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Nonlocality of Energy in General Relativity



 
 
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Old October 26th 04 posted to sci.physics.relativity,sci.math,sci.astro,sci.space,sci.military
Jack Sarfatti
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Posts: 2,218
Default Nonlocality of Energy in General Relativity

How to really lose weight - Einstein's Equivalence Principle


On Oct 25, 2004, at 4:06 PM, wrote:

Jack Sarfatti wrote:

Reply to Zielinski below but first:

[deleted]
----------------------------- Reply to Zielinski:

Paul,

We are spinning our wheels here. You ask questions that make no sense to
me. You seem to think that P_k being "frame dependent" is a problem. Are
you saying P_kP^-k is not frame invariant?

I am saying what Pauli says: in Einstein GR, the energy-momentum content
computed for closed systems residing
in finite regions of space where a gravitational field is present
depends on the choice of coordinates system, and can even be made
infinite in certain coordinate systems all other things being held equal..

This statement is meaningless without the math. What is "energy-momentum
content"? Is that P_k? Give a proof that one can make the global
integral either P_k = infinite or zero in ALL components with a single
x^u -- x^u'(x^u) in the region of integration defining P_k.

PROVE IT! Let's see the math.


Einstein's explanation for this bizarre situation was that the
energy-momentum content of the field is *not physically localizable*.

That is what I have been saying all along and it is what I am saying now.

First of all it is not clear what it is you are saying. First give the
math formula for P_k and then prove what you say above is possible.

Second of all WHAT set of "frames" do you mean? Define them!

I am talking about *general coordinate transformations*, as I have said
many times.

Then you talking gibberish.

P_k is a global integral of a local pseudo-tensor.

P_k itself is NOT subject to GCT!

GCT is a LOCAL transformation

x^u(E) -- x^u'(E) = x^u'(x^u(E))

where E is a FIXED PHYSICAL "POINT" EVENT that actually also needs the
EM Fuv field to FIX. This solve the Einstein "hole" active/passive
DIFF(4) problem as shown by Rovelli. E is defined as a RELATION between
guv and Fuv since all measurements require Fuv as well as Dirac electron
field that must also be included for completeness.

Indeed guv is a macro-quantum emergent field from QED! i.e. Dirac Sea
-- Higgs Ocean

Goldstone phase of Higgs Ocean --- Einstein's guv gravity field.

P_k itself is a global 4-vector under the approximate Poincare group in
the asymptotic 4D flat region OUTSIDE the region of the integral
defining P_k. Without that P_k has no physical meaning as the 4-momentum
of gravity waves from that region of integration.

In canonical GR this means *arbitrary motion of the observer*, including
accelerating frames of reference.

So you can forget about any restrictions to your "local Poincare group".

When you do you will see they must be global frames in the
asymptotically flat region outside the finite region of curvature.

Completely irrelevant to the *general* problem as stated by Pauli..

Diff(4) only has LOCAL FRAMES.

Irrelevant, since we are talking about physical field energy-momentum
content computed over arbitrary finite regions by integration
of a pseudo-tensor stress-energy density.

You are being irrational here. First show what integral you mean. Write
its formula. Then we can proceed to the next step.

Therefore the frame of the integrated quantity P_k is NOT part of
Diff(4) but is for the asymptotically flat approximate Poincare group!

You have completely inverted Pauli's logic.

The point is that the energy-momentum contribution of the field is
generally a frame-dependent quantity, which depends in Einstein
GR on the choice of spacetime coordinates.

Just how do you think you can refute or even defuse this by pointing out
that this is even true in the special case of an asymptotically flat
region spacetime, even when we restrict our attention to linear
transformations within such a finite region?

I'm sorry, Jack, but your argument makes no sense to me.

I realize that. You are posing a pseudo-problem. Until you can write the
math for it, you are not saying anything. It's just word salad so far.

Yet you say Pauli does not mention that. That is a contradiction. Pauli
probably assumed that was so obvious that he was not explicit about it.

He didn't mention it because it was obviously irrelevant.

Look do not use e-mail. Use equation editor in WORD and send me the pdf
and put in ALL the math. Otherwise we cannot communicate about this.
Your verbal descriptions are too ambiguous. This is a technical problem
that requires a close examination - a deconstruction of the mathematical
text. OK?

Let's put this on hold because I would have to do a careful reread of
Pauli, MTW etc. on this that will take a lot of time.

OK.

I would seriously recommend that you get a copy of Landau & Lif****z
(Addison-Wesley, 1951), which is very good on this subject.

I have it. Classical Theory of Fields. What pages? I have other things
to do first however.

The physical reason for the use of the pseudo-tensor for stress-energy
density currents is the splitting of the dynamical degrees of freedom of
the full metric field into off-mass-shell nonpropagating near field
background + propagating on-mass-shell far field gravity waves.

This is about matter vs field, not near-field vs. far-field.

Again, you are talking here about a *different problem*.

Also you need to put in the EM field explicitly as part of the detectors
- a point made by Rovelli BTW.

What Pauli is talking about does not depend in any way on the presence
or absence of EM fields.

Yes because Pauli wrote in 1921!


Einstein's GR Diff(4) field equations TRIVIALLY conserve stress-energy
density currents LOCALLY.

Not according to Einstein and Pauli.

However, I'll look at what MTW have to say about this.

GR is only a local field theory. The P_k are NOT local Diff(4) objects.

Yes, exactly.

They only have meaning in special space-times that are asympotically
flat with a DIFFERENT emergent approximate asymptotic GLOBAL Poincare
group that has no Diff(4) anymore. The "global frames" for P_k are NOT
Diff(4) local frames!

Exactly. Which is one *specific* example of what causes the problem with
getting exact conservation
principles for closed matter + field systems, which is what Pauli is
talking about.

That this is all still true, strictly speaking, even in an
asymptotically flat region of spacetime under a restricted set of
coordinate transformations simply supports Pauli's point.

So I think you have your wires crossed here.

If you confuse apples with oranges you get in trouble.

I can see.:-)

Doing global integrals in curved space-time is tricky business and
involves topology - global constraints beyond the local field equations.
So what you have is a new set of theories i.e.

Local GR (1915) + Global Topological Constraints

The latter introduced "nonlocality" - not same as "quantum"

Einstein's local field equations are simply

Sum of all relevant stress-energy density current tensors = 0

Over what region?

All regions.

For an open or a closed system?

Both - BTW define "open" and "closed" here.


In the presence or absence of gravitational field?

Obviously in the presence of. In the absence of it's special relativity
not general relativity.

See you do not understand here. This is a LOCAL field equation at a
POINT EVENT of course in the presence of gravity fields! That's what
"geometry" means below!


