+W0W-, massless photon

One Higgs particle as small vibration the single real Higgs amplitude
whose real conjugate Goldstone phase modulation gives Einstein's GR via

B^a = Lp(Goldstone Phase)^,a

Note in SU(2)weak group parameter fiber space - the one real NON-ZERO
VEV points along the 3-axis. Therefore the Goldstone Phase for the
emergence of gravity's curved spacetime is the rotation angle in the 1-2
plane about the 3-axis.

The NASA Pioneer anomaly is a HEDGEHOG showing that the vacuum order
parameter is in the 3-adjoint irrep of SU(2) as we expect from the
Standard Model of Leptons & Quarks.

but

S from local gauging of O(1,3)

i.e. S ~ Sa^b in the Lie Algebra of O(1,3) but with SINGULAR
MULTI-VALUED GAUGE TRANSFORMATIONS, i.e.

S ~ d'd'(Goldstone Phase) =/= 0

Note that W ~ Wa^b is also in Lie Algebra of O(1,3) but in a TRIVIAL
NON-SINGULAR WAY where

d'd'(Goldstone Phase) = 0

i.e. dB + W/\(1 + B) = 0

Now

D' = d + W/\ + S/\

The curvature 2-form is

R' = R + S/\W

D' = D + S/\

The field equations for R' are

D'R' = 0

Note that

D'R' = DR + D(S/\W) + S/\(R + S/\W)

= D(S/\W) + S/\(R + S/\W) = 0 Bianchi identities

D'*W = *J'1

D'*J'1 = 0

Similarly for the TORSION 2-FORM

T = D'S = DS + S/\S =/= 0 when S =/= 0

D'T = 0

D'*S = *J2

D'*J2 = 0

That's IT FROM BIT in a NUTSHELL prior to trying to quantize, which one
should not do for the R' & T' curvature and torsion 2-form fields that
are ODLRO VACUUM MACRO-QUANTUM COHERENT emergent low-energy c-number
local fields. You CAN MICRO-QUANTIZE only their SMALL VIBRATIONS
relative to them as Diff(4) & higher group COVARIANT dynamical
backgrounds. When the vacuum coherence vanishes like in a topological
defect core you are back to the UNSTABLE FALSE VACUUM in the Higgs
Mexican Hat Potential.

One Dirac vortex string ending on a ONE magnetic monopole in our causal
universe is enough to quantize ALL electric charges everywhere in the
universe (Hubble Bubble).

One geometrodynamical point defect in the universe from the B =
Lp'd'(Goldstone Phase) curved tetrad field is enough to quantize all
geometry on the 't Hooft-Susskind Causal Screen of their World Hologram.

That is, the information content of the universe is only of order ~
[c/H(t)]^2/4Lp^2 ~ 10^56/10^-66 ~ 10^122 BITS.

i.e. Surface integral of *R enclosing the point defect in spacelike
slice will be quantized as

Area of Surface/Lp^2 ~ Integer WRAPPING NUMBER of times the S2 VACUUM
MANIFOLD U(1)xSU(2)/U(1) is wrapped for a single wrapping of the surface
in physical 3D space.

"It is a mistake, Jack. The structural Cartan equations of group of
translations Ò(4) do not contain curvature R, as the translations
generate only torsion (see Cartan works). Witten, Baez et-al know this
and I agree with this scientists."


What I say is basically in Rovelli's book Ch 2. Also if you look at
Kibble's famous paper he has essentially what I have.
Gennady Shipov

"Rovelli and Kibble respected people, but about what they write all was
made by Cartan."


Jack Sarfatti

Rovelli has spin connection W 1-form

D = d + W/\

Gennady Shipov wrote:

"I think, that It is absolute external differential, which contains
spin connection W 1-form. In metric geometry of the general view W is
submitted as the sum

W = G + T

where G - Levi-Civita connection, T - Ricci rotation coefficients.
Structural Cartan equationsof group of translations T(4) look like

De = de + W/\e = 0 (A)

if Cartan torsion is equal to zero and if it is distinct from zero we have

De = de + W/\e = S (A')
where S is Cartan torsion 2-form.

Equations (A) are integrable, equations (A') not.

W - is the structural function of the translational grup T(4).

which satisfy Jacoby identity (Bianchi identity )

and

DW=R"

OK I think we agree now, but our notation is not same.

