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Re: absence of local gravity stress energy density

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  • Paul Zielinski
    ... I am not arguing that the Yilmaz proposal is necessarily correct. As a by-product of this Newtonian interpretation of the EEP, I am simply eliminating
    Message 1 of 2 , Nov 12, 2002
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      ISEP Theoretical Physics Group wrote:

      > On Monday, November 11, 2002, at 02:52 PM, Paul Zielinski wrote:
      >
      > > 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.

      I am not arguing that the Yilmaz proposal is necessarily correct. As a by-product
      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 is
      >
      > 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).

      Right.

      > Metricity may mean no extra dimensional intrusion from hyperspace.
      >
      > 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!

      Yes. Which makes sense since this treatment is only approximately valid
      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
      > momenergy from the geometry to matter and vice versa!

      "Field to matter". You don't really believe in this curved air stuff, do you? :-)

      > This is essentially Deser's point! IMO.

      OK.

      > If you want to think local stress energy density of geometry

      That'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 is
      > 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).

      I have no idea what you mean by "Tuv is only for spin 2 field".

      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
      gravitational stress-energy.

      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
      all.

      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
      acausality.

      The "archaeology of knowledge" (Foucault).

      Z.
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