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Science Forum Index » Mathematics Forum » Ed Witten's Uncertainty
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| Jack Sarfatti |
 Posted: Sun Dec 28, 2003 9:38 pm |
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On Sunday, December 28, 2003, at 04:31 PM, Jack Sarfatti wrote:
"There was a time when people spoke their minds, and were not afraid to
offend -
and that since then, too many truths have been buried."
Mark Kurlansky, "1968: The Year That Rocked The World"
(Ballantine, 2004) thanks to Frank Lauria
In 1968 I was in La Jolla CA at UCSD during time Greg Benford describes in
"Timescape" living on Bonair Street Wind an Sea Beach near Unicorn
Theater with Ken Kesey's "Merry Prankster" Bus parked nearby frequently.
I was also teaching at San Diego State with Fred Alan Wolf.
....
PZ: I can't imagine anything more wrong-headed. And you say Rovelli is a
"big
shot"?
That is why I say Rovelli's position is incoherent.
JS: Is coherence in the mind of the beholder?
PZ: If you want to treat g_uv as a physical field, based on its
"dynamical character"
(i.e. matter-dependence), then the natural thing to do is separate the
background
generalized Minkowski kinematical metric (which is NOT matter dependent) as
chronogeometric, and treat the gravitational g_uv alone as "physical" -- by
Rovelli's own argument.
JS: That will not work. It will not tip the light cones. It will not
give the correct bending of light.
Also you are too vague on what you mean by "matter" on the RHS of
Guv(Einstein) = -(alpha)(alpha')Tuv(Matter)
alpha = e^2/hc ~ 1/137
alpha' = 8pi(Witten's reciprocal string tension)
alpha' ~ (10^-32 cm)^2 in a common convention.
I also include on RHS
tuv(Vacuum) ~ [(alpha)(alpha')]^-1/\zpfguv
/\zpf = Lp^-1[Lp^3|Vacuum Coherence|^2 - 1]
Repulsive dark energy is /\zpf > 0
Attractive dark matter is /\zpf < 0
FRW Omega(Dark Energy + Dark Matter) ~ 0.96
With Omega(Total) = 1
i.e. FLAT SPACE
Preferred foliation is where CMB is maximally isotropic to ~ 10^-5.
This allows accurate navigation with weightless warp drive and
traversable wormholes both supported by configurations of dark energy
and dark matter exotic w = -1 vacua.
PZ: Yet he doesn't even mention this.
JS: "There was a time when people spoke their minds, and were not afraid
to offend -
and that since then, too many truths have been buried."
Mark Kurlansky, "1968: The Year That Rocked The World"
....
JS: Also at quantum level Rovelli
mention's Dirac's insight that the Heisenberg Picture is better than
Schrodinger Picture and that "time" as in the "flow" of "time's arrow"
is not dynamical time but is a statistical thermodynamic construct.
PZ: Sure, if you want to quantize everything and abandon "time".
JS: Read Goldstein's article in the same volume. It is very clear unlike
Unruh's for example, and some of the others.
Unruh has some important ideas however.
PZ: But then I fail to see any material distinction between relabeling
the bare unindividuated
spacetime points (passive diffeomorphism), on the one hand, and
shifting all physical
"fields" (including the GR metric field) with respect to such a raw
manifold (active
diffeomorphism), on the other. Kretschman's point appears to be fully
valid in both cases:
how can physics in general -- any sensible physics -- possibly depend
on a mere re-labeling
of raw unindividuated spacetime points; or, for that matter, on a
common shift of all physical
systems, including the *physical* metric field g_uv, with respect to
such a set of unindividuated
points?
JS: Admittedly a sticky wicket that I also need to understand more
deeply.
PZ: It's an artificial model that has nothing to do with physical
relativity IMO.
JS: I found this remark by Goldstein helpful:
"In the ADM formulation 4-diffeomorphism invariance amounts to the
requirement that one ends up with the same space-time, up to coordinate
transformations, regardless of which path in multi-fingered space-time
is followed, i.e. which lapse function N is uses." p.278
OK so this idea goes back to the archetypal notions of classical
mechanics of a particle in a conservative potential, to reversible
thermodynamics with a "state function", to holonomic "integrability" of
equality of mixed partial derivatives with not multiply-connected
manifolds, to a closed Cartan exterior differential form on a cycle (no
boundary), no topological defects and all that.
The passive coordinate transformations are like EM gauge transformation
(e/c)Au -> (e/c)Au + hChi,u in a fixed gauge constraint.
PZ: Rotating a system in isotropic space is connected with a true
physical symmetry
of the system including the vacuum in which it is embedded. Yes, the
symmetry
of the system Hamiltonian under such a transformation is an active
transformational
symmetry that is characteristic of the particular system -- unlike the
invariance of the
proper formal expression of any physical law under a *mere* coordinate
transformation.
JS: Note also 12.2.2 p.279 alluding to your digging up Kretchmann from
Dr. Frankenstein's favorite graveyard. ;-)
"The fundamental symmetry at the heart of general relativity is its
invariance under general coordinate transformations of spacetime. It is
important to stress that almost any theory can be formulated in such a
4-diffeomorphism invariant manner by adding further structure to the
theory (e.g. a preferred foliation of spacetime as a dynamical object).
General relativity has what is sometimes called serious diffeomorphism
invariance, meaning that it involves no spacetime structure beyond the
4-metric and, in particular, singles out no special foliation of spacetime."