My "W + S" is same as your "G + T".

R = DW is curvature 2-form

DR = 0 is Bianchi identity

Gennady Shipov wrote:

"For absolute parallelism geometry we have

DW=0, (B)

and in general case

DW=R' (B')

Equations (B) are integrable, equations (B') not.

R' = DW is Cartan curvature 2-form

From (B) we have

R=DT

where R is Riemann curvature 2-form,

T is Ricci rotation coefficients 1-form.

Jack Sarfatti wrote earlier:

D*R = *J is Einstein's field eq.

Jack Sarfatti writes now:

That is an ERROR I made. A TYPO. I SHOULD HAVE WRITTEN

D*W = *J 2-form eq.

Gennady Shipov wrote:

"I suppouse *R is dual Riemann curvature 2-form. In this case the equations

D*R = *J

contain third derivatives of metric tensor."

These equations cannot be Einstein's equations!!!"

Jack Sarfatti wrote: Yes, Gennady you are correct.

Gennady Shipov wrote:

"The equations

D*R = *J

are ill-defined Einstein equations."

Jack Sarfatti writes:

Yes, Gennady thank you for pointing out my error putting in "R" where I
should have put "W" the spin connection.

Corrected version
On Nov 4, 2005, at 11:32 AM, Jack Sarfatti wrote:

I here UNIFY the Electro-Weak Force with Einstein's Gravity
Geometrodynamics.
I think this is the first time anyone has even thought of doing this?
Why did I think of this?
Simple!
Einstein's Equivalence Principle
That's why!
If leptons and quarks get their rest inertia from the Electro-weak force
vacuum symmetry breaking Higgs mechanism then so must gravity (curved
space-time) emerge from that because:

Any physical theory that does not have gravity and inertia emergent
together is a wrong theory.

Theorem of 'tHooft & Polyakov

"If the manifold of degenerate vacua contains non-contractible
two-surfaces lije the sphere S2. This corresponds to the vacuum manifold
V = G/H having a non-trivial second homotopy group PI2(G/H) =/= I. If
the unbroken VEV invariant normal subgroup G of H has a non-trivial
FUNDAMENTAL GROUP PI1(H)" HENCE A CONJUGATE GRAVITY-GENERATING GOLDSTONE
PHASE IS GUARANTEED! "then there are point defect 'monopole' solutions from

PI1(U(1)) = Z"

IN FACT IN GENERAL

"Grand unified models based on simple groups G which break to leave H =
U(1)EM must produce MONOPOLES.

The simplest monopole is the 't Hooft-Polyakov ... which appears when
SU(2) is broken to U(1) ... the 3-component Higgs field phi far from the
core of the monopole takes a HEDGEHOG configuration

VEV = (0|phi|0)3r^

where r^ is the unit radial vector in physical 3D spacelike slice of 4D
space-time."

p. 64 "Cosmic Strings & Topological Defects"

In this case however we do not have a magnetic monopole, but a charge
neutral geometrodynamic monopole because the gauge potential is not Aem,
but the curved tetrad

B = (hG/c^3)^1/2'd'(Goldstone Phase) Translation group to Diff(4)

The effective vacuum order parameter here in the 3-irrep of SU(2)weak is

a_g = -dV(Dark Energy)/dr = cH(t)r^

From Einstein's eq using w = -1

G00 ~ c^2/\zpfg00

/\zpf ~ H(t)/cr

g00 ~ 1

See below.

NOTE TO HISTORIANS:

I thought of the HEDGEHOG from the NASA Pioneer data alone BEFORE I knew
of the 't Hooft-Polyakov "theorem".


I claim that Einstein's gravity emerges from the single Goldstone phase in

e^-i(Goldstone Phase)T3

that leaves the only non-vanishing VEV (0|Higgs Field|0)3 invariant in
the 3-adjoint irrep of SU(2)weak spontaneous symmetry breaking of the vacuum

G = U(1)hypercharge SU(2)weak --3-- H = U(1)EM (photon)

i.e.

The degenerate vacuum manifold for constant (0|Higgs|0)3 is S2.

n' = 3 is the number of real scalar Higgs fields in the 3x3 irrep of
SU(2) in which the VEV is taken along the 3-direction in fiber group
parameter space.

