Sunday, July 29, 2007

R^a^b = Dw^a^bce^c = d(w^a^bce^c) + w^a^a'ce^a'/\w^c^bb'ce^b'

d(w^a^bce^c) = d(w^a^bc)/\e^c + w^a^bcde^c

R^a^b = d(w^a^bc)/\e^c + w^a^bcde^c + w^a^a'ce^a'/\w^c^bb'ce^b'

T^a(P10) = w^abc(SO(1,3))e^b/\e^c = w^abc(SO(1,3))(I^b + (1/N)^1/3A^b)/\(I^c + (1/N)^1/3A^c)

Note that the torsion field 2-form does not depend upon F^a = DA^a.

G. Shipov's "teleparallel" theory I think means

R^a^b(P10) = 0


R^a^b(P10) = R^a^b(T4) + R^a^b(SO(1,3) + curvature-torsion couplings

R^a^b(T4) is Einstein's 1916 torsion-free disclination curvature

R^a^b(SO(1,3) is Utiyama's 1956 torsion-gap dislocation defect induction of disclination curvature defects in the geometrodynamic monopole nodes of the Kleinert "world crystal lattice".

w^aa'c(T4)e^a'/\w^c^b'(SO(1,3)]ce^b'+ w^aa'c(SO(1,3)]e^a'/\w^c^bb'(T4)e^b'

Are the curvature-torsion coupling cross terms.

However, I see no compelling physical reason to make the restrictive choice

R^a^b(P10) = 0

R^a^b(P10) = D[w^a^bc(T4) + w^a^bc(SO(1,3)]e^c

= d([w^a^bc(T4) + w^a^bc(SO(1,3)]e^c)

+ [w^aa'c(T4) + w^aa'c(SO(1,3)]e^a'/\[w^c^bb'(T4) + w^c^b'(SO(1,3)]ce^b'

= R^a^b(T4) + R^ab(SO(1,3) + w^aa'c(T4)e^a'/\w^c^b'(SO(1,3)]ce^b'+ w^aa'c(SO(1,3)]e^a'/\w^c^bb'(T4)e^b'

Math typo corrected draft 2
On Jul 29, 2007, at 9:53 AM, Jack Sarfatti wrote:

John A Wheeler coined

"Mass without mass"

"Charge without charge"

"Spin without spin."

"Law without law."

in his mid-1950's classical geometrodynamics where he also introduced "quantum foam" elucidated below.

World Hologram is "Space without space" (my term for the record)

L(Einstein-Hilbert) = *(R^a^b/\e^c/\e^d + Lambda e^a/\e^b/\e^c/\e^d)

e^a = I^a + (1/N)^1/3A^a

R^a^b = DS^a^b = dS^a^b + S^ac/\S^cb

S^a^b = w^a^bce^c

R^a^b = Dw^a^bce^c = d(w^a^bce^c) + w^a^a'ce^a'/\w^c^bb'ce^b'

The Ricci rotation coefficients (like Lie algebra structure constants in internal symmetries) are local functions so that dw^a^bc =/= 0 - use product rule.

We see that the spin 1 effective Yang-Mills potential does not have terms higher than quartic in the intrinsic spin 1 warp fields A^a. Therefore, the quantum field theory is renormalizable using the Veltman-t'Hooft analysis. See Sidney Coleman's Erice Lectures.

The effective warp field potential in the Lagrangian density has the form

*{C3/\A^a + C2/\A^a/\A^b + C1/\A^a/\A^b/\A^c + C0/\A^a/\A^b/\A^c/\A^d}

Where Cp are p-forms from the Minkowski global tetrads I^a whose components I^au(x) are curvilinear functions encoding the inertial accelerations, Coriolis, centrifugal forces on local detectors in non-geodesic motion in the fully warped spacetime. These inertial forces are the g-forces that are locally equivalent to the Newtonian "gravity forces" on the centers of mass of extended test objects. Warp drive eliminates all non-tensor g-forces on the center of mass coordinates. Curvature and torsion forces on the relative coordinates of extended objects are still there because they are T4(x) GCT tensors. They must be kept small.

The Ricci rotation coefficients w^abc(x) are also there in the Cp from the R^a^b term. There are also kinetic energy density terms from the d operator, i.e. gradient terms in A^a, I^a & w^abc(x).

d(w^a^bce^c) = d(w^a^bc)/\e^c + w^a^bcde^c

d(w^a^bc) = w^a^bc,udx^u

T^a(P10) = D(P10)e^a = de^a + w^abce^b(P10)/\e^c = w^abce^b(SO(1,3))/\e^c


T^a(T4) = D(T4)e^a = de^a + w^abce^b(T4)/\e^c = 0

w^a^bc(P10) = w^a^bc(T4) + w^a^bc(SO(1,3)

So we want to substitute

T^a(P10) = w^abc(SO(1,3))e^b/\e^c



to see how the torsion field 2-form T^a(P10) couples to Einstein's curvature 2-form R^a^b(T4)

R^a^b = Dw^a^bce^c = d(w^a^bce^c) + w^a^a'ce^a'/\w^c^bb'ce^b'

= R^a^b(T4) + R^a^b(SO(1,3) + Curvature-Torsion Field Cross-Terms

Note that torsion dislocation fields by themselves also induce curvature disclination fields, but NOT vice versa!

