Gravity and the principle of equivalence
Now we are ready to discuss the laws of gravitation. Einstein was trying to generate a theory of gravitation that would fit with the relativity theory that he had developed earlier. He was struggling along until he latched onto one important principle which guided him into getting the correct laws. That principle is based on the idea that when a thing is falling freely everything inside it seems weightless. For example, a satellite in orbit is falling freely in the earth’s gravity, and an astronaut in it feels weightless. This idea, when stated with greater precision, is called Einstein’s principle of equivalence. It depends on the fact that all objects fall with exactly the same acceleration no matter what their mass, or what they are made of. If we have a spaceship that is “coasting”—so it’s in a free fall—and there is a man inside, then the laws governing the fall of the man and the ship are the same. So if he puts himself in the middle of the ship he will stay there. He doesn’t fall with respect to the ship. That’s what we mean when we say he is “weightless.” Now suppose you are in a rocket ship which is accelerating. Accelerating with respect to what? Let’s just say that its engines are on and generating a thrust so that it is not coasting in a free fall. Also imagine that you are way out in empty space so that there are practically no gravitational forces on the ship. If the ship is accelerating with “$1$ g” you will be able to stand on the “floor” and will feel your normal weight. Also if you let go of a ball, it will “fall” toward the floor. Why? Because the ship is accelerating “upward,” but the ball has no forces on it, so it will not accelerate; it will get left behind. Inside the ship the ball will appear to have a downward acceleration of “$1$ g.” Now let’s compare that with the situation in a spaceship sitting at rest on the surface of the earth. Everything is the same! You would be pressed toward the floor, a ball would fall with an acceleration of $1$ g, and so on. In fact, how could you tell inside a space ship whether you are sitting on the earth or are accelerating in free space? According to Einstein’s equivalence principle there is no way to tell if you only make measurements of what happens to things inside! To be strictly correct, that is true only for one point inside the ship. The gravitational field of the earth is not precisely uniform, so a freely falling ball has a slightly different acceleration at different places—the direction changes and the magnitude changes. But if we imagine a strictly uniform gravitational field, it is completely imitated in every respect by a system with a constant acceleration. That is the basis of the principle of equivalence.