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Bottom line, for a thin spherical shell capacitor filled with appropriate meta-material of thickness d << Area A of concentric shells - the anomalous Newtonian g-force field just outside the outer electrically charged spherical shell should be of order of magnitude
g(anomalous repulsion) = c^2rs(applied EM field)/r^2
r ~ A^1/2
~  (index of refraction)^4G(-E^2d/c^2
(- = negative permittivity

Therefore, without the index to the fourth power amplification we cannot hope to nullify g(Earth) ~ 10 meters/sec^2 with practical small amounts of applied electric field/voltage gradient between the inner and outer spherical shells filled with a properly designed meta-material.

On Mar 12, 2011, at 10:17 PM, jfwoodward wrote:
Well, certainly the metamaterial is worth testing.  And producing as much exoticity as possible makes sense.  But reducing c (as in a superconductor) I don't think will matter much. 
I disagree. If we cannot greatly reduce "c" via a Bose-Einstein condensate and/or http://en.wikipedia.org/wiki/Slow_light enormous increase of index of refraction I don't think there is a chance it will work. Could be wrong of course - and it may not work because my basic Ansatz may not be true - empirical issue, but these are desperate times and we should try everything not obviously not even wrong.
You are thinking that by reducing c, m (= E/c^2) will be increased I'll bet.
My idea is motivated by Sakharov 1967 that gravity is an emergent macroscopic IR effective c-number field from the electro-weak-strong forces and sources as a substrate as VIRTUAL quanta inside the physical vacuum.
My idea is motivated by
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and Einstein's field equation that I conjecture is, in a material,
Guv(gravity) + [8pi(index of refraction)^4G/c^4]Tuv(applied EM field) = 0
But I don't think that changing c by an index of refraction makes any difference as c in m = E/c^2 is the vacuum speed of light (not whatever it may be in some material medium).  As I said, reducing c can increase the energy density (as the stuff traveling at c gets stacked up if you will as it passes into the refracting medium), but it cannot change the total energy (which is compressed into a smaller volume in the refracting medium but not changed in total amount).
But let's say I'm wrong about the c issue.  Thinking in terms of non-transparent media, you don't need a superconductor.  Think in terms of materials with very large dielectric constants.  10^3 is easy.  That's the k of ferroelectric materials.  And I've heard that ks of 10^6 are possible.  It's not 10^10.  But it should be more than enough for the purpose. . . .

Update on
On Mar 12, 2011, at 5:13 PM, JACK SARFATTI wrote:
The capacitor has to have negative permittivity at DC or at least at ELF range.
But that's not good enough to measure anomalous repulsive gravity if the effective index of refraction is normal ~ 1
The important thing we want to measure is (index of refraction)^4G/c(vacuum)^4
to test my conjecture
Guv +  [(index of refraction)^4G/c(vacuum)^4(E.D)] = 0
inside a material despite apparent breaking of general covariance
D = (permittivity)E
The effective induced radius of curvature R is
1/R^2 ~ (index of refraction)^4G/c(vacuum)^4(E.D)
comparing to an idealized spherical mass equivalent
rs/r^3 = 1/R^2 ~ curvature estimate for Guv in Einstein's equation in the meta-material spherical shell region where Tuv =/= 0
rs/r^3 ~  [(index of refraction)^4G/c(vacuum)^4](E.D)
What is rs here?
We need to take the total EM field SOURCE energy in the "capacitor" on the RHS, divide by c^2 etc.
From that we compute r self-consistently.
E.D = (-E^2
(- = electrical permittivity that we want negative in an ELF band in a spherical thin shell capacitor filled with a meta-material of volume V that is also superconducting at high Tc.
The total non-radiative near field ELF electric field mass-energy M (neglect magnetic part in first approximation)
M = (-E^2V/c^2
Therefore, assuming a spherically symmetric shell "capacitor" of thickness d and area A, V = Ad with E ~ constant inside the thin shell
d << A^1/2 (neglecting 4pi etc for now)
rs = 2GM/c^2 = (index of refraction)^4G(-E^2Ad/c^4
and
r ~ A^1/2
so in vacuum just outside the shell of the spherical capacitor
g(anomalous) = c^2rs/r^2 ~  (index of refraction)^4G(-E^2d/c^2
The effective static LNIF anomalous g-force is then c^2rs/r^2 to compare with local Earth g of 10meters/sec^2
Unless we can get (index of refraction) way up to ~ 10^10 in the relevant frequency band I doubt we will be able to measure anything.
Clearly, this theoretical issue needs to be more carefully studied first - this is only off the cuff back of envelope sort of hand waving.