Warped Spacetime Rubber Sheet Gimmick in General Relativity
(Adapted from the cover of Spacetime and Geometry by Sean M. Carroll)
According to GR gravity is due to the warpage of spacetime. In this context we often find images like that shown above. The accompanying explanations state or imply that light or test objects in the vicinity of the dimple are constrained to follow geodesics on the surface.
What's missing is an explanation as to why anything moves at all!
Due to an Earthian viewer's built-in prejudices, he or she may unwittingly think the illustration makes sense. Round objects (for example) placed on inclined surfaces do always roll downwards.
The kicker is that this illustration has the same meaning whether its drawn "sideways" or "upside down" in the middle of outer space. It represents a cross-section of a geometrical construct (Schwarzschild field) that is supposed to be utterly static. Therefore, no matter how the surface is oriented, if we place an object on the "incline" there is no reason (short of a miracle) to expect it to move.
Rejecting the miraculous, to get the massive object to make the dimple in the sheet or to get anything to move in this picture we have two possibilities: 1) We slip in another gravitational field whose "downward" direction is defined by the dimple, or 2) We accelerate the whole sheet upwardly (perpendicular to the concavity).
Our conscience and our intellect prevent us from cheating in this manner, however. So we surmise that something huge is missing. A possible clue (to which we will return) is contained in the second possibility above: We can mimmick the effect of gravity by acceleration. The idea that static spacetime curvature causes motion leaves much to be desired. But perhaps the inverse of this logic holds more promise. Perhaps motion causes spacetime curvature; perhaps a "gravitational field" is a state of perpetual motion.