In the 1915 theory

tuv(geometry) + Tuv(matter) = 0

where

tuv(geometry) = (c^4/8piG)Guv

Guv = Ruv - (1/2)Rguv

This may be true globally,

No, it's true LOCALLY it's a LOCAL c-number field theory. The global
topology and boundary conditions are yet to be specified!

The general LOCAL field equation is

Guv(E) + /\zpf(E)guv(E) = -(8piG/c^4)Tuv(E)matter

where E is a "point event" i.e. a region of space-time SMALL compared to
the local radii of curvature r*.

On surface of Earth r

1/r*^2 ~ GM(Earth)/c^2r^3

You need EM Fuv to really fix E. Note that we live in an LIF and there
would be no "weight" without Fuv!

That is the equation of motion of a test particle is

d^2X^u/ds^2 + (Connection Field)^uvw(dX^v/ds)(dX^w/ds) = Sum over e of
e(dX^v/ds)F^uv (em Lorentz force) with QM Pauli principle effects as well

The connection field is a 3rd rank PSEUDO-tensor with an inhomogeneous
term in the LOCAL GCT at E.

In the non-geodesic REST LNIF that we stand on

d^2X^k/ds^2 = dX^k/ds = 0

where k = 1,2,3 space components

"0" time components do not vanish.

Therefore, the 3-vector WEIGHT that the scale shows when you step on it is

W^k = (Connection Field)^k00(dX^0/ds)^2 = Sum over e of e(dX^v/ds)F^kv

Now when you locally make

(Connection Field)^k00 = 0 only at E with some GCT.

That formal move physically describes you jumping off a ladder or in
this case a tall building - with a parachute of course. As soon as you
open the parachute you are on a non-geodesic from air pressure - also we
ignored the air resistance, which is not really a good approximation. So
as soon as air resistance is important you are on a non-geodesic also.

Although the Connection Field is effective zero continuously as you
weightlessly free fall on the timelike geodesic, technically you need a
new GCT at every point on the geodesic. No single GCT will make the
connection field vanish all along the timelike geodesic UNLESS the
spacetime is really 4D flat globally! Similarly for P_k using that
second rank t_uv pseudo-tensor.

but the problem, as I have explained, arises when you look at a closed
matter + field system
in a limited region of space.

What do you mean by "closed"? Finite support for non-vanishing matter
density? That automatically implies an asymptotic flat boundary region
that is OUTSIDE the closed 4D "source" region. So you cannot talk
"closed" without "asymptotic flat". You can also use deSitter spacetime
with asymptotic constant curvature.


Now in 1915 theory the Bianchi identities give the vanishing covariant
divergence

tuv(geometry)^;v = 0

Therefore, the "wood" matter currents are locally CONSERVED separately
without any direct exchange with geometry.

The "marble geometry" is in a separate compartment from the "wood matter".

That is

Tuv(matter)^;v = 0

ALL BY ITSELF!

This only gives sensible conservation laws in the absence of the
gravitational field.

WRONG. You completely misunderstand! You do not understand the Bianchi
identities!

See Pauli. See Landau & Lif****z.
See just about anyone who is serious.

You have misread them. The equations I give above are simple and
complete here. You are very confused on this fundamental point.

The covariant 4-divergence of the matter stress-energy current density
tensor vanishes under these orthodox conditions of the 1915 GR. This
means a sensible local conservation law IN THE PRESENCE OF EVEN A STRONG
GRAVITATIONAL FIELD! Indeed even when the Bianchi identities fail you
still have overall conservation with a direct exchange intermingling of
matter and geometry currents forbidden in the 1915 theory.

LOCAL CONSERVATION means VANISHING COVARIANT DIVERGENCE of the TENSOR
representing the CURRENT DENSITY.

The stress-energy current density is a second rank GCT tensor.

The electromagnetic current density is a first rank GCT tensor.

Also they are O(1,3) tensors from the tetrad EEP.


Metric engineering of warp, wormhole and weapon is IMPOSSIBLE in this limit!

Indeed, metric engineering requires the violation of the 1915 Bianchi
identities.

Furthermore in this limit in VACUUM defined by

Tuv(matter) = 0

Obviously

tuv(geometry) = 0

Therefore the total local stress-energy current density Diff(4) tensor
is WELL DEFINED and is EXACTLY ZERO!

No, in the presence of field this depends in a limited region of vacuum
on the choice of coordinates.

I think you are simply wrong here.

You do not understand what you are talking about here. You are dead wrong.

Guv is a TRUE GCT tensor. It is NOT the pseudo-tensor Pauli talked
about! You are lost in the limbo of dangling symbols divorced from context.

You are seriously confused Paul about what Einstein's field equations
are and what they mean.



P_u is a horse of a different color - an integral of a far field
pseudo-tensor piece of tuv(geometry) = 0

Your P_u is a kind of approximate "4-pseudo-vector" which is only useful
in approximately flat spacetime
regions.

Pauli's J_i is a 1-index quantity that is not locally a full tensor
(true world-tensor) under *any* circumstances
where there exists a gravitational field.

That's the whole point.

So it is simply irrelevant to point out that P_u is approximately a
tensor with respect to linear transformations
only. IMO this establishes precisely nothing about the nature or
validity of Pauli's argument.

You are confused about the above fundamentals, and confused here as well.

Now in my theory I DERIVE Einstein's GR theory of gravity as a limiting
case of the variations in the Goldstone Phase Field of the
post-inflationary macro-quantum coherent calm partially random
highly-ordered massive Higgs Ocean that emerges from the spontaneous
symmetry-breaking instability in the micro-quantum incoherent stormy
completely random massless clothed Dirac Sea including w = -1 zero point
virtual bosons of positive energy density and equal and opposite
negative pressure as well as w = -1 zero point virtual
fermion-antifermion pairs of negative energy density and equal and
opposite positive pressure.

OK, good.

Well you do not understand this because you have contradicted yourself
because your


No, in the presence of field this depends in a limited region of vacuum
on the choice of coordinates.

I think you are simply wrong here.

IS NOT CONSISTENT with my theory at all.



Also I throw away Tuv(matter) completely in first approximation as a
small perturbation because in the FRW limit of cosmology

Omega(matter) ~ 0.04 with w = 0 and w = 1/3 components

w = pressure/(energy density)

Omega(exotic vacuum) ~ 0.96 with w = -1

Dark matter detectors will not click with The Right Stuff, i.e. dark
matter is virtual exotic vacuum not real exotic particle on mass shell.

Exotic vacuum can either anomalously gravitate or ANTI-GRAVITATE
depending on TWO FACTORS

1. Sign of the virtual energy density

2. Space distribution of the energy density.

The exotic vacuum field equation is

Guv + /\zpfguv = 0

In general

Guv^;v =/= 0

This is necessary for metric engineering.

I have to say that this all makes more sense to me than your position
Pauli and gravitational energy-momentum.

