Electron as point particle
Jack Sarfatti
Warps" of 3D space around a black hole. The ratio of circumference to
radius (2D) and of surface area to radius (3D) is non-Euclidean. The
physical radius is much larger relative to circumference and surface
area than in flat space. One needs a radial integral of dr/(1 -
2GM/c^2r)^1/2.
Similarly, for the electron as an IT Bohm "hidden variable" surfing on a
BIT pilot wave of "active information". You can think of the electron as
an extreme non-radiating Kerr-Newmann black hole modified of course to
include its exotic vacuum /\zpf < 0 "dark matter" core that stabilizes
the electric charge and provides the residual physical renormalized mass
~ 0.5 Mev. The extreme short range effective gravity of the dark matter
core will cause a huge "gravitational lens" bending of light probes
scattering from the electron. This is like Rutherford's scattering in
1913 that showed a tiny nucleus in the atom from the anomalous large
angle scattering! Similarly here. The strong short range gravity causes
large angle photon scattering making the effective form factor of the
electron look like a "point".
The string picture below was only a half-baked guess. One could,
alternatively, picture a shell of electric charge of "radius" ~ 1 fermi
(i.e. e^2/mc^2) with /\zpf ~ -(1 fermi)^-2 inside so that the
renormalized mass m is ~ (e/c)^2/\zpf^1/2 with a thin shell of /\'zpf ~
(e^2/hc)Lp^-2 binding the electric charge and canceling its Coulomb
barrier. I ignore spin in first approximation. That is, most of the dark
matter core providing the physical rest mass of the electron is the
hadronic /\zpf ~ 1/(1fermi)^2 . You only need a thin surface region of
/\zpf' 1/(Kaluza-Klein)^2 to prevent the electric charge from exploding.
The extreme black hole condition with exotic vacuum stabilizing core is
probably
(G*m/c^2)^2 = (hc/e^2)/\zpf^-2 + G*Q^2/c^4 + (J/mc)^2
where
G*m^2 ~ Q^2
Q is electric charge, i.e. e in this case.
Therefore, since /\zpf < 0 for dark matter
(hc/e^2)|/\zpf|^-2 ~ 137(fermi)^2 = (J/mc)^2
J/mc ~ 10^-12 cm
forgetting factors of pi.
Recall also
Lp*^2 = Lp^2 - /\zpf^-1 = hG*/c^3
On Saturday, April 19, 2003, at 10:16 PM, Jack Sarfatti wrote:
Why take /\zpf = - 1/(1fermi)^2 for universal exotic vacuum dark matter
core of elementary particles?
Is it from the World Hologram ? (L. Susskind) since
Lp* = Lp^2/2(c/H)^1/3 ~ 1 fermi
H is the Hubble.
Note, to make sure the electric charge of electron does not explode, we
need a second length scale
/\zpf' = -(e^2/hc)Lp^-2 = -1/(Kaluza-Klein Compactification Scale)
That is, the electron IT Bohm hidden variable moved by its qubit pilot
field of "active information" is 2 2-Brane, i.e. a tube with two ends
about 1 fermi in length with a dark matter core of thickness ~
Lp/(square root of Planck length) ~ 10Lp.
(Mc/h)^2 = /\zpf'
i.e. e^2 ~ GM^2 = G/\zpf'(h/c)^2
e^2/hc = (Gh/c^3)/\zpf'
On Saturday, April 19, 2003, at 09:52 PM, Jack Sarfatti wrote:
Have you seen Smolin's paper?
http://arxiv.org/abs/hep-th/0303185
Smolin wrote:
"... standard perturbative approaches, which attempted to base
quantum gravity on a Feynman perturbation theory for graviton modes, of
the form,
gab = nab + hab (1)
Here hab is defined to be a small excitation on a flat background nab.
All such approaches to
the quantization of general relativity were found to fail at some low
order in perturbation
theory, yielding theories that were perturbatively nonrenormalizable.
Various attempts were
made to save the situation at the level of an expansion of the form of
(1) and they all failed.
For example, one can add to the Einstein action terms in the square of
the curvature; pertur-
bative renormalizability is then accomplished, but at the expense of
perturbative unitarity.
The same holds for attempts to resolve the problem by adding new degrees
of freedom,
such as dynamical torsion or non-metricity. In each case one can
construct theories that are
perturbatively unitary and theories that are perturbatively
renormalizable, but not theories
that have both properties. .... There were, nevertheless, significant
advances in the 1970’s. Around 1971 several striking results were found,
concerning the behavior of quantum fields on a few spacetime backgrounds"
Note in contrast in my version of Sakharov's induced gravity, I get
gab = <gab> + h'ab (1')
where <gab> is an already curved c-number background from the "more is
different" "off-diagonal-long range order" vacuum condensate
<0|e+(x)e-(x)|0>. This vacuum expectation value is not the "inflaton" BTW.
<gab> = nab + (da,b + db,a)/2
da = Lp^2[arg<0|e+(x)e-(x)|0>,a - 2(e/hc)Aa] = World Crystal distortion
field
/\zpf = Lp^-2[1 - Lp^3|<0|e+(x)e-(x)|0>|^2]
Lp^2 = hG/c^3
/\zpf = 0 in the "equilibrium vacuum" that does not gravitate nor does
it anti-gravitate.
/\zpf > 0 is dark energy exotic vacuum that anti-gravitates, i.e.
Omega(dark energy) ~ 0.73 ? accelerating the universe (Mike Turner says
it's more like 2/3 than 3/4?)
/\zpf < 0 is dark matter exotic vacuum that gravitates, i.e. Omega(dark
matter) ~ 0.23
Omega(ordinary matter) ~ 0.04
Total Omega = 1 i.e. flat space.
h'ab is the spin 2 quantum field on curved c-number superfluid background.
In the physical vacuum case, h'ab makes virtual off mass shell gravitons
not real gravity waves.
The vacuum field equation is
Guv + /\zpfguv = 0
The physics is that nab is unstable to non-perturbative BCS pairing of
virtual electron-positron pairs at the edge of the Dirac negative energy
virtual electron Fermi sphere in momentum space.
<0|e+(x)e-(x)|0> persists as it is the backbone of both c-number
macro-quantum curved spacetime & unified dark energy-matter as exotic
vacuum regions.
<0|e+(x)e-(x)|0> may be the surviving long range part of a
U(1)xSU(2)xSU(3) multiplet. The short range part decays as the
"inflaton" perhaps?
/\zpf ~ -1/(fermi)^2 universal dark matter core at 1Gev scale explains
Regge trajectory string data for hadronic resonances.
J ~ |/\zpf|^-1(mc/h)^2 + intercept = integer
This is like quantization of magnetic flux in a Josephson weak link
since <0|e+(x)e-(x)|0> must be single-valued.
|/\zpf|^-1c^2/h^2 = G*/hc
G* = |/\zpf|^-1c^3/h
|/\zpf|^-1 ~ Lp*^2 >> Lp^2
In general
Lp*^2 = Lp^2 -/\zpf^-1
Note rest mass of the electron me ~ (e^2/c^2)/\zpf^1/2 ~ 0.5 Mev