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On the nonlocality of gravity energy 1
Posted on Saturday, August 27, 2005 @ 17:48:05 GMT by vlad

Science Dr. Jack Sarfatti writes (not for general public): Any attempt, like Yilmaz's, to localize the classical vacuum energy of the pure gravity field violates the local equivalence principle and is in contradiction with Einstein's theory of General Relativity. One can define a covariant local gravity stress-energy tensor in a classical vacuum (i.e. vanishing zero point energy density and equal and opposite pressure). It will be exactly zero. However, you cannot compute the total energy-momentum of the gravity field at asymptotically flat infinity with that covariant tensor.

The use of a coordinate-dependent pseudo-tensor is completely physical because in order to make a g-force one must use a non-gravity force. The g-force detector is, therefore, not on a time-like geodesic. Consequently, the non-vanishing value of the pseudo-tensor is precisely from the work done and stresses induced by the external non-gravity forces on the detectors.

Mathematically the argument goes like this. Assume 1915 GR with vanishing torsion. The Bianchi identities then ensure that

Guv^;v = 0

where ;v is the gauge covariant derivative from the local gauging of the global translation group T4 down to the Diff(4) local group of general coordinate transformations. This local gauging gives a non- trivial warp part compensating gauge potential 1-form B to the Einstein-Cartan tetrad that in local frame-invariant form can be written as

e = 1 + B

The Levi-Civita connection is derived from this e. When there is torsion we have

e' = e + S

where S is the torsion 1-form

S = De = de + WΛe

W is the spin-connection 1-form

The gauge-covariant derivative with respect to e' is then ;;

The generalized Bianchi identity then gives the "teleparallel"

Guv^;;v = 0

Note that the metric field g is still bilinear in e not e' as demanded by the Einstein Equivalence Principle (EEP).

Therefore, now the original Bianchi identity is violated with

Guv^;v ~ cross-terms S with B and S^2 terms =/= 0

B is ~ the disclination defect density and S is ~ the dislocation defect density in the vacuum condensate Goldstone phase (see Hagen Kleinert's home page for curvature as disclination and torsion as dislocation without any mention of vacuum condensate however).

OK, but going back to 1915 GR, with zero torsion

Guv^;v = 0

Implies that

Tuv^;v = 0

The above equation means

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

Where ,v is the flat space-time partial derivative and

tuv(Matter-Geometry) is the pseudo-tensor that rattles a lot of people like Yilmaz and Zielinski.

tuv(Matter-Gravity)^,v consists of terms like (LC)ul^wT^lw

Where (LC) is the connection that is only non-zero when non-gravity forces do work on the detectors pushing them off the natural timelike geodesics in curved space-time. That is (LC) is the "Gravity" and T is the "Matter" in the "Matter-Gravity" coupling that is the pseudo- tensor.

The "nonlocality of the gravity energy" means that the above pseudo- tensor vanishes in Local Inertial Frames (LIFs), but does not vanish in Local Non-Inertial Frames (LNIFS). The LNIFs only exist because of work done by non-gravity forces on the detectors. Nevertheless, under certain conditions, gravity waves will propagate energy-momentum to infinity causing detectors to click with irreversible generation of heat. The background space-time is of course flat in this asymptotic region that is like in S-Matrix theory in quantum scattering.

To be continued.

(See attached poll on the top right of the page -Vlad)

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"On the nonlocality of gravity energy 1" | Login/Create an Account | 2 comments | Search Discussion
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Re: On the nonlocality of gravity energy 1 (Score: 1)
by irjsi on Saturday, August 27, 2005 @ 22:14:52 GMT
(User Info | Send a Message)
Hello Vlad,
A. I thought you were taking the weekend off, and
B. I remain convinced that there must be a better way of providing energy to the rapidly expanding numbers of 'humans with disposable income' on the Planet.
C. As a member of 'the general public',
I ask: Is there a 'thesauraus' of mathematical terms and symbols available to the general public? (^) ( ; ) ? ? ?

( The above equation means

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

Where ,v is the flat space-time partial derivative and

tuv(Matter-Geometry) is the pseudo-tensor that rattles a lot of people like Yilmaz and Zielinski.

tuv(Matter-Gravity)^,v consists of terms like (LC)ul^wT^lw" ) ? ? ?

An Engineer (related to me), and now deceased, was convinced that nuclear power is 'safe'.
My response to him: "If the only solution to the energy problems of the World is 'nuclear'; I would prefer to turn-off the lights!"
The 'nuclear priesthood' has yet to safely sequester the first ounce of nuclear waste. And the 'nuclear priesthood has opted to increase the 'safe' dose of radiation from, as I recall: allowable dosage to increase from about 12 rems? to 350 rems?
Do not recall the source! Had to do with not guaranteeing security/exposure of nuclear waste after the 10 millenia required to detect meaningful reduction/attrition of radiation.

I remain convinced that there must be a better way of providing energy to the rapidly expanding numbers of 'humans with disposable income' on the Planet.

Roy Stewart
Phoenix AZ


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