Science > Physics > Extending Einstein's Gravity Theory to Metric Engineering
| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
18 Nov 2003 11:32:37 PM |
| Object: |
Extending Einstein's Gravity Theory to Metric Engineering |
On Tuesday, November 18, 2003, at 08:34 PM, Alex Poltorak wrote:
How do you mean "nonmetricity."?
By "nonmetricity" I understand the nonmetric part of an affine
connection which is generally composed of three terms: Levi Civita
connection + nonmetricity + torsion.
Yes, OK.
I use "metricity" in Hagen Kleinert's sense
guv^;v = 0
i.e. Diff(4) divergence vanishes.
I use the term metricity in the same way as you: if the covariant
divergence of a connection vanishes, it is "metric" or, when there is no
torsion, a Levi Civita connection.
In general, for every Riemmanian manifold without torsion, Levi Civita
connecion {} and and an affine connecion A, there is one and only one
(1,2) tensor of nonmetricity S, that the the affine connection is the
sum of the Levi Civita and the nonmetricity tensor (A = {} + S) and the
curvature tensor of the affine connection R(A) splits into a sum of a
Riemmanian curvature tensor on {} and a nonmetric curvature tensor of
the same structure wherein the affine connection A is replaced by the
nonmetricity tensor S. The Einstein tensor G likewise splits into
affine G(A) and nonmetric G(S) parts and can be rewritten as G = G(A) -
G(S). Thus the Einstein field equations take form of
G(S) = -(8piG/c^4)T + G(A)
In my view, the tensor of nonmetricity describes gravity, while the
affine connection describes a chosen frame of reference. The second
member on the right side of the equation describes the contribution of
the inertial forces to the energy-momentum. In an inertial frame it, of
course, vanishes.
These field equations are completely covariant with a covariant
energy-momentum (instead of pseudotensor) tensor t.
Alex.
OK, I need to study what you say above. :-)
With regard to odd claims from Akimov's group in Russia today about
"torsion fields" based on Gennady Shipov's theories:
Again the physics issue here is whether or not:
1. Do torsion fields exist in Nature?
2. Is the coupling of torsion fields to electron and proton spins is
sufficiently strong to have a large
bio-weapons effect on living matter as claimed by the Akimov School in
Russia today?
3. Einstein's gravity field guv(x) of curved spacetime is the local
compensating gauge force field from the 4-parameter translation group
generated by total energy-momentum. Obviously curved space-time breaks
space-time translational symmetry upon which the rigid Fourier
transforms depend (as distinct from wavelet transforms). Curvature is
the stringy topological disclination defect density in the large scale
Lp^2 = hG(Newton)/c^3 ~ 10^-66 cm^2 (Hagen Kleinert).
guv = Flat Minkowksi + huv
The degrees of freedom of the local gauge force compensating huv restore
local conservation of stress-energy density current in the sense that
Tuv(matter/radiation)^;v = 0
only when the two Bianchi identities manage to hold so that
Guv(space-time geometry)^;v = 0
;v is the Diff(4) covariant partial derivative using the symmetric
Levi-Civita connection for parallel transport of tensor fields along
vector fields in the curved base space-time of the tangent bundle of
Einstein's GR.
Einstein's local geometrodynamic field equation with zero torsion and no
zero point energy density "exotic vacuum" "dark energy/matter" term is
Guv(geometry) = -(string tension)^-1Tuv(matter/radiation)
"matter" means "on-mass-shell" i.e. particles whizzing around that can
trigger detectors to "click".
4. Adding the exotic vacuum term gives
Guv(geometry) + /\zpfguv = -(string tension)^-1Tuv(matter/radiation)
Or, you can write this in terms of the perfectly balanced local
stress-energy density tensors
tuv(geometry) + tuv(exotic vacuum) + Tuv(matter/radiation) = 0
The Bianchi identities break down which means direct cross-transfer of
stress-energy density currents between geometry, zero point vacuum
energy and ordinary matter-energy such that the total currents are
conserved.
This is essential for the "metric engineering" of Star Gates and
Weightless Warp Drives as well as the Doomsday WMD of Chapter 9 of Sir
Martin Rees's "Our Final Hour" "ripping space" in a kind of "Ice Nine"
effect.
