Casimir force detection of extra space dimensions in the 't Hooft-Susskind World Hologram Theory
On Nov 6, 2005, at 12:16 PM, Jack Sarfatti wrote:
On Dec 31, 2004, at 1:20 PM, Leonard Susskind wrote:
To whom it may concern,
The Glogower Susskind Paper of 1963 which introduced phase operators for a quantum oscillator was in direct response to discussions between Glogower, Susskind and A Jack Sarfatti. Sarfatti's contributions were significant. The correct attribution should be to the "Glowgower, Sarfatti, Susskind" operators.
Jack Sarfatti wrote:
Casimir force measurements are an extremely sensitive test for extra space dimensions.
If 't Hooft & Susskind are correct, then on the basis of their theory, I predict a new "gravity" term for the Casimir force that can be used to test for extra space dimensions. Indeed, it is pretty safe to say that extra space dimensions have already been detected via current observations of the Casimir force without people realizing it - provided that 't Hooft & Susskind's basic idea is correct.
The simplest model of the QED Casimir force uses the OLD form of Heisenberg's uncertainty principle
&p ~ h/&r
& means "uncertainty" (root mean square fluctuation of "ensemble" of identically prepared micro-quantum systems subject to the Born probabilty rules with "signal locality" from "sub-quantal equilibrium" - A. Valentini)
&p < h/&r for virtual off-mass-shell zero point processes inside the vacuum
&p > h/&r for real on-mass-shell excited states outside the vacuum
't Hooft & Susskind show that gravity (formation of a tiny black hole at large momentum transfer in scattering) modifies the uncertainty principle to
&p ~ h/&r + (h/Lp)^2&r/h = h/&r + (c^3/G)&r
Its dual is
&r ~ h/&p + Lp^2&p/h = h/&p + (G/c^3)&p
Therefore, the Casimir force equation needs to be changed from
F = ahcA/L^4 = a(h/L)cA/L^3 = a&pcA/L^3
F = [a&pc + b(h/Lp)^2c&r]A/L^3
F(Casimir) = (ahc/L + b(c^4/G)L)A/L^3 = ahcA/L^4 + b(c^4/G)A/L^2
= QED Casimir Force + (G-STRING TENSION)(A/L)^2
where a & b are dimensionless coefficients to be calculated by renormalization/regularization algorithms.
c^4/G = G-string tension (Energy/Length) = (Force)
Extra space dimensions increase G* at small scales. Note that c^4/G is a big number because G is small and c is large.
Therefore, the fact that such a huge Casimir force ~ (10^19Gev/10-33cm)A/L^2 is clearly not seen implies either:
1. The 't Hooft-Susskind idea is wrong.
2. There are already extra space dimensions at the scale of Casimir force measurements that make
c^4/G* << c^4/G
Note, in a spherical conducting cavity A/L^2 is a constant.
Therefore, the gravity Casimir force is a constant = G-STRING TENSION
The potential is linear
V(Casimir Gravity Potential ~ (G-STRING TENSION)r
For positive dark energy density with negative pressure from w = -1 inside the cavity V > 0 and the radial force -dV/dr is attractive pointing toward the center of the spherical cavity i.e. a CONFINEMENT FORCE like the quarks inside hadrons.