Nonlocality of Gravity Energy
- From: Jack Sarfatti <sarfatti@xxxxxxxxxxx>
- Date: Fri, 26 Aug 2005 06:58:02 +0000 (UTC)
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 + W/\e
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.
.
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