re: Guv(induced space-time warp) ~ [(index of refraction)^4G/c^4]Tuv(applied electromagnetic field stress-energy density)
n < 0 meta-material
|n| >> 1 superconductor
James Woodward wrote:
"On the contrary, I get exactly what you are up to with your speculative idea. It is predicated on the assumption that the electromagnetic index of refraction is the determinant of the stiffness of spacetime."
James: This, of course, is not correct.
Jack: I am of course aware, that my premise may be false. However, you cannot say a-priori it is wrong. It's entirely an empirical question. Also, if it's wrong, there is no other way to make a low-power warp drive.
James: The electromagnetic index of refraction has nothing to do with the stiffness of spacetime. It is a measure of the
propagation characteristics of EM waves in material media in FLAT spacetime.
Jack: This is a false argument in my opinion. First, the permittivity of free space, vacuum impedance, is mostly from the scattering of real photons off virtual electron positron pairs in the vacuum. Similarly, the permittivity of materials is from the scattering of real photons off real electrons & ions etc. However, the equivalence principle demands that both real and virtual particles have direct gravity effects. Also, curvature is a Red Herring, since space-time is locally flat and the index of refraction is clearly definable even when spacetime is curved. For example, simply take the 2nd rank electromagnetic response tensor in a LIF and multiply it by the tetrad components appropriate to the desired LNIF, e.g. a static LNIF in the simplest SSS problem where
gtt = - 1/grr = 1 - rs/r
James: So putting a small amount of energy -- as you propose -- into a metamaterial with a large negative index of refraction -- even if the energy density of the field becomes negative by virtue of being in the metamaterial (which it almost certainly doesn't) -- will not produce the spacetime warps needed for wormholes, warp drives, and stargates.
Jack: There is no way to know this without actually doing the experiment.
James: There are decades of orders of magnitude more negative energy needed to do this, and a small amount of energy doesn't get transformed in to the large amount of energy needed simply by the passive action of a metamaterial.
Jack: I repeat: There is no way to know this without actually doing the experiment.
James: This does not mean that it is impossible to engineer wormholes and stargates. I just means that it almost certainly can't be done on the cheap in the way you propose.
Jack: So, what do you propose as an alternative?
James has either forgotten or is not aware of Ray Chiao's very similar proposal on gravity amplification in superconductors (though without the metamaterial factor).