| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
25 Jul 2005 05:52:43 PM |
| Object: |
Tetrads & Dirac Strings |
My basic formula for the Einstein-Cartan tetrad gravity field is
e^I = 1 + Lp(theta)^,I = 1 + B^I
theta is the Goldstone phase of the vacuum ODLRO condensate.
Therefore, B^I = Lp(theta)^,I is the compensating local gauge potential
from forcing T4 to the GCT Diff(4), but that would not be possible
without the QED spontaneous breaking of U(1) symmetry in the physical
vacuum. Both effects happen together in my new original theory.
The anholonomic character of B^I is related obviously to the notion of
the "Dirac string".
Notice that in my theory, curved space-time is impossible if the speed
of light is infinite, if Planck's quantum of action were to disappear,
even if Newton's constant G were not zero.
Note also Wigner's limits on measurement of curvature change if G* >> G
on small scale of 1 fermi for example, i.e. electron shell stabilized by
dark energy interior core micro-geon of
Mass without mass
Charge without charge
Electric flux without electric flux?
i.e. Wheeler-Feynman idea that EM fields are redundant, and the
"electron" field is in the multiple-connectivity of space i.e.
non-bounding 1-cycles. Primacy of 2D areas is the World Hologram idea
that seems natural here in my theory.
e.g.
From Wikipedia, the free encyclopedia.
"In physics, a Dirac string is a fictitious one-dimensional curve in
space, stretched from a magnetic monopole - also called the Dirac
monopole - to infinity. The gauge potential cannot be defined on the
Dirac string, but it is defined everywhere else. The Dirac string acts
as the solenoid in the Aharonov-Bohm effect, and the requirement that
the position of the Dirac string should not be observable implies the
Dirac quantization rule: the product of a magnetic charge and an
electric charge must always be an integer multiple of 2?."
On Jul 25, 2005, at 3:17 PM, Jack Sarfatti wrote:
I will use Rovelli's notation in his free on-line book on "Quantum
Gravity" even though Lubos Motl from the Harvard String Quintet panned
it. ;-)
Indices I, J ... are Minkowski, raised and lowered with LIF flat metric.
Indices u,v ... are raised and lowered with LNIF curved metric guv.
In a globally flat space-time if you fire your rocket (we will always
imagine we are out there in Deep Space Nine) you do not generally stand
still relative to some arbitrary reference object. On the other hand, if
you are near some big object you need to fire your rocket merely to keep
at a constant distance from it (as measured by radar). This, therefore,
is a contingent correlation between the non-geodesic "weight" (AKA
"g-force") and the local curvature. Indeed, it is your rocket engine
firing that is causing your sensation of weight, which vanishes
completely as soon as you switch off the engine and jump automatically
on the closest geodesic. So even in this case you have created the
"g-force" with a non-gravity force and the presence or absence of
curvature is contingent on whether or not you feel heavy. So far we are
in Earth like conditions amenable to our comfort so that we can safely
ignore unpleasant tidal stretch-squeeze on our bodies also felt on
geodesics of course.
Rovelli uses "gravitational field" to mean the Minkowski-valued Cartan
1-form
e^I(x) = eu^I(x)dx^u
In my theory, we have the beautiful prediction
e^I(x) = 1 + Lp(argVacuumODLRO)^,I
Lp = (hG/c^3)^1/2
,I is ordinary partial derivative. Look at John Baez's Gravity Knots
book to see how multiple-connectivity (also Berry phase singularities)
give us flux-without-flux. That is, in spite of appearance (bad
notation) Lp(argVacuumODLRO)^,I is not an ordinary holonomic
path-independent when integrated "gradient" of a scalar function in a
simply-connected space. That is, e^I is anholonomic closed but not
exact. Therefore, its integral around a closed loop (1-coform) that is
not a boundary of a multiply-connected area (think annulus cross section
of a vortex core tube in superfluid helium) is not zero and is indeed
quantized in equilibrium from the single-valuedness of the macro-quantum
order parameter PSI(x) = Vacuum ODLRO in my theory. Of course one can
force more flux through in a transient non-equilibrium process. The
vortex will vibrate and shake off the excess circulation settling into a
stationary "eigenstate" ~ Nh/m for example. Josephson interference
effects for the coupling of two interfering order parameters will
produce the Josephson term cos2pi(Applied Flux/Quantum of Flux) where
one gets the interference max cos = 1 at the quantized flux values 2piN.
Because of the above considerations there is an effective F* = dB* if we
only measure a Bohm-Aharonov fringe shift for, say, an electron beam
through only one several non-bounding closed loops. The above is for a
U(1) order parameter space. One can also have, for example, an SU(2)
order parameter space etc.
Einstein's curved metric is
guv(x) = eu^I(x)(Minkowski)IJev^J(x)
The key physical invariant is the BEAUTIFUL FORMULA
ds^2 = guvdx^udx^v = (1^I + B^I(x))(Minkowski)IJ(1^J + B^J(x))
With terms linear and bi-linear in Lp(argPSI(x))^,I.
Only ds^2 is the fundamental local frame invariant physical observable
in General Relativity.
.
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