Monday, November 22, 2004

Theorem: The tensor T = 0 in {LC} = T + N in 1916 Einstein GR

Proof: (the proof is trivial, Zielinski's claim is obviously wrong, i.e. inconsistent with Einstein's 1916 GR)

I thought of this several days ago but forgot to write it up.

The Levi-Civita connection field for the non-geodesic inertial forces in non-inertial frames {LC} is a sum of partial derivatives of the metric tensor gij (here i,j,l, a,b,c,d = 0,1,2,3)

{LC}^lki = (1/2)g^l^j(gij,k + gjk,i - gki,j)

,j is the ordinary partial derivative

the LC covariant partial derivative is ;j

Given the metric tensor gab, the ONLY way to make a tensor 3rd-rank tensor T^lki from it, is to take its {LC} covariant derivative (sum over repeated indices o)

Tki;^l =gki^,l - {LC}^ok^lgoi - {LC}^oi^lgko = NON-METRICITY tensor = 0 in Einstein's 1916 GR.

Therefore T = 0

{LC} = N (not a GCT tensor)

{LC} -> {LC}' = XXX{LC} + XY

Y is an ordinary partial derivative of the GCT Jacobian matrix X.

Therefore, {LC} is a tensor relative to the SUBGROUP of LINEAR i.e. Y = 0 GEODESIC coordinate transformations where by definition Y = 0. Such transformations cannot generate inertial forces i.e. {LC} = 0 under those restricted transformations that only connect INERTIAL FRAMES on timelike geodesics in curved spacetime.

All formal coordinate transformations, whether global (in flat spacetime) or local (in curved spacetime), correspond to physical gedankenexperiments that in principle can be real experiments.

All NONLINEAR COORDINATE TRANSFORMATIONS to NON-INERTIAL FRAMES with INERTIAL FORCES ~ {LC} =/= 0, i.e. Y =/= 0 are NON-GEODESIC and require NON-GRAVITY FORCES or initial TORQUES to set sources in rotation with conserved angular momentum, to implement physically.

Note that Alex Poltorak's theory introducing a rigid non-dynamical connection field with non-zero non-metricity and a new covariant derivative |l is not allowed in Einstein's plain vanilla 1916 GR to which this discussion is confined. Alex's idea is a NEW THEORY not equivalent to Einstein's 1916 GR and this is not the place to discuss it.

On Nov 21, 2004, at 8:27 PM, Jack Sarfatti wrote:

Paul, from simple dimensional analysis the basic components of the 4th rank stretch-squeeze tidal curvature tensor scale as GM/c^2r^3, i.e. 1/(area). Therefore, the CONNECTION FIELD piece for T you are looking for must have the factors GM/c^2r^2 where r is the Schwarzschild coordinate that Hal Puthoff in PV does not distinguish from the isotropic coordinate. Here r > 2GM/c^2, i.e. not a black hole.

Therefore, given the definition of {LC} starting in the LNIF rest frame you must show

T' = f(GM/c^2r^2)

N' = ?

in terms of first order partial derivatives of guv & g^u^v.

What is the function f explicitly for this case in the LNIF rest frame at r, where

{LC}' = T' + N'

Remember, I say that even in this case T' = 0, that there is only N'.

Unless you can produce an explicit solution in terms of your Ansatz for this next simplest possible problem, i.e. "Helium atom" analog, you have no real theory.

On Nov 21, 2004, at 5:12 PM, Jack Sarfatti wrote:


OK, we do not disagree in that simple example. You agree with me T = 0 there.

Next problem is Schwarzschild solution. Compute T there!

On Nov 21, 2004, at 4:45 PM, wrote:

1. A pseudotensor can "be zero" in one cooridnate system -- meaning that in this
CS the pseudotensor is represented by a matrix whose composnents are all zero --
and can "be non-zero" in another -- meaning that is represented in that CS by a
matrix whose components are not all zero.

Of course. So what? I never denied that. You keep citing obvious things that have no bearing on the issue.

This is a very good example in mathematics of how a certain kind of non-scalar
quantity can "be zero" at yet still be present.

Yes, at least in some cases.

So I would rather say that the zero matrix representing a pseudotensor in a certain
CS is the ghost of a *non-departed* quantity.


2. The physical vacuum is the ghost of the departed mechanical aether: not exactly
something, but not exactly nothing either.

I disagree with the spin in your 2. It's ordinary matter that is more ghostly in that it's only ~ 4% of the universe.

The real point is that "off-mass-shell" is as physical as "on-mass-shell" when it comes to gravity!
That is not the case for electromagnetism. The difference is the equivalence principle that you and Hal Puthoff seem to want to violate in profound ways.

What you should do ASAP is collect relevant quotes on the "energy problem" and "general covariance" and put them in a pdf with standard math notation.

If you cannot compute a T =/= 0 for the Schwarzschild solution in the REST LNIF then you need to get off your hobby horse.

BTW Note:

gtt = -(1 - 2GM/c^2r)

grr = +(1 - 2GM/c^2r)^-1

gtheta,theta = +1

gphi,phi = + 1


ds^2 = gtt(cdt)^2 + grrdr^2 + gtheta,theta(rdtheta)^2 + gphi,phi(rsinthetadphi)^2

Note that I used the dimensionally consistent tetrad basis in spherical polar LOCAL coordinates

(det,der, detheta, dephi) = (cdt, dr, rdtheta, rsinthetadphi) all with physical dimension of length

When you take partial derivatives for example you have





Jack Sarfatti wrote:

re: Metric Engineering W^3

Zielinski inadvertently draws attention to the "ghosts of departed quantities" in this case the creative tension between the formal idea of "zero" and the physical idea of a property vanishing as when we say, for example:

1. The motion of the Earth through the aether is undetectable, i.e. zero fringe shift in Michelson-Morley interferometer experiment.

2. Dark matter detectors cannot click with the right stuff to explain Omega(CDM) ~ 0.23 because CDM is virtual off-mass-shell exotic vacuum with w = -1 that MIMICS w = 0.

3. The voltage drop across a resistor is zero.

4. The room is dark.

5. T + 0 = T (see below)

When a physical property is "zero" is it not there? Or is it there in potential form actuated when it is not zero?
That depends on each case, especially when the "zero" has arbitrary gauge freedom (E. Wigner).

Formally "0" is a perfectly good number.

On the other hand 1 + 0 = 1

6. When the zero point vacuum pressure is zero in ordinary vacuum it is still there in a sense because in anti-gravity dark energy exotic vacuum (from outside an exotic compact source) the pressure goes negative and in gravitating dark matter exotic vacuum the pressure goes positive. Whether the zero point vacuum pressure is zero, negative or positive depends on the local intensity of the Higgs Ocean macro-quantum coherent vacuum order parameter that we control in the metric engineering of warp, wormhole and weapon (W^3).

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