Re: absence of local gravity stress energy density
- ISEP Theoretical Physics Group wrote:
> On Monday, November 11, 2002, at 02:52 PM, Paul Zielinski wrote:I am not arguing that the Yilmaz proposal is necessarily correct. As a by-product
> > More comments:
> > ISEP Theoretical Physics Group wrote:
> >> No radiation until one jerks the world line with acceleration of
> >> acceleration corresponding to time-changing gravity as well.
> > This is another question entirely. My use of the classical freely
> > moving
> > charged particle in a pure electrostatic field to illustrate
> > "Newtonian"
> > inertial cancellation of forces does not depend upon the question of
> > radiation of a uniformly accelerated charge.
> > In fact, its better for my present purposes if Feynman was right,
> > since it
> > simplifies my thought experiment.
> > Paul
> Agreed. I showed in last message that standard GR without any Yilmaz
> baggage suffices for your example.
of this "Newtonian" interpretation of the EEP, I am simply eliminating one class
of objections to Yilmaz's theory (Yilmaz poses a number of other problems).
IMHO, Yilmaz will probably eventually boil down to an empirical question.
I am arguing here only for an alternative consistent interpretation of the *standard
GR formalism* (without any "Yilmaz term" on the RHS of the field equations).
The believe the approach I am advocating here could be applied to the
standard GR weak-field model, and might throw some light on the question of
gravitational stress-energy in the strong field, and the phenomenon of gravitational
self-interaction in GR.
> BTW note that local conservation of momenergy isRight.
> Guv^;v + /\^,vguv = - 8pi(G/c^4)Tuv^;v
> Take /\ = 0 for now.
> The Bianchi identity is
> Guv,^;v = 0
> this assumes zero torsion and metricity (guv^;v = 0).
> Metricity may mean no extra dimensional intrusion from hyperspace.Yes. Which makes sense since this treatment is only approximately valid
> Tuv^;v = Tuv^,v (Linear) + Ju(Non_Linear) = 0
> Tuv^,v(Linear) is not a Diff(4) tensor. Neither is Ju.
> They are tensors under local Lorentz group!
in asymptotically flat regions.
> Their sum is a Diff(4) 1st rank tensor that vanishes.Yes, the energy-momentum *integrals* are fine, but the approximate
linearized pseudotensor "densities" that they are derived from are all
over the place. It's a mess.
> This is local conservation of momenergy where Ju is the transfer of"Field to matter". You don't really believe in this curved air stuff, do you? :-)
> momenergy from the geometry to matter and vice versa!
> This is essentially Deser's point! IMO.OK.
> If you want to think local stress energy density of geometryThat's begging the question. In the "best" interpretation of the standard formalism,
GR may turn out to be simply a metric expression of a physical field in a physical
vacuum extending over a flat spacetime.
As far as I can see, your theory comes close to this. You recover standard GR
as an "effective" theory out of a more fundamental theory of the quantum vacuum.
> this isI have no idea what you mean by "Tuv is only for spin 2 field".
> how to do it. It's not a Diff(4) tensor on its own!
> When /\ = 0
> Tuv,^;v = 0
> is the ebb and flow of momenergy between geometry and matter.
> Tuv is only for spin 0, 1/2, 1, 3/2 fields.
> Guv is for spin 2 field.
> /\ as a local quintessent field opens the Star Gate and allows
> weightless warp drive (Bondi-Terletskii-Forward-Sarfatti).
There is no question in GR that the gravitational field itself gravitates;
this is necessary for internal consistency. The only real questions here
are: How is the field stress-energy to be properly defined in GR; and
under the proper definition, (1) is it generally covariant, (2) is it localizable,
and if so, how localizable; and (3) if so, is it locally conserved?
However, I completely agree that the relationship between gravitational
self-interaction and non-linearity of the GR field equations, as revealed
in the massless spin-2 quantum vacuum treatments of Feynman-Gupta and
of Deser, is of pivotal importance in arriving at deeper physical
understanding of the GR formalism.
I simply think that the original concept of Einstein equivalence does not
stand up to objective criticism, and I am trying to point to the fact
(as authoritatively reported by Fock) that this pseudo-positivist "principle"
has in reality been abandoned -- even by Einstein -- except for certain
inconsistent positions taken by those such as MTW on localizability of
Now, just a few weeks ago (before I reminded you about Pauli's book), you
yourself were aggressively arguing the fundamental distinction between
a real physical gravitational field and a "fictitious" inertial field. I guess
you were not then cognizant of the inconsistency of this position with
the crude argument against localized field stress-energy that appears on
MTW p 467, with its mischievous pun on "gravitational field".
I cannot imagine why you think the utterly arbitrary (and IMO heuristically
incoherent) separation of the gravitational field into absolutely existent and
only relatively existent aspects (curvature and connections resp.) makes any
physical sense -- even while the only heuristic scalpel (Einstein equivalence)
that could make such a painful dissection feasible has long been thrown away
by leading theorists.
From an interpretive standpoint, I view this as a chimera reminiscent of Bohr's
monstrous quantum theory of the hydrogen atom.
You might as well say that the mathematical reality of the curvature of a circle
is absolute, but the mathematical reality of the gradient of a tangent to any point
on the circle is not, since we can always tilt our heads and make the tangent
appear level from that point of view -- that the reality of the gradients is therefore
*purely relative*. But obviously, a *zero gradient is still a gradient*.
Or that a physical field described by a potential phi(x,y,z) "disappears" or is
"annihilated" at any point where the gradients of the potential vanish.
Do we say in GR that the gravitational field is "locally eliminated" at the null
point between two gravitating objects (e.g., the earth and the moon) simply
because the gradients of the metric all vanish there? Of course not.
I see all this as nothing more than a slick "papering over" that simply supports
the superficial pretense that the currently formulated "EEP" has something to
do with Einstein equivalence -- whereas in fact it has nothing to do with it at
After all, even Einstein himself said, "only to first order".
So from my perspective, Einstein equivalence is just a pseudo-positivistic
relic of the historical "context of discovery" of GR -- to be admired for what
it is, but to be allowed to rust in peace after a decent burial.
Along with Heisenberg's bizarre pseudo-positivistic 1926 "proof" of quantum
The "archaeology of knowledge" (Foucault).