Tuesday, August 29, 2006

Emergent Gravity from Quarks and Leptons
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


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