Which only shows you are being internally inconsistent. What I say here
demands everything I said above that you disagreed with!

For one thing you have garbled Pauli's GCT pseudo-tensor t_ik with the
GCT true tensor (c^4/8piG)Guv.


On Oct 25, 2004, at 11:05 AM, Jack Sarfatti wrote:

Reply to Zielinski below but first:

Hedgehog Day

“Origin of the Blueshift in Signals from Pioneer 10 and 11”

Kris Krogh

Neuroscience Research Institute University of California, Santa Barbara,
CA 93106,

September 28, 2004

Abstract

“… Doppler tracking signals returned by the Pioneer 10 and 11 space
probes … Analysis by Anderson, Laing, Lau, Liu, Neito and Turyshev …
finds a persistent blueshift, equivalent to an extra acceleration of the
probes toward the Sun … unexplained by general relativity or prevailing
cosmology … NASA’s Pioneer 10 probe was launched in 1972, and sent the
first close-up pictures of Jupiter. Pioneer 11, launched the following
year, showed us Saturn. In addition to those revealing images, they sent
a puzzle: Doppler tracking signals returned by both probes indicated an
anomalous acceleration toward the Sun …. Pioneer 10 crossed Pluto’s
orbit in 1983 and continued sending data until last year, when it was 82
AU from the Sun. Pioneer 11 relayed tracking signals until 1990, when an
electronics unit failed, at a distance of 30 AU. Microwave signals were
sent from Earth stations to the probes, which transmitted phase-locked
signals back. Each station’s signal was derived from a hydrogen
maser frequency reference with an accuracy exceeding 1 part in 10^12,
and the Doppler-shifted frequency of the returning signal was compared
continuously. Unlike the subsequent Voyager missions to the outer
planets, the Pioneers used spin stabilization, which maintains a
spacecraft’s orientation without frequent use of thrusters.
Consequently, Doppler data was accumulated over long periods during
which the motions of the craft were undisturbed. The Doppler data was
checked against models of the probes’ motions by separate groups at
NASA’s Jet Propulsion Laboratory and The Aerospace Corporation. An
unmodeled blueshift was found in each case, equivalent to an
acceleration ap of ~8x10-8 cm/s2. Extensive further analysis of the
Pioneer 10 data by Anderson, Laing, Lau, Liu, Neito and Turyshev …
arrived at (8.74 ±1.33)x10-8 cm/s2, in the approximate direction of the
Sun and Earth. This effect hasn’t been reconciled with general
relativity. According to general relativity, space-time is curved by
mass-energy. Quantum mechanics says space is filled with vacuum energy.
Yet measurements of the universe’s large-scale curvature show none.
Wilczek .. writes:

‘Any theory of gravity that fails to explain why our richly structured
vacuum, full of symmetry-breaking condensates and virtual particles,
does not weigh much more than it does is a profoundly incomplete
theory.’ Frank Wilczek, “Scaling Mount Planck III: Is that all there
is?” Physics Today, 55(8), 10 (2002). And ‘Since gravity is sensitive to
all forms of energy it really ought to see this stuff. . . . A
straightforward estimation suggests empty space should weigh several
orders of magnitude (no misprint here!) more than it does. It “should”
be much denser than a neutron star, for example. The expected energy of
empty space acts like dark energy, with negative pressure, but there’s
much too much of it. To me this discrepancy is the most mysterious fact
in all of physical science, the fact with the greatest potential to rock
the foundations.’ F. Wilczek, “The universe is a strange place,”
astro-ph/0401347.”

Frank Wilczek, who just won a Nobel Prize in 2004, is correct and I
propose an original solution to this problem in this book. I show how
the coherence of the post-inflationary calm ordered Higgs Ocean that
emerges from the pre-inflationary turbulent disorder of the Dirac Sea
removes almost all of the vacuum zero point energy. When I first became
aware of this Pioneer anomaly only a few days ago (it’s now Oct 24, 2004
as I type from Caffe Trieste in Sausalito, California), I immediately
thought of a spherical halo of exotic vacuum centered at the Sun similar
to the galactic halo surrounding the large black hole at the center of
our galaxy. This galactic exotic vacuum halo keeps the circulating
motion of the stars around the black hole fairly constant and prevents
the galaxy from fragmenting. Creon Levit of NASA AMES quickly told me of
the “ephemeris constraint” which does not allow the required density of
vacuum needed in a sphere centered at the Sun out to the orbit of Uranus
20AU from the Sun. 1 AU is the mean Earth-Sun distance of about 10^13 cm
or 93 million miles to be a bit more accurate. The exact numbers do not
matter for now. Tony Smith also suggested a hollow sphere. I thought
about that for a few days and then suddenly realized that the data shows
that the Sun is surrounded by what soft-condensed matter physicists call
a “hedgehog” topological defect! Such a structure in a solid, for
example, can be pictured as two concentric spheres. The inner sphere is
“empty” but the space between the two spheres is filled with a field
with a constant density of Faraday lines of force. This is analogous to
the constant electric field in a parallel plate capacitor ignoring edge
effects. However here we have two concentric spheres not parallel plates
and it’s all “vacuum” i.e. empty space that is not really empty but is
filled with a coherent Higgs Ocean “virtual condensate” as well as some
“normal” plasma of uncondensed virtual particles that actually make the
exotic vacua of either positive or negative pressure and different space
distributions. The constant acceleration back to the Sun is this uniform
radial gradient flow between the inner and outer spherical
surfaces. This inward radial acceleration is in the warp and woof of
space-time itself like the cosmological Hubble recessional velocity of
distant galaxies and quasars. It is not a strange new non-gravity force!
You can also think of this radial tug on Pioneer, or anything else out
there as a centripetal acceleration from a warped rotation of the exotic
vacuum dark zero point energy currents.

There is NO ZERO POINT ENERGY in ordinary non-exotic vacuum. It is all
absorbed into the Higgs Ocean that is then completely calm without any
surfy foam of breaking waves.

Exotic vacuum means foamy breaking waves in the Higgs Ocean for UFOs
with warp drive to SURF on! These foamy waves are not to be confused
with quantum gravity foam, which does not exist in this theory!

The exotic vacuum effective gravity potential energy per unit test
particle mass induced by its zero point energy is in the spherically
symmetric S wave case of the static Green's function multipole expansion
of the Poisson equation weak field slow speed limit of Einstein's field
equation is

Vzpf ~ c^2/\zpfr^2

Example 1: Pioneer Anomaly with local SINGLE-VALUED Higgs Ocean Order
Parameter in S^2 space;

In the case of the Pioneer anomaly, the Higgs Ocean has an exotic vacuum
hedgehog point topological defect at the center of the Sun.

