Monday, December 06, 2004

Gravity's Force without force in Einstein's General Relativity

On Dec 6, 2004, at 10:41 AM, Jack Sarfatti wrote:

III Z's Cognitive Dissonance on Newton to Einstein Gestalt Shift in meaning of the "inertial/non-inertial motion" creative tension.

Also message from retired USAF SAC scientist R. Kiehn on Cartan, Stoke's theorem, Bohm-Aharonov, aerodynamic lift etc.

On Dec 6, 2004, at 8:53 AM, Jack Sarfatti wrote:

On Dec 5, 2004, at 10:25 PM, wrote:

Jack Sarfatti wrote:

On Dec 5, 2004, at 6:41 PM, wrote:

The metric for an x-y vacuum domain wall can be written as

ds^2 = -(1 - g|z|/c^2)^2 . d(ct)^2 + (1 - g|z|/c^2)^2 .e^-(2kappa ct).(dx^2 + dy^2) + dz^2

JS: So what?

1. That is ONLY the linear weak field approximation I suspect.

PZ: This is the exact solution for the vacuum domain wall. It is not a weak-field approximation.

JS: What equation in the paper? Even if it is exact solution so what? This or that solution, exact or not, has nothing whatever to do with the real problem here, which is your deep confusion over the meaning of "inertial motion". Indeed YOU VIOLATE NEWTON'S FIRST LAW as well as Einstein's GR. You confound Newton's first and second laws.

"Inertial motion" means FORCE-FREE MOTION.

There is NO INERTIAL COMPENSATION of forces in inertial motion.

Let's take your misbegotten idea in its simplest application to Newton's mechanics in Galilean relativity.

Inertial motion there means motion of a point test particle in a straight line in Euclidean space at constant speed.

There is ZERO FORCE there. "Zero" means zero. Your confused idea is that even in that case you have INERTIAL COMPENSATION, i.e.

F(real force) + F(inertial force) = 0

This is obviously wrong.

Your equation for curved space-time that in inertial motion (i.e. timelike geodesic in curved space-time) along which the torsion-free plain vanilla Levi-Civita connection {LC} can be set to zero in a sequence of LIFs (geodesic coordinates) is

0 = {LC} = T + N

where you say T is a GCT 3rd rank tensor =/= 0 but that you have "inertial compensation", i.e.

T + N = 0

T = - N =/= 0

But this is the same as saying that in Newtonian inertial motion

F(real force) + F(inertial force) = 0


T = F(real force)

N = F(inertial force)

Now, why have you made such an obvious mistake?

You are suffering a common cognitive dissonance missing the switch in the meaning of "inertial motion" in the paradigm shift from Newton's mechanics of forces acting at a distance to Einstein's LOCAL geometrodynamics. Now this cognitive dissonance is epidemic and accounts for a lot of crackpot psychoceramic attacks on Einstein and general relativity. So it is worth explicating it. Traces of it underly Hal Puthoff's PV "electro-gravitic" or "dielectric" theory eschewing tensors and general coordinate covariance (GCT) of the local classical field equations. Indeed, Paul your rhetoric shows a lack of respect, stemming from a superficial understanding of the "equivalence principle" and "covariance". Note also that Michael Ibison has correctly written that Hal Puthoff's PV model claims for the metric engineering of warp, wormhole and weapon W^3, is not consistent with "GCT" nor, I add, is it consistent with experiment/observation beyond the 3 basic weak field tests such as the 1913+16 Pulsar data on gravity radiation. Einstein's GCT theory is in agreement with that data to 10^-14 while Puthoff's PV is off by a whopping 33% as I recall? But at least Paul, Puthoff makes a falsifiable prediction, which is good, and which you never do. You know what Wolfgang Pauli always said about bogus physics being "not even wrong". Note Newton's gravity theory is accurate to 10^-7 in most NASA applications.

One comment on Puthoff's brute force approach to metric engineering with Eric Davis of WARP METRICS in Las Vegas recently in the news because of the USAF contract on "teleportation" and "stargates", using only Einstein's

Guv = 8pi(G/c^4)Tuv(electrostatic capacitor)

where Guv ~ g/c^2(radius of Earth) for geodesic gliding warp drive in atmosphere

Tuv ~ E.D/2

MKS SI units

I get a critical lift voltage gradient

V/d ~ 10^16/k^1/2 volts per meter

to nullify the Earth's 1g field for non-inertial observers

k is the dielectric coefficient that can have a resonance peak.