However, U(1)xSU(2) has n = 4 real scalar fields in d = 4 space-time
corresponding to group U(2). That is one mode for each generator in the
Lie algebra.

e^-i(Goldstone Phase)T3(0|Higgs|0)3 = (0|Higgs|0)3

Einstein's geometrodynamic field, therefore is the curved tetrad 1-form

B = (hG/c^3)^1/2'd'(Goldstone Phase of U(1)xSU(2) --3-- U(1))

'd' means topological singularities in the vacuum manifold

V = G/H = U(1)hyperchargexSU(2)weak/U(1)em = S2

N = 4 = number of generators of G = U(1)xSU(2).

N - K = 1 is number of generators of H = U(1)

Therefore,

K = 3

is the number of massive SU(2)weak force gauge bosons

i.e.

W+, W0, W-

On the other hand, the number of real Higgs quanta is

n - K = 4 - 3 = 1

This provides our UNIQUE Goldstone phase for emergent Einstein-Gravity
as a c-number low-energy long range effective field theory.

The Higgs quanta on mass shell are small vibrations of the single real
Higgs VEV along the 3-direction in SU(2) group parameter space in the
3x3 matrix adjoint irrep. The physical Goldstone phase leaving that
(0|Higgs Field|0) invariant mod small oscillations is the S1 circle of
renormalizable Mexican Hat minima in the 1-2 plane of internal weak
force 3x3 group representation fiber space.

The number of massless gauge quanta is

N - K = 1, i.e. H = U(1)em.

OK, think of U(1)hypercharge SU(2)weak as a 4D group parameter space.

One real dimension for each Lie algebra generator. We have 4 with 4
conjugate phase parameter.

2 orthogonal TRANSVERSE directions are W+ & W- they are T1 & T2.

T3 is electrically charged neutral.

T4 the hypercharge is also electrically charged neutral.

The T4-T1 plane (like longitudinal-timelike virtual photon polarizations)

has a rotated frame in which one axis is W0 the massive weak
electrically neutral weak current boson

and the orthogonal axis is the MASSLESS electrically neutral PHOTON!

So that's ELECTRO-WEAK THEORY in a NUT SHELL without the PARITY
VIOLATION - we stick that in later. Now for the emergence of gravity:

Suppressing the tangent fiber indices, in compact symbolic form

ds^2 = guvdx^udx^v = (1 + B)(Minkowski)(1 + B)

D = d + W/\

De = dB + W/\B = 0

R = DW = curvature 2-form

Einstein-Hilbert Lagrangian density is for /\zpf = 0

L = R/\e/\e

DR = 0 is Bianchi identity

D*W = *J(Matter) is Einstein's field equation.

* = Hodge dual

D*J(Matter) = 0 is local conservation of matter stress-energy current
densities.


TYPO-CORRECTED Draft 3
On Nov 3, 2005, at 7:35 PM, Jack Sarfatti wrote:

On Nov 3, 2005, at 2:42 PM, art wagner wrote:

Are you totally anti-Chaplygin...? Is Lobo loco...?

No.


(http://xxx.lanl.gov/PS_cache/gr-qc/pdf/0511/0511003.pdf)


http://www-conf.slac.stanford.edu/ss...age_05_jpg.htm

Note that the energy density in the expanding universe scales as

energy density ~ (space expansion factor)^-3(1 + w) = a^-3(1 + w)

OK the skewon field has w = -1/3, therefore

skewon energy density ~ a^-3(2/3) = a^-2

Phantom energy has w - 1 therefore its energy density increases as
universe expands. This causes the BIG RIP totally destroying the universe.

However, Lorentz invariance and equivalence principle DEMAND UNIVERSALLY
for ALL vacuum ZPF

w = - 1 EXACTLY (at least for isotropic fields).

Einstein's equation for ZPF i.e.

D*W = *J(ZPF)

W = SPIN CONNECTION

translates to the w = -1 exotic vacuum equation

Guv + /\zpfguv = 0

In general in the Newtonian weak curvature Galilean v/c 1 limit

Guv + kTuv(sources) = 0

in the 00 component

G00 ~ Grad^2V ~ (G/c^2)(Energy Density)(1 + 3w)

For w = 0 we have Newton's gravity theory in Poisson eq. form.

for radiation w = +1/3 we have the famous Einstein factor of 2 in
gravity bending of light. Note that fast matter looks like light in this
regard.

