Memorandum For The Record

The complete solution to Sakharov's "Metric Elasticity" 1967 problem for
the emergence of gravity from zero point energy is given below. The
competing program of Haisch, Puthoff and Rueda does not work as
advertised by Eric Davis, Nick Cook, STAIF et-al.

Einstein-Cartan theory extends general relativity to correctly handle
spin angular momentum. There is a qualitative theoretical proof showing
that general relativity must be extended to Einstein-Cartan theory when
matter with spin is present. Experimental effects are too small to be
observed at the present time.

------------------------------------------------------------------------------------------


That experimental effects of torsion fields are too small to be detected
is controversial. Richard Hammond of the Department of Physics at the
University in Fargo (the Dakotas US), then working on a US Navy
contract, reported torsion radiation that is forbidden in some versions
of torsion theory. Torsion radiation has also been reported by Akimov in
Moscow based on a very controversial theory by Gennady Shipov. Akimov
and Shipov have been harshly attacked by their Russian colleagues.
However, it's much too soon to rush to premature judgment on the reality
of torsion fields although the extraordinary claims by Akimov are
suspect and cannot be taken on face value.

All the dynamical force fields of physics come from the principle of
local gauge invariance. Start with a global symmetry group G of the
action S of some dynamical system. Let L be a member of the Lie algebra
generating G. The local action density is &S/&V^4. The unitary operator
for a symmetry transformation is of the form U(L) = e^iL@/h, where @ is
a global phase (constant over space-time region V4). Invariance of the
dynamical action under the global symmetry is expressed by &S/&V^4 =
U(L)^-1&S/&V^4U(L). The principle of local gauge invariance means
allowing the phase @ to be an arbitrary function over space-time. The
ordinary partial derivatives ,u need to be replaced by a gauge-covariant
partial derivative ;u = ,u - Bu where Bu is the compensating gauge
potential that is a new independent dynamical "force" field that
restores the dynamically broken global symmetry to the extended action
S' that now includes Bu. For example, if G = U(1) and the original
source field is the Dirac field of the electron, then Bu -> Au the
well-known "4-vector potential" of Maxwell's EM field theory. In terms
of Cartan forms, the EM Maxwell field equations are simply F = dA, where
d = exterior derivative, d^2 = 0, therefore, dF = 0 contains both
Faraday's law of induction and no magnetic monopoles. Taking the
Hodge-dual *F of F = "curvature", gives d*F = J which contains both
Ampere's law and Gauss's law. The first equation dF = 0 is topological
independent of arbitrary metrics. The second equation with the *
operation is metric-dependent. The metric is a kind of covariant
"aether" combining the Lorentz-Fitzgerald substratum dynamical
hidden-variable model for the emergence of the Lorentz group O(1,3) with
Einstein's phenomenological geometrodynamics. See also G.E. Volovik's
book "The Universe in a Helium Drop" for details on the used of
renormalization group flow to a fixed point for the emergence of O(1,3)
from a Galilean relativity substratum where Bohm's quantum potential
acts instantly. The gauge force picture with Bu is dual to the
geometrodynamic "Force-without-force" picture developed by John
Archibald Wheeler. You can switch between them like going back and forth
between the Schrodinger and Heisenberg pictures in quantum field theory.
When G = U(1)xSU(2)xSU(3) on the parity-violating Dirac lepto-quarks we
get the standard model of elementary particles in globally flat
space-time without gravity prior to the Higgs-Goldstone spontaneous
breaking of symmetry (SBS) for the SU(2) weak sector of the physical
vacuum that allegedly should generate all the rest masses m of the
lepto-quarks and weak bosons. See for example, "In search of symmetry
lost" Frank Wilczek (Nobel Physics Prize 2004), NATURE, 433, 20 Jan.
2005. The model for the origin of rest inertia from friction in the sea
of virtual transverse photons suggested by Haisch, Puthoff and Rueda has
been rejected by experts as too simple and "not-even-wrong" in Wolfgang
Pauli's sense (e.g. Space-Time and Beyond II by Jack Sarfatti, Author
House (2002))

Einstein's 1916 General Relativity (GR) comes from locally gauging T4
the translation subgroup of the Poincare symmetry group of Einstein's
1905 Special Relativity (SR). The early version of this theory is in
"Wheeler's World: It From Bit?" pp. 41-84, "Developments in Quantum
Physics", F. Columbus, V. Krsnoholovets ed., Nova Science Publishers,
2004 ISBN 1-59454-003-9.

