I think the missing piece in your puzzle is adding the "time" to space-time. A particle moving through time is "falling" in the time dimension. The curvature of

I think the missing piece in your puzzle is adding the "time" to space-time. A particle moving through time is "falling" in the time dimension. The curvature of the 4d space makes this movement through time also move through space due to the warping effect of a gravity well.