Macro-Quantum Emergent Gravity
- From: Jack Sarfatti <sarfatti@xxxxxxxxxxx>
- Date: Wed, 6 Jul 2005 05:29:40 +0000 (UTC)
The big questions are
1. How does inflation work in the creation of the universe?
2. Why is the entropy low in the early universe?
3. What is dark energy and dark matter?
4. Why is the electron stable? (implication for Ken Shoulders EVOs)
5. What is the Galactic Halo? Why is the stellar rotation curve flat in
a wide region?
6. What is causing the gravity anomaly in the two NASA Pioneer space probes?
7. What makes the gamma ray bursts?
8. Why the universal slope of the Regge paths of the hadronic resonances?
I suppress indices as much as possible for brevity in e-mail. When I am
forced to use them, a,b,c in tangent fiber, u,v,w in base space, with I
= Kronecker delta &u^a in the global aligned frame in flat Minkowski
space-time. This frame is physical i.e. all non-rotating inertial
detectors are on globally flat timelike geodesics where the geodesic
deviation tidal curvature tensor field is identically zero in that
limiting case.
The Einstein-Cartan tetrad is
e = I + B
I = identity
When the substratum warp field B = 0 identically, the tangent fiber is
aligned with the base space in the "convenient" global frame. Of course
Diff(4) transformations in this globally flat B = 0 everywhere-when
limit will misalign the fiber with the base describing inertial forces
on globally flat non-geodesic detectors. These inertial forces, that are
locally equivalent, to gravity cannot exist without non-gravity
electrical forces. In this B = 0 limit the geodesic deviation tidal
tensor field AKA Cartan-Einstein curvature 2-form is identically zero.
B ~ Lp^2GradargPSI
Goldstone phase of vacuum ODLRO is argPSI, Grad is 4D.
In terms of Cartan's exterior derivative d with d^2 = 0
argPsi is a 0-form
B ~ Lp^2dargPSI
dB =/= 0 only because of multiple connectivity, i.e. singularities in
argPSI that make B closed but not exact despite the notation dargPSI.
See John Baez's book, on Gravity and Knots for example. The cohomology
is non-trivial like vortex lines in superfluid helium which is, like the
Higgs Ocean post-inflationary vacuum, a macro-quantum condensed system
of real quanta rather than, as in our problem of emergent gravity,
virtual zero-point quanta.
Technically H1, the first cohomology group of the local macro-quantum
ODLRO order parameter PSI is larger than the trivial identity group that
describes a simply-connected manifold.
PSI = LOCAL post-inflation order parameter (a complex-numbered scalar
field in a 4D real manifold)
This explains why macro-spacetime physics is local and why the early
universe has a small entropy.
Lp^2 = hG/c^3 = Loop quantum of area
Therefore
1. if c -> infinity a real geodesic deviation tidal curvature warp field
is impossible. That is, no gravity possible in Galilean relativity. You
need special relativity as the local limit AKA the Einstein Equivalence
Principle (EEP).
2. if h -> 0 a real geodesic deviation tidal curvature warp field is
impossible. That is, you need a finite quantum of action to get Einstein
gravity as a "More is different" (PW Anderson) Andrei Sakharov emergent
macro-quantum phenomenon.
These two conditions are non-trivial and are only explained clearly in
my theory. The third condition is trivial, i.e.
4. if G -> 0 a real geodesic deviation tidal curvature warp field is
impossible.
In essence I show here how Loop Quantum Gravity gives classical Einstein
theory.
EEP (Einstein's Equivalence Principle) in this formalism is symbolically
g(curved) = (I + B)(flat)(I + B)
= In(flat)I + I(flat)B + B(flat)I + B(flat)B
The terms of the curved metric field g linear in B are "elastic" terms
and the nonlinear terms quadratic in B are the "plastic" terms causing
the "cracking" of the world crystal lattice whose defects appear as
curvature and torsion.
Under X in Diff(4), which is the locally gauged T4, with B as the
substratum's compensating warp Yang-Mills gauge force potential of "spin
1" not spin 2, which appears only at the bi-linear level.
e' = Xe
That is total tetrad e is a Diff(4) first rank tensor.
e is also a Cartan 1-form in the substratum
Under L in tangent fiber Lorentz group SO(1,3)
e'' = Le
Note that XI = I' =/= I
What is physical meaning of X?