For Skewons we have w = -1/3 so that the source term on RHS VANISHES.

Skewons DO NOT BEND SPACE-TIME (at least on large scale isotropic case -
that may be the loophole).

ZPF BENDS SPACE-TIME ABSOLUTELY, i.e. NO CASIMIR FORCE SUBTRACT NO
BOUNDARY FROM BOUNDARY as in QED. QED thinking FAILS for gravity. That's
one of Hal Puthoff's BIG BLUNDERS in his attempt at metric engineering.
Another is his naive use of a single global coordinate system - another
story.

For zero point energy w = -1 ON THE NOSE and in isotropic case

G00(ZPF) ~ Grad^2V(ZPF) ~ -2(G/c^2)(Energy Density)

Therefore,

POSITIVE ZPF ENERGY DENSITY ANTIGRAVITATES with a UNIVERSAL REPULSION

NEGATIVE ZPF ENERGY DENSITY GRAVITATES with a UNIVERSAL ATTRACTION

Put them together for NEGATIVE MATTER PROPULSION of the GEODESIC KIND -
no g-forces!

The basic story is simple!

You need torsion to make /\zpf inhomogeneous. Maybe you need a Skewon as
well as an auxilliary field? I don't know yet.

Also small scale anistropies may be important. Above is only for FRW
cosmology very large scale homogeneous isotropic "aether".

Further

Total Exotic Vacuum Virtual Particle "4D Super-Solid" Density = Higgs
Vacuum Locally Coherent Condensate Density + Nonlocally Coherent Locally
Incoherent EPR ZPF density

The second term on RHS can be locally negative as can the LHS.

Remember in the Einstein-Podolsky-Rosen-Bohm effect, the photon pair
state is nonlocally coherent but locally incoherent. Same for momentum
pair correlated interferometry. The Higgs field however is also LOCALLY
COHERENT and it is that LOCAL COHERENCE that Einstein's curved
space-time gravity emerges from!

B(curved) ~ 'd'(Goldstone Phase of U(1)yxSU(2)weak - U(1)em)

i.e. point defects like Pioneer anomaly since

n = 4 real scalar fields

N = 4 generators of U(1)hyperchargexSU(2)weak

N - K = 1 = number of generators of U(1)em

K = 3

n - K = 1 is the single Higgs boson amplitude oscillation whose
conjugate phase is the Goldstone phase out of which Einstein's 1915 GR
field equations emerge quite simply.

K = 3 massive weak force bosons W+, W0, W-

N - K = 1 is the massless photon of H = U(1)em

The NASA PIONEER gravity anomaly data show this effect clearly on
macro-scale of tens of AU with the point defect d' = 0 at center of our Sun

i.e.
hedgehog.gif

This is a point defect with "wrapping number" = -1.

Instead of magnetization we have

a_g = -cH(t) ~ 1 nanometer per sec^2 anomalous dark energy blue shift
between the two S2 spherical surfaces. First one at ~ 20AU. Don't know
where 2nd one ends.

That is anomalous part of the radial geodesic equation is

dr^2/dt^2 - a_g = 0

a_g as a vector is constant

/\zpf = H(t)/cr

V(ZPF) = c^2/\zpfr^2

= cH(t)r

a_g = - dV(ZPF)/dr = - cH(t)

as observed.

Most of this is in my book Super Cosmos.
http://amazon.com

But the U(1)hyperchargeSU(2)weak --- U(1)em

will be in book #4 of

Space-Time and Beyond: The Series

you still working on the Shipov frictionless table-top drive,
Jack-o?

thus:
George Bush has always loved secrecy, and this appears to have extended

to the business activities -- or alleged business activities -- of
Zapata Offshore. A small window on a whole range of secret and
semisecret activities and transactions during these years is provided
by recently published information about Bush's shady business relations

with Jorge Diaz Serrano of Mexico, the former head (1976-1981) of the
Mexican national oil company Pemex, who was convicted and jailed for
defrauding the Mexican government of $58 million....
http://tarpley.net/bush8.htm

http://www.rwgrayprojects.com/synerg.../plate03z.html.

--ducs chez Kyoto!
http://tarpley.net/bush8.htm