Goldstein and Teufel then knock standard QGrav including even Ashtekar
-> Loop Spin Foams that are perhaps near to being falsified by NASA's
EINSTEIN in
On Sunday, December 28, 2003, at 02:29 PM, Gary S. Bekkum wrote:
Jack better check this story out:
http://www.gsfc.nasa.gov/topstory/2003/1212einstein.html
Gary S. Bekkum
garysbekkum@hotmail.com
....
How to get
localization in space and the flow of time as we experience it in our
immediate inner consciousness
has nothing to do with the particular local coordinate representation
like "r" and "t" in, for example,
Puthoff's "PV" challenge to "GR" as when he writes
K = e^2GM/c^2r
dr/dt = c/K
for null geodesic
and in his Tables generally in the context of potentially practical
metric engineering of the guv field using the EM Au field in spite of
the enormous gravity string tension ~ c^4/G ~ 10^19 Gev per 10^-33 cm.
PZ: You are blocking his actual definition of r. Classic operationalism
does not
apply to a theory of this type. That is a critical point. Miss that and
of course
nothing makes sense.
JS: I am not ready to renounce PW Bridgman's "Operationalism". Indeed,
nothing Hal Puthoff says about the foundations of his PV makes any sense
to my mind. "If it ain't broke, don't fix it." Of course I am not a
doctrinaire "positivist" like Stephen Hawking proudly proclaims he is.
....
JS: Correct, with the proviso that "matter" includes both "real", i.e.
"on mass shell", sources" as well as "virtual", i.e. "off mass shell"
sources. The virtual sources divide into two classes:
I. Non-exotic near EM field Fuv giant coherent quantum states of
virtual photons that contribute to Omega(Matter) of the FRW metric and
to Tuv in Einstein's local field equation.
II. Exotic vacuum w = -1 zero point stress-energy density local tensor
~ (String Tension)/\zpfguv for both repulsive dark energy /\zpf > 0 of
negative pressure and attractive dark matter /\zpf < 0 of positive
pressure.
These exotic vacuum virtual sources contribute Omega(Exotic Vacua) ~
0.96 to Omega(Total) = 1 in our large-scale spatially flat
post-inflationary local "Level I" "Hubble sphere" "brane world" as in
Max Tegmark's May 2003 Scientific American's "Parallel Universes" on
Lenny Susskind's megalopolis "Landscape" subject to the natural
selection of the Weak Anthropic Principle ("WAP")
OK, I think I made an error above including "brane worlds" in sense of
"parallel worlds"?
Here is why I think I made an error (If I did so did Hawking and
Scientific American in their popular science reports):
"D-Branes are extended surfaces without edges. In order that the black
hole be a localized object, it is assumed that our ordinary four
dimensions (three space and one time) are all orthogonal to these
D-Brane surfaces ... Thus to us these D-Branes would look as though they
were located at a point (or at least a very small region) of our
observable three dimensions of space." W. G. Unruh p. 168 "Black holes,
dumb holes, and entropy", i.e. the D-Branes are in the compactified
Calabi-Yau space. I have to look again at Hawking's "The Universe in a
Nutshell" that seems to give the wrong idea here? Perhaps I mis-remember?
Note also Ed Witten's formula generalizing Heisenberg's quantum
uncertainty principle, i.e. eq. (5.9) p. 136
Delta X > h/DeltaP + alpha'(DeltaP)/h
The second gravity-string source of uncertainty should give the
irreversible statistical arrow of time not found when alpha' = 0 i.e.
infinite string tension, or infinite space-time stiffness of action
without reaction as is also found in the "signal locality" of orthodox
quantum theory in sense of Antony Valentini's papers.
Consider a model for an elementary particle as a Wheeler wormhole of
"Mass without mass", but with a strong micro-gravity
G* ~ 10^40G on 1 fermi scale. The wormhole has an attractive dark
matter exotic vacuum core where
Vacuum Coherence --> 0
just like inside a quantized vortex of circulation in superfluid HeII.
Therefore, in the core
/\zpf ~ - (1 fermi)^-2
w = -1
Therefore the quantum pressure is positive and the exotic vacuum core
gravitates as
Grad^2V(Exotic Vacuum) ~ -c^2(1 fermi)^-2
this prevents the spread out electric charge from exploding and also
compensates any quantized rotation centrifugal forces. For now keep
charge and rotation zero for simplicity. That is I here only model a
spin 0 neutral micro-geon. That means I would need a high-power
graviton laser as the Heisenberg uncertainty scattering probe
microscope. That's OK since this is only a gedankenexperiment.
The SSS metric then has the factor
1 - 2GM/c2r
Where G(mass density) is replaced by c^2/\zpf
GM is replaced by ~ c^2/\zpfR^3
for a micro-geon of size R
r is DeltaX as in Witten's formula above with DeltaP as the scattering
momentum transfer between gravitons and the micro-geon.
Therefore, the Schwarzschild factor is (neglecting factors of 2, pi etc
all lumped into dimensionless parameter b
1 - bc^2/\zpfR^3/DeltaX
The critical value of Delta X is then the "event horizon" where the
Schwarzschild factor vanishes - can it be reached?
This micro-geon is a solution of the exotic vacuum local field equation
Guv(Einstein) + /\zpfguv = 0
At critical Delta X, the geon looks like a POINT PARTICLE from the huge
space-warp induced by the probe's momentum transfer Delta P.
C is the circumference
dC/dR = 2pi (1 - bc^2/\zpfR^3/DeltaX)^1/2
Where one considers the radial size fixed at R the scale of the throat
of the wormhole.
So when can we have
DeltaX = bc^2/\zpfR^3 ?
Note that alpha' may be large of order (10^-11 cm)^2 not (10^-32 cm)^2
as in Witten's idea. |
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