Einstein vs. Newton:
•Newton: everything falls to Earth due to an
  instantaneous force of attraction.
• Empirical fact: everything falls to Earth at
   the same rate, independent of its composition
 
•Einstein: everything moves along the straightest
   possible line in the curved space-time around the
   Earth (gravitation is a “fictitious” force)
As stated above, Newton explained why objects fall towards the earth by postulating an instantaneous force of attraction between all objects. This works really well to a point, but it leaves at least unexplained one startling fact: all objects fall towards the earth at the same rate. This is a complete mystery in Newton's gravity theory. In order to explain this simple fact, Einstein had to completely overturn the Newtonian view of the Universe. In particular, Einstein taught us that that gravity (as an instantaneous force of attraction between two objects) is a myth. Morever, space is not merely an inert stage on which physical phenomena occur. Space is a dynamical entity: it has a shape and structure that is determined by the matter it contains. Objects fall towards the earth at the same rate because they are all trying to follow the (same) straightest possible trajectory in the curved space surrounding the Earth. (Actually, I should be talking not just about space, but space and time together, but it is easier to visualize the geometry of space, rather than spacetime .) A simple sheet, or membrane, like a stretched piece of spandex, can provide a very accurate two dimensional representation of how gravity works, as shown on the next transparency.