Sakharov's Emergent Gravity

On Monday, November 17, 2003, at 11:08 AM, Tony Smith wrote:

Jack, you ask:
"... Tony what do you mean by D5 describing Gravity?
What that would mean to me is that start from the D5 group
and end up with Einstein's local field equation
Guv = (superstring tension)^-1Tuv
can you actually do that?
Similarly, start from D4 and get the U(1)xSU(2)xSU(3) principal fiber
bundle of the
electroweak-strong gauge forces with the associated vector bundle of
the lepto-quark
sources. Can you do that? ...".

"Yes, to both questions (although I don't use the conventional
superstring structure that you mention)."

I am trying to see if there is a precise mathematical connection between
what you are doing and
what I am doing in http://qedcorp.com/APS/EmergentGravity.pdf

In my theory Einstein's gravity field plus exotic vacuum w = -1 dark
energy/matter fields are all ODLRO c-number collective emergent low
energy effective MACRO-QUANTUM fields in which Diff(4) is an emergent
symmetry from the spontaneous breaking of the U(1) EM symmetry at the
unstable "false vacuum" micro-quantum level of the lepto-quark
sources/electroweak-strong gauge forces level.

More specifically, I get an emergent c-number LOCAL giant MACRO-QUANTUM
VACUUM COHERENT WAVE

Vacuum Coherent Field = (Higgs Amplitude Field)e^i(Goldstone Phase Field)

World Crystal Lattice Distortion Field = Lp*^2(Goldstone Phase Field),u

Einstein's guv field is the flat Minkowski metric + the Strain Tensor of
the Distortion Field

Therefore, Einstein's Gravity Field emerges as modulation of the
Goldstone Phase Field consistent with Andrei Sakharov's "metric
elasticity", which is the complementary view of P.W. Anderson's
"generalized phase rigidity" in his "More is different" paradigm. That
is, the basic emergent gravity coupling is precisely Ed Witten's

alpha' = 1/(string tension) = 8piG*/c^4

where I allow G* to be a scale-dependent variable that is 10^40
G(Newton) at the 1 fermi scale.

Unified Exotic Vacuum Dark Energy/Matter Field is from the modulation of
the Higgs Amplitude Field which also provides the rest mass of the
lepto-quarks as

mc^2 ~ e^2/\zpf^1/2

where /\zpf ~ -1/(1 fermi)^2 at the 1 fermi scale in the vibrating "
dark matter" quantized vortex string core where the
Higgs Field is zero.

Where with h = c = 1 convention

/\zpf = (alpha')^-1[(alpha')^3/2|Higgs|^2 -1]

alpha' is a scale-dependent variable not fixed at 10^-66 cm^2.

BTW I have come to the tentative conclusion that the alleged
"Holographic Universe" formula

Lp* = Lp^2/3L^1/3

found in the LNL e-prints has serious problems of interpretation.

My basic theory does not essentially depend on that additional assumption.

While I see no basic problem in you getting the micro-quantum
U(1)xSU(2)xSU(3) from your group theory, I do
not understand how you get Einstein's Gravity. The Ed Witten argument
that one gets a "spin 2" quantum is not good enough for me since in the
"More is different" emergence the consensus "quantum gravity" idea is
not correct at all and that is what non-renormalizability of Einstein's
GR in the low-energy sector is telling us.

There may be some linear spin 2 perturbative random gravitons as
micro-quantum noise or "normal fluid" in the emergent curved spacetime
"superfluid" background from the modulation of the c-number Goldstone phase.

So I am asking where is the MACRO-QUANTUM EMERGENCE in your group theory
approach to deriving Einstein's Gravity from a more fundamental level?

Tony:
"Those things (the forces of Gravity and the Standard Model) all
come from the 28-dim adjoint rep of the D4 subalgebra of D5.

More particularly:

As to Gravity (and Higgs, and special conformal generators):

D4 has a 15-dimensional D3 subalgebra that is the conformal
algebra SU(2,2) = Spin(2,4). It has:
1 dilation generator (corresponds to Higgs)
OK
4 special conformal generators

What do they locally gauge to?
My hunch is /\zpf,u

10 anti-deSitter generators.

The 4 Pu of T4 locally gauge to Einstein's guv.

The 6 Muv of O(1,3) locally gauge to a Torsion Field.

By a modified conformal MacDowell-Mansouri mechanism,

Is this where ODLRO MACRO-QUANTUM EMERGENCE is buried?

you get the Einstein-Hilbert Lagrangian.
All this is at conventional textbook level, for example,
section 14.6 of Unification and Supersymmetry, 2nd edition,
by Rabindra Mohapatra, Springer-Verlag 1992.
If you want a prominent establishment name dropped, Frank Wilczek
mentions the MacDowell-Mansouri mechanism in
http://xxx.lanl.gov/abs/hep-th/9801184
where he notes that the mechanism was also independently
formulated by Chamseddine and West.
The mechanism was invented to make it possible to get gravity
from the anti-deSitter part of Lie superalgebras used in
supergravity theories.


As to the Standard Model,

look at the 28 generators of the D4 Lie algebra.
Use 15 of them as above, and 1 more
to "complete" the SU(2,2) to U(2,2) = SU(2,2)xU(1).
Then you have 12 generators left.
The form the 12-dim Standard Model SU(3) x SU(2) x U(1).
Here is how you can see that structure geometrically,
and unambiguously:
If you look at things (here I was inspired by Saul-Paul) in
terms of the Weyl reflection group of the root vector space,
and take away the 12 root vectors of the U(2,2) and the 4 Cartan
algebra elements of the 16-dim rank 4 U(2,2), that leaves you
with 28-12-4 = 12 root vectors.
Since the root vectors of D4 form a 24-cell, which can be seen
as a 12-vertex cuboctahedron plus two 6-vertex octahedra,
you see that the remaining 12 root vectors form a pair of octahedra.
Line the two octahedra up so that they share a common axis,
and project the two octahedra into a space perpendicular to that axis,
so that the 4 axis vertices fall on a line that forms the
root vector diagram (including Cartan origin vertices) of
the 4-dim Lie algebra U(2) = SU(2) x U(1).
The remaining 8 can be seen as the vertices of a cube:

tb----xb
|\ | \
| zb----yb
| | | |
yr-|--zr |
\| \|
xr----tr

Now look at the cube along its tb-tr diagonal axis,
and project all 8 vertices onto a plane perpendicular
to the tb-tr axis, giving the diagram


yb

xb zb

tb tr

zr xr

yr

with two central points surrounded by two interpenetrating triangles,
which is the root vector diagram of SU(3).


Therefore,
the 16 of the 28 D4 generators give us Gravity, Higgs, and special
conformal,
and
the remaining 12 give us the Standard Model SU(3) x SU(2) x U(1).

Consideration of the relevant geometries and combinatorics give
the particle content, particle masses, and relative force strengths
of ALL the observed particles and forces. I have mostly done only tree-
level calculations, so such higher order things as neutrino masses
(they are in my model tree-level massless) remain to be fully calculated.
Details are in my papers, including a paper at
http://www.innerx.net/personal/tsmit...I1vNFadd97.pdf
that contains material barred from the Cornell arXiv due to
me being blacklisted by them.

Tony"