The UFO would then be a kind of flying capacitor. However, there are other ways to accomplish The Mission. This is just an obvious way that even the Nazis who attended Arnold Sommerfeld's lectures in Munich in the 1920's & 1930's would have easily figured out if they had the right dielectric and good U-Boat batteries for their "Model T" wobbly flying tin cans. See Nick Cook's "The Hunt for Zero Point" from Jane's Defence Weekly on the Nazi UFO folklore leading to current reports of flying Black Triangles with rumored electro-antigravitic propulsion.

Start with Chapter 10 of Landau & Lifshitz's The Classical Theory of Fields for Newtonian mechanics in Galilean relativity with absolute simultaneity.

Consider the APPROXIMATE Lagrangian L for a uniform constant gravity field g in the reference frame of the surface of the Earth, which in Newtonian 17th century mechanics is considered an INERTIAL FRAME (neglecting relatively small Coriolis inertial forces from the fact that the Earth rotates once every 24 hours etc.)

L = (1/2)mv^2 - mgz

z = altitude from surface of Earth where z = 0

In Newton's paradigm GRAVITY IS AN EXTERNAL FORCE in the INERTIAL FRAME of the Earth. Gravity's potential energy in this approximation is

V(gravity) ~ mgz

The REAL FORCE of gravity in Newton's picture is

F(real force of gravity) = -dV(gravity)/dz = - mg pointing downward to surface of Earth.

Consider the test particle m. Since it is in a real external gravity force field, no different ontologically from an external electric field in Newton's world picture, the REST FRAME of the test particle is NON-INERTIAL. Therefore, you can and do use INERTIAL COMPENSATION in that case. INERTIAL COMPENSATION, i.e. the cancellation of a real with a "fictitious" inertial force only has meaning in NON-INERTIAL FRAMES OF REFERENCE.

The Newtonian NON-INERTIAL REST FRAME of the test particle executing a parabolic path in general in this uniform gravity force field, trivially obeys

g - g = 0

where the first g is from the inertial "fictitious" force of the accelerating rest frame of the test particle, and the second g is from the Newtonian external field. But since m(gravity) = m(inertial) the common m cancels out.

To make this more clear, change the problem for a moment. Suppose the test particle has charge e in electrostatic field E without gravity. Then the inertial compensation in the non-inertial rest frame of the charge of mass m is

ma - eE = 0

That is

a = eE/m

Obviously Paul, your fancy words "inertial compensation" really mean

Newton's Second Law of Motion

F(external real force) = ma

seen from the POV of the test particle's non-inertial rest frame.

Now Paul your fundamental blunder at the heart of your darkness is trying to apply Newton's distinction between inertial and non-inertial motion to Einstein's theory!

In the Paradigm Shift from Newton to Einstein the very idea of an objective external gravity force is completely eliminated! Back to the problem

L = (1/2)mv^2 - mgz

The test particle m is now in INERTIAL MOTION, i.e. on a timelike geodesic in curved spacetime. Therefore "inertial compensation" makes no sense other than to say

F = ma = 0

i.e. F = 0

i.e. your T = 0

A timelike geodesic is the straightest possible line with the most uniform possible motion in the curved spacetime. It is by definition FREE OF OBJECTIVE (e.g. GCT tensor forces). In Einstein's theory it is the surface of the Earth that is in non-inertial motion and the test particle on the parabola is in inertial motion. We feel weight on the surface of the Earth because of inertial compensation of the inertial g-force {LC}^z't't' against the electrical reaction real force of the rock pushing us off timelike geodesics.

Now, Paul you have confused all this! BTW I do not deny that one can have approximately uniform g-fields for some non-inertial observers from a Tuv(matter) source like an unstable short-lived vacuum wall. I never denied that. You keep raising this Red Herring. Indeed my vacuum defect hedgehog explanation of the observed anomaly in NASA Pioneer 10&11 motion of cH ~ 10^-7 cm/sec^2 pointing back to the Sun is very similar to Vilenkin's basic idea, but with a different topology for the vacuum coherence!