5. Gravity is emergent (Andrei Sakharov) out of micro-quantum vacuum
instability and is non-perturbative like the BCS superconducting ground
state which cannot be derived in a finite analytic perturbation series
from the normal metal ground state.
6. The torsion field of skewed or twisted space-time is from locally
gauging the 6-parameter Lorentz group O(1,3). This local gauging should
not be confused with the freedom to make local Lorentz transformations
of the tetrads in the tangent space. That freedom is already in
torsion-free Einstein 1915 geometrodynamics with a symmetric connection.
The local gauging in the sense here gives a compensating gauge "torsion
force field" that manifests as an additional Diff(4) antisymmetric (3rd
rank) tensor term added to the non-tensorial symmetric
Levi-Civita-Christoffel connection. This torsion field corresponds to
stringy topological dislocation defect densities in the large scale
limit (Hagen Kleinert).
7. The "string" is because gravity and torsion emerge from a
MACRO-QUANTUM Vacuum Coherence Field with O(2) symmetry at least in the
low-energy effective emergent "More is different" (P.W. Anderson) ODLRO
(Oliver Penrose) c-number "superfluid" local field theory sense.
8. One need not stop there. Look at the De Sitter Group for space-times
of constant curvature corresponding to Einstein's cosmological constant"
There is it appears from other's work, a duality between zero and
infinite cosmological constant that brings in the 4 parameter "special
conformal transformation" of uniformly proper acclerating "hyperbolic
motion" of special relativity that is a subgroup of the 15 parameter
Penrose massless twistor conformal group as the infinite cosmological
constant limit of the De Sitter Group.
Locally gauge the De Sitter Group to get gravity + torsion + ??? (new
stuff like variable /\zpf of exotic vacuum unified dark energy/matter
which has a Bondi-Terletskii "vacuum propeller" weightless warp drive
possibility built in.
I rewrite Einstein's zero torsion 1915 geometrodynamic "classical"
local field equaton
Guv = -(8piG/c^4)Tuv
as
Guv = -alpha'Tuv
alpha' = (string tension)^-1 = Witten parameter
Infinite string tension means no gravity because space-time geometry is
too stiff to bend.
The local stress-energy density tensor of pure geometry is then
trivially
Tuv(Geometry) = (alpha')^-1Guv
Einstein's field equation is then simply the balance
Tuv(Geometry) + Tuv(Ordinary Mass-Energy) = 0
Adding random micro-quantum zero point energy density from all quantum
fields of spin 1/2 lepto-quarks and spin 1 gauge force bosons gives
additional term
tuv(zpf) = (alpha')-1/\zpfguv
/\zpf > 0 is exotic vacuum "dark energy" with w = -1 negative pressure.
/\zpf < 0 is exotic vacuum "dark matter" with w = -1 positive pressure
"Dark matter" detectors will never "click" except by false positives in
my theory.
Einstein's equation is then
Tuv(Geometry) + Tuv(Ordinary Mass-Energy) + tuv(zpf) = 0
In the 1915 theory with /\zpf = 0
Tuv(Geometry)^;v = 0
from the Bianchi identities.
However these identities FAIL IMHO when /\zpf =/= 0 and is variable
and if there are torsion fields.
In my theory (with Witten's h = c =1 convention)
/\zpf = (alpha')^-1[(alpha')^3/2[|MACRO-QUANTUM VACUUM COHERENCE|^2 - 1]
guv = Minkowski metric + Kleinert World Crystal Lattice Strain Tensor
Make the Levi-Civita connection from guv in the usual way.
World Crystal Lattice Distortion Field = du(x) = alpha'(Goldstone Phase
of MACRO-QUANTUM VACUUM COHERENCE),u
Strain Tensor = du(x),v + dv(x),u
Diff(4) Landau-Ginzburg eq for VACUUM COHERENCE in a two-way feedback
loop between IT World Crystal Lattice Distortion Field and
BIT VACUUM COHERENCE in sense of Bohm's interpretation of IT(hidden
variable) + BIT(Pilot Wave of "Active Information")
Torsion fields mean
du(x),v - dv(x),u =/= 0
.
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