Einstein's Muddle
Free lunch means that flying saucers may only need ONE Energizer AAA Battery to out fly the MIG 29? Perhaps I exaggerate? OK maybe TWO AAA batteries? :-)

Memorandum For The Record

Subject: How The Flying Saucers Render Conventional 21st Century Military Hardware Impotent and Obsolete.

On May 12, 2005, at 11:24 AM, Jack Sarfatti wrote:

Note corrected eqs (adding second term on RHS) below for the covariant 4-divergence.

On May 11, 2005, at 6:35 PM, iksnileiz@earthlink.net wrote:

J: The tuv(Matter-Gravity) pseudo-tensor is not needed for anything important. It's only there because of the arbitrary demand that

Tuv(Matter)^;v = 0

be replaced by

Tuv(Matter)^,v + tuv(Matter-Gravity)^,v = 0

Where, by definition we have the partial differential equations

(Corrected eqs )

tuv(Matter-Gravity)^,v =

-{LC(Gravity)}u^l^vTlv(Matter) - {LC(Gravity)}l^l^vTuv(Matter)

In principle this is difficult problem to solve for tuv(Matter-Gravity) explicitly.

There is no reason to do so, since it is a fictitious non-physical quantity from asking the wrong question to begin with!

The analogous eq. in flat space-time would be something like

A(x)u^,u = L(x)F(x)

Where L(x) and F(x) are independent functions.

Obviously though one needs to specify some kind of boundary condition, e.g. asymptotic flatness for the GR problem.

J: Einstein unfortunately misidentified tuv(Matter-Gravity) as the energy of the gravity field. In fact this tuv = 0 when Tuv(Matter) = 0 everywhere-when.

Z: I think you are mistaken. Or at least, you are talking about another theory.

J: Just look at (61) eqs (341), (406) & (447) pp 175-176.

Z: You need an asymptotically Galilean spacetime in order to recover anything resembling an objective conserved energy-momentum for a closed system

J: Not the point about tuv requiring Tuv(Matter) =/= 0 to exist. You jumped the gun.

Z: since this means there is *no radiative leakage* out of the closed system, and it also means that the Einstein stress-energy density is *asymptotically zero*. Basically, it's a fudge.

J: You misunderstand the meaning of (447)

Ju = constant

That will include any gravity waves propagating to the asymptotic flat region.

Einstein's field equations MEAN

Sum of all local OBJECTIVELY MEASURABLE Diff(4) stress-energy density tensors from all causes exactly vanish.

Einstein had a peculiar failure of nerve in his own theory on this issue.

Pauli wrote p. 176 - 177 in 61

"Lorentz and Levi-Civita made the suggestion to denote as energy components of the gravitational field, NOT THE QUANTITIES tuv(Matter-Gravity), but (c^4/8piG)Guv."

This is EXACTLY what I have done independently mind you.

Einstein's objection to this was lame and muddled. He had a peculiar failure of nerve and Pauli blindly followed! Thus,

"But Einstein QUITE RIGHTLY (actually quite wrongly IMHO) raised the objection, that with this definition of the gravitational energy, the total energy of a closed system (why "closed"? Who ordered that?) would always be zero."

That is, Einstein did not like the idea of a "free lunch"!

With the initial white hole singularity at the beginning of our local Hubble horizoned universe (Max Tegmark's "Level 1") the universe is not "closed", but even if it were, the total energy density is zero, but that does not imply the total energy is zero.
Einstein in 1921 was not aware of wormholes! Einstein would not discover wormholes until ten years later! The wormhole mouths are closed 2D surfaces that are NOT BOUNDARIES of the seemingly "enclosed" 3D space. It's like Mr Sphere passing through Flatland! One can rob the locked safe! Einstein in 1921 did not have much understanding of modern cohomology theory! When he did discover the Einstein-Rosen Bridge he did not put 2 + 2 together to make 4 by seeing how it affected the energy problem.

Wormholes are extra space dimensions without extra space dimensions!

More with less.

Mass-Energy without mass-energy.

Quantized flux without flux.

11D without 11D

11-11

Replace extra dimensions with non-trivial homotopy, homology & cohomology?

Have your cake and eat it too.

Dark energy keeps the wormholes open so that you can fly, or even walk, through the Looking Glass to the Universes Next Door.

Free lunch means that flying saucers may only need ONE Energizer AAA Battery to out fly the MIG 29? Perhaps I exaggerate? OK maybe TWO AAA batteries? :-)

Pauli continued: "that the maintenance of this [zero] value of the energy does not require the continued existence of the system in some form or other"

There was low power consumption metric engineering of warp, wormhole and weapon staring Einstein and Pauli in the face in 1921. The Light outside Plato's Cave was too bright even for Einstein & Pauli and so they went back into The Cave and confused everyone until this moment!

Also I have shown WHY BIG BANG is necessary!
The claims the "Big Bang never happened" are wrong.
You need the white hole singularity to
1. Explain the arrow of time (low entropy of early universe)
2. Energy without energy as in Wheeler geon.

Further clarification there are two meanings ("marble" & "wood") to "gravity energy". Einstein made a muddle when he called tuv(matter) the "gravity energy".

Z: Well, I personally think the whole theory is a "muddle".

J: Your cure is worse than the disease. This is only a minor bump in the road.
I do agree however that Einstein was in a muddle about this and so was Pauli and so has been everyone else.

Z: I don't think it's quite so simple, since in GR the LC connection -- on which the definition of the covariant derivative is based -- is interpreted as representing the unified gravitational-inertial field. So the difference between ";" and "," is more than purely mathematical.

J: Of course it's both physical and mathematical. There is no logic in your comment. It has no connection with what I have shown. Another isolated insight from you leading nowhere - like the Mars Rover stuck in the sand dune.

