Thanks Tashja, I was hoping you would do that.
Using a geometrical theory about the manifold of space and time means you don't have to invoke a force or fictional force to find the path (geodesic )of a particle. I was wondering, would a force have to be invoked to explain a path in what Prof: G. Lewis is saying about 'matter tells matter how to move'.
It depends on what you mean by explain!
The reason I reposted that portion of Prof. Lewis' comment, in the post above, is because it speaks directly about the issue. GR is not a theory of fundamental
cause and
effect. It is a descriptive field theory that describes only the effect. It does not say anything about the why or how, matter tells space-time or other matter how to move, it only describes the result. I have had a long standing disagreement with Brucep on this point, where I have referred to his interpretation as a modern interpretation. A view that does think of space-time as a thing.
I am not sure I agree entirely with Prof. Lewis as he describes space-time in that last sentence, though I agree completely with what I understand of its intent. It is not clear to me, whether space-time is a thing, as in has some quasi-independent substance, or just a mathematical representation of a gravitational field. However in either case, anytime the path through space over time of matter, meaning a massive object, be it a particle, a rock or a planet, changes.., some force must be involved. It is just that in the case where changes in motion or path, through a gravitational field are involved, through we can describe the path and changes, we have no clear understanding of the fundamental mechanism(s)/force(s). Newton just labeled it/them action at a distance. Einstein, at least in the beginning seemed more interested in describing the dynamics, than in attempting to isolate the fundamental origin, and gave us GR.
As you may have noticed in the above, I am stuck somewhere between the idea that space-time is just a mathematical field theory, describing the dynamics.., and that it, space-time does have some undefined pseudo-independent substance of its own. But before this question has any place in the discussion it is important to understand exactly what is meant by the idea of warp speed.
I have not read the Alcubierre drive paper recently, or even Prof. Lewis' paper referenced earlier, so I cannot answer that question in the context of the OP.
I will say this much, again.., it is my belief that any time there is a relative change in the path of a massive object - a change in direction or speed - there is some force involved. Where gravitation is concerned the dynamics is described by GR and a space-time model, without needing to identify the fundamental force... That does not mean there is no fundamental force, just that it is not needed to describe the dynamics, of the field.