23rd April 03:28
Renormalizable Emergent Quantum Gravity & Supersolids
"If we knew what it was we were doing, it would not be called research,
- Albert Einstein
Jack Sarfatti wrote:
So how does this process generate a gravitational field that depends on
in Kibble's model? By imposing invariance of the action under the
displacements in T4*?
Of course - that's the generic trick to get the electromagnetic field
from the electron source field using U(1) instead of T4.
Right. Except that there U(1) is clearly a physical symmetry group.
So is the Poincare group!
In the GR case, we are treating a covariance group T4 as a physical
symmetry group, because we are using spacetime CSs to represent
measurements of space and time intervals performed in relativistic
Any more deep insights? ;-)
The T4 "charge" is 4-momentum hence the universality of gravity minimal
coupling - equivalence principle.
OK, so 4-momentum acts as the source of the gravitational field in this
IN ALL MODELS!
So we are really dealing with a kind of "matter field" that originates
from the invariance of the action with respect to the locally gauged
translation group T4*?
NO! That's the GRAVITY FIELD!
Puthoff's ZPE theory is wrong on this count BTW. Puthoff says that
uniform ZPF does not (anti)gravitate. WRONG!
Whatever. I'm not selling Puthoff's theory.
If so, this is where I see a subtle shift in interpretation, since this
would only make sense to me if T4* is now understood as a set of
(locally gauged) *physical displacements* of a specified physical system
relative to the spacetime manifold, regardless of the assignment of
There you go again. It's ALL non-gravity physical fields.
OK. Then in Kibble's model it looks like you do in fact get an ****og of
spacetime curvature without actual Riemann curvature.
NO! YOU GET actual RIEMANN CURVATURE! It's bilinear in the tetrads. You
also get torsion.
The fundamental gravity fields are the tetrads and the spin connections.
Locally gauge T4 for all non-gravity matter fields and get universal
This gives a dependent spin connection A^a^bu(T4*) - corresponding to
disclination defects for zero torsion 2-form T^a.
dA^a + S^ac(T*4)/\(I^c + A^c) = T^a = 0
Similarly, locally gauge O(1,3) and get additional independent
contribution to the spin connection A^a^bu(O(1,3)*) that gives non-zero
torsion as dislocation defects.
S^ac(O(1,3)*)/\(I^c + A^c) = T^a =/= 0
Meantime the Riemann curvature tensor is
R^luvw = e^la[(d/dx^u)(d/dx^v) - (d/dx^v)(d/dx^u)]e^aw
Where in general
A^a^bu = A^a^bu(T4*) + A^a^bu(O(1,3)*)
R^a^b = dA^a^b + A^ac/\A^c^b
R^a^b = R^a^buvdx^u/\dx^v
R^luv^w = ea^leb^wR^a^buv
Note cross terms
What you get is a total action that is invariant relative to the locally
gauged covariance group T4*, which is being treated in this model as a
physical symmetry group for the matter-vacuum system.
IT IS A UNIVERSAL ACTION SYMMETRY GROUP called 1905 Special Relativity!
If T4 invariance of the action is understood as representing the
uniformity of the conditions of inertial motion of test bodies in
gravity-free spacetime, then T4* invariance of the action can be
understood as representing *variable*
energy-momentum dependent conditions of inertial motion that precisely
replicate the effects of the matter-dependent gravitational field of GR.
What happens to this gauge field in an LIF, and why? How does this model
recover the GR effects of frame acceleration?
The SPIN 1 RENORMALIZABLE (as a quantum field) tetrad Au^a is the gauge
field from T4* The 1915 zero torsion Levi-Civita (disclination-only
defect) connection is
(LC)^luv = e^la(d/dx^u)e^av = (I^1a + A^la)dA^av/dx^u
In a timelike geodesic LIF (zero torsion limiting case) zero g-force for
observer's center of mass at rest in the sequence of LIFs on the
geodesic (relative coordinate tidal forces irrelevant to center of mass
of the extended test body that could be a spinning gyroscope)
(LC)^luv = (I^1a + A^la)dA^av/dx^u = 0
Locally a sufficient condition is dA^av/dx^u = 0, i.e. CRITICAL POINT in
same gauge orbit A^av = Xv^uAu^a
note d/dx^u is ordinary partial derivative.
Note that(I^1a + A^la)dA^av/dx^u = 0
is a homogeneous set of nonlinear first order partial differential
With constraints (LC)^luv = (LC)^lvu zero torsion field case i.e. no
Note also from Kleinert - SINGULAR MULTI-VALUED MAPPINGS FROM
DEFECT-FREE GLOBAL MINKOWSKI SPACE-TIME PERFECT WORLD CRYSTAL PLANCK
LATTICE CHANGE TOPOLOGY AND INTRODUCE DISCLINATION AND DISLOCATION
DEFECTS. This happens in the BIG BANG. Therefore those singular
multi-valued mappings represent the physical false -> true micro-quantum
-> macro-quantum ODLRO "More is different" spontaneous broken symmetry
vacuum phase transitions of eternal chaotic inflation. They are similar
to the formation of quantized vortices in superfluid helium, which is my
1969 PhD I tried to model as a local U(1) gauge field (not EM of
course). I also predicted supersolid in thin He films at that time
published in Physics Letters months before Tony Leggett's paper. Note my
paper gives credit to David Goodstein at Cal Tech and Israeli physicist
David Bergmann who helped me write the paper back then. I was an Asst
Prof at San Diego State back then with Fred Alan Wolf when he was
"straight" (well almost);-)