Z: Do you really imagine that Pauli could have been confused about this?

J: Just read Pauli's text. He bought Einstein's blunders and quotes them.

"Einstein calls the tuv the energy components of the gravitional field." p. 176

That's Einstein's Blunder 1.

tuv is, in fact, a COMPOSITE of the "marble", i.e. (LC)uv^l of the gravitational field MULTIPLIED by the "wood", i.e Tuv(Matter).

When Tuv(Matter) = 0 GLOBALLY then tuv VANISHES!

There is no tuv in pure nonexotic vacuum theory where Ruv = 0 GLOBALLY as in the Wheeler geon of "Mass without mass".


"The Question is: What is The Question?"

That is

Tuv(Matter)^;v = Tuv(Matter)^,v + tuv^,v(Matter-Gravity) = 0

Are you still saying that tuv^,v(Matter-Gravity) = 0 wherever T_uv = 0?

No! I am saying that the solution for tuv(Matter-Gravity) is an integral over 4D space-time with a Green's function multiplying the source, which is (LC Gravity)u^v^lTuv(Matter). Therefore IF Tuv(Matter) is IDENTICALLY zero EVERYWHERE-WHEN  in the 4D region of interest, obviously

tuv(Matter-Gravity) = 0 EVERYWHERE-WHEN

Z: Since Einstein's t_uv is a pseudotensor, this depends on the coordinates. So what you are saying can't be true.

J: What you just said is mathematically FALSE!

You have confused tuv = 0 in an LIF at P with tuv = 0 GLOBALLY, i.e. not existing.

You are confused on a very fundamental point.

Take the (LC) field.

In say the SSS solution.

There is a real (LC) =/= 0 field even though choosing an event P and a LIF at P

(LC) = 0 in LIF(P).

For example, in the HOVERING LNIF's at fixed r, theta, phi for r > 2GM/c^2

(LC)10^0 = (GM/c^2r^2)(1 - 2GM/c^2r)^-1

(LC)00^1 = (GM/c^2r^2)(1 - 2GM/c^2r)

(LC)33^1 = -(1/r)(1 - 2GM/c^2r)

(LC)13^3 = 1/r

etc.

All of these (LC) components = 0 in any COINCIDENT LIF, but that is not to be confused with saying that (LC) = 0 globally.

It is true however, that in any NIF there is an (LC) =/= 0 even when the space-time is globally flat Minkowski.

That is, the (LC) representation is locally a property of the LNIF!

But the (LC) FIELD globally as a whole has a physical meaning, i.e. measurable, detectable, making pointers move on a scale. In Minkowski space you do not have to fire a rocket to stand still relative to some marker. In the space around the Earth you do. Therefore, the (LC) field is locally observable as "weight" or "g-force" even though it is not a Diff(4) tensor!

Note that (LC) is a Poincare group tensor. It is not a Diff(4) tensor.

(LC) is a tensor under space-time displacements and under all 4D rigid rotations (special relativity).

That (LC) = 0 in the LIF is the analytic continuation from T4 -> Diff(4) of the fact that it takes no force to stand still in empty space relative, to say, some distant star.

We have a Great Chain of Being and Becoming of Groups in a Lattice.

(LC) is objectively real, coordinate independent, for the Poincare symmetry group of 1905 Special Relativity, but not for the Diff(4) symmetry group of 1916 General Relativity.

The GROUP STRUCTURE defines the reference frame structure!

But the fact that (LC) takes a definite form in a special class of HOVERING LNIFs as the above formulae show for the HOVERING LNIF REPRESENTATION

ds^2 = (1 - 2GM/c^2r)(cdt)^2 - (1 - 2GM/c^2r)^-1dr^2 + r^2(dtheta^2 + sin^2thetadphi^2)

r > 2GM/c^2

Note that the guv are dimensionless & (LC) have dimension 1/(length) with curvature dimension 1/Area



In the case of tuv(Matter-Gravity) - it depends on the product (LC)T(Matter).

Its non-tensor property relative to Diff(4) of vanishing in a LIF at P comes from its (LC) dependence in the source PRODUCT, but if T(Matter) = 0 GLOBALLY then, since T(Matter) is a Diff(4) tensor, tuv will be zero in all local frames GLOBALLY, therefore there is no possibility of tuv =/= 0 in such a case! tuv is a HYBRID of (LC) and T(Matter). That's what you do not understand!

Z: Einstein's t_uv can be made non-zero or even infinite inside a source-free region simply by going to polar coordinates.

J: Hogwash. You have confounded the purely marble (LC) non-tensor with the composite marble-wood tuv. What is true for (LC) is NOT necessarily true for tuv.

You are alluding to Pauli's "Bauer showed that by simply introducing polar coordinates into the Euclidean line element ... the [tuv] energy components are found to have values different from zero, in fact the total energy becomes infinite" p. 176

That Bauer paper is from 1918 and we really do not know if it is correct! It must assume that the Diff(4) tensor Tuv(Matter) =/= 0 somewhere-when in the problem. The issue is what happens in Bauer's model when Tuv(Matter) is globally identically zero so that the ONLY relevant field equation is Ruv = 0?

Where did you get "source free"? How can it be source free? That is nonsense, if you look at 61.

Essentially

tuv(x)(Matter-Gravity)

= |d^4x'G(x'x)[{LC(Gravity x')}u^l^vTlv(Matter x') + {LC(Gravity x')}l^l^vTuv(Matter x')]

Therefore, if the Diff(4) tensor Tuv(Matter) is globally identically zero, so must be tuv(Matter-Geometry).


This is why tuv has nothing to do with the real issue that is

tuv(gravity vacuum) = (c^4/8piG)Guv = (c^4/8piG)/\zpfguv =/= tuv(Matter-Gravity)