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

AVOID RIGID CONNECTIONS! They are not BACKGROUND INDEPENDENT.

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.

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, sarfatti@pacbell.net 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.


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 chain,s 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)

http://www.lulu.com/kiehn



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 eigen vectors 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.)

It 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 eigen values, and one real eigenvector of eigen value 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 asumptions.

Regards

RMK

On Dec 5, 2004, at 10:25 PM, iksnileiz@earthlink.net wrote:


Jack Sarfatti wrote:


On Dec 5, 2004, at 6:41 PM, iksnileiz@earthlink.net 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

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

You "suspect". You *are* a suspect!

Loopy polemics. Look I am too busy to read the paper in detail. From my quick scan he only does a weak field case.

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

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 clueless confusion, worthy of Mrs Malaprop, over the meaning of "inertial motion". Indeed YOU VIOLATE NEWTON'S FIRST LAW as well as Einstein's GR.

"Inertial motion" means FORCE-FREE MOTION.

There is NO INERTIAL COMPENSATION of forces in inertial motion.

Let's take your really stupid 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 kakamany idea is that even in that case you have INERTIAL COMPENSATION i.e.

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

This is obviously stupid.

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

where

T = F(real force)

N = F(inertial force)

Now, why have you made such an incompetent stupid mistake?

I have seen a lot of stupid mistakes in physics but really Paul, you take the cake on this one. This is the stupidest mistake I have seen in a long time and you have wasted years of futile effort on it.

You are suffering cognitive dissonance in 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 theory.

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!