See below on Minkowski metric discussion with Alex & Paul

To be adapted for the stage:

On Nov 9, 2004, at 12:35 AM, iksnileiz@earthlink.net wrote:

"You are like some Kafka bureaucrat who is fixated on a literal interpretation of The Bible" [JS]

Actually I'm not fixated at all.

You are sure fooling me. ;-)

I am simply pointing out that there is a perfectly consistent
alternative physical interpretation of GR, in addition to the traditional Einsteinian model.

You are wrong on that. In fact, you are not even wrong on that. This is your Quixotic Delusion. That's how any editor of a mainstream journal in relativity will view it. I guarantee it. Try it. Prove me wrong. Surprise me.

This means we can get all the essential physical content of GR, and the same formalism,
without an Einstein equivalence principle and without Einsteinian "general relativity".

My psychoceramic meter just went off scale past the redline and exploded psychokinetically! I must say however that this is an improvement on Hal Puthoff's "PV without PV" sold in the Eric Davis USAF teleportation report. You at least admit you violate the equivalence principle (WEP not SEP is understood). Hal thinks he does not violate it even though his co-worker at IAS Austin, Mike Ibison, wrote that PV is not consistent with GCT, nor does it agree with the pulsar 1913 + 16 data. In contrast, Einstein's GR with WEP & GCT, agrees with that data to one part in 10^14 (100 trillion!).

Also, part of what I am doing is exposing what I consider to be the *metaphorical character* of
some of Einstein's most fundamental ideas in relativity physics. So the shoe is really on the other foot.

All of theoretical physics has a "metaphorical character". So what do you mean exactly?


Jack seems to think that anyone who argues critically against the canonical GR texts such as Misner,
Thorne, and Wheeler, or against any of Einstein's ideas regarding special and general relativity,
is somehow *ipso facto* a "crackpot" or an "Einstein-basher" with dark ulterior motives
and a low IQ. Unquestioning obedience to The Master has somehow become a Procrustean benchmark
for all "right thinking" in physics.

"Psychoceramics warning: ... There are no inconsistencies in special relativity." Lorentzian Wormholes, p.204
Matt Visser.

But all I have really been saying is that we had been led to believe that the formalism of GR only
supports the classic Einsteinian model, based on the equivalence hypothesis, but this turns out not
to be the case -- because the LC connection of 1916 GR is linearly decomposable into a tensor and
a non-tensor.

There you go again with nonsense.

Theorem: Using only the methods of Einstein GR 1916, i.e. not allowing the additional adhoc excess baggage of Alex Poltorak's second "affine connection", essentially a new theory beyond 1916 GR, there is no way to write

{L-C} = GCT tensor + non-GCT tensor.

BTW, the Minkowski metric nuv is not a GCT tensor. It is only a Poincare group tensor.

When Feynman writes

guv = nuv + huv

in the sense of spin 2 quantum field theory, huv and guv are NOT GCT tensors in perturbation theory out to a finite number of terms.

Feynman only gets GCT Einstein GR in a Poincare group vacuum instability like ODLRO BCS theory with a non-perturbative sum of an infinity of restricted Feynman diagrams. This is like my pre-inflationary Dirac Sea --> Higgs Ocean with a collapse of vacuum phase space volume explaining the "Arrow of Time" in the sense posed by Roger Penrose in "Fashion, Faith and Fantasy". Zielinski's program here is not at all fashionable. It is pure fantasy.


I have not even asserted at this point that the alternative interpretation I am proposing is the uniquely
correct model -- just that it is available, is internally coherent, and is fully compatible with the GR
formalism.

I deny that it is internally coherent.


Neither have I said that the mere existence of this alternative model in and of itself necessarily invalidates
the Einsteinian approach and its "equivalence hypothesis". However, there are additional arguments that
have been advanced in the literature on this subject that do raise serious questions about the original
heuristic motivation for GR and how seriously it is to be taken at this point.

Extraordinary claims require extraordinary proof.

If it is true that there is a viable alternative model for physically interpreting the formalism of GR
in its current stage of development, then I am simply suggesting that it might be interesting to
explore the ramifications of this alternative; although as a matter of fact these ramifications have
already been explored by many well-qualified authors in thoroughly competent papers published
in leading peer-reviewed journals such as Il Nuovo Cimento, the AJP, and Physical Review.

So judging by your reactions I think it is you who is thoroughly fixated and borderline irrational.

You seem to be desperately circling the wagons.

Z.

I have not read these alleged articles. I am only going by what you actually write - obscure though it is most of the time.

Minkowski Metric & Curvilinear Coordinates

People are sloppy. You can get away with using inconsistent units virtually in intermediate steps as long as one checks the final "real" equations dealing with the actual physics for dimensional consistency.

Example http://arXiv/gr-qc/9712019
pp 60-61:






However, since the metric tensor and the {L-C} connection in 1916 GR have direct physical meaning, I insist that a consistent choice be made at each step of the way. This means that guv must be dimensionless and {L-C} has dimension (length)^-1 (or (time)^-1). Curvature then has dimension (Area)^-1 (or (time)^-2).

Example 1. Plane polar coordinates on a truly FLAT plane.

