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Remember however these papers only deal with "plane wave far field radiation (real photons in coherent states) not near-fields (virtual photons in coherent states) that do not propagate.

Gravitation and electromagnetic wave propagation
with negative phase velocity
Tom G Mackay1,3, Akhlesh Lakhtakia2,4 and Sandi Setiawan1
1 School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK
2 CATMAS—Computational & Theoretical Materials Sciences Group,
Department of Engineering Science and Mechanics, Pennsylvania State
University, University Park, PA 16802–6812, USA
E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., This email address is being protected from spambots. You need JavaScript enabled to view it. and This email address is being protected from spambots. You need JavaScript enabled to view it.
New Journal of Physics 7 (2005) 75
Received 25 October 2004
Published 8 March 2005
Online at http://www.njp.org/
doi:10.1088/1367-2630/7/1/075
Abstract. Gravitation has interesting consequences for electromagnetic wave
propagation in vacuum. The propagation of plane waves with phase velocity
directed opposite to the time-averaged Poynting vector is investigated for a
generally curved spacetime. Conditions for such negative-phase-velocity (NPV)
propagation are established in terms of the spacetime metric components for
general and special cases. Implications of the negative energy density of NPV
propagation are discussed.
3

Obstacle to the goal of low power warp drive

A simplistic expression of the (monochromatic) electromagnetic energy density turns out to yield negative values [8], which are generally held as impossible in the electromagnetics research community, but more sophisticated investigations indicate that the
electromagnetic energy density in NPV materials is indeed positive when account is taken of the frequency-dependent constitutive properties ...

The possibility of a negative electromagnetic energy density requires discussion. In the
research on isotropic, homogeneous, dielectric-magnetic NPV materials, the negative value
has been noted [8]. Equally important is the fact that such materials have been artificially
fabricated as composite materials comprising various types of electrically small inclusions, and their plane wave response characteristics (over limited ω-ranges) are substantially as predicted [7]. This implies the aforementioned procedure to compute W(ω/c, k, r)t may not be always correct. Indeed it is not, because it applies only to nondissipative and nondispersive mediums. When account is taken of the dissipative and the dispersive nature of the NPV materials [26], W(ω/c, k, r)t does turn out to be positive [9].

Change G above to n^4G in the superconducting |n| ~ 10^10 meta-material n < 0.

3) The primary area of research in metamaterials is investigation of materials with a negative refractive index.
This appears to permit the creation of 'superlenses' which can have a spatial resolution below that of the
wavelength, and a form of 'invisibility' has been demonstrated at least over a narrow wave band. Although the
first metamaterials were electromagnetic, acoustic and seismic metamaterials are also areas of active research.
Metamaterial potential applications are diverse and include remote aerospace applications, sensor detection
and infrastructure monitoring, smart solar power management, public safety, radomes, high-frequency
battlefield communication and lenses for high-gain antennas,[4] improving ultrasonic sensors and even
shielding structures from earthquakes. ...

Metamaterials as left-handed media occur when both permittivity ε and permeability μ are negative. Furthermore, left handedness occurs mathematically from the handedness of the vector triplet E, H and k. ...

In natural occurring transmission media right handedness dominates, i.e., permittivity and permeability are
both positive resulting in an ordinary positive index of refraction. However, metamaterials have the capability
to exhibit a state where both permittivity and permeability are negative, resulting in an extraordinary index of
negative refraction, i.e. a left-handed material.[2] The term Left Handed Material (LHM), is interchangeable
with the term Double Negative metamaterials (DNG).[7]

In DNG metamaterials both permittivity and permeability are negative resulting in a negative
index of refraction. The index of refraction, n, has been shown to be negative in theory, and several research
experiments have reported a negative index of refraction for DNG metamaterials.[1] Studies have created
applications for producing a negative refractive index. These applications are "phase compensation with
electrically small resonators, negative angles of refraction, subwavelength-waveguides, backward wave
antennae, Cerenkov radiation, photon tunnelling, and enhanced electrically small antenna". The concept of
continuous wave excitation is a key component of these studies to obtain the negative index refraction of DNG
media, and introduce these applications.[1] DNG metamaterials are innately dispersive, so their permittivity ε,
permeability μ, and refraction index n, will alter with changes in frequency.

Main article: Negative index metamaterials
The greatest potential of metamaterials is the possibility to create a structure with a negative refractive index, since this property is not found in any non-synthetic material. Almost all materials encountered in optics, such as glass or water, have positive values for both permittivity ε and permeability µ. However, many metals (such as silver and gold) have negative ε at visible wavelengths. A material having either (but not both) ε or µ negative is opaque to electromagnetic radiation (see surface plasmon for more details).
Although the optical properties of a transparent material are fully specified by the parameters ε and µ, refractive index n is often used in practice, which can be determined from . All known non-metamaterial transparent materials possess positive ε and µ. By convention the positive square root is used for n.
However, some engineered metamaterials have ε < 0 and µ < 0. Because the product εµ is positive, n is real. Under such circumstances, it is necessary to take the negative square root for n. Physicist Victor Veselago proved that such substances can transmit light.

