Monday, November 08, 2004

Typo-corrected expanded draft #2:

On Nov 8, 2004, at 11:22 AM, Jack Sarfatti wrote:

See p. 73 on "negative energy". There is a lot of confusion on this in the literature.

Eric says "mass energy density < "stress"

What Eric should say is that for positive energy density

w = pressure/(energy density) < -1/3

pressure < -(1/3)(energy density)

We see below that the key equation is (weak limit)

Grad^2V = 4piGrho(1 + 3w)

Where a positive RHS gravitates and a negative RHS anti-gravitates outside the boundary of a compact source.

"Exotic" means "anti-gravitates".

If, on the other hand, the energy density is negative, then one wants w > -1/3.

Therefore, there are more possibilities than Eric mentions.

The key is the frame-invariant trace T of the stress-energy source tensor Tuv(Source) in Einstein's GR field equation

Guv(Geometry) = -(8piG/c^4)Tuv(Source)

If we assume an isotropic perfect fluid source, mass density rho, pressure p

T^u^v = c^2rho(1 + w)(dX^u/ds)(dX^v/ds) - pg^u^v

T = c^2rho(1 - 3w)

R^u^v = -(8piG/c^4)(T^u^v - (1/2)g^u^vT)

R00 = -{L-C}^i00,i ordinary partial derivative of the Levi-Civita connection field.

Note that

W^i = mc^2{L-C}^i00

is the 3-vector "weight" of m in its rest LNIF.

W^i = 0 in the rest LIF consistent with WEP (Weak Equivalence Principle)

In the weak-field slow-speed Newtonian-Galilean relativity limit of Einstein's GR

G^0^0 = 2R^0^0 --> - (2/c^2)Grad^2V

V = Newtonian gravity potential energy per unit test mass

Grad^2V ~ 4piGrho(1 + 3w)


1. Ordinary slowly-moving on-mass-shell matter w ~ 0

T^u^v(matter) ~ c^2rho(dX^u/ds)(dX^v/ds) - pg^u^v

T(matter) ~ c^2rho

Grad^2V ~ 4piGrho

2. Relativistic matter & radiation

w --> +1/3

T^u^v(radiation) = (4/3)c^2rho(dX^u/ds)(dX^v/ds) - pg^u^v

T(radiation) = c^2rho(1 - 1) = 0

Grad^2V(radiation) = 8piGrho(radiation)

3. Zero point micro-quantum vacuum fluctuations (all spins).

Lorentz invariance + WEP minimal gravity coupling --> w = -1

T^u^v(zpf) = - p(zpf)g^u^v

/\zpf = (c^4/8piG)p(zpf) = Einstein's cosmological "constant".

For virtual photons, completely random, with the usual Planck scale cutoff

/\zpf ~ Lp^-2 ~ 10^+66 cm^-2

This is 122 Powers of Ten too big compared to dark energy observations (Type 1a supernovae data)

*This is the cosmological constant problem.

Grad^2V(zpf) ~ -(8piG/c^2)p(zpf) = - c^2/\zpf

Virtual (off-mass-shell) photons (3 independent spin components) have negative zpf pressure from Bose-Einstein quantum statistics commutation rules of creation and destruction.

Therefore a compact source of completely random virtual photons anti-gravitate as "dark energy" outside its boundary.

Virtual electron-positron pairs (2 independent spin components) have positive zpf pressure from the Pauli Exclusion Principle anti-commutation rules of creation and destruction operators. Therefore, a compact source of virtual electron-positron pairs will gravitate like "dark matter" outside its boundary. From a distance they gravity lens like w = 0 CDM.

* Note, you get the opposite inside the boundaries!

For example, the Pioneer 10-11 anomaly is a dark energy hedgehog exotic vacuum topological defect centered at Sun starting at 20 AU from the Sun.

Ordinary vacua have p(zpf) = 0.

OK to sharpen what Eric Davis says on p. 73

The real criterion for "exotic matter" with anti-gravity outside compact exotic sources is

w < -1/3

At least for isotropic perfect fluid sources like zpf in bulk.

On Nov 4, 2004, at 11:26 AM, Gary S. Bekkum wrote:

Air Force report calls for $7.5M to study psychic teleportation

I do not support any of the recommendations in 2.3 for the following reasons:

1. The correct calculations give effects that are much too small.

2. There are serious conceptual errors starting with the use of Puthoff's PV theory giving the false impression that it is plausible and viable for metric engineering warp, wormhole and weapon (W^3) in the context of UFOs. Davis worked for the UFO NIDS in Las Vegas now defunct although Bigelow Aerospace is still going. For example, the idea that you need negative zero point energy density for a stargate is wrong. You need positive zero point energy density (zpf) with equal and opposite negative pressure w = -1 because the gravity source created from the zpf is, for all sources real and virtual, proportional to (1 + 3w) as shown by Mike Turner in the recent Rev Mod Physics article on precision cosmology. One cannot ignore the cosmological constant problem even on small scales.

3. Davis's reference to work by Robert Forward, Puthoff & Cole on extraction of vacuum energy by the Casimir force has been disputed by Ian Peterson of the University of Coventry UK. In any case, you do not get a lot of energy and the energy you might get is very small from the electrostatic energy of the mutually induced electric dipoles in the neutral molecules of the plates.

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