You see in Carroll's discussion his guv is dimensionally inconsistent as are his Christoffel symbols. You have more freedom in pure math than in using the math in a physical model. Carroll's eq (3.22) is in fact

dl^2 = (drer + rdthetaetheta)^2 = grr(der)^2 + gthetatheta(detheta)^2

Where er and etheta are the radial and tangential orthonormal basis vectors in plane polar coordinates.

der = drer is an infinitesimal radial vector

detheta = rdthetaetheta is an infinitesimal tangential vector

The gij are mutually consistent dimensionless numbers!

Indeed

gij = Kronecker delta, i,j = r,theta

gij,k = 0

All Christoffel symbols = 0

Now if you used an arbitrary basis of dimensionless e1, e2 unit vectors that are not orthogonal, but still linearly independent

dl^2 = (dx1e1 + dx2e2)^2 = dx1^2 + dx2^2 + 2e1.e2dx1dx2

g11 = 1

g22 = 1

g21 = g12 = e1.e2 = cos(phi)

These are still linear transformations.

Let's start with

dl^2 = dx^2 + dy^2 = nijdx^idx^j

A flat metric on the plane.

Make a GCT

x -> x'(x,y)

y -> y'(x,y)

x,y, x',y' all have same physical dimensions i.e. "length".

Define, the Jacobian matrix of this GCT as the dimensionless 2x2 matrix

X^x'x X^x'y
X^y'x X^y'y

where

X^x'x = x',x

X^x'y = x',y

X^y'x = y',x

X^y'y = y',y

, means partial derivative

Also there is its inverse matrix since det(Jacobian) =/= 0 for a proper GCT.

nij = Kronecker delta

i.e.

nij = 1 if i = j

nij = 0 if i =/= j

nij is a GCT metric tensor, therefore

ni'j' = Xi'^iXj'^jnij = Xi'^iXj'^inii = X^i'1X^j'1 + X^i'2Xj'2

So that in general the FLAT metric tensor has off-diagonal terms in curvilinear coordinates.

This generalizes obviously to N-dim space.

However, in orthogonal transformations

X^i'1X^j'1 + X^i'2Xj'2 = Kronecker Delta i.e. = 1 if i'=j' = 0 if i' =/= j'

Example,

x' = xcos@ + ysin@

y' = -xsin@ + ycos@

X^x'x = cos@

X^x'y = sin@

X^y'x = -sin@

X^y'y = cos@

X^x'xXx'x + X^x'yX^x'y = cos^2@ + sin^2@ = 1

the off diagonals are

cos@sin@ - sin@cos@ = 0

Example 2 GCT in 4D GR

Let's start with a curved space-time metric GCT tensor guv

I make the split

guv = nuv + huv

where nuv is DEFINED as the CONSTANT Minkowski metric MATRIX, i.e. -1,1,1,1 along diagonal , 0's off-diagonal

NOTE that nuv and huv need NOT be GCT tensors separately, ONLY THEIR SUM NEED BE!

Note that all the nuv, huv and guv are pure numbers no physical dimensions

The GCT scalar invariant is

ds^2 = guvdx^udx^v

The dx^u all have the same physical dimensions UNLIKE some of the purely formal math discussions you cite.

Also this is not perturbation theory. In no sense is huv << nuv.

Next make a multi-linear GCT tensor transformation X (note that X is dimensionless):

guv -> gu'v' = Xu'^uXv'^vguv = Xu'^uXv'^v(nuv + huv) = Xu'^uXv'^vnuv + Xu'^uXv'huv

OK define THE OBVIOUS GCT TENSORS

n'u'v' = Xu'^uXv'^vnuv

h'u'v' = Xu'^uXv'^vhuv

Therefore,

guv -> gu'v' = Xu'^uXv'^vguv = n'u'v' + h'u'v'

But the game is not over. I now define

gu'v' = nu'v' + hu'v'

Where AGAIN like originally

nu'v' is DEFINED as the CONSTANT Minkowski metric MATRIX, i.e. -1,1,1,1 along diagonal , 0's off-diagonal.

Therefore

hu'v' = gu'v' - nu'v'

This is a well-defined algorithm associated with each GCT. It's a kind of additional compensating gauge transformation associated with the GCT.

Again note that

n'u'v'(GCT tensor) =/= nu'v'(non-GCT tensor)

h'u'v'(GCT tensor) =/= hu'v'(non-GCT tensor)

Hey, if Alex can do his shenanigans with a SECOND AFFINE CONNECTION completely different from the FIRST PLAIN VANILLA {L-C} connection, I can certainly do this.

Now in my MACRO-QUANTUM theory of EMERGENT EINSTEIN 1915 PLAIN VANILLA GR

hu'v'(non-GCT tensor) = Strain Tensor of the World Distortion Field

i.e.

huv = Lp^2(Higgs Ocean Goldstone Phase)(,u,v) note it is dimensionless

( ) = symmetrizer

The dimensionless ANHOLONOMIC FIELD is

Suv = Lp^2(Higgs Ocean Goldstone Phase)[,u,v]

[ ] is anti-symmetrizer

We can use {L-C} from guv to make L-C GCT covariant derivatives and get a torsion tensor with same dimensions as the {L-C} connection field itself.

The GCT X^u'u come from local phase transformations on the Goldstone phase field of the post-inflationary Higgs Ocean.