Sweetpea, the following is an attempt to explain how I have come to interpret the issue.., and I have been on both sides of the debate, in the past and may yet change my view point, in the future... But as long as we discuss theory the way we do, there must be room to question and present different approaches and interpretations, for there to be any chance that we will ever be able to improve on what we know and understand of what is real.
How have I taken this out of context...There you say" in either case", you are referring to both models and saying a 'force' is at play in each.
Just because it is not known why mass and energy affect space-time has not stopped the development of a geometrical space-time manifold model. On that altered space-time manifold model-- find the path of maximum aging for the rock and you will have its worldline on that manifold. No force needed ,If that sounds like magic then your forgetting this is a model.
On the Newtoinan force picture...explain the mechanism that acts at a distance which results in two bodies coming together (attraction), you can can describe the motions ( by using a convenient force) but not the why. Again sounds like magic.
The above quote shows you want to add a convenient magic 'force' model to the geometrical space-time manifold model without even knowing how that 'force' works. And yet that geometrical model doesn't need a force to describe a rock's worldline in an altered space-time. Their both models.
I believe the problem here centers on how one interprets GR as a field theory and whether that tends toward curvature being a cause of how matter moves or just a description of how matter moves.
A Wheeler quote that pops up a lot, especially in lay oriented discussions is,
John Wheeler said:
Spacetime tells matter how to move, matter tells spacetime how to curve.
One can assume that the above statement suggests that spacetime actually tells matter how to move, because that is a literal interpretation of that last bit... And that kind of interpretation is what I have been referring to as a modern interpretation... But that interpretation also, leads to the idea that spacetime itself has some kind of substance that allows or results in matter and spacetime interactions. (A further comment about this later on.)
Or, as suggested in the following quote from Prof. Lewis, originally quoted in tashja's post #55 and reposted in my post #56 for emphasis,
Prof. Lewis said:
The concept of space-time is not banished – you just have to realise what it is – the mathematical medium that tells you how mass and energy influences mass and energy. Relativity tells you how to connect events with particles and photons, and this depends upon the mass and energy distribution around it.
The mistake people make is to treat space-time as a thing and then make suppositions of what happens in relativity based on this.
... we can accept spacetime as a mathematical model that describes,"
how mass and energy influences mass and energy."... without spacetime being the cause of that interaction.
The fundamental cause or origin then becomes a problem for a theory of quantum gravity, where force remains an important mechanism of change...
I believe one of your issues with my comments has been the idea of gravitation being the result of some fundamental force and the impression that, that would not be consistent with a field theory. I don't believe that is necessisarily true.., that there is a conflict between the concepts of force and field.., especially if one begins to consider that gravitation may emerge from quantum field interactions, perhaps including a graviton as a force carrier. In that case the GR field description would be a macroscopic field description, of an exchange or transfer of momentum, that begins or originates somewhere in quantum theory... (And no we are not there yet!)
If I were to restate Wheeler's catch phrase, which I believe has taken on a life greater than its original intent,
I would say, "Matter tells spacetime how to curve, and spacetime describes how matter moves."
Even still I like the way Prof. Lewis put it better, and I believe his last sentence in the quote above,
"The mistake people make is to treat space-time as a thing and then make suppositions of what happens in relativity based on this."
.., is a telling commentary on how the Wheeler quote is often misunderstood, or perhaps just misapplied.
--------
One of my earlier comments above,
"But that interpretation also, leads to the idea that spacetime itself has some kind of substance that allows or results in matter and spacetime interactions.
Touches on an issue from earlier in the thread, where I said, in different words, that I was on the fence about spacetime having some kind of intrinsically substance or being just a geometric description. Where that comes from, is the concept that matter interacts with the quantum vacuum. Whether you think of the vacuum as filled with virtual particles (or virtual quantum fields), or just a broad spectrum of EM radiation, it is not unreasonable to consider that any interaction involves influences that go both ways. Which at least implies that matter is affected by the vacuum and the vacuum is affected by matter. The question then is, is the vacuum part of what we refer to as spacetime? And if so does spacetime then have some independent substance, even if that is thought of as a virtual substance?
I don't know the answer, but I am open minded enough on the issue(s), to be on the fence.
This could keep on going deeper into opinion and speculation, but this has already been a long post. I don't like long posts, and I am not sure much of where it would lead, is even appropriate for this thread.
