Weightless Warp Drive with Curvature and Torsion Fields


math typo - final equation on previous message on emergent gravity should have been

R/\e + Lambda e/\e/\e = 0 vacuum equation

Memorandum for the Record

Military Applications of the Emergent Gravity Theory

Bottom Line:

*Military Applications:

Stealth cloaking of attack fighter-bombers and cruise missiles

Silent running, e.g. "Black Triangle" UFO craft

Tapping of zero point energy for power as in the "energy device" allegedly delivering up to 100,000 watts CW at 100 amps continuously for past 60 years reported by Robert Collins (USAF Intelligence ret) in "Exempt from Disclosure."

All of the above are without torsion fields. Torsion fields give more capabilities of course.

I. Plain Vanilla 1915 Einstein gravity "The Cake"

The vacuum equation is the 1-form equation

*[R/\e + Lambda e/\e/\e] = 0


The 1-form matter source equation is


*[R/\e + Lambda e/\e/\e] = *J


*J is the stress-energy source current density 1-form, so that J is a 3-form.

The torsion 2-form is

S = De

First consider only 1915 GR i.e.

S = De = 0

e = 1 + B

D = d + W/
Therefore the torsion-free spin connection 1-form is

W = -*[dB/\(1 - B)]

Note the subspace nonlinearity ~ dB/\B not found in electromagnetism.

Look at Maxwell's E&M gauge force theory

The U(1) internal symmetry gauge invariant exterior derivative on source fields is

D = d + A/
Compare this to the Diff(4) (AKA locally gauged T4) "background independent" space-time covariant exterior derivative

D = d + W/
So that A is analogous to W not to B. B lives in the antisymmetric "square root" tetrad subspace of the symmetric geometrodynamic space. The boson elements of space-time are pairs of the tetrads. That's one way of thinking of the equivalence principle, AKA EEP.

In abelian U(1) electrodynamics

F = dA

is the 2-form EM field tensor

dF = 0 is the "Bianchi identity"

i.e. Faraday's law & no magnetic monopoles law

from d^2 = 0 locally ignoring global EMERGENT "More is different" topological defects for now.

* is Hodge dual, i.e. 4D antisymmetric tensor depends on vacuum (or material) structure.

d*F = *J this is a 3-form since *F is a 2-form in 4D space-time

(no extra dimensions here)

i.e., Ampere's law with displacement (transverse radiation) current) + Gauss's law

Again from d^2 = 0 locally NOT generically GLOBALLY in DeRham integration

d^2*F = d*J = 0

i.e. local conservation of electric current source density.

One can generalize this to non-Abelian SU(2) & SU(3) Yang-Mills gauge force theories using

D = d + A/
where

F = DA = dA + A/\A

A/\A = 0 in U(1) EM

A/\A =/= 0 in SU(2) weak force and in SU(3) strong force because of non-trivial Lie algebra

[A^a,A^b] = fc^a^bA^c

Note that

A/\A means A^a^c/\Ac^b = (A/\A)^a^b

DF = 0 Bianchi identities

D*F = *J (source equations)

D^2 = 0 locally

D*J = 0

local conservation of Yang-Mills source current densities for weak and strong internal gauge forces of the standard model without gravity.

What about gravity?

Obviously, the geodesic deviation tidal curvature 2-form is

R = DW = dW + W/\W

W = -*[dB/\(1 - B)]

Note Einstein's local invariant is the symmetric bilinear expression (indices suppressed)

ds^2(curved) = guvdx^udx^v = (1 + B)(Minkowski)(1 + B)

= 1(Minkowski)1 + B(Minkowski)1 + 1(Minkowski)B + B(Minkowski)B

Note the nonlinear PLASTIC FRACTURE term B(Minkowski)B that gives "geon" spontaneous self-organization to the fabric of space-time even in the absence of "sources".

B = 0 globally means NO REAL GRAVITY FIELDS in sense of Landau & Lifshitz "Classical Theory of Fields".

Rovelli shows that the Einstein-Hilbert action gives the field vacuum equation

R/\e + (Lambda)e/\e/\e = 0

This is a 3-form equation

Note that

DR = 0 and De = 0

imply that in VACUUM

D(Lambda) = d(Lambda) ---> 4D gradient of 0-form Lambda = 0

i.e. Lambda is a uniform constant in this limiting case, though not in general. This is so in the FRW cosmology of "dark energy" from Type 1a supernovae anomalous redshifts.

The source equation is

R/\e + (Lambda)e/\e/\e = J

Still if no torsion

d(Lambda)e/\e/\e = DJ =/= 0

That is the locally conserved stress-energy density current is

J' = J - (Lambda)e/\e/\e

DJ' = 0

d(Lambda) =/= 0 locally coincident with DJ =/= 0

* This is a sloshing back and forth between off-mass-shell virtual zero point vacuum stress-energy current densities and on-mass-shell real matter-EM field stress-energy current densities.

*Military Applications:

Stealth cloaking of attack fighter-bombers and cruise missiles

Silent running, e.g. "Black Triangle" UFO craft

Tapping of zero point energy for power as in the "energy device" allegedly delivering up to 100,000 watts CW at 100 amps continuously for past 60 years reported by Robert Collins (USAF Intelligence ret) in "Exempt from Disclosure."

II. Add the Russian Torsion Field from local gauging of O(1,3). This is a poor man's string theory with a 10D manifold. The Whipped Cream with the Cherry on Top.

S = De =/= 0

Obviously then we have WWD i.e. Weightless Warp Drive ("G-Engine" of George Trimble, "acceleration field" of Paul Hill)

In vacuum

R/\e + Lambda e/\e/\e = 0

Therefore,

DR = 0 still true, but

R/\De + d(Lambda)e/\e/\e + (Lambda)d(e/\e/\e) = 0

Note the curvature-torsion coupling

R/\De = R/\S =/= 0

and the pure zero point energy torsion propellantless propulsion term

(Lambda)d(e/\e/\e) =/= 0

as well as the WWD term

d(Lambda)e/\e/\e =/= 0

One gets additional effect when J =/= 0

"Nuff said"

On Jan 26, 2006, at 9:29 PM, Jack Sarfatti wrote:


Let (hG/c^3) = 1 for now.

I have derived at least Einstein's classical GR vacuum equation as an emergent Goldstone phase modulation.

I assume a Planck-scale emergence where the degenerate vacuum manifold

G/H ~ S2

So there are 2 independent local Goldstone phase coherent fields theta & phi

I define the invariant 1-form

B = (dtheta)/\(phi) - (theta)/\(dphi)

so that

dB = 2(dtheta)/\(dphi) =/= 0

d^2B = 0 locally

The invariant Einstein-Cartan 1-form is

e = 1 + B

where

e = eudx^u

eu = eu^a&a

Einstein's symmetric metric tensor is by the equivalence principle

guv = eu^a(Minkowski)abev^b

Note the nonlinear terms ~ B^2.

The spin connection is the 1-form W^a^b = Wu^a^bdx^u

The exterior covariant derivative is

D = d + W/
Zero torsion means

De = 0

Therefore

W = -*[dB/\(1 - B)]

* is the Hodge dual

The curvature 2-form is

R = DW = dW + W/\W

i.e.

R^a^b = DW^a^b + Wa^c/\Wc^b

The Bianchi identities are

DR = 0

Define

The vacuum equation is the 1-form equation

*[R/\e + Lambda e/\e/\e] = 0