On Dec 6, 2004, at 7:40 AM, Jack Sarfatti wrote:

Yes, thanks. Will incorporate what you say. I was writing fast off the cuff not focused on that particular important detail.

In a message dated 12/6/2004 1:36:10 AM Romance Standard Time, writes:

Note that Ruvwl has physical dimensions of 1/Area, and the {LC} has
physical dimensions 1/Length. The line integral and the surface
integral in the generalized Stoke's theorem of manifold topology
(independent of metric)

i.e. DeRham-Hodge integral of p-Cartan form about a closed p-boundary
of a p+1 co-form = integral of the exterior derivative p + 1 form of
the p-form over the bounded p + 1 co-form (manifold)

Gives the curvature flux through any bounded area in curved space-time.
This is analogous to the magnetic flux. What is the analog of the
"fringe shift"? Is it the change in the orientation of a vector
parallel transported around the closed loop boundary of that arbitrary
2-surface in curved spacetime?

If you do a macro-quantum interference experiment, you will get a Berry
phase shift as well. How can you do that? That's where metric
engineering the fabric of spacetime for warp, wormhole and weapon W^3
comes in. Another story coming soon to a computer screen near you.

Kiehn comments:

"JACK:  This is not correct.

Stokes theorem is valid only if the integration chain is a boundary.

But there are closed circulation chains which are NOT boundaries."

The BA effect is related to the integration of closed, but not exact, forms around closed integration chains WHICH ARE NOT BOUNDARIES.

Stokes theorem is not valid for closed chains which are not boundaries.

However, those p-forms which are exact have ZERO circulation integrals whether or not the integration chain is a cycle or a boundary.

It is the integration around closed chains of closed, but not exact, p-forms that gives the deRham topological quantization.

Examples :  A =(ydx-xdy)/(x^2+y^2),

            dA = 0

Integral (A) around a closed chain that encircles the origin is 2pi, not zero.

(See Chapter 6 of my monograph on Non Equilibrium Themodynamics)

It is also the integration around a closed chain (the airfoil), not a boundary, of a non exact, but closed. form (which has ZERO vorticity and therefor no E or B field in the EM sense ) that produces lift and makes a wing fly!  Vorticity does not make a wing fly!

Lift is NOT due to a (V x B) component of a Lorentz-type force (as B = 0) outside the airfoil.

Vorticity usually causes drag in deformable viscous fluids.

Note that the Fields F=dA of MAxwell theory are related to a completely anti symmetric matrix of functions.  The set induces a symplectic structure on the variety of independent variables if the matrix is of maximal (even) rank 4. The eigenvectors of such matrices are two spinor pairs of complex components, and of equal and opposite pure imaginary eigenvalues.  (The eigenvectors are said to be isotropic.) The matrix rank is 3, then a contact structure is introduced, and the eigenvectors consist of  one pair of spinors with complex components of pure imaginary eigenvalues, and one real eigenvector of eigenvalue zero. The spinors do NOT behave as vectors with a uniquely defined connection. See last page of E. Cartan's book on Spinors) However, spinor pairs can be combined to form well behaved vectors wrt to connections. Note that these spinor properties have little to do with symmetric concepts of elasticity deformation theory, for the eigen vectors of a symmetric real matrix are real, not complex. 

Bottom line, spinors are not strangers to classical Maxwell theory defined by the topological constraint, F = dA = 0.

It does not take relativity, nor QM, to produce spinors.  They are artifacts of antisymmetric matrices.

IMO Yang-Mills is NOT the same as EM, but has some formal similarities. The problem is that Yang-Mills fields can be compact, but Maxwell EB fields are usually NOT COMPACT (this is known as Gromov's theorem, and follows as F = dA, not dA+A^A.) Also, EM fields are rarely self-dual in the real world. This is not to say that YM theory should be neglected, but only that it is NOT equivalent to EM theory without the addition of constraints. I do not recommend the using a Maxwell analogy for trying to justify Yang Mills assumptions.



