The dark matter (negative zero point energy density in a vortex filament) induced IR long-wave quark-quark force per unit mass is
f(IR) = c^2/Lp* = constant
Lp* ~ 1 fermi ~ (Lp^2Hubble radius of future dark energy retro-causal de Sitter horizon)^1/3
Lp ~ 10^-33 cm
Hubble "radius" ~ 10^28 cm
This means that the dark matter vortex filament core zero point energy density scales as
1/Lp*r in IR limit
but scales as 1/Lp*^2 in the UV limit where
f(UV) ~ c^2r/Lp*^2 -> 0 as r -> 0
i.e. asymptotic freedom of QCD
Therefore, there is a connection of SU(3) internal symmetry with localized conformal group symmetry which may be there perhaps in Carlos Castro's model?
Obviously SU(3) is the symmetry of the 3D quantum harmonic oscillator which is precisely what we have in a sphere of uniform zpe density. Therefore, the two ends of the open string are point monopole defects with spherical symmetry connected by a dark matter zpe vortex filament tube - this is a pretty picture not needing extra space dimensions. Roger Penrose does not like extra space dimensions (e.g. "The Road to Reality") too much excess math baggage - that's "The Trouble With Physics" - what I just gave you is a Michael Faraday picture in 3D space consistent with Einstein's GR and ordinary QM.
On Oct 21, 2007, at 4:35 PM, Jack Sarfatti wrote:
What do they have in common?
"the force between two quarks approaches a constant strength as we pull the quarks apart ..."
p. 104 "The Trouble With Physics" Lee Smolin
In the simple weak curvature slow speed Galilean limit of Einstein's 1916 General Relativity (GR) with additional torsion, the quantum exotic vacuum zero point energy (ZPE) induced Sakharov (1967) gravity potential energy per unit test particle mass is (in a static spherically symmetric toy model)
Vzpf(r) = -(1/2)c^2/\zpf(r)r^2
In Einstein's GR
g00 = (1 + 2Vzpf/c^2) = - 1/grr
for static LNIF observers outside the event horizon g00 = 0.
ZPF induced Newtonian "gravity force per unit test mass is
f = - dVzpf/dr
In the case of the two NASA Pioneer space probes at the outer edge of the solar system now beyond Saturn in different directions on the celestial sphere the anomalous gravity pull fits the adhoc assumption
|/\zpf| = H/cr
H = Hubble's cosmological constant
Vzpf ~ cHr
f = cH ~ 1 nanometer/sec^2 agrees with observed data
this universal anomalous "gravity" force can point either radially inward or radially outward depending on the sign of the exotic vacuum zero point energy density (w = -1).
Dark matter has /\zpf < 0, i.e. negative zero point exotic vacuum energy with positive pressure and this gives the force pointing inwards to the center of the Sun if we imagine a possibly expanding hollow concentric spherical shell "pulse" starting presently around the orbit of Saturn - blown off in a "vacuum quake" from the center of the Sun. K Tangen says the anomaly is non-geodesic, this model says it's geodesic - however since there must be a torsion field to allow /\zpf to be variable, there may not be a conflict using the "auto-parallel" generalized "geodesic".
Carlos Castro has a new duality argument from localizing the full conformal group to explain why Hubble's parameter shows up at this small scale, i.e. in my paradigm this is tantamount to curvature + torsion + conformal boost and dilation compensating geometrodynamic gauge potentials.
Obviously this same picture can work for hadronic strings i.e. quarks at the end of a rubber band string that is a vortex filament whose "core" is dark matter but of larger density than in the Pioneer case.
i.e. /\zpf ~ 1/Lp*r
Lp*^2 ~ hG*/c^3
G* ~ 10^40G(Newton)
as in Abdus Salam's strong short-range f-gravity and my paper of 1973 "Collective Phenomena" ed. H. Frohlich & FW Cummings when I was at Salam's ICTP in Trieste, Italy.
This gives universal slope of hadronic resonance Regge trajectories
Spin ~ (1Gev)^-2E^2 + intercept
also interpreted as small Kerr black holes in strong short range zero point energy induced Sakharov gravity