General relativity was founded on the belief that we live in a four dimensional universe known as space-time. In the past, scientists had always treated space (the three dimensions of height, width, and depth) and time as two separate things, yet Einstein taught that they were, in fact, very closely related and could be treated as one entity. Scientists had also believed that space was a flat, rigid structure that was not affected by the objects that moved through it. It was simply there. But Einstein said that his space-time could be bent or curved, so to speak, and that these curves were created by the matter that it contained.
But what did Einstein mean by curved space? For that matter, what is flat space and why is it important? To make this easier to visualize, lets work in a more two-dimensional universe. To start with, picture a hard, smooth, wooden table top. The surface of this table top represents our two-dimensional space. If you roll a small metal ball across the table top it will travel in a straight line, from one end to the other, at a constant speed. Now place a large metal ball on the center of the table. Because the wooden table top is rigid, the large ball will not change its shape. The surface of the table is still a perfectly flat two-dimensoinal space. If you roll a small ball across it, the ball will still travel in a straight line (provided that it doesn’t collide with the large ball).Now, lets take away the wooden table top and replace it with a sheet of some sturdy yet elastic material that is attached securely to the edges of the wooden table frame. At first, the surface of this sheet would also seem to represent an area of flat space. But if we again take the large metal ball and place it in the center of the elastic sheet, it will create a noticeable depression in the area of the sheet surrounding the ball. The surface of the sheet will no longer be flat. It represents a two-dimensional curved space. Now take the small metal ball again. Roll it across the surface of the sheet, but not directly towards the large ball. Instead, roll it so that it will pass near the other ball, within the surface curve. (For this experiment, pretend that the elastic sheet has no friction so that the small ball will not lose any speed just by rolling across it.)
When the small ball reaches the curve in the sheet which is created by the presence of the large ball, it can no longer continue to travel in a straight line. It will begin to follow what is known as a geodesic, the straightest possible path in a curved space. Its path will begin to bend in the direction of the large ball.
If the ball is traveling fast enough, or if the curve is shallow enough, the bending will not be great and the ball will leave the curved space and continue to the edge of the table. But, if the curve is too steep or the ball too slow, the path of the ball will bend so much that it will curve towards the center of the depression and collide with the large ball. However, if conditions are exactly right, the small ball, upon entering the curve will have its path bent just so much that it will circle around and around the large ball forever in a kind of dance that looks suspiciously like the orbit of a planet around the Sun!
If someone watching this experiment was, for some reason, not able to see the depression in the surface of the elastic sheet, it might seem to them that the small ball’s path was being bent by some invisible attractive force coming from the large ball when in fact it was simply following the straightest possible path in a curved space. According to the theory of relativity, this is very similar to what happens to objects traveling through curved space-time.
In short, Einstein’s theory of gravity tells us that all objects create curves in space-time and in turn, these curves determine how objects travel through space-time. Like the large ball in our experiment, the Sun creates a great depression in space-time and, like the small ball, the planets follow the curve of this depression as they orbit around the Sun. There is no invisible bond that exists directly between the Sun and the planets. It is all a matter of how objects shape space and move within it. And that, according to Einstein, is what gravity really is: an object’s ability to bend the space that it travels in.
For more on Albert Einstein and the history of general relativity see History Page 7.
