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Christopher:

According to your comment:

As I understand the orthodoxy, it is futile to speak of the speed of propagation of gravitational causal agency, because gravity is geometry, and the notions of its "propagation" and of its "causal agency" are both sheer nonsense, devoid of meaning.

You either don't understand "the orthodoxy", or "the orthodoxy" is not what you believe it to be (very nearly the same thing), or I have simply never experienced such an "orthodoxy" (which causes me to wonder whether such exists). (Of course this "causal agency" thing does appear to be a rather nebulous concept for geometry.)

(It might be of interest to note that Jim Arnold's "heretical" views of Gravitation fit into the category of "Gravitation as Geometry" precludes "energy bearing" gravitational waves. So if his views are "heresy", even though he appears to strongly adhere to the "orthodox" view that "Gravitation is Geometry" [including, it would appear, that "propagation" is not meaningful within such a context] then where is "the orthodoxy" here?)

I consider Feynman to be quite right in his observation: “It is one of the peculiar aspects of the theory of gravitation, that it has both a field interpretation and a geometrical interpretation.” (In fact, it can even be interpreted as a "dynamical aether" theory.)

You say:

I think the Whitehead position is that "Within General Relativity" one can accept nothing, not the "metric", not the "effective" metric. He thinks it is physically meaningless nonsense, because it abandons causality. He wants to refer to a single underlying Minkowski geometry (such as is not admitted by ‘the general theory of relativity’) and build effective geometries on that. Zeeman’s causality argument seems to support him.

Unfortunately, you either have misinterpreted Whitehead, or he has a far different view of "causality" than I, at least, do. (Unfortunately, I'm not sure what Zeeman's causality argument is, so I'm not sure what the disagreement is, here.)

Within General Relativity causality is fully preserved, at least locally. The only sense in which causality is even potentially violated is when the topology (non-local, an essentially global characteristic) is taken into account. However, this is way outside the purview of the Hilbert-Einstein equations, since they only apply locally. (Even Special Relativity, or even Newtonian Mechanics [Galilean Relativity], can succumb to this issue.)

Furthermore, on the matter of "conservation laws" you state:

I think Logunov also thinks that the ‘general theory of relativity’ is seriously deficient in physical meaning, but for slightly different reasons. He thinks that the ‘general theory of relativity’ is incomplete, so that it does not make definite predictions for empirical testing, and because it would leave physics crippled and incapacitated, lacking the conservations laws.

I'm not sure what "conservation laws" he appears to think are "lacking". Going from Newtonian to Relativistic views did loose, or at least modify, some "conservation laws" (similarly going to the Quantum Mechanical view). And it is true that there are some "conservation laws" that are modified and/or combined into more general "conservation laws" within General Relativity.* However, this is far from "lacking conservation laws".

As for the assertion that General Relativity "does not make definite predictions for empirical testing", I'm not sure what is being referred to here, either. Surely he, and you, know of the myriad of tests General Relativity has inspired and passed. Is it simply the fact that there is no one-single answer for the "metric" when solving the equations? You do know there is a very physical reason for this, right?

I'll have to see when I can devote the time it appears I'll need to track down some of these issues/questions.

Personally, I prefer the "Gravity is Geometry" viewpoint. Within this viewpoint, I have no problem trying to trace the "propagation" of "disturbances" within this geometry (such as the propagation of waves). (In fact, I believe it may be instructive to take a look at the treatment of Gravitational Waves within Misner, Thorne, and Wheeler's Gravitation tome. They look at it both as a perturbation on an "underlying" geometry [the linear approximation, as in "perturbation", not to be confused with "prior geometry"], and at least one exact solution where all can be viewed as geometry. As they put it, it can aid the understanding to take a look at phenomena from a variety of perspectives.)

However, in order to view "propagation" of anything within a spacetime (a space that combines space and time) one has to shift one's perspective down to one of space plus time (the usual old "pre-relativistic" perspective), rather than the global spacetime perspective (that, frankly, most people appear to have a hard time actually achieving, or at least maintaining for long). After all, within the global spacetime perspective all of space and time is rolled into one single entity that is "static" in that it doesn't change (not in this global perspective), it just "is". It's really a matter of perspective.

David

NOTE: I have now edited this post. So, hopefully, it's improved. :-)

* For instance, the separate conservations of mass, energy, and momentum, within Newtonian Mechanics, are changed into a combined conservation of mass-energy-momentum (as a four-vector quantity) within Special Relativity. Furthermore, within General Relativity, this gets combined and generalized into a conservation of mass-energy-momentum-stress (as a tensor quantity). Even within Newtonian mechanics one has to add a new form of energy, gravitational "potential" energy, in order to preserve conservation of energy with gravity.**

** Incidentally, are you aware how distasteful Newton's own theory of gravity was to Newton? This whole "action at a distance" thing was just too much for him to accept. Of course, then "physics" invented the concept of "fields" to handle such issues. Is that the "reality", or simply "man's" own limited way of explaining what is not "fully understood"? (Is it too similar to invention of "gods" to explain things?)