This has caused confusion in the literature over the physical meaning of Utiyama's 1956 paper where he only locally gauges the Lorentz group and sticks in Einstein's GCTs by hand ad-hoc - corrected by Kibble in 1961.

On Jul 28, 2007, at 7:12 PM, Jack Sarfatti wrote:

The Grand Illusion, The New Paradigm

Quantum Gravity for Dummies

The basic classical field Lagrangian density template for all spin connections S^a^b corresponding to localized spacetime symmetry Lie group G(x) is

L(Einstein-Hilbert) = *(R^a^b/\e^c/\e^d + Lambda e^a/\e^b/\e^c/\e^d)

G(x) --> T4(x) is 1916 GR

G(x) --> P10(x) is Einstein-Cartan extension of 1916 GR

G(x) --> Conformal Group (15 parameters) Tony Smith's theory?

G(x) --> GL(4,R)

G(x) --> GL(4,C) Penrose Twistors?

G(x) --> GL(4,Q) Supersymmetric Twistors? Q = quaternions

My theory uses only P10(x) at the present time. The additional 6 parameters of P10(x) beyond the 4 of T4(x) form the extra space-dimensions for the torsion field (e.g. G. Shipov) out of which using Kaluza-Klein maybe we can get U(1) SU(2) SU(3) "internal symmetries" of EM, weak, strong?

World Holography eq.

e^a = I^a + (1/N)^1/3A^a

I^a = globally flat Minkowski S-T tetrad 1-form

A^a = the real intrinsic warp SPIN 1 renormalizable (if quantized) Yang-Mills geometrodynamic field

Lp^2 = hG/c^3 = 10^-66 cm^2

N = (Lp^2Lambda)^-1 = Bekenstein BIT number of a closed 2D surface surrounding N point geometrodynamic unit wrapping number monopoles at center of quantum gravity foam bubble N^1/6Lp across.

Each quantum gravity foam bubble has "volume without volume" &V = N^1/2Lp^3, the total volume without volume V is N^3/2Lp^3 therefore exactly N close-packed quantum foam bubbles in the interior of a surrounding surface with N area quanta each Lp^2. Therefore, V/&V = N^3/2/N^1/2 = N QED. This is the 2D point defect (3 real vacuum ODLRO order parameters) analog of a 1D vortex line defect(2 real superfluid ground state order parameters).

s^2 = nabx^ax^b = Integral{I^aIa} = global Minkowski space-time interval.

Integrating dx^a in that case is holonomic, i.e. path-independent

All closed geometrodynamic 1-forms are exact 1-forms in 1905 SR.

ds^2 = guvdx^udx^v = e^aea = I^aIa + (1/N)^1/3(I^aAa + A^aIa) + (1/N)^2/3A^aAa

F^a = dA^a + w^abcA^b/\A^c

DF^a = 0 Yang-Mills Faraday & no geometrodynamic "magnetic" monopole laws

D*F^a = *J^a Yang-Mills Ampere & Gauss's laws

D*J^a = 0 local conservation of warp current densities

Lagrangian density ~ *(1/4)F^a/\*Fa

Note the relation to the torsion field T^a is

T^a = De^a = de^a + w^abce^b/\e^c

= d(I^a + (1/N)^1/3A^a) + w^abc(I^b + (1/N)^1/3A^b/\(I^c + (1/N)^1/3A^c)

Note that

w^abc = w^abc(T4) + w^abc(SO(1,3)


T^a(T4) = de^a + w^abc(T4)e^b/\e^c = 0 i.e. 1916 GR

R^a^b = DS^a^b = dS^a^b + S^ac/\S^cb

S^a^b = w^a^bce^c

to be continued

On Jul 28, 2007, at 4:02 PM, Jack Sarfatti wrote:

On Jul 28, 2007, at 1:44 PM, Paul J. Werbos, Dr. wrote:

Hi, Jack!

I think I see the story now...


I asked:

2. What would Hehl's kinds of alternative models imply for the possibility of something
like warp drive in the SPIRIT of the Alcubierre solutions? (Not the same equations or solutions,
but paying serious attention when they appear to allow FTL patterns as solutions.)

You answered:

>Don't know.

