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Joined: 06 Oct 2005
Posts: 602
Location: Toon Town
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Globally flat Minkowski space has a finite conformal image on the
Einstein static universe "cylinder." Similarly for DeSitter dark zero
point energy space /\ > 0 with negative pressure making a cosmic
antigravity repulsive field accelerating the expansion of 3D space from
the initial "singularity", for dark matter Anti-DeSitter space with /\ <
0, positive pressure and closed timelike worldline as in Godel rotating
universe and for Bondi-Gold "steady state universe." Closed timelike
worldlines in the dark matter Galactic Halo? All these solutions have
different finite conformal images on the above archetypal "Einstein
cylinder." The boundaries of these images are "infinities" of various
kinds. The Big Bang may not be a singularity in sense of infinite
curvature, but rather a vacuum ODLRO phase transition in which curved
spacetime as a smooth number geometrodynamic field emerges.
That is the identity tetrad action on the tangent bundle is the local
scalar Cartan IT 1-form
e = I + A
A encodes all the geodesic deviation curvature information from
A ~ Theta/\dPhi - dTheta/\Phi
F = dA ~ dTheta/\dPhi
Theta & Phi are the 0-form macro-quantum coherent Goldstone phases of
the World Hologram that encodes all curvature BITS in the three real
component Higgsian vacuum ODLRO inflation field that may be related to
electroweak symmetry breaking giving an effective Planck area of 10^-32
cm^2 rather than 10^-66 cm^2?
If A is Abelian U(1)
dF = 0
d*F = *J(source)
d*J = 0 (local conservation of source currents in goemetrodynamic subtratum)
* is Hodge dual
if A is SU(2) electroweak
D = d + A/\
i.e. A has two internal indices
The Yang-Mills field equations in geometrodynamic substratum are
F' = DA
DF' = 0
D*F' = *J'
D*J' = 0
Einstein's GR is recovered from
e = eu^adx^u&a = e^a&a
ds^2 = e^a(Minkowski)abe^b
This is Einstein's equivalence principle in Cartan tetrad formalism.
That is, geodesic observers are weightless. Pure gravity force is always
zero. It is eliminated in Einstein's GR. Non-zero pure gravity force
only has meaning in Newton's theory. Whenever you pull g's and feel
weight that is caused by a non-gravity force that pushes you off the
geodesic of the curved spacetime you are in. Weight is always a reaction
to a non-gravity force like when you stand on the surface of Earth, your
weight is from the quantum electrical forces in the rock you stand on.
When you choose a "hovering" or "shell" non-geodesic local frame (LNIF)
by applying a non-gravity external force, then you get an accidental
relation of the non-gravity force to the geometrodynamic connection
field. The latter is not a tensor field. It adapts to the non-gravity
force and locally vanishes when the non-gravity force locally vanishes. |
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