On Dec 5, 2004, at 6:32 PM, Jack Sarfatti wrote:

II The principle of equivalence requires nonlocality of the pure gravity energy: "We take note of the fact that in Einstein's theory, the symmetric tensor Tuv that appears in his field equation is to include the energy-momentum of all NON-gravitational fields (and particles). Whatever energy there is in the gravitational field itself is to be excluded from having any representation within Tuv. This point of view is made somewhat plausible if we think again of the principle of equivalence. Imagine an [LIF] observer in free orbit ... within some spaceship without windows, so that it appears, at least to a first approximation, that there is no gravitational field. That observer would expect that energy is conserved within the spaceship ... without there being any contribution from the gravitational field. This 'conservation' is only an approximation, which is expected to need correction as soon as the relative acceleration (tidal) effects due to the non-uniformity of the gravitational field begin to play a role. The upshot of it all is that the [the conservation of the non-gravity fields in Tuv] should [approximately] remain undisturbed by the non-uniformity of the gravity field - unaffected by the spacetime curvature of the [Levi-Civita] connection - and that the contributions of gravity to energy-momentum conservation should SOMEHOW enter NON-LOCALLY as corrections to the calculation of the total energy-momentum. ... gravitational contributions to energy-momentum ... 'slip in through the cracks' that separate the LOCAL equation Tuv(non-gravity)^;v = 0 from an integral conservation law for TOTAL energy-momentum." p. 458 Roger Penrose "The Road to Reality".

On torsion field propulsion:

"Recall the discussion of Einstein's equivalence principle, and of why this leads to a curved spacetime. Thus when gravity is present, we must take into account the fact that [the GCT covariant partial derivative] is no longer simply [the ordinary partial derivative] ... but there are extra [Levi-Civita {LC}] terms that confuse the very meaning of Tuv^,v and which certainly prevent us from deriving an integral conservation law for energy-momentum JUST from our 'conservation equation' Tuv^,v = 0. The problem can be phrased as the fact that the extra index v in Tuv prevents it from being the dual of a 3-form, and we cannot write a coordinate-independent formulation of a 'conservation equation' (like the vanishing exterior derivative of the 3-form *J in d*J = 0 [in Maxwell's EM]) ... there is a more satisfactory perspective ... suppose we have a Killing vector K(u;v) = 0 [symmetrized indices] ... which describes some continuous symmetry of the [base space]. In Minkowski space, there are 10 independent such symmetries ... Thus Minkowski space has 10 independent Killing vectors ...[the action principle and] Noether's theorem allows us to derive a conservation law from each continuous symmetry ... there are also 3 components coming from the the Lorentzian boosts that take us from one velocity to the other. THESE GIVE US THE CONSERVATION OF CENTER OF MASS MOVEMENT." p. 457 Penrose

The absence of a torsion field ensures this conservation of center of mass movement. If you locally gauge the 3 Lorentz boosts along with the three rotations for the entire Lorentz group O(1,3) you do get Gennady Shipov's torsion field as shown by Kibble et-al years ago in the 1960's. Obviously this suggests torsion propulsion since we now have additional field degrees of freedom beyond Einstein's 1916 GR Levi-Civita connection non-GCT tensor field and tidal curvature GCT tensor field that comes from locally gauging ONLY the four translations! Even beyond that there are the 4 conformal boosts that take us from one proper LNIF acceleration to another. What if we also locally gauge that? Finally what if we locally gauge the dilation i.e. the 15th element of the Lie algebra of the Conformal Group? Will the purely translational weightless geodesic glider warp drive continue to hold if we have these additional dynamical fields beyond Einstein's plain vanilla 1916 GR? That is a key question for metric engineering of warp, wormhole and weapon W^3.

On Dec 5, 2004, at 4:16 PM, Jack Sarfatti wrote:

Inertial compensation in REST LIF? NO!
Inertial compensation in REST LNIF? YES!

"The Question is: What is The Question?" John A. Wheeler

We want to make Einstein's GR look as much like Maxwell's EM as possible. Actually like non-Abelian Yang-Mills since gravity carries its own charge like W bosons and gluons but unlike photons. Lots of papers on this of course including tetrads and also Ashtekar's (more on that down the line).

Maxwell connection for parallel transport in the internal fiber space is the vector potential Au with the U(1) gauge covariant derivative

Du = ,u - ieAu

Au is not a U(1) tensor it transforms as

Au -> Au' = Au + Chi,u

this is the NON-TENSOR connection transform relative to the U(1) internal symmetry group.

