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Suppose we could make a very high Tc superconducting meta-material.

The effective speed of light is then c/n where n < 0 and |n| >> 1. Of course there will be dispersion, i.e. n(k,w) including virtual photons.
Let's be naive and look what happens to the Planck units.
LP* = (hGn^3/c^3)^1/2 >> LP ~ 10^-33 cm
TP* = LP*/c = (hGn^5/c^5)^1/2 >> TP ~ 10^-43sec
P*P = h/LP = h/(hGn^3/c^3)^1/2 << PP
does the "i" have any physical meaning?
The Planck energy is 
EP* = (hc^5/n^5G)^1/2 << EP ~ 10^19 Gev
again all of these parameters get an i because n is negative
The Action Cartan 1-form is 
S = Et - Px ---> -S
So the Feynman amplitudes go to their complex conjugates.
The gravity coupling of matter to curvature is now n^4G/c^4 = 1/G-string tension
suppose n ~ 10^10

EP* ~ 10^-2510^19Gev ~ 10^-6Gev ~ 1Kev

Furthermore the classical coherent electromagnetic field energy density is negative - for classical fields this should produce antigravity for non-radiative near fields (coherent states of virtual photons) trapped inside the superconducting meta-material as confined quantized magnetic vortices (Abrikosov lattice) under Type II conditions.

The coupling of these magnetic vortices to the geometrodynamic field will be 10^40 times stronger than normal.

This amazing material in my imagination at the moment would also have stealth cloaking functionality.