….
There is another issue that just occurred to me that makes Wheeler's statement
Spacetime tells matter how to move; matter tells spacetime how to curve
particularly true, now that we know for a fact (from cosmological measurements) that the expansion of the universe is accelerating and that the cosmological constant is real (and so is dark energy).
Referring again to the General Relativity's field equation:

A spacetime completely free of any matter sources (Tμν=0) with a positive cosmological constant Λ>0 must always be curved , because for Tμν=0, the Ricci tensor Rμν will not vanish.
For Tμν=0, we have
Rμν - ½ R g μν = - Λ g μν
In essence, you can think of the cosmological constant Λ as a source of energy, by bringing this Λ term to the right hand side. That is one of the reasons is it called dark energy, it curves space.
Thus Wheeler was right once again, considering dark energy, spacetime tells matter how to move: it tells matter to move as spacetime accelerates its expansion and carries matter with it.
General Relativity is not just a geometric description of gravity: spacetime itself has energy (both dark energy and is capable of having gravitational waves carrying energy). That is why Wheeler, Kip Thorne and others refer to General Relativity as "Geometrodynamics". Spacetime without matter in General Relativity is not empty (it has gravitational waves and dark energy). Spacetime tells matter how to move [due to dark energy and due to gravitational waves]; and matter tells spacetime how to curve as well (gravitation due to matter).
Dr. Rodal,
The following portions of your above comment concern me, in that they represent assertions of certainty or fact, based on inherently theoretical conclusions and/or interpretations. And please accept that I am not challenging here whether these conclusions and/or interpretations represent reality, just that they should not be represented as having attained the status of facts.
“… now that we know
for a fact (from cosmological measurements) …”
“… A spacetime completely
free of any matter sources … must always be curved , …”
First, and without comment on validity of those conclusions and interpretations.., as I am sure your know, virtually all of cosmology is, or at least at present is, inherently theoretical and relies heavily on the interpretation and projection of locally defined understanding of gravitation and the propagation of light, both of which occur within an essentially flat Spacetime, to the larger context of galaxies and the universe which can only be thought of and evaluated within the variable time and spacial scales, of GR and its associated 4D Spacetime metric. What we believe to be true, even if it is true should not be referred to as having attained the status of fact, until it has been directly observe to be fact.
In the second, instance noted above, when you reference, “A spacetime completely
free of any matter sources…” you stear the discussion into an area that is inherently beyond our ability to ever test and confirm the theoretical assertion and perhaps, since it is understood that a gravitational field, propagating at the speed of light, extends at least to the light horizon beyond the location of any massive object, there is and can be no space within our observable universe completely free of any matter source. The argument is based on a theoretical extension of a portion of the involved math, to a hypothetical space or Spacetime, which cannot exist within the observable universe. Again though exploring the implications this portion of your comments can and almost certainly has value, in our attempts to understand the physical reality of the universe around us, it should not be thought of even approaching the status of a fact, or that it provides a basis to assert that this interpretation of General Relativity's field equation, represents reality.., as a matter of fact.
Setting my above interpretation (comments about what may or may not be fact) aside and attempting to return to my original intent…
In your later or following comments (quoted above), you seem to equate the existence of dark energy and gravitational waves with evidence that Spacetime exists as a causative component of gravitation. In response I would assert that whether we are talking about the presence of, matter, dark energy, gravitational waves or even the quantum vacuum or vacuum energy, a ZPF etc., we are talking about things that exist or may exist in space over time, and whose dynamic interaction can be or is described by the Spacetime model. It is the distribution of matter and energy that are at least a causative component of gravitation, not the Spacetime model that describes that distribution.
Step back for a moment and imagine a room containing a clock which can be seen from anywhere in the room. The clock represents an indication of the progression of time and the length, width and height of the room establish a 4D special frame of reference. Since the room is small relative to the speed of light both with respect to time and the 4 spatial dimensions the room can be treated as defining a flat Minkowski spacetime. It is unlikely that anyone would assert that by describing the location or motion of any object inside the room as being the result of the time and spatial measurements. In effect when one asserts that Spacetime, within the context of GR, is the cause of the location of or how an object moves, they are asserting that just because the time and spatial dimensions involved are variable, endows that Spacetime with causative attributes.
My assertion has been and remains that, it is the effect of the distribution of matter and energy that affects how an object will move through a gravitational field and what the location specific potential of the gravitational field may be… And that GR and Spacetime are descriptive of just how the distribution of matter and energy affect both the location specific potential and the motion over time, of matter and perhaps even energy, due to a gravitational field. In a lay context the words, "Spacetime tells matter how to move..." seems to suggest that Spacetime itself has some physical or sudo-physical property that allows it to directly affect the path of an object through a gravitational field, it is the distribution of matter and energy, rather than a description of its distribution that affects the path of an object through a gravitational field.
I believe that when WarpTech says,
….
... The very notion that spacetime is more than a mathematical convenience, seems to me to be absurd.
….
he goes a little to far, only in his assertion that Spacetime is reduced to a
mathematical convenience. I do agree that both GR and spacetime are descriptive rather than causative, but more than just convenient, they have proven to be both descriptive and predictive, useful and powerful tools.
I don't believe that most of this discussion would be important if the discussion were not open to the lay public. Though theoretical physicists of differing views may use these terms and arguments without detailed clarifications, they generally understand the differing definitions and interpretations of one another, at least to a greater extent than the lay reader. Where the discussion is being held in a open forum some greater clarity of the difference between what has been proven and what remains a matter of interpretation is more important.
You are correct when you list physicists who share the interpretation you have presented. It is not a perspective I have not shared in the past. What I would say today is that, that perspective/interpretation is one that is generally made while interpreting the world through rose colored glasses, in that the interpretations and conclusions seem limited to evaluation within the context of a modern interpretation of GR, and without care as too lay interpretations.
One further point, it seems to me that if one accepts GR and Spacetime as descriptive rather than causative it does nothing to undermine the success of GR and Spacetime. What it might do is open the way to the possibility of, if not a unification of GR and quantum mechanics, at lest the inclusion of mechanisms originating within some part of quantum mechanics, as functional components of an underlying mechanism, resulting in what we experience as gravitation. IOW as a desiptive model Spacetime could incorporate mechanisms originating as quantum phenomena, as sources of the energy component of the field equations. The equations of the quantum mechanisms do not have to lead to or even be consistent with the field equation of General Relativity, as long as the energy associated with the quantum mechanism can be incorporated.