On Oct 3, 2010, at 1:57 PM, Paul Zielinski wrote:
On Sun, Oct 3, 2010 at 1:22 PM, JACK SARFATTI <
Z
see your Sean Carroll notes
basic ambiguity is split between background and wave metrics
Yes of course.
physical metric = background metric + gravity wave metric
The argument was made that since any gravity wave could be eliminated ("zeroed out") by a suitable choice of coordinates,
gravity waves were not real. This is closely related to the EP argument against objective local gravitational energy. I understand that in the case of gravity waves at least this argument is no longer taken seriously.
also need to restrict to Minkowski background for Hulse-Taylor to get the quadrupole formula that is actually measured.
Of course -- because the actual gravity wave is defined as the coordinate-invariant deviation from flat vacuum geometry.
The true observable is the 4th rank curvature tensor of the complete physical metric field.
This is what I've been saying all along. You cannot actually get around this with quasi-local quantities. You have to abandon the classic EP argument that frame transformations literally cancel first-order geometric distortions of a flat Minkowski geometry in GR.
As you know, I think you are in serious error on this specific point. The first order Levi-Civita connections are only zero at the Centers Of Mass (COMs) of the LIFs that are not rotating and on timelike geodesics of the complete metric. If you exceed the local curvature radius at that COM then you are in a new LIF' and need to zero the Levi Civita terms at that new COM'. The covariant curl of the Levi-Civita connection is not zero'd out by this NON-SINGULAR local transformation. This is different from Hagen-Kleinert's multi-valued maps corresponding to real invariant topological, e.g. disclination defects that are not found in Einstein's 1916 restricted GCTs. What you were looking for Z is in Kleinert's work.
Amazon.com: Multivalued Fields: In Condensed Matter ...
Multivalued Fields: In Condensed Matter, Electromagnetism, and Gravitation by HagenKleinert Paperback 4.0 out of 5 stars (1) ...
www.amazon.com › ... › Physics › Mathematical Physics - Cached
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Multivalued fields in condensed matter, electromagnetism, and ... - Google Books Result
Hagen Kleinert - 2008 - Science - 497 pages
Kleinert's work includes flexible manipulation of coordinates that led to his evaluation of the path integral for the Coulomb potential.
books.google.com/books?isbn=981279171X...
Multivalued function - Wikipedia, the free encyclopedia
The multivalued function corresponds to this inverse relation. .... 1992; Kleinert, Hagen,Multivalued Fields in in Condensed Matter, Electrodynamics, ...
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Multivalued function
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Phys. Rev. D 81, 084030 (2010): Jizba et al. - Uncertainty ...
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gravity wave is because the source is not on a timelike geodesic relative to the full physical metric.
e.g. the Hulse-Taylor case - on timelike geodesics relative to background metric that accelerate relative to full physical metric?
OK....
There should be no radiation on true geodesics - this is one aspect of the classical nonlocality of gravity energy.
It's very tricky.
Then each LIF constitutes a preferred frame relative to which accelerating motion of gravitational sources is judged.
Is this really what you mean to argue here?
Yes.