General Relativity The General Theory of Relativity is even more subtle and even farther beyond the scope of this course. Nevertheless, some of the basic ideas can be described. First note that SPECIAL RELATIVITY effects show up for fast moving objects which are in relative motion but where the relative motion has CONSTANT VELOCITY. GENERAL RELATIVITY INCORPORATES FAST MOTIONS AND ACCELERATION.

General Relativity: the Principle of Equivalence Einstein first noted that freely falling in a gravitational field results in a constant acceleration (velocity changes but at a constant rate). He then realized that it is impossible for an observer to distinguish between freely falling in a gravitational field, and some other mechanism of uniform acceleration such as a rocket. This is the PRINCIPLE OF EQUIVALENCE Einstein was then led to consider that since acceleration describes how objects move through space and time, and free fall in gravity and any uniform acceleration were indistinguishable, that gravity's effect on objects may actually be describable by it direct influence on space itself. This turned out to be a profound insight.

A physical picture of what is going on is something like the following: Consider a very large trampoline with nothing on the trampoline pad. The trampoline pad remains flat and parallel to the ground. Now place a heavy bowling ball at the center of the trampoline pad. The center of the pad will sag downward. If we assume the analogy that the trampoline pad represents space-time, and the bowling ball a gravitating object, then the sagging of the trampoline represents the curvature of space time under the influence of gravity. We can now see that if we take a lighter ball, and place it at the edge of the trampoline bad, it will roll down toward the bowling ball. This attraction to the bowling ball is because the path toward the bowling ball through space is favorably curved. In general relativity, however, it is not only balls that would follow that curved path but light as well.

Consequences of the Principle of Equivalence Said another way, as light passes a massive object, the path of light is actually bent by a gravitational field. This effect is even measurable during a solar eclipse. Stars whose locations we know to be behind the position of the sun are actually observable during a solar eclipse because the light is bent around on a curved path! Here, I summarize the differences between Newton's theory of gravitation and the theory of gravitation implied by the General Theory of Relativity. They make essentially identical predictions as long as the strength of the gravitational field is weak, which is our usual experience. However, there are crucial predictions where the two theories diverge, and thus can be tested with careful experiments.