How does curved spacetime result in an effective gravitational force?

[Pete62]

[/QUOTE] From A.T. Nothing is stationary or at rest in spacetime. Everything moves trough space or time or both.[/QUOTE]

Getting your head around the time part of space-time was the biggest hurdle for me. Remember, the only way to not be moving in time (not including black hole event horizons) is to be moving at the speed of light.

 

[meteor9]

exactly Pete62 , not only at the speed of light but also at the 'speed' of 'stationary dimension' . By this i mean that if we consider the 'parallel worlds' which have been mentioned so many times in 'quantum physics' , we even would not need any 'speed' , you can 'move' or 'enter' easily to lot of other 'worlds, and why not to 'other' planets or galaxies , without spending energy to produce 'speed' . In my opinion the theory of einstein about the 'curved ' space-time , has stopped all sort of 'different considereations' of space-time concept and has made the physics to remain at a stagnation point. Since then we don't search elswhere to find some other sort of explanations of the 'physics' , 'quantum physics or rather the 'metaphysics' and why not the 'metarealism'

 

[altonhare]

I think the original question has been answered but I thought I'd add my own analogy in case it helps the poster more.

The geometric aspect of acceleration/force in GR is explained more or less by our inability to "see" the "temporal dimension". By this I mean the object may appear to be taking a linear path to us only because we cannot see its path "in time".

As always, let's consider Flatland. There's two stick figure Flatlanders here. There is a big depression in Flatland and one of the sticks is down in the depression, moving out. The other stick is in a flat region watching the other stick coming toward him. These Flatlanders cannot perceive nor conceive of the "up" direction, however the stick at the bottom of the depression is doing most of his motion "upward". The observing stick, then, sees the traveler moving very slowly at first, then faster and faster as the traveler moves out of the depression. The up component of the traveler's velocity is decreasing as its rightward velocity component is increasing. The whole time the magnitude of the traveler's velocity was actually constant, but it appeared to change to the observer because s/he could not see the decreasing velocity in the "up" direction, but only the increasing velocity in the "rightward" direction.

Does that make sense?