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David,

Thank you for your reply that starts by referring to Whitehead’s illustrative model.

I am wary of talking at this stage of what is “true” or “observable” or “prior”.

Perhaps it may be useful to distinguish several viewpoints.

I am saying that as for how to read the equations, Whitehead is ceremoniously kicked down the front entrance steps by the palace guard of the orthodoxy, and then, because the lights go out and the stove goes cold and the clocks stop when he leaves, he is taken in again by the butler through the back door, so that the meals can be ready on time.

It is not common for a practical physical problem to be dealt with from first principles in full detail and with full rigour by the pure methods of strict orthodoxy. Mostly, I think people think and talk and calculate real physical problems in the heretical way, but when pressed on certain occasions, they report this as if they were doing it orthodoxly, and most readers are not too fussed by this.

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.

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. (By way of correction of a previous remark of mine, Logunov seems to think that Hilbert is orthodox.)

Steven Weinberg at page 147 tells us that he is unfussed but in brackets he warns the reader that some others are not:
“ … the geometric interpretation of the theory of gravitation has dwindled to a mere analogy, which lingers in our heritage in terms like “metric” … … it simply doesn’t matter whether we ascribe these predictions to the physical effect of gravitational fields … or to a curvature of space and time. (The reader should be warned that these views are heterodox and would meet with objections from many general relativists.)”

Feynman is also unfussed, on page 113:
“It is one of the peculiar aspects of the theory of gravitation, that it has both a field interpretation and a geometrical interpretation.”

But Whitehead and Logunov are careful to argue that this should be fussed about: it is not a matter of two valid interpretations, but of one physically incapacitated or nonsensical and the other valid.

Perhaps I may unpack the nutshell a little.

In the Whitehead view, the speed constant that relates time and space for quasi-static geometry far from heavy things is the empirically apparently universally constant maximum speed of propagation of causal agency, and is the speed constant that appears in the Lorentz-Minkowski formulas. Experience tells us that far from heavy things, light travels very nearly that fast, but that is an empirical finding, not a definition. It is only since Shapiro that we have tried to directly measure the speed of light near a heavy thing, to compare it with the speed far from a heavy thing.

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.

According to the heresy, as I understand it, it makes sense to speak of the speed of propagation of gravitational causal agency. It has not proved easy to make empirical measurements of it (supposing it does have physical meaning). Far from a heavy thing, gravity is weak and hard to measure. Also we want to measure the speed of its propagation near heavy things, but there the climate can be uncomfortable. So far as I know, it is empirically an open question whether gravity travels perhaps at the speed of light, or perhaps at the (in principle not necessarily the same) universally constant maximum speed of propagation of causal agency, and whether it travels more slowly near heavy things.

I read Clifford Will, a redoubtable scholar, saying on the internet at http://physics.wustl.edu/cmw/SpeedofGravity.html
that the right way to measure the speed of gravity is by observations of gravity waves. Will there and also at http://arxiv.org/abs/astro-ph/0301145 comments on another proposed way to measure the speed of gravity. Will uses the post-Newtonian account for his analysis of the matter. I think the post-Newtonian account is a Whitehead way of doing things. Logunov also thinks that, like the speed of gravity, gravity waves have no meaning in the orthodoxy, but they have a meaning in the heretical view; Logunov thinks that Einstein adopts the heretical view when he talks about this, because, he says, of Einstein’s “formidable intuition” for physics. Caused by cyclical processes in far-off heavy things, gravity waves propagating to us have not yet been observed. We owe it largely to Will’s fine scholarship that we know and thoroughly understand that Whitehead’s illustrative model is empirically wrong.

Sincerely,

Christopher