More…

Video representing negative refraction of light at uniform planar interface.
The foregoing considerations are simplistic for actual materials, which must have complex-valued ε and µ. The real parts of both ε and µ do not have to be negative for a passive material to display negative refraction.[23] Metamaterials with negative n have numerous interesting properties:
Snell's law (n1sinθ1 = n2sinθ2), but as n2 is negative, the rays will be refracted on the same side of the normal on entering the material.
The Doppler shift is reversed: that is, a light source moving toward an observer appears to reduce its frequency.
Cherenkov radiation points the other way.
The time-averaged Poynting vector is antiparallel to phase velocity. This means that unlike a normal right-handed material, the wave fronts are moving in the opposite direction to the flow of energy.
For plane waves propagating in electromagnetic metamaterials, the electric field, magnetic field and wave vector follow a left-hand rule, thus giving rise to the name left-handed (meta)materials. It should be noted that the terms left-handed and right-handed can also arise in the study of chiral media, but their use in that context is unrelated to this effect. The effect of negative refraction is analogous to wave propagation in a left-handed transmission line, and such structures have been used to verify some of the effects described here.
Handedness is an important characteristic in metamaterial design and fabrication as it relates to the direction of wave propagation. Metamaterials as left-handed media occur when both permittivity ε and permeability µ are negative. Furthermore, left handedness occurs mathematically from the handedness of the vector triplet E, H and k.[2]
In ordinary, everyday materials - solid, liquid, or gas; transparent or opaque; conductor or insulator - right handedness dominates. This means that permittivity and permeability are both positive resulting in an ordinary positive index of refraction. However, metamaterials have the capability to exhibit a state where both permittivity and permeability are negative, resulting in an extraordinary, index of negative refraction, i.e. a left-handed material.[2][24]
http://en.wikipedia.org/wiki/Metamaterial

On Aug 15, 2010, at 2:11 PM, JACK SARFATTI wrote:

Given a dispersive dissipative medium, the Fourier transform of the index of refraction is n(f,k) which has an imaginary part for dissipation - see Kramer's Kronig dispersion relations for causality

for far-field radiation f = kc (on classical light cone "mass-shell")

for non-radiative near fields f =/= kc i.e. macrocoherent Glauber states of virtual photons correspond to induction fields of motors, generators, transformers, power lines etc.

formally

phase velocity is

vphase =  c/n(f,k)

for near fields f, k are independent variables

group velocity of energy transport is

vgroup = df/dk

which is physically meaningless for near fields, but not for far fields.

when f = [c/n(f,k)]k

vgroup = df/dk = [c/n(f,k)]dk/dk + ck(d/dk)(1/n(f,k))

note that d/dk is the gradient Del 3-vector operator in k-space

so causality i.e. no FTL signal requires
vgroup = df/dk < 0

Now some of the meta-material papers Waldyr sent seem to require gradient terms in the near-field EM density to avoid negative energy - of course we want negative EM energy to get the "lift" of anti-gravity for low-power warp drive (zero g-force and no time dilation) - so that's the problem where

|n(f,k)| >> 1 superconductor

http://www.news.harvard.edu/gazette/2001/01.24/01-stoplight.html

& n(f,k) < 0 meta-material


On Aug 15, 2010, at 9:41 AM, JACK SARFATTI wrote:

PS

coupling of stress-energy density Tuv to gravity Guv is ~ G/c^4 that I replace by n^4G/c^4

when |n| >> 1 as in a superconductor

a small stress-energy density induces a large curvature (in some range of f & k) in the exotic superconducting meta-material - that then ripples out to vacuum via

Green's function propagators of the gravity field

Guv ~ n^4(G/c^4)Tuv in sc meta-material

Guv = 0 in vacuum - neglect / here.

On Aug 15, 2010, at 9:34 AM, JACK SARFATTI wrote:

Paul
My idea is simple

in the stress-energy tensor Tuv replace c by c/n

n = index of refraction

in a meta-material n < 0

not only that but permittivity and permeability separately negative

now there are unresolved problems of dispersion and dissipation, however (as noted by Waldyr Rodrigues Jr)

most papers try to eliminate negative energy density.

T00(EM) = (permittivity)(electric field)^2 + (permeability)(magnetic field)^2 < 0 in some range of frequencies f and wave vectors k

think non-radiating near fields not far fields so that f =/= ck i.e., off light cone coherent states of virtual photons

a negative energy density creates anti-gravity repulsion in this case where w > -1/3 as in Casimir plates geometry (e.g. Puthoff's papers)

in addition in a superconductor |n| >> 1 i.e. stopping light

therefore, I suggest that a high Tc superconducting meta-material will show anomalous repulsive gravity


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