The compensating gauge potential Bu from locally gauging T4 is

Bu = (Goldstone Macro-Quantum World Hologram Coherent Phase of the SBS
"multi-layered multi-colored" (Wilczek) Higgs Field),u = bu^aPa/h

{Pa} = mom-energy Lie algebra of T4 in tangent space indices a = 0,1,2,3,4

h = Planck's quantum of action

The local gauge transformations on Bu -> local GCT tensor Diff(4)
transformations of Einstein's geometrodynamics.

bu^a is the non-trivial nonholonomic piece of the Einstein-Cartan tetrad
eu^a, where u indices are in the warped base space of the tangent bundle
of Einstein's GR.

eu^a = &u^a + bu^a

&u^a = trivial Kronecker delta holonomic tetrads of 1905 SR where the
tangent space is degenerate with the base space. Local gauging of T4
removes the degenerary replacing global inertial frames (GIF) with local
frames, both inertial non-rotating timelike Levi-Civita connection
geodesic (LIF) and non-inertial off-geodesic (LNIF). Einstein's curved
metric guv is only for the LNIF where the local equivalence principle
(EEP) is

guv(LNIF) = eu^anab(LIF)eu^b

Note the linear elastic terms ~ bu^a and the nonlinear quadratic plastic
terms ~ bu^abv^b in the EEP. The latter are the spontaneous
self-organizing couplings allowing the Wheeler geons of "Mass without
mass" solutions of the non-exotic vacuum equation for the Ricci tensor

Ruv = 0

The Ricci rotation coefficients Au^b^c needed for the Riemann tidal
stretch-squeeze curvature and for the dynamics of Dirac spinors on
curved space-time are

Au^b^c = eu^aAa^b^c

Where, in 1916 GR without torsion fields, the Aa^b^c are constant global
phases conjugate to Sbc the space-space rotation and space-time rotation
(rapidity) boost Lie algebra of O(1,3) the local Lorentz group in the
tangent vector fiber space. If we locally gauge O(1,3) as Gennady Shipov
does and as Kibble and Utiyama did in the 1960's, then Aa^bc are
arbitrary functions, the torsion field is then

Tu = eu^aAa^b^cSbc/h

The extended covariant derivative is then

Du = ;u - Tu = ,u - Bu - Tu

we then expect Einstein-Cartan field equations of the same Cartan form
as Maxwell theory, ie.

R = DB

DR = D^2B = 0

Bianchi identities for local conservation of both curvature and torsion
current densities (the key to practical metric engineering the fabric of
space-time using the generalized Bohm-Aharonov-Josephson-Berry effect
from the weak link/\ZPF ~ cosine(phase difference) between a real
macro-quantum control system and the virtual physical macro-quantum
coherent vacuum.

D*B = J

i.e., generalized Einstein field equations with both translational
curvature and rotational torsion sources from exotic vacuum virtual
(off-mass-shell) dark energy/matter sources as well as real
(on-mass-shell) sources like rotating superconductors (e.g.
Podkletnov/Ning Li - both highly controversial like Akimov's claims. See
Marc Millis NASA BPP and STAIF Exotic Propulsion Proceedings of AIP).

D^2*B = DJ = 0

mutual transfer of source current densities to curvature and torsion
current densities with total local conservation.

D = Dudx^u

B = Budx^u

John Archibald Wheeler calls these kinds of dynamics "The boundary of a
boundary is zero."

R = DB is a boundary, but D*B is not a boundary.

Thanks to R. Kiehn for explaining Cartan's forms and to Art Wagner for
telling me about an interesting paper from Brazil from Arcos and Peiera
(sp?).