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Science Forum Index » Mathematics Forum » Strings and Sakharov's G from QED
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| Jack Sarfatti |
 Posted: Sun Dec 28, 2003 5:14 pm |
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Jack Sarfatti wrote on Dec 28, 2003
Thanks for this insight.
PS I will review "Physics Meets Philosophy at the Planck Scale".
There seems to be a misconception about D Branes starting in Hawking's
new popular book "The Universe in a Nutshell" ("O Brane New Worlds")
and also pictures in Scientific American showing gravitons (closed strings)
moving through all of hyperspace with lepto-quarks and photons (open
strings) stuck to "D Branes" pictured as "parallel universes" as
in Max Tegmark's "Level 1" May 2003 Scientific American. The way Unruh
describes a D Brane seems incompatible with that picture?
Also Witten seems to think his alpha' = 1/(string tension) ~ (10^-32
cm)^2 is a new independent fundamental constant (a moduls or
compactification scale) rather than
Lp^2 = hG(Newton)/c^3 = hc(alpha'alpha) = alpha'e^2
hG/e^2c^3 = alpha'
Think first in quantum field theory of a virtual electron-positron pair
"vacuum bubble", i.e. closed world line with no free ends. Then imagine
one virtual photon bisecting the the closed world line. This is the
basic virtual bound state into which a huge number of these vacuum
bubbles Bose-Einstein condense to form the vacuum coherence field whose
Goldstone phase ripples form Einstein's guv c-number ODLRO field.
The Higgs amplitude ripples of the vacuum coherence condensate form the
dark energy and dark matter exotic vacuum w = -1 phases that is 96% of
the large-scale stuff of the world.
For strings imagine a closed strip - two-sided orientable - maybe also
Mobius one-sided strips.
The smallest quantized area of these vacuum bubbles is obviously
hcalpha' in Witten's sense.
The single virtual photon gives a factor of alpha = e^2/hc since each
fuzzed out vertex is (alpha)^1/2
i.e. basic diagram is <|> | is the virtual photon and <> is the virtual
electron-positron vacuum loop or bubble.
Therefore, this is a simple Mickey Mouse derivation of Andrei Sakharov's
emergence of gravity G from QED and Witten's basic
modulus or string tension parameter, i.e.
G = e^2c^3alpha'/h = c^4(alpha)(alpha')
So that to be more precise Einstein's GR equation is
Guv = (8piG/c^4)Tuv
8piGh/hc^4 = 8piLp^2/hc = (alpha)(alpha')
Guv = (alpha)(alpha')Tuv
alpha' is Witten's modulus.
On Saturday, December 27, 2003, at 11:30 PM, Carlos Castro wrote:
"Dear Friends :
Recently there has been a lot of work dedicated to
Fisher information theory, entropy.... see the book by
Frieden, Cambridge University Press :
" Physics from Fisher Information "
that claims/suggests to derive all of physics from
Fisher information theory. If you look at the
literature about QM and Fisher you will see that there
is a Fisher information term in the Schroedinger
equation that is related to Bohm's quantum potential =
Weyl scalar curvature induced by the ensemble density
of particle paths. Although the authors never pointed
this out to my amazement !
So yes, information theory, entropy and Weyl-Bohm have
a lot in common. Call it " Information Geometry "
which is very popular today.
also
Dear Jack :
The title of Christian Beck's book is :
Spatio-temporal vacuum fluctuations of quantized fields...
World Scientific 2002. Nonlinear sciences.
His papers are in the hep-th, condensed matter and astrophysics
archives. You can download them.
His book is based on his paper : Chaotic Strings that is on the archives.
Best wishes
Carlos"
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