/\zpf = 0 from r = 0 at center of the Sun out to r ~ 20AU at the orbit
of Uranus.

From that point on out to some outer limit r* yet to be measured by
future spinning space-probes

/\zpf = H(t)/cr

H(t) = R(t)^-1dR(t)/dt

R(t) is the DIMENSIONLESS FRW scale factor for the currently
accelerating expansion of 3D space.

Therefore, in this zero point energy exotic vacuum hedgehog region
between the inner and outer spherical surfaces centered at the Sun

V(zpf) = cHr = (speed of light)(Hubble recession speed)

The observed Pioneer anomalous acceleration is

a_P = cH ~ 10^-7 cm/sec^2

This is known to a precision of ~ 10^-8 cm/sec^2 therefore all claims of
a minimal acceleration of c^2/(Hubble scale) from the quantum gravity
foam of geometry are falsified.

Example 2: Quantum Gravity Foam does not exist! - prediction

There is no quantum gravity foam in the Higgs Ocean! Therefore,
anomalous dispersion of cosmic gamma rays from

E^2 = [(pc)^2 + (mc^2)^2]/[1 + (pc)^2/Ep^2]

With E -- Ep as pc/mc^2 1

should NOT be seen. So far they haven't been seen.

Example 3: Dark Matter Galactic Halo of "Dark Matter" surrounding the
central large black hole keeping the outer stars in the galaxy

There may also be a hole in the zero point energy exotic vacuum halo
there as well, but it is not a hedgehog, the flat circulating tangential
velocity v* rotation curves imply

/\zpf ~ 1/r^2

Therefore

V(zpf) independent of r

We can also write

V(zpf) = cv*

where v* is the constant circulating tangential speed of the stars in
the dark matter Galactic Halo

-----------------------------
Reply to Zielinski:

Paul,

We are spinning our wheels here. You ask questions that make no sense to
me. You seem to think that P_k being "frame dependent" is a problem. Are
you saying P_kP^-k is not frame invariant?

Second of all WHAT set of "frames" do you mean? Define them! When you do
you will see they must be global frames in the asymptotically flat
region outside the finite region of curvature.
Diff(4) only has LOCAL FRAMES. Therefore the frame of the integrated
quantity P_k is NOT part of Diff(4) but is for the asymptotically flat
approximate Poincare group! Yet you say Pauli does not mention that.
That is a contradiction. Pauli probably assumed that was so obvious that
he was not explicit about it.

Let's put this on hold because I would have to do a careful reread of
Pauli, MTW etc. on this that will take a lot of time.

The physical reason for the use of the pseudo-tensor for stress-energy
density currents is the splitting of the dynamical degrees of freedom of
the full metric field into off-mass-shell nonpropagating near field
background + propagating on-mass-shell far field gravity waves. Also you
need to put in the EM field explicitly as part of the detectors - a
point made by Rovelli BTW.

Einstein's GR Diff(4) field equations TRIVIALLY conserve stress-energy
density currents LOCALLY. GR is only a local field theory. The P_k are
NOT local Diff(4) objects. They only have meaning in special space-times
that are asympotically flat with a DIFFERENT emergent approximate
asymptotic GLOBAL Poincare group that has no Diff(4) anymore. The
"global frames" for P_k are NOT Diff(4) local frames! If you confuse
apples with oranges you get in trouble.

Doing global integrals in curved space-time is tricky business and
involves topology - global constraints beyond the local field equations.
So what you have is a new set of theories i.e.

Local GR (1915) + Global Topological Constraints

The latter introduced "nonlocality" - not same as "quantum"

Einstein's local field equations are simply

Sum of all relevant stress-energy density current tensors = 0

In the 1915 theory

tuv(geometry) + Tuv(matter) = 0

where

tuv(geometry) = (c^4/8piG)Guv

Guv = Ruv - (1/2)Rguv

Now in 1915 theory the Bianchi identities give the vanishing covariant
divergence

tuv(geometry)^;v = 0

Therefore, the "wood" matter currents are locally CONSERVED separately
without any direct exchange with geometry.

The "marble geometry" is in a separate compartment from the "wood matter".

That is

Tuv(matter)^;v = 0

ALL BY ITSELF!

Metric engineering of warp, wormhole and weapon is IMPOSSIBLE in this limit!

Indeed, metric engineering requires the violation of the 1915 Bianchi
identities.

Furthermore in this limit in VACUUM defined by

Tuv(matter) = 0

Obviously

tuv(geometry) = 0

Therefore the total local stress-energy current density Diff(4) tensor
is WELL DEFINED and is EXACTLY ZERO!

P_u is a horse of a different color - an integral of a far field
pseudo-tensor piece of tuv(geometry) = 0

Now in my theory I DERIVE Einstein's GR theory of gravity as a limiting
case of the variations in the Goldstone Phase Field of the
post-inflationary macro-quantum coherent calm partially random
highly-ordered massive Higgs Ocean that emerges from the spontaneous
symmetry-breaking instability in the micro-quantum incoherent stormy
completely random massless clothed Dirac Sea including w = -1 zero point
virtual bosons of positive energy density and equal and opposite
negative pressure as well as w = -1 zero point virtual
fermion-antifermion pairs of negative energy density and equal and
opposite positive pressure.

Also I throw away Tuv(matter) completely in first approximation as a
small perturbation because in the FRW limit of cosmology

Omega(matter) ~ 0.04 with w = 0 and w = 1/3 components

w = pressure/(energy density)

Omega(exotic vacuum) ~ 0.96 with w = -1

Dark matter detectors will not click with The Right Stuff, i.e. dark
matter is virtual exotic vacuum not real exotic particle on mass shell.

Exotic vacuum can either anomalously gravitate or ANTI-GRAVITATE
depending on TWO FACTORS

1. Sign of the virtual energy density

2. Space distribution of the energy density.

The exotic vacuum field equation is

Guv + /\zpfguv = 0

In general

Guv^;v =/= 0

This is necessary for metric engineering.


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  #2  
Old October 26th 04 posted to sci.physics.relativity,sci.math,sci.astro,sci.space,sci.military
John Crichton
external usenet poster
 
Posts: 1
Default Nonlocality of Energy in General Relativity

I can't figure out whether or not you are on to something here or you
drank the bong water (never, never drink the bong water). I am pretty
sure those are the choices. I do see the huge hole in that our current
understanding of how the universe works has not a clue as to how to
explain consciousness. Very interesting.

Jon




Jack Sarfatti wrote:
How to really lose weight - Einstein's Equivalence Principle


On Oct 25, 2004, at 4:06 PM, wrote:

Jack Sarfatti wrote:

Reply to Zielinski below but first:

[deleted]
----------------------------- Reply to Zielinski:

Paul,

We are spinning our wheels here. You ask questions that make no sense to
me. You seem to think that P_k being "frame dependent" is a problem. Are
you saying P_kP^-k is not frame invariant?

