The equivalence suggested to Einstein that the path an object follows is a property of space itself, rather than having anything to do with the specific properties of the object.
We know that in the absence of any forces, objects follow straight lines, and
we also know that straight lines are the shortest possible paths……
Perhaps gravity is a manifestation of objects in free fall following the shortest
possible paths, known as geodesics, in curved spacetimes
It is difficult to visualize curved spacetimes, but the surface of a sphere is a simple curved space. Geodesics are great circles that pass through both poles. We see that they can pull apart and then meet up again….
COSMOS to HUMANITY, Spring 2008
Lecture 2 , slide 4