Friday, March 04, 2005

Gauge Force/Geometrodynamic Duality

On Mar 4, 2005, at 12:11 PM, Jack Sarfatti wrote:

Written at Kavli Institute for Theoretical Physics, UCSB

I make notation change at end so as not to confound "T" as stress-energy density source tensor bending geometry from T as torsion field 1-form. I use S for torsion.

On longitudinal EM waves. If photon has a rest mass then there would be such a component. Vigier suggests a very small photon rest mass of

mc^2 = hH(t)

H(t) = Hubble.

What about vacuum phonons asks R. Kiehn? One would have to do make a calculation of the correlations of virtual electron-positron zero point density fluctuations to compute the effective elastic PV parameters from QED with vacuum coherence. However, Zielinski is still wrong since these hypothetical vacuum phonons would have to obey O(1,3)Diff(4) dynamical symmetry with possible SBS of course. No reason at all to impose Galilean boosts except as the limiting case of v/c < 0, where v is observer velocity relative to another observer. We know that the virtual quanta have NO direct "clicks" on QED-based detectors. They could only be detected by their DIRECT gravity effects via Einstein's exotic vacuum field equation

Guv + /\zpfguv = 0

Virtual electron-positron quasi BCS vacuum coherence macro-quantum local "More is different" order parameter is a complex numbered Cartan 0-form PSI with Higgs amplitude |PSI| and Goldstone phase argPSI.

Local gauge force picture:
The Einstein-Cartan tetrad is

e = I + B

I is the holonomic tetrad for pre-inflationary false-vacuum globally flat 1905 SR without gravity and without inertia, where the tangent space and base space are globally identical, i.e. Kronecker delta &u^a, u is in base space. All quantum field theories in the false vacuum are conformal with zero rest mass.

B is the anholonomic tetrad compensating field from locally gauging the translation group T4 generated by energy-momentum Pa, a is in tangent space.

B = Bu^adx^u(dargPSI/dx^a) = Bu^adx^u(Pa/h)argPSI = *d^-1*argPSI

*argPSI = 4-form

d^-1argPSI = 3-form

*d^-1argPSI = 1-form

Einstein's local equivalence principle EEP is

g(LNIF) = en(LIF)e' = (I + B)n(LIF)(I' + B')

= InI' + BnI' + InB' + BnB'

U(1)em SBS in the false vacuum triggers the post-inflationary Big Bang and the emergence of our universe (among many) with gravity and inertia, i.e. m =/= 0 rest masses of lepto-quarks, W bosons.

Gauge transforms on B in gauge force picture <---> Diff(4) in geometrodynamic picture

(LC) when we only locally gauge T4 is the Levi-Civita connection (with no torsion fields for now) in the geometrodynamic curved space-time representation.

D = d + (LC) =

The 4th rank tidal stretch-squeeze curvature tensor is

C = D(LC)

It's 2nd rank contraction is

G = T = stress-energy density source tensor

DG = 0 are the Bianchi identities

DT = 0 is local stress-energy current density source conservation

note again EEP

g(LNIF) = In(LIF)I' + Bn(LIFI' + In(LIF)B' + Bn(LIF)B'

this is the explicit connection of the gauge force picture to the geometrodynamic picture

Locally gauging O(1,3) gives the torsion field extension of above 1915 plain vanilla GR.

S = Su^a^bdx^u(d/dx^a)(d/dx^b) =Su^a^bdx^uSab/h = Torsion field in base space

{Sab} = Lie algebra of Lorentz group O(1,3).

D* = D + S

Sua^b = eu^cAc^a^b

Ac^a^b = Ricci rotation coefficients

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