Frank Morgan

Actor Alan Alda appears with mathematician Bob Osserman in a video of a Berkeley Repertory Theatre conversation sponsored by the Mathematical Sciences Research Institute. It is a wonderful conversation between two very intelligent and curious individuals. Here I want to comment on Alda’s implicit, unanswered question:

          What is meant by curvature in space-time?In space alone, e.g. in the Euclidean plane, a path is straight if it has constant slope, never getting more or less steep. In space-time, a path is straight if it has constant velocity, i.e., if it never changes slope or speed. Galileo observed that in free space, objects move in straight lines at constant speed, i.e., move in straight lines in space-time. They do not “curve” in space-time by speeding up or slowing down or changing direction. Gravity, however, causes a ball thrown in the air to deviate from such straight lines and continually change speed and direction. In this sense, gravity causes objects to curve in space-time, to change speed as well as direction.

Of course as Osserman explains, Einstein’s Theory of General Relativity (see also my books on applied real analysis and Riemannian geometry) is fundamentally deeper than this, but this is something I wished I could have told Alda first.