Here, one important point to keep in mind is that I discuss particle physics. This means that our problem lies in the context of the elementary particles and their interactions. Gravitational effects are here tiny, as they are proportional to the masses involved. Elementary particle masses are indeed so small that anything related to gravity is negligible compared to the effects associated with any of the other three fundamental interactions. This obviously change at super high energies, much higher than anything we can conceive as humans (we are talking about a factor of 1015 more or less).
In addition, we do not know how to include gravity in the Standard Model, and this lies at the heart of many on-going researches today. But for anything that concerns us, this problem is a non problem (as whatever is the way gravity will be incorporated to the Standard Model, it will have a non-measurable effect on any observable).
Dropping a stone into a pond results in pressure on the water to move to accept the volume displaced by the stone, and similarly mass affecting spacetime produces warping as a result, and neither volume nor gravity are forces per se, although producing affects involving forces.
As a side note, we cannot really discuss "volumes", because this does not involve time. Gravitational effects of massive bodies act on all four dimensions of space time, according to general relativity.
Gravity is a force in the context of mechanics. On the other hand, general relativity tells us that this force is not an ordinary force.
At the end of the day, what matters is the context. For slowly moving and not too heavy objects, Newtonian mechanics is a very good approximation, with its context of forces, acceleration, etc. Otherwise, we need to rely on relativity in which what we interpret as a force is the curvature of spacetime. This seems to agree with what you wrote, if I got it correctly.
Since gravity affects spacetime, which is neither space nor time, I understand it's affects to extend across the full breadth of that medium, and it seems to me that dark matter is proposed to account for the affects of matter at other times that is not apparent presently in the visible space.
This does not accord with the standard model as I understand it, and I am incompetent to even contemplate treating this understanding mathematically. Frankly I can count past twenty if I am without pants, so am curious if my understanding has any basis in such facts as you believe demonstrable, or if it is contradicted.
I don't understand the above paragraph. Why do you say that there is no dark matter in space today? If we assume that the standard model of cosmology is valid, with dark matter in it, then we can explain varied cosmological observations (galaxy rotation curves, the cosmic microwave background, structure formation, etc., to quote a few of them). Do you therefore mind clarifying your comment? Thanks in advance!
Cheers, and thanks again for passing by!