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Unformatted text preview: Chapter 15 Introduction to General Relativity 15.1 The Problem After 1905 and the success of the Special Theory of Relativity, Einstein turned his attention to the problem of making the other known fundamental force of his time, gravitation, consistent with Special Theory of Relativity. Remember that the electromagnetic theory of Maxwell was consistent with the Special Theory from the start. The other force systems that we now know about such as the strong or nuclear force and weak force had not yet been identified. At this time, gravitation was still described by the action at a distance formulation identified with Newton, see Section 4.1. This theory was intrinsically inconsistent with speed of light restrictions on the propa- gation of energy and momentum. In Newtonian Gravity, the acceleration of the moon due to the presence of the earth as a moon =- G N M earth r r , where r is the separation vector between the moon and the earth. If, for some reason, the mass of the earth would change, the acceleration of the moon is instantly changed to accommodate the new mass. The moon instantly changes its orbit to a new one to accommodate the change. In essence, there is momentum and energy transferred to the moon. This implies that the information about the earth’s mass in the form of energy an momentum is propagated to the moon faster than the speed of light. This violates the basic premises of the Special Theory. The theory that he developed was rather long in gestation. It was not until 1916 –1917 that he was finally able to articulate the basic principles of what is now called the General Theory of Relativity. This name is both a 337 338 CHAPTER 15. INTRODUCTION TO GENERAL RELATIVITY misnomer and yet an insightful appellation. It was a modern theory of the effects of gravitation and thus should be called by that name – The Modern Theory of Gravity. But it was only after he took the fullest advantage of the underlying concepts of relativity that he was able to find the correct formulation of the theory and, in fact, it was through a generalization of the principles of relativity that he was able to develop the theory. We will follow this thread of development. The problem is that it is rather abstract and there is some tendency to lose track of the fact that it is a theory of gravity. On the other hand, it has the advantage of making it clear that a modern theory of gravitation is, in fact, a theory of the structure of space-time. 15.2 Free Fall Observers and the Equivalence Prin- ciple In Section 10.3, we discussed the physical implications of Galilean invariance. One of the ways of describing the meaning of this invariance was that you were always at rest in your own rest frame. In other words, there was an infinite set of related observers all of whom thought that they were at rest....
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