I am saying what Pauli says: in Einstein GR, the energy-momentum content
computed for closed systems residing
in finite regions of space where a gravitational field is present
depends on the choice of coordinates system, and can even be made
infinite in certain coordinate systems all other things being held equal..

This statement is meaningless without the math. What is "energy-momentum
content"? Is that P_k? Give a proof that one can make the global
integral either P_k = infinite or zero in ALL components with a single
x^u -- x^u'(x^u) in the region of integration defining P_k.

PROVE IT! Let's see the math.


Einstein's explanation for this bizarre situation was that the
energy-momentum content of the field is *not physically localizable*.

That is what I have been saying all along and it is what I am saying now.

First of all it is not clear what it is you are saying. First give the
math formula for P_k and then prove what you say above is possible.

Second of all WHAT set of "frames" do you mean? Define them!

I am talking about *general coordinate transformations*, as I have said
many times.

Then you talking gibberish.

P_k is a global integral of a local pseudo-tensor.

P_k itself is NOT subject to GCT!

GCT is a LOCAL transformation

x^u(E) -- x^u'(E) = x^u'(x^u(E))

where E is a FIXED PHYSICAL "POINT" EVENT that actually also needs the
EM Fuv field to FIX. This solve the Einstein "hole" active/passive
DIFF(4) problem as shown by Rovelli. E is defined as a RELATION between
guv and Fuv since all measurements require Fuv as well as Dirac electron
field that must also be included for completeness.

Indeed guv is a macro-quantum emergent field from QED! i.e. Dirac Sea
-- Higgs Ocean

Goldstone phase of Higgs Ocean --- Einstein's guv gravity field.

P_k itself is a global 4-vector under the approximate Poincare group in
the asymptotic 4D flat region OUTSIDE the region of the integral
defining P_k. Without that P_k has no physical meaning as the 4-momentum
of gravity waves from that region of integration.

In canonical GR this means *arbitrary motion of the observer*, including
accelerating frames of reference.

So you can forget about any restrictions to your "local Poincare group".

When you do you will see they must be global frames in the
asymptotically flat region outside the finite region of curvature.

Completely irrelevant to the *general* problem as stated by Pauli..

Diff(4) only has LOCAL FRAMES.

Irrelevant, since we are talking about physical field energy-momentum
content computed over arbitrary finite regions by integration
of a pseudo-tensor stress-energy density.

You are being irrational here. First show what integral you mean. Write
its formula. Then we can proceed to the next step.

Therefore the frame of the integrated quantity P_k is NOT part of
Diff(4) but is for the asymptotically flat approximate Poincare group!

You have completely inverted Pauli's logic.

The point is that the energy-momentum contribution of the field is
generally a frame-dependent quantity, which depends in Einstein
GR on the choice of spacetime coordinates.

Just how do you think you can refute or even defuse this by pointing out
that this is even true in the special case of an asymptotically flat
region spacetime, even when we restrict our attention to linear
transformations within such a finite region?

I'm sorry, Jack, but your argument makes no sense to me.

I realize that. You are posing a pseudo-problem. Until you can write the
math for it, you are not saying anything. It's just word salad so far.

Yet you say Pauli does not mention that. That is a contradiction. Pauli
probably assumed that was so obvious that he was not explicit about it.

He didn't mention it because it was obviously irrelevant.

Look do not use e-mail. Use equation editor in WORD and send me the pdf
and put in ALL the math. Otherwise we cannot communicate about this.
Your verbal descriptions are too ambiguous. This is a technical problem
that requires a close examination - a deconstruction of the mathematical
text. OK?

Let's put this on hold because I would have to do a careful reread of
Pauli, MTW etc. on this that will take a lot of time.

OK.

I would seriously recommend that you get a copy of Landau & Lif****z
(Addison-Wesley, 1951), which is very good on this subject.

I have it. Classical Theory of Fields. What pages? I have other things
to do first however.

The physical reason for the use of the pseudo-tensor for stress-energy
density currents is the splitting of the dynamical degrees of freedom of
the full metric field into off-mass-shell nonpropagating near field
background + propagating on-mass-shell far field gravity waves.

This is about matter vs field, not near-field vs. far-field.

Again, you are talking here about a *different problem*.

Also you need to put in the EM field explicitly as part of the detectors
- a point made by Rovelli BTW.

What Pauli is talking about does not depend in any way on the presence
or absence of EM fields.

Yes because Pauli wrote in 1921!


Einstein's GR Diff(4) field equations TRIVIALLY conserve stress-energy
density currents LOCALLY.

Not according to Einstein and Pauli.

However, I'll look at what MTW have to say about this.

GR is only a local field theory. The P_k are NOT local Diff(4) objects.

Yes, exactly.

They only have meaning in special space-times that are asympotically
flat with a DIFFERENT emergent approximate asymptotic GLOBAL Poincare
group that has no Diff(4) anymore. The "global frames" for P_k are NOT
Diff(4) local frames!

Exactly. Which is one *specific* example of what causes the problem with
getting exact conservation
principles for closed matter + field systems, which is what Pauli is
talking about.

That this is all still true, strictly speaking, even in an
asymptotically flat region of spacetime under a restricted set of
coordinate transformations simply supports Pauli's point.

So I think you have your wires crossed here.

If you confuse apples with oranges you get in trouble.

I can see.:-)

Doing global integrals in curved space-time is tricky business and
involves topology - global constraints beyond the local field equations.
So what you have is a new set of theories i.e.

Local GR (1915) + Global Topological Constraints

The latter introduced "nonlocality" - not same as "quantum"

Einstein's local field equations are simply

Sum of all relevant stress-energy density current tensors = 0

Over what region?

All regions.

For an open or a closed system?

Both - BTW define "open" and "closed" here.


In the presence or absence of gravitational field?

Obviously in the presence of. In the absence of it's special relativity
not general relativity.

See you do not understand here. This is a LOCAL field equation at a
POINT EVENT of course in the presence of gravity fields! That's what
"geometry" means below!


In the 1915 theory

tuv(geometry) + Tuv(matter) = 0

where

tuv(geometry) = (c^4/8piG)Guv

Guv = Ruv - (1/2)Rguv

This may be true globally,

No, it's true LOCALLY it's a LOCAL c-number field theory. The global
topology and boundary conditions are yet to be specified!

The general LOCAL field equation is

Guv(E) + /\zpf(E)guv(E) = -(8piG/c^4)Tuv(E)matter

where E is a "point event" i.e. a region of space-time SMALL compared to
the local radii of curvature r*.

On surface of Earth r

1/r*^2 ~ GM(Earth)/c^2r^3

You need EM Fuv to really fix E. Note that we live in an LIF and there
would be no "weight" without Fuv!

