There was a previous question titled "Why would spacetime curvature cause gravity?" asked March 10, 2014.
The answer given was essentially that since the time component of an object in curved space slows that automatically has to generate a motion in space so the total spacetime velocity is still c.
So far so good but there seems to be a problem. Suppose another object is sitting on the surface of the earth. Its clock is also slowed due to curved space but there is NO motion in space.
So how can the object still have a total spacetime velocity of c if its coordinate time is slowed but it is not moving in space?
It doesn’t seem like the answer to the original question works if the slowing of coordinate time has to produce motion in space because there isn’t any motion in space in this case but there is still slowing of coordinate time. Is this correct?
In light of this how does curved spacetime cause motion? Is there some other explanation that works or am I missing something?