Question

You are watching a baseball game and the batter has just hit a high fly ball into the outfield. The outfielder gets into position and waits for the balls arrival and makes the catch. From the perspective of Einstein's General Theory of Relativity, why did the ball follow a curved path that was originally moving upwards and then back downward to the ground where the outfielder caught the ball?

Answer 1

Consider the diagram below, which shows the situation you describe in your question. The ball and the bullet both start off along the same path in space. However as we know, their paths quickly diverge -- the bullet will travel much farther before hitting the ground than the ball does.

SPACE Ball Bullet Space (eft / right)

This might not seem strange at first, but under Einstein's reconception of gravity, it's a major problem! Einstein was that there is no such thing as a "force" of gravity which pulls things to the Earth;

If this is true, then the ball and the bullet which start off on the same path should logically continue on the same path.

After all, if you imagine walking on a curved surface such as the Earth, if you start off walking in a straight line towards the east and your friend starts from the same location running in a straight line towards the east, you'll both follow the exact same path! It doesn't matter how fast you're going; you'll both (eventually) reach the same location. So why don't the ball and the bullet wind up in the same location too?

The only way to get around this problem in Einstein's theory is to say that it is not just "space" which is curved; rather, it is "space-time."

To understand this, it's helpful to look at the illustration below. This illustration shows the same ball and bullet as above, only now they are plotted on a diagram of space AND time together ("space-time").

SPACE-TIME ● Ball Bullet Space (left / right)

The above diagrams show that although the ball and the bullet start off along the same direction in space, they actually start off along different directions in space-time. So if we agree that space-time, and not space, is the proper arena in which to consider the question, then we can understand why the ball and the bullet don't wind up in the same place at the end of their trip.
Just like it's not surprising that if you start off walking east and your friend starts off walking northeast, you will end up in different places, it also isn't surprising that the ball and the bullet end up in different places, since they started off in different directions!

This is completely consistent with Einstein's theory -- the path that an object takes through space-time doesn't depend on the mass of the object or on the material it is made of; it only depends on the initial direction that the object in which the start to move.

In some sense, therefore, what Einstein's theory tells us is that we really need to consider space-time, rather than space, as the fundamental "playing field" upon which the events of the universe occur. It is a profound realization to understand this fact -- all the objects around us actually exist in a realm of "space-time" that is much more complex than the simple realm of space in which we perceive them.