That is the equation of motion of a test particle is

d^2X^u/ds^2 + (Connection Field)^uvw(dX^v/ds)(dX^w/ds) = Sum over e of
e(dX^v/ds)F^uv (em Lorentz force) with QM Pauli principle effects as well

The connection field is a 3rd rank PSEUDO-tensor with an inhomogeneous
term in the LOCAL GCT at E.

In the non-geodesic REST LNIF that we stand on

d^2X^k/ds^2 = dX^k/ds = 0

where k = 1,2,3 space components

"0" time components do not vanish.

Therefore, the 3-vector WEIGHT that the scale shows when you step on it is

W^k = (Connection Field)^k00(dX^0/ds)^2 = Sum over e of e(dX^v/ds)F^kv

Now when you locally make

(Connection Field)^k00 = 0 only at E with some GCT.

That formal move physically describes you jumping off a ladder or in
this case a tall building - with a parachute of course. As soon as you
open the parachute you are on a non-geodesic from air pressure - also we
ignored the air resistance, which is not really a good approximation. So
as soon as air resistance is important you are on a non-geodesic also.

Although the Connection Field is effective zero continuously as you
weightlessly free fall on the timelike geodesic, technically you need a
new GCT at every point on the geodesic. No single GCT will make the
connection field vanish all along the timelike geodesic UNLESS the
spacetime is really 4D flat globally! Similarly for P_k using that
second rank t_uv pseudo-tensor.

but the problem, as I have explained, arises when you look at a closed
matter + field system
in a limited region of space.

What do you mean by "closed"? Finite support for non-vanishing matter
density? That automatically implies an asymptotic flat boundary region
that is OUTSIDE the closed 4D "source" region. So you cannot talk
"closed" without "asymptotic flat". You can also use deSitter spacetime
with asymptotic constant curvature.


Now in 1915 theory the Bianchi identities give the vanishing covariant
divergence

tuv(geometry)^;v = 0

Therefore, the "wood" matter currents are locally CONSERVED separately
without any direct exchange with geometry.

The "marble geometry" is in a separate compartment from the "wood matter".

That is

Tuv(matter)^;v = 0

ALL BY ITSELF!

This only gives sensible conservation laws in the absence of the
gravitational field.

WRONG. You completely misunderstand! You do not understand the Bianchi
identities!

See Pauli. See Landau & Lif****z.
See just about anyone who is serious.

You have misread them. The equations I give above are simple and
complete here. You are very confused on this fundamental point.

The covariant 4-divergence of the matter stress-energy current density
tensor vanishes under these orthodox conditions of the 1915 GR. This
means a sensible local conservation law IN THE PRESENCE OF EVEN A STRONG
GRAVITATIONAL FIELD! Indeed even when the Bianchi identities fail you
still have overall conservation with a direct exchange intermingling of
matter and geometry currents forbidden in the 1915 theory.

LOCAL CONSERVATION means VANISHING COVARIANT DIVERGENCE of the TENSOR
representing the CURRENT DENSITY.

The stress-energy current density is a second rank GCT tensor.

The electromagnetic current density is a first rank GCT tensor.

Also they are O(1,3) tensors from the tetrad EEP.


Metric engineering of warp, wormhole and weapon is IMPOSSIBLE in this
limit!

Indeed, metric engineering requires the violation of the 1915 Bianchi
identities.

Furthermore in this limit in VACUUM defined by

Tuv(matter) = 0

Obviously

tuv(geometry) = 0

Therefore the total local stress-energy current density Diff(4) tensor
is WELL DEFINED and is EXACTLY ZERO!

No, in the presence of field this depends in a limited region of vacuum
on the choice of coordinates.

I think you are simply wrong here.

You do not understand what you are talking about here. You are dead wrong.

Guv is a TRUE GCT tensor. It is NOT the pseudo-tensor Pauli talked
about! You are lost in the limbo of dangling symbols divorced from context.

You are seriously confused Paul about what Einstein's field equations
are and what they mean.



P_u is a horse of a different color - an integral of a far field
pseudo-tensor piece of tuv(geometry) = 0

Your P_u is a kind of approximate "4-pseudo-vector" which is only useful
in approximately flat spacetime
regions.

Pauli's J_i is a 1-index quantity that is not locally a full tensor
(true world-tensor) under *any* circumstances
where there exists a gravitational field.

That's the whole point.

So it is simply irrelevant to point out that P_u is approximately a
tensor with respect to linear transformations
only. IMO this establishes precisely nothing about the nature or
validity of Pauli's argument.

You are confused about the above fundamentals, and confused here as well.

Now in my theory I DERIVE Einstein's GR theory of gravity as a limiting
case of the variations in the Goldstone Phase Field of the
post-inflationary macro-quantum coherent calm partially random
highly-ordered massive Higgs Ocean that emerges from the spontaneous
symmetry-breaking instability in the micro-quantum incoherent stormy
completely random massless clothed Dirac Sea including w = -1 zero point
virtual bosons of positive energy density and equal and opposite
negative pressure as well as w = -1 zero point virtual
fermion-antifermion pairs of negative energy density and equal and
opposite positive pressure.

OK, good.

Well you do not understand this because you have contradicted yourself
because your


No, in the presence of field this depends in a limited region of vacuum
on the choice of coordinates.

I think you are simply wrong here.

IS NOT CONSISTENT with my theory at all.



Also I throw away Tuv(matter) completely in first approximation as a
small perturbation because in the FRW limit of cosmology

Omega(matter) ~ 0.04 with w = 0 and w = 1/3 components

w = pressure/(energy density)

Omega(exotic vacuum) ~ 0.96 with w = -1

Dark matter detectors will not click with The Right Stuff, i.e. dark
matter is virtual exotic vacuum not real exotic particle on mass shell.

Exotic vacuum can either anomalously gravitate or ANTI-GRAVITATE
depending on TWO FACTORS

1. Sign of the virtual energy density

2. Space distribution of the energy density.

The exotic vacuum field equation is

Guv + /\zpfguv = 0

In general

Guv^;v =/= 0

This is necessary for metric engineering.

I have to say that this all makes more sense to me than your position
Pauli and gravitational energy-momentum.

Which only shows you are being internally inconsistent. What I say here
demands everything I said above that you disagreed with!

For one thing you have garbled Pauli's GCT pseudo-tensor t_ik with the
GCT true tensor (c^4/8piG)Guv.