Neither do I. So far as either of us knows, no one has done the mathematical work needed
to know whether something like warp drive (Alburierre-type solutions but more implementable)
would be possible, in alternatives to GR.

Let me qualify that. I was only referring to Hehl. It's clear to me that you need the torsion field to mutate Einstein's cosmological constant Lambda into a locally variable quintessent field Lambda(x) that you then need to modulate with electromagnetic fields in order to get a practical low-energy zero-g force "geodesic" warp drive.

P10 here is localized Poincare group

In Einstein's curvature-only 1916 approximation

Guv^;v = 0 Bianchi identities i.e.

R^a^b(T4) = D(T4)S^a^b(T4) = curvature 2-form

D(T4)R^a^b = 0


Lambda^,v = 0 i.e. uniform constant

But in Einstein-Cartan theory

R^a^b(P10) = D(P10)S^a^b(P10)

D(P10)R^a^b(P10) = 0

D(P10) = D(T4) + D(SO(1,3)

S(P10)^a^b = S(T4)^a^b + S(SO(1,3)^a^b

R^a^b(P10) = d(S(T4)^a^b + S(SO(1,3)^a^b) + (S(T4)^ac + S(SO(1,3)^ac)/\(S(T4)^c^b + S(SO(1,3)^c^b)

So we now have all these extra terms!

D(T4)R^a^b =/= 0 with torsion, hence

Lambda^,v need no longer vanish.

Second ----------------------------------------------------------------------------

The existence of something like dark matter is the one data point you cite telling us that
SOMETHING is going on, beyond the usual standard model plus GR combination.
But what in particular? With one data point, and hundreds of possible things to play with,
we don't yet have empirical evidence.

First of all it's dark matter and dark energy. We have many data points. I don't understand what you are even saying here? "One data point"? "hundreds of possible things"? I don't think so.

Thus in addition to not knowing what a PARTICULAR Hehl-like model implies for
warp drive, we do not know which alternative model
we should believe anyway -- except if one makes a choice based on some kind
of religious or estehetic conviction, which sounds to me like picking a "system"
at Las Vegas.

You lost me completely. I am talking precise equations and also many precise observations.

Third ---------------------------------------------------------------------------------------------

Is warp drive possible at all?

In the absence of clear empirical or mathematical evidence (except for
the GR case, where there exist the Alcubierre solutions)... we certainly
do not KNOW, one way or another.

First of all there are many good data points in the UFO evidence. That's the whole point here. The Pope's Men also refused to look through Galileo's telescope. If you throw the baby out with the bathwater then as King Lear says
"From nothing comes nothing." (my paraphrase from memory)

You cite UFO sightings as evidence it must be possible.
You might be amused by a link a friend pointed me to yesterday (by accident!!):

Is that the "rebuttal" by that Christian Evangelist? URL too long to work.

HOWEVER -- uncertainty cuts two ways. If we do not KNOW whether warp drive is possible,

Wrong. Fact is we observe such craft. Look at Paul Hill's book for example. Talk to Bruce Maccabee.

and we DO know
something highly unknown is out there (the role of your "dark matter" stuff)...

You must distinguish "dark matter" from "dark energy".

it is rational
to try to find out, by filling in those gaps in empirical data and in mathematical
knowledge, rather than flipping dice and guessing, or wasting time trying to be Holy Inquisition or Defenders
of old things that do not address the real issues here.

Vague, of course. We all like Apple Pie and Ice cream. The real situation is not as hopeless as you paint it.

I thank you very much for pointing me towards Hehl, who does seem to be one of the very few
people out there actually living the full scientific method in fundamental physics.

S. Weinberg wrote a strange letter in Physics Today mentioning Hehl.

If there were more such people, perhaps humans really would have some chance
of making progress, and surviving in the long term. However, I worry here.
Chimpanzee society once made progress long ago, and then reached the limits of
the technology and understanding that such creatures were capable; have humans now
reached that point as well, in their understanding of basic physics and in
the technologies which that would otherwise make possible? For example --
is the full-up mathematics of operator fields simply so difficult that humans do not learn it until
an age when they are less flexible, and prone to becoming overwhelmed or ossified by it,
to the extend that they understand it at all? On the bright side, the adult Sophists
of Greece seemed equally befuddled by easier things, so perhaps there is hope for progress;
yet it is hard to see, in concrete terms.

Eric Davis would disagree with the above.

What do you mean?

He would claim he has a viable theory of how the universe works
(though he may be humble enough to say it comes from other people),

Such as?

AND a way to show how to design a warp drive based on definite predictions of that theory.
But I do not feel convinced as yet that the connections he proposes would really work.

What connections? References?

At best, it would require new mathematical work to properly evaluate.

I don't think so.

Best of luck to us all,


No comments: