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GENERAL THEORY OF RELATIVITY GTR is an extension of STR. While STR has to do with the identity of laws in different inertial reference frames, GTR is concerned with the relations that hold between laws expressed in any reference frames, inertial or not, even accelerated (i.e., curvilinear). The motivation for this is the belief that physics should not depend upon the point of view of an observer. The laws of physics should not depend upon the state of motion of any observer. Start with the universal character of gravity. When you think about it, gravity is very odd. When you apply any other force to an object, the effect is dependent upon the inertial mass of the object. If you run a proton and an electron through a magnetic field, their behavior (ignoring their different charges and hence the different directions in which they are deflected) is quite different. The electron “feels” the force field much more strongly, in that it is affected much more radically. If you use a magnet to move two iron balls of different masses, the lighter will be moved faster than the heavier. In a gravitational field, on the other hand, all bodies are affected in exactly the same way. All bodies fall with the same velocity. Noticing this, Einstein formulated his Principle of Equivalence, which states that a body free falling in a gravitational field is indistinguishable from a body experiencing inertial motion. Conversely, a body accelerating uniformly outside a gravitational field is indistinguishable from a body at rest in a gravitational field. This is illustrated by the famous elevator gedanken experiment. Consider the following diagrams. The left hand picture illustrates the equivalence of acceleration and gravitation. In the right hand picture, we see what happens to a light ray shining through an accelerating elevator. It curves. But, the accelerating elevator is indistinguishable from the elevator at rest in a gravitational field, so, by the PII, the light ray should curve in a gravitational field, an effect that was verified in 1919. (Actually, Einstein predicted this behavior of light some years before the full GTR was developed.
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This note was uploaded on 02/14/2011 for the course PHIL 124c taught by Professor Humphrey during the Spring '11 term at UCSB.

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