On Oct 25, 2004, at 11:05 AM, Jack Sarfatti wrote:

Reply to Zielinski below but first:

Hedgehog Day

“Origin of the Blueshift in Signals from Pioneer 10 and 11”

Kris Krogh
Neuroscience Research Institute University of California, Santa Barbara,
CA 93106,

September 28, 2004

Abstract

“… Doppler tracking signals returned by the Pioneer 10 and 11 space
probes … Analysis by Anderson, Laing, Lau, Liu, Neito and Turyshev …
finds a persistent blueshift, equivalent to an extra acceleration of the
probes toward the Sun … unexplained by general relativity or prevailing
cosmology … NASA’s Pioneer 10 probe was launched in 1972, and sent the
first close-up pictures of Jupiter. Pioneer 11, launched the following
year, showed us Saturn. In addition to those revealing images, they sent
a puzzle: Doppler tracking signals returned by both probes indicated an
anomalous acceleration toward the Sun …. Pioneer 10 crossed Pluto’s
orbit in 1983 and continued sending data until last year, when it was 82
AU from the Sun. Pioneer 11 relayed tracking signals until 1990, when an
electronics unit failed, at a distance of 30 AU. Microwave signals were
sent from Earth stations to the probes, which transmitted phase-locked
signals back. Each station’s signal was derived from a hydrogen maser
frequency reference with an accuracy exceeding 1 part in 10^12, and the
Doppler-shifted frequency of the returning signal was compared
continuously. Unlike the subsequent Voyager missions to the outer
planets, the Pioneers used spin stabilization, which maintains a
spacecraft’s orientation without frequent use of thrusters.
Consequently, Doppler data was accumulated over long periods during
which the motions of the craft were undisturbed. The Doppler data was
checked against models of the probes’ motions by separate groups at
NASA’s Jet Propulsion Laboratory and The Aerospace Corporation. An
unmodeled blueshift was found in each case, equivalent to an
acceleration ap of ~8x10-8 cm/s2. Extensive further analysis of the
Pioneer 10 data by Anderson, Laing, Lau, Liu, Neito and Turyshev …
arrived at (8.74 ±1.33)x10-8 cm/s2, in the approximate direction of the
Sun and Earth. This effect hasn’t been reconciled with general
relativity. According to general relativity, space-time is curved by
mass-energy. Quantum mechanics says space is filled with vacuum energy.
Yet measurements of the universe’s large-scale curvature show none.
Wilczek .. writes:

‘Any theory of gravity that fails to explain why our richly structured
vacuum, full of symmetry-breaking condensates and virtual particles,
does not weigh much more than it does is a profoundly incomplete
theory.’ Frank Wilczek, “Scaling Mount Planck III: Is that all there
is?” Physics Today, 55(8), 10 (2002). And ‘Since gravity is sensitive to
all forms of energy it really ought to see this stuff. . . . A
straightforward estimation suggests empty space should weigh several
orders of magnitude (no misprint here!) more than it does. It “should”
be much denser than a neutron star, for example. The expected energy of
empty space acts like dark energy, with negative pressure, but there’s
much too much of it. To me this discrepancy is the most mysterious fact
in all of physical science, the fact with the greatest potential to rock
the foundations.’ F. Wilczek, “The universe is a strange place,”
astro-ph/0401347.”

Frank Wilczek, who just won a Nobel Prize in 2004, is correct and I
propose an original solution to this problem in this book. I show how
the coherence of the post-inflationary calm ordered Higgs Ocean that
emerges from the pre-inflationary turbulent disorder of the Dirac Sea
removes almost all of the vacuum zero point energy. When I first became
aware of this Pioneer anomaly only a few days ago (it’s now Oct 24, 2004
as I type from Caffe Trieste in Sausalito, California), I immediately
thought of a spherical halo of exotic vacuum centered at the Sun similar
to the galactic halo surrounding the large black hole at the center of
our galaxy. This galactic exotic vacuum halo keeps the circulating
motion of the stars around the black hole fairly constant and prevents
the galaxy from fragmenting. Creon Levit of NASA AMES quickly told me of
the “ephemeris constraint” which does not allow the required density of
vacuum needed in a sphere centered at the Sun out to the orbit of Uranus
20AU from the Sun. 1 AU is the mean Earth-Sun distance of about 10^13 cm
or 93 million miles to be a bit more accurate. The exact numbers do not
matter for now. Tony Smith also suggested a hollow sphere. I thought
about that for a few days and then suddenly realized that the data shows
that the Sun is surrounded by what soft-condensed matter physicists call
a “hedgehog” topological defect! Such a structure in a solid, for
example, can be pictured as two concentric spheres. The inner sphere is
“empty” but the space between the two spheres is filled with a field
with a constant density of Faraday lines of force. This is analogous to
the constant electric field in a parallel plate capacitor ignoring edge
effects. However here we have two concentric spheres not parallel plates
and it’s all “vacuum” i.e. empty space that is not really empty but is
filled with a coherent Higgs Ocean “virtual condensate” as well as some
“normal” plasma of uncondensed virtual particles that actually make the
exotic vacua of either positive or negative pressure and different space
distributions. The constant acceleration back to the Sun is this uniform
radial gradient flow between the inner and outer spherical surfaces.
This inward radial acceleration is in the warp and woof of space-time
itself like the cosmological Hubble recessional velocity of distant
galaxies and quasars. It is not a strange new non-gravity force! You can
also think of this radial tug on Pioneer, or anything else out there as
a centripetal acceleration from a warped rotation of the exotic vacuum
dark zero point energy currents.
There is NO ZERO POINT ENERGY in ordinary non-exotic vacuum. It is all
absorbed into the Higgs Ocean that is then completely calm without any
surfy foam of breaking waves.

Exotic vacuum means foamy breaking waves in the Higgs Ocean for UFOs
with warp drive to SURF on! These foamy waves are not to be confused
with quantum gravity foam, which does not exist in this theory!

The exotic vacuum effective gravity potential energy per unit test
particle mass induced by its zero point energy is in the spherically
symmetric S wave case of the static Green's function multipole expansion
of the Poisson equation weak field slow speed limit of Einstein's field
equation is

Vzpf ~ c^2/\zpfr^2

Example 1: Pioneer Anomaly with local SINGLE-VALUED Higgs Ocean Order
Parameter in S^2 space;

In the case of the Pioneer anomaly, the Higgs Ocean has an exotic vacuum
hedgehog point topological defect at the center of the Sun.

/\zpf = 0 from r = 0 at center of the Sun out to r ~ 20AU at the orbit
of Uranus.

From that point on out to some outer limit r* yet to be measured by
future spinning space-probes

/\zpf = H(t)/cr

H(t) = R(t)^-1dR(t)/dt

R(t) is the DIMENSIONLESS FRW scale factor for the currently
accelerating expansion of 3D space.

Therefore, in this zero point energy exotic vacuum hedgehog region
between the inner and outer spherical surfaces centered at the Sun

V(zpf) = cHr = (speed of light)(Hubble recession speed)

The observed Pioneer anomalous acceleration is

a_P = cH ~ 10^-7 cm/sec^2

This is known to a precision of ~ 10^-8 cm/sec^2 therefore all claims of
a minimal acceleration of c^2/(Hubble scale) from the quantum gravity
foam of geometry are falsified.

