My rebuttal to New Scientist May 22, 2004 Open Letter: http://www.cosmologystatement.org/
and Commentary on:
The warp drive: hyper-fast travel within general relativity
Authors: Miguel Alcubierre
Comments: 10 pages, 1 figure. Not previously available in gr-qc
Journal-ref: Class.Quant.Grav. 11 (1994) L73-L77
It is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed. By a purely local expansion of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light as seen by observers outside the disturbed region is possible. The resulting distortion is reminiscent of the ``warp drive'' of science fiction. However, just as it happens with wormholes, exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.
My comments on this paper:
The metric squared interval in Einstein's GR os
ds^2 = guvdx^udx^v
Use the ADM 3+1 canonical decomposition
ds^2 = -(a^2 - b^2)(cdt)^2 + 2bidx^i(cdt) + gijdx^idx^j
u,v = 0,1,2,3
i,j = 1,2,3
a = lapse function
b = (b1,b2,b3) = shift 3-vector = gravimagnetic field of frame drag Lense-Thirring effect to be tested in EINSTEIN NASA space probe.
b also plays key role in Ray Chiao's "gravity radio" superconducting transducer to convert far field gravity waves to electro-magnetic waves and vice versa via the b.A coupling Hamiltonian, where A is the EM vector potential. We need the near-field "induction" case for metric engineering the fabric of space-time (AKA the geometrodynamic field).
Note that Hal Puthoff's PV challenge to Einstein's GR is not able to describe the gravimagnetic field at all so far. We will see that the gravimagnetic field is essential to practical metric engineering on small scales where G* >> G. Therefore, PV as formulated up to present time in publications by Puthoff is irrelevant to the metric engineering of weightless warp drive and traversable wormhole star gate time travel portals.
Alcubierre's lapse function a = 1, which is a sufficient condition for weightlessness, i.e. the timelike world lines normal to the spacelike slices of space-time in the ADM 3+1 decomposition are free float geodesics for the Eulerian observers inside the "flying saucer" who are able to shape their own flight geodesic - to steer it at will including hair-pin 180 degree turns with zero g-force inside the saucer because the spacelike 3D metric gij inside the saucer is flat Euclidean.
Since the interior of the alleged alien ET flying saucer is spatially flat all of the curvature is extrinsic given by the second fundamental form
Kij = (1/2)(bj,i + bi,j)
where ,j denotes ordinary partial derivative in the usual notation.
A key parameter is the expansion of volume elements for the Eulerian observers inside the flat 3D geometry of the saucer's interior, which turns out to be simply the negative divergence of the gravimagnetic field! This is what is plotted in Alcubierre's picture in his paper.
Therefore, in terms of my theory of metric engineering controlled saucer flight
Div.b ~ /\zpf
That is, the exotic vacuum zero point energy density is a source for the gravimagnetic 3-vector field of the engineered warp drive/star gate metric field!
In the electromagnetic analogy, the zero point energy density is a gravimagnetic monopole density!
We will also need, in the special case of Alcubierre's toy model
1 - b^2 ~ /\zpf
with the critical exotic vacuum phase transition from universally repulsive dark energy density to universally attractive dark matter density at |b| = 1.
The recent letter in New Scientist (May 22, 2004) signed by 33 dissident cosmologists that
"The big bang today relies on a growing number of hypothetical entities, things that we have never observed-- inflation, dark matter and dark energy are the most prominent examples. ... The successes claimed by the theory's supporters consist of its ability to retrospectively fit observations with a steadily increasing array of adjustable parameters, just as the old Earth-centred cosmology of Ptolemy needed layer upon layer of epicycles."
is very wrong-headed in my opinion.
Note that Alcubierre's eq. (19) for Goo ~ -|/\zpf|^2 because goo ~ /\zpf and Einstein's exotic vacuum field equation is simply
Guv + /\zpfguv = 0
The statements by the 33 dissident cosmologists that dark energy, dark matter and the inflation field are epicyclic fudge factors are false.
Dark energy is /\zpf > 0/
Dark matter is /\zpf < 0
The inflation field is the vacuum coherence in the large scale sense of a wavelet transform where the vacuum coherence local field is dominated by the physical vacuum ODLRO order parameter
Vacuum Coherence = <0|e+e-|0>
for a macro-quantum condensate of virtual electron-positron bound states.