The Maxwell field tensor Fuv is the curl of Au


Similarly, Levi-Civita connection for parallel transport of vector fields in curved spacetime "base space" (no torsion no Poltorak RIGID "affine connection" etc, just plain vanilla 1916 GR) has a GCT SPACETIME SYMMETRY GROUP gauge covariant derivative, symbolically like

Du* = ,u - {LC} ...

example, for any GCT first rank tensor we get the second rank tensor

DuB^v = B^v,u + {LC}^vuwB^w

The NON GCT TENSOR "gauge transform" analogous to

Au -> Au' = Au + Chi,u

in Maxwell's EM is precisely

{LC} = N -> {LC}' = N' = XXXN + XY

where X is the GCT Jacobian matrix and Y is a partial derivative of X.

I can provide the indices but they are unwieldy.

Just as Au is not a U(1) tensor so also is {LC} not a GCT tensor.

Z's attempt to use Newtonian "inertial compensation" here is wrong. The shift from Newton to Einstein is a profound change in the meaning of "inertial motion" in which the idea of an objective Newtonian force of gravity in an inertial frame is completely eliminated. Hence there is nothing to compensate!

The inertial g-force, which is {LC}^i00, i = 1,2,3 in the REST LNIF of a test particle not on a timelike geodesic acted on by a non-gravity force is always caused by the latter. The inertial g-force indeed compensates the non-gravity force in the REST LNIF. But that is not what Z proposes. Z wants to compensate a gravity force in a REST LIF - a profoundly wrong idea!

That is, Z proposes that in the REST LIF where {LC} = 0 that

{LC} = T + N = 0

T =/= 0

where T is a GCT tensor of rank 3.

Do not confuse this with torsion. Z is only talking 1916 GR.

This is profoundly wrong.

What is correct is that in the REST LNIF

{LC)^i00 + (External Non-Gravity Force)^i = 0

That is, the inertial g-force in the non-inertial frame exactly compensates the non-gravity external force pushing the particle off a timelike geodesic.

For example, here on surface of the Earth we are in a local non-inertial frame (LNIF) from the electrical reaction forces and quantum Fermi-Dirac pressure of the rock on which we stand. That's why we feel weight.

Z's deep error is to apply "inertial compensation" not to the REST LNIF of the test object where it does apply, to the REST LIF where it does not apply.

Back to the connections and Stoke's theorem & Bohm-Aharonov Effect

The local vector potential U(1) EM connection Au is not a local classical observable, but it is a nonlocal quantum observable because from Stoke's theorem the closed loop line integral of Au is the magnetic flux integral through the enclosed surface. From micro quantum mechanics this causes a fringe shift in a double slit experiment with electrons passing through a region free from magnetic field but with nonzero Au connection field.

Similarly in general relativity, where the macro-quantum vacuum coherence, which makes Einstein's cosmological constant near zero, is a giant quantum wave, there will be an analogous "fringe shift"!

From Stoke's theorem now in curved spacetime, the Riemann-Christoffel tidal stretch-squeeze geodesic deviation curvature 4th rank GCT tensor Ruvwl is the analog to the Fuv Maxwell field tensor. Ruvwl is the GCT covariant curl of the Levi-Civita {LC}uvw connection just like Fuv is the curl of Au.

Note that Ruvwl has physical dimensions of 1/Area, and the {LC} has physical dimensions 1/Length. The line integral and the surface integral in the generalized Stoke's theorem of manifold topology (independent of metric)

i.e. DeRham-Hodge integral of p-Cartan form about a closed p-boundary of a p+1 co-form = integral of the exterior derivative p + 1 form of the p-form over the bounded p + 1 co-form (manifold)

Gives the curvature flux through any bounded area in curved space-time. This is analogous to the magnetic flux. What is the analog of the "fringe shift"? Is it the change in the orientation of a vector parallel transported around the closed loop boundary of that arbitrary 2-surface in curved spacetime?

If you do a macro-quantum interference experiment, you will get a Berry phase shift as well. How can you do that? That's where metric engineering the fabric of spacetime for warp, wormhole and weapon W^3 comes in. Another story coming soon to a computer screen near you.

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