Example 2: Quantum Gravity Foam does not exist! - prediction

There is no quantum gravity foam in the Higgs Ocean! Therefore,
anomalous dispersion of cosmic gamma rays from

E^2 = [(pc)^2 + (mc^2)^2]/[1 + (pc)^2/Ep^2]

With E -- Ep as pc/mc^2 1

should NOT be seen. So far they haven't been seen.

Example 3: Dark Matter Galactic Halo of "Dark Matter" surrounding the
central large black hole keeping the outer stars in the galaxy

There may also be a hole in the zero point energy exotic vacuum halo
there as well, but it is not a hedgehog, the flat circulating tangential
velocity v* rotation curves imply

/\zpf ~ 1/r^2

Therefore

V(zpf) independent of r

We can also write

V(zpf) = cv*

where v* is the constant circulating tangential speed of the stars in
the dark matter Galactic Halo

----------------------------- Reply to Zielinski:

Paul,

We are spinning our wheels here. You ask questions that make no sense to
me. You seem to think that P_k being "frame dependent" is a problem. Are
you saying P_kP^-k is not frame invariant?

Second of all WHAT set of "frames" do you mean? Define them! When you do
you will see they must be global frames in the asymptotically flat
region outside the finite region of curvature.
Diff(4) only has LOCAL FRAMES. Therefore the frame of the integrated
quantity P_k is NOT part of Diff(4) but is for the asymptotically flat
approximate Poincare group! Yet you say Pauli does not mention that.
That is a contradiction. Pauli probably assumed that was so obvious that
he was not explicit about it.

Let's put this on hold because I would have to do a careful reread of
Pauli, MTW etc. on this that will take a lot of time.

The physical reason for the use of the pseudo-tensor for stress-energy
density currents is the splitting of the dynamical degrees of freedom of
the full metric field into off-mass-shell nonpropagating near field
background + propagating on-mass-shell far field gravity waves. Also you
need to put in the EM field explicitly as part of the detectors - a
point made by Rovelli BTW.

Einstein's GR Diff(4) field equations TRIVIALLY conserve stress-energy
density currents LOCALLY. GR is only a local field theory. The P_k are
NOT local Diff(4) objects. They only have meaning in special space-times
that are asympotically flat with a DIFFERENT emergent approximate
asymptotic GLOBAL Poincare group that has no Diff(4) anymore. The
"global frames" for P_k are NOT Diff(4) local frames! If you confuse
apples with oranges you get in trouble.

Doing global integrals in curved space-time is tricky business and
involves topology - global constraints beyond the local field equations.
So what you have is a new set of theories i.e.

Local GR (1915) + Global Topological Constraints

The latter introduced "nonlocality" - not same as "quantum"

Einstein's local field equations are simply

Sum of all relevant stress-energy density current tensors = 0

In the 1915 theory

tuv(geometry) + Tuv(matter) = 0

where

tuv(geometry) = (c^4/8piG)Guv

Guv = Ruv - (1/2)Rguv

Now in 1915 theory the Bianchi identities give the vanishing covariant
divergence

tuv(geometry)^;v = 0

Therefore, the "wood" matter currents are locally CONSERVED separately
without any direct exchange with geometry.

The "marble geometry" is in a separate compartment from the "wood matter".

That is

Tuv(matter)^;v = 0

ALL BY ITSELF!

Metric engineering of warp, wormhole and weapon is IMPOSSIBLE in this
limit!

Indeed, metric engineering requires the violation of the 1915 Bianchi
identities.

Furthermore in this limit in VACUUM defined by

Tuv(matter) = 0

Obviously

tuv(geometry) = 0

Therefore the total local stress-energy current density Diff(4) tensor
is WELL DEFINED and is EXACTLY ZERO!

P_u is a horse of a different color - an integral of a far field
pseudo-tensor piece of tuv(geometry) = 0

Now in my theory I DERIVE Einstein's GR theory of gravity as a limiting
case of the variations in the Goldstone Phase Field of the
post-inflationary macro-quantum coherent calm partially random
highly-ordered massive Higgs Ocean that emerges from the spontaneous
symmetry-breaking instability in the micro-quantum incoherent stormy
completely random massless clothed Dirac Sea including w = -1 zero point
virtual bosons of positive energy density and equal and opposite
negative pressure as well as w = -1 zero point virtual
fermion-antifermion pairs of negative energy density and equal and
opposite positive pressure.

Also I throw away Tuv(matter) completely in first approximation as a
small perturbation because in the FRW limit of cosmology

Omega(matter) ~ 0.04 with w = 0 and w = 1/3 components

w = pressure/(energy density)

Omega(exotic vacuum) ~ 0.96 with w = -1

Dark matter detectors will not click with The Right Stuff, i.e. dark
matter is virtual exotic vacuum not real exotic particle on mass shell.

Exotic vacuum can either anomalously gravitate or ANTI-GRAVITATE
depending on TWO FACTORS

1. Sign of the virtual energy density

2. Space distribution of the energy density.

The exotic vacuum field equation is

Guv + /\zpfguv = 0

In general

Guv^;v =/= 0

This is necessary for metric engineering.


  #3  
Old October 26th 04 posted to sci.physics.relativity,sci.math,sci.astro
Luigi Caselli
external usenet poster
 
Posts: 63
Default Nonlocality of Energy in General Relativity

"John Crichton" ha scritto nel messaggio
news:aBifd.7463$R05.4632@attbi_s53...
I can't figure out whether or not you are on to something here or you
drank the bong water (never, never drink the bong water). I am pretty
sure those are the choices. I do see the huge hole in that our current
understanding of how the universe works has not a clue as to how to
explain consciousness. Very interesting.

Jon


Unfortunatly Jack Sarfatti only write on newsgroups, but almost never reply
to us and so leave us in the huge holes of not understanding...
Maybe this is a good thing... instead we'll be covered by tons of formulas
that only few person in the world can understand (maybe only him).

Luigi Caselli


  #4  
Old October 26th 04 posted to sci.physics.relativity,sci.math,sci.astro,sci.space,sci.military
Fred McGalliard
external usenet poster
 
Posts: 77
Default Nonlocality of Energy in General Relativity


"John Crichton"
....
I do see the huge hole in that our current
understanding of how the universe works has not a clue as to how to
explain consciousness. Very interesting.


I thought the universe explained it's thoughts on the subject very well,
when last we talked. I hope it is not offended by my infinitesmal
summarization of "Huh? You call that barest glimmer of a half formed thought
consciousness? (followed by a billion years of ROTFLOL)"


 




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