Torsion Fields

Some toy model calculations
I. 1 + 1 string spacetime slice, neglecting Weyl conformal dilation but
including energy and momentum translation generators i.e. A00 = Energy
Generator, A11 = Linear Momentum Generator in sense of Noether's theorem
relating symmetries to conservation laws for continuous groups. We mean
appropriate matrix representations of the Lie algebra depending on what
physical vector space they operate on, e.g. Cartan mobile tetrad local
frames of reference for gravity and internal vector spaces for "charges"
of U(1), SU(2) & SU(3).

The geometrodynamic gauge-covariant partial derivatives acting on
Tuv(source) matter fields are

,u --- ;u = ,u + (Connection)u^a^bAab

(use ' for base space indices)

;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11

+ (Connection)0'^1^0A10 + (Connection)0'^0^1A01

A01 = - A10 = space-time Lorentz boost

;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Linear
Momentum)

+ [(Connection)0'^1^0 - (Connection)0'^0^1]A10

;0' = ,0' + (LC Connection)0'^0^0(Energy) + (LC Connection)0'^1^1(Linear
Momentum)

+ (Tensor Torsion Field)0'^1^0(Lorentz Boost)

Note how the String Torsion Field is the Yang-Mills "Phase" of the
Lorentz Boost.

The Equivalence Principle is encoded in the (LC Connection) terms.

Similarly for ;1

The tetrads tilt in infinitesimal displacements as:

ea(x + dx) = eb(x)(Connection at x)u^badx^u

e0(x + dx) = [(Connection at x)0'^00dx^0' + (Connection at
x)1'^00dx^1']e0(x)

+ [(Connection at x)0'^10dx^0' + (Connection at x)1'^10dx^1']e1(x)

e1(x + dx) = [(Connection at x)0'^01dx^0' + (Connection at
x)1'^01dx^1']e0(x)

+ [(Connection at x)0'^11dx^0' + (Connection at x)1'^11dx^1']e1(x)

II 2 + 1 slice for anyonic vacuum ODLRO fractional charge/quantum
statistics "World Hologram Plate"

cc* + c*ce^i(Anyonic Phase) = 1

Anyonic Phase = 0 2D fermions

Anyonic Phase = pi 2D bosons

Control Anyonic Phase with perpendicular magnetic field on a 2D nano
quantum well showing fractional quantum Hall effect.



Exotic matter effects are neither fermion nor boson.

What does that do to the spin-statistics connection?

Flux tubes pin to charged fermions. Effective charges are fractional
like quarks, but only in 2D + 1 space-time "surfaces". In world
holography there are no dynamically independent volume degrees of
freedom for the geometrodynamic field, hence the Bekenstein bound for
black hole thermodynamics and the amount of bits that can be packed into
a Volume V ~ V^2/3/Lp^2 ~ (/\Lp^2)^-1 for our pocket universe on the
cosmic landscape of parallel universes.

,u --- ;u = ,u + (Connection)u^a^bAab

;0' = ,0' + (Connection)0'^a^bAab

;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11 +
(Connection)0'^2^2A22

+ (Connection)0'^0^1A01 + (Connection)0'^1^0A10

+ (Connection)0'^0^2A02 + (Connection)0'^2^0A20

+ (Connection)0'^1^2A12 + (Connection)0'^2^1A21

;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +

(Connection)0'^2^2(Momentum2)

+ [(Connection)0'^0^1 - (Connection)0'^1^0]A01

+ [(Connection)0'^0^2 - (Connection)0'^2^0]A02

+ [(Connection)0'^1^2 - (Connection)0'^2^1]A12

;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +

(Connection)0'^2^2(Momentum2)

+ (TORSION)0'^0^1 (LORENTZ BOOST)01

+ (TORSION)0'^0^2 (LORENTZ BOOST)02

+ (TORSION)0'^1^2 (ROTATION)12

Similarly for ;1'

Note that in Einstein's 1916 theory, TORSION = 0, therefore the Lorentz
boost and rotation terms vanish!

Homework, do this for 3D + 1.


On Aug 29, 2006, at 8:32 AM, Jack Sarfatti wrote:

Bottom Line
Gravity is "More is different" emergent from the Standard Model of
quarks & leptons with gauge bosons. Standard quantum gravity theories
are not even wrong, i.e. loop quantum gravity, string theory, canonical
quantization are like trying to quantize elasticity theory.

This is the 11th dimension so to speak. 10 from the Poincare group.
From the principle fiber bundle

M(Base Space) = Cartan Mobile Tetrad Frame Fiber Bundle/(Poincare Group
+ Weyl Dilation)

dimM = 11?

This is intuitive - still thinking about it - non-rigorous.

That is, 4 translations of the tetrad local frame, 3 rotations, 3 boosts
+ 1 Weyl dilation. Each parameter "phase" "angle of rotation" is a
"dimension" of M.

11 G-Orbit equivalence classes partition of the tetrad bundle.

G = Poincare Group + Weyl Dilation
(universal symmetry group for emergent spacetime physics)

Also an addition 4 special conformal transformations not accounted for
(Tony Smith)

,u --- ;u = ,u + (Connection)u^a^bAab

"Gauge covariant partial derivative" analog to internal symmetry
Yang-Mills SU(2), SU(3) ...

{Aab} = Lie Algebra of G

The Cartan mobile tetrad frames tilt & stretch/contract relative to each
other

ea(x + dx) = eb(x)(Connection at x)u^badx^u

(ea|eb) = (Minkowski metric)ab = nab

(eu|ev) = (Curvilinear Metric)uv = guv

e^a = eu^adx^u

eu = eu^a&a

Identity action = I = e^a&a = I' + B

F = dB ~ dTheta/\dPhi

Theta & Phi = Goldstone phases of vacuum ODLRO Higgs inflation field
with 3 real components (in one toy model)

B ~ Theta/\dPhi - dTheta/\Phi

d^2 = 0

D = d + B/\

DF = 0

D*F = *J

D*J = 0

Yang-Mills field equations for U(1)xSU(2)xSU(3) of standard model in
false vacuum that is globally flat.

i.e. Gravity emergent from the Standard Model of quarks & leptons with
gauge bosons.

On Aug 29, 2006, at 2:05 AM, Carlos Castro wrote:

Dear Jack :

Also in Weyl's geometry the non-metricity tensor Q is
zero as well.

The Weyl covariant derivative of the metric is zero.
Despite that the lengths of vectors change under
parallel transport (in Weyl spacetime )
the angle of two vectors remains the same ( conformal
property ) under paralell transport.

Best wishes

Carlos

What utter nonsence - Isacc Asimov is far better.

By the way did anyone notice Aldabron expoding in a supernova a few days
ago, I slept throught it.

The light must have only just got here, bit slow, light!

--
Golden Helmet
"Jack Sarfatti" wrote in message
om...
Some toy model calculations
I. 1 + 1 string spacetime slice, neglecting Weyl conformal dilation but
including energy and momentum translation generators i.e. A00 = Energy
Generator, A11 = Linear Momentum Generator in sense of Noether's theorem
relating symmetries to conservation laws for continuous groups. We mean
appropriate matrix representations of the Lie algebra depending on what
physical vector space they operate on, e.g. Cartan mobile tetrad local
frames of reference for gravity and internal vector spaces for "charges"
of U(1), SU(2) & SU(3).

The geometrodynamic gauge-covariant partial derivatives acting on
Tuv(source) matter fields are

,u --- ;u = ,u + (Connection)u^a^bAab

(use ' for base space indices)

;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11

+ (Connection)0'^1^0A10 + (Connection)0'^0^1A01

A01 = - A10 = space-time Lorentz boost

;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Linear
Momentum)

+ [(Connection)0'^1^0 - (Connection)0'^0^1]A10

;0' = ,0' + (LC Connection)0'^0^0(Energy) + (LC Connection)0'^1^1(Linear
Momentum)

+ (Tensor Torsion Field)0'^1^0(Lorentz Boost)

Note how the String Torsion Field is the Yang-Mills "Phase" of the Lorentz
Boost.

The Equivalence Principle is encoded in the (LC Connection) terms.

Similarly for ;1

The tetrads tilt in infinitesimal displacements as:

ea(x + dx) = eb(x)(Connection at x)u^badx^u

e0(x + dx) = [(Connection at x)0'^00dx^0' + (Connection at
x)1'^00dx^1']e0(x)

+ [(Connection at x)0'^10dx^0' + (Connection at x)1'^10dx^1']e1(x)

e1(x + dx) = [(Connection at x)0'^01dx^0' + (Connection at
x)1'^01dx^1']e0(x)

+ [(Connection at x)0'^11dx^0' + (Connection at x)1'^11dx^1']e1(x)

II 2 + 1 slice for anyonic vacuum ODLRO fractional charge/quantum
statistics "World Hologram Plate"

cc* + c*ce^i(Anyonic Phase) = 1

Anyonic Phase = 0 2D fermions

Anyonic Phase = pi 2D bosons

Control Anyonic Phase with perpendicular magnetic field on a 2D nano
quantum well showing fractional quantum Hall effect.



Exotic matter effects are neither fermion nor boson.

What does that do to the spin-statistics connection?

Flux tubes pin to charged fermions. Effective charges are fractional like
quarks, but only in 2D + 1 space-time "surfaces". In world holography
there are no dynamically independent volume degrees of freedom for the
geometrodynamic field, hence the Bekenstein bound for black hole
thermodynamics and the amount of bits that can be packed into a Volume V ~
V^2/3/Lp^2 ~ (/\Lp^2)^-1 for our pocket universe on the cosmic landscape
of parallel universes.