X is the field mapping of possible coincident detectors in arbitrary
relative motion to each other in the neighborhood of the same physical
event P. Such a mapping corresponds to a transition function connecting
overlapping local coordinate charts. However, there are more such
transition functions then physically significant Diff(4) X. Therefore X
is a quotient set mod the equivalence relation ~ that leaves the
relative motion of coincident detector sets invariant. That is
X = {transition functions}/~
i.e. X is a non-overlapping "coset" equivalence class mod ~ in the
quotient group with the unphysical gauge freedom factored out.
Note that
e' = Xe = XI + XB = I' + XB = I + B'
Therefore,
B' = (I'-I) + XB = XI - I + XB
Therefore, B' has an inhomogeneous term under Diff(4) if we wish to make
the split into a globally flat part and a warped part post the X
transition. On the other hand, if we are content to use I' = XI, then B
is a tensor under X. So it depends on how we want to make the split.
Obviously, when B = 0 identically
g' = XI(flat)XI
is the apparent curved metric from the non-geodesic motion of the
detectors. However, locally there is no way to distinguish an apparent
gravity force from an actual gravity force. Globally we can, of course
tell the difference. EEP is only a local principle. Geodesic deviation
stretch-squeeze measurements of B in the relative coordinates are
forbidden in this statement since they do not affect the actual force on
the center of mass of an extended test object. You need non-gravity
forces to create such non-geodesic motions in the detectors. Here we are
talking about globally flat timelike geodesics when B is identically zero.
To proceed further we need to define the spin-connection W that is more
fundamental physically than the Levi-Civita connection. W is a Cartan 1
form with values in the Lorentz Lie Algebra.
The gauge covariant exterior derivative at the bi-linear level of the
geometrodynamic field is
D = d + W/\
where d^2 = 0 ONLY in SIMPLY-CONNECTED manifolds without holes. /\ is
the Cartan exterior product.
Do not confuse D with
D* = d + B/\ in the substratum of the fabric of spacetime!
D & D* are qualitatively physically different. I will use * on right of
a symbol for substratum quantities, not to be confused with same * to
left for the Hodge dual using the fully anti-symmetric tensors of
different ranks 2 to 4. The Yang-Mills spin 1 substratum field is the 2-form
F* = D*B = dB + B/\B
The Bianchi identities in the substratum give
DF* = 0
i.e. the 3-form equation
dF* + B/\F* = d^2B + d(B/\B) + B/\dB + B/\B/\B = 0
The 1-form Yang-Mills source equation is
D*F* = *J
Remember B is from the local gauging of T4 a 4-parameter commutative
group unless you deform it to a non-commutative space-time geometry
where it may look like U(1)xSU(2)?
Next, I go to the bi-linear geometrodynamic level. The Cartan-Shipov
torsion 2-form is defined as
T = De = de + W/\e
Since the tetrad is a 1-form.
Einstein's 1915 GR has T = 0 identically. This is what you get when you
do NOT locally gauge SO(1,3) the 6-parameter Lorentz Lie Group.
Therefore
de + W/\e = 0
implicitly determines the spin-connection 1-form W in terms of the
tetrad e = I + B
That is
d(I + B) + W/\(I + B) = 0
Since I is a constant, dI = 0
dB = - W/\(I + B)
Note, we cannot assume dX = 0 in a Diff(4) transformation.
When B = 0 identically, obviously W = 0 because
0 = - W/\I
The Levi-Civita connection is
(LC) = eWe = (I + B)W(I + B) = IWI + BWI + IWB + BWB
EEP here then implies that
(LC) = 0 in local curved spacetime geodesic coordinates only at a point
event P - not identically. That is, one must make a different choice as
one moves about in curved spacetime.
The stretch-squeeze geodesic deviation tidal curvature Cartan 2-form is
R = DW = dW + W/\W
Globally-flat Minkowski space-time has R = 0 identically.
The 1915 zero torsion Einstein-Hilbert classical action density is the
0-form
&S/&V^4 = *(e/\e/\R) + /\zpfe/\e/\e/\e)
Note that the Hodge star dual of a 4-form is a 0-scalar form.
where /\zpf is the dark zero point energy term shown now by observation
to be 96% of the large-scale limit of the universe.
However, it is not required to form the nonlocal unitary Feynman
micro-quantum gravity amplitudes
<i|e^iPathIntegral &S/&V^4|f>
When
B ~ Lp^2GradargPSI
Instead one must use the NON-UNITARY local macro-quantum coherent
Landau-Ginzburg equation with a micro-quantum dark energy noise term
against a coherent vacuum ODLRO dynamical background.
.
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