,u --- ;u = ,u + (Connection)u^a^bAab

;0' = ,0' + (Connection)0'^a^bAab

;0' = ,0' + (Connection)0'^0^0A00 + (Connection)0'^1^1A11 +
(Connection)0'^2^2A22

+ (Connection)0'^0^1A01 + (Connection)0'^1^0A10

+ (Connection)0'^0^2A02 + (Connection)0'^2^0A20

+ (Connection)0'^1^2A12 + (Connection)0'^2^1A21

;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +

(Connection)0'^2^2(Momentum2)

+ [(Connection)0'^0^1 - (Connection)0'^1^0]A01

+ [(Connection)0'^0^2 - (Connection)0'^2^0]A02

+ [(Connection)0'^1^2 - (Connection)0'^2^1]A12

;0' = ,0' + (Connection)0'^0^0(Energy) + (Connection)0'^1^1(Momentum1) +

(Connection)0'^2^2(Momentum2)

+ (TORSION)0'^0^1 (LORENTZ BOOST)01

+ (TORSION)0'^0^2 (LORENTZ BOOST)02

+ (TORSION)0'^1^2 (ROTATION)12

Similarly for ;1'

Note that in Einstein's 1916 theory, TORSION = 0, therefore the Lorentz
boost and rotation terms vanish!

Homework, do this for 3D + 1.


On Aug 29, 2006, at 8:32 AM, Jack Sarfatti wrote:

Bottom Line
Gravity is "More is different" emergent from the Standard Model of quarks
& leptons with gauge bosons. Standard quantum gravity theories are not
even wrong, i.e. loop quantum gravity, string theory, canonical
quantization are like trying to quantize elasticity theory.

This is the 11th dimension so to speak. 10 from the Poincare group.
From the principle fiber bundle

M(Base Space) = Cartan Mobile Tetrad Frame Fiber Bundle/(Poincare Group +
Weyl Dilation)

dimM = 11?

This is intuitive - still thinking about it - non-rigorous.

That is, 4 translations of the tetrad local frame, 3 rotations, 3 boosts +
1 Weyl dilation. Each parameter "phase" "angle of rotation" is a
"dimension" of M.

11 G-Orbit equivalence classes partition of the tetrad bundle.

G = Poincare Group + Weyl Dilation
(universal symmetry group for emergent spacetime physics)

Also an addition 4 special conformal transformations not accounted for
(Tony Smith)

,u --- ;u = ,u + (Connection)u^a^bAab

"Gauge covariant partial derivative" analog to internal symmetry
Yang-Mills SU(2), SU(3) ...

{Aab} = Lie Algebra of G

The Cartan mobile tetrad frames tilt & stretch/contract relative to each
other

ea(x + dx) = eb(x)(Connection at x)u^badx^u

(ea|eb) = (Minkowski metric)ab = nab

(eu|ev) = (Curvilinear Metric)uv = guv

e^a = eu^adx^u

eu = eu^a&a

Identity action = I = e^a&a = I' + B

F = dB ~ dTheta/\dPhi

Theta & Phi = Goldstone phases of vacuum ODLRO Higgs inflation field with
3 real components (in one toy model)

B ~ Theta/\dPhi - dTheta/\Phi

d^2 = 0

D = d + B/\

DF = 0

D*F = *J

D*J = 0

Yang-Mills field equations for U(1)xSU(2)xSU(3) of standard model in false
vacuum that is globally flat.

i.e. Gravity emergent from the Standard Model of quarks & leptons with
gauge bosons.

On Aug 29, 2006, at 2:05 AM, Carlos Castro wrote:

Dear Jack :

Also in Weyl's geometry the non-metricity tensor Q is
zero as well.

The Weyl covariant derivative of the metric is zero.
Despite that the lengths of vectors change under
parallel transport (in Weyl spacetime )
the angle of two vectors remains the same ( conformal
property ) under paralell transport.

Best wishes

Carlos

Golden helmet wrote:
What utter nonsence - Isacc Asimov is far better.

I personally prefer John Stuart Mill. Asimov wrote about the laws of
robotics. However he begs an awful lot of questions. One of the things
dogging Christian moral philosophy thoughout the centuries has been the
question of pacifism. Asimov gives us absolutely no clues. No robot
hurting a human. Suppose someone is going for you?

I prefer to have a moral philosopher with some credentials like Aquinas
with his concept of "just war", or John Stuart Mill for a completely
secular approach. Asimov you see played at being a moral philosopher,
and he isn't.

As far as robotic behaviour is concerned, this is what the manufacturer
programs in. If you want to destroy a target in Beirut and place your
bomb with 2m accuracy the electronic system will do it for you. Is this
a moral desire? Pass, however Sheik Nasrallah has said that the ****es
cannot fight another war in the forseeable future, so perhaps it was
right.