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Unformatted text preview: Chapter 11 Kinematics of special relativity 11.1 Special Relativity 11.1.1 Principles of Relativity Einstein postulated that there was still Galilean invariance, i. e. all uni formly moving observers had the same laws of physics; there was still no way to determine a velocity. The thing that they also agreed upon included Maxwell’s equations and thus the speed of light. The problem then becomes one of defining lengths and times so that this can be done. From Section ?? , we realize that, instead of an arbitrary distance between scratches on a bar being the standard, distance can be defined from a velocity and a time. Thus, if we have a time such as the period of light from a particular atom, we can define lengths from the speed of light. If Maxwell’s Equations are to be valid in all frames the speed of light , c, must be a universal constant. We will examine this concept later. We can use this so that we no longer have a fundamental unit of length. Lengths follow from this velocity and a standard to time. In other words, we use a time and c as our fundamental units and c is defined in such a way that we recover the usual meter. This change in the definition of length manifests itself in a good table of physical values by having the speed of light given as c = 2 . 99792458 × 10 8 m sec (exact) . (11.1) In other words, we can pick the value for c since it is the standard. It is chosen so that the distance that we called the meter is what it was before. 255 256 CHAPTER 11. KINEMATICS OF SPECIAL RELATIVITY Said another way, the meter is the length of the path traveled by light in vacuum during the time interval of 1 299 , 792 , 458 of a second. Digression on Dimensions In olden times, the basic measured quantities were a mass, a length and a time. The standards were arbitrary and chosen for convenience. We then chose to use standards that were stable, accessible, and easy to use: the kilogram, the meter, and the second. We realized though in Section ?? that we could use any set of algebraically independent combination of the three fundamental dimensional entities such as an energy, velocity, and a momentum. Then, you may ask, what could be more accessible and stable than the fundamental dimensional constants? The problem is to chose. There are lots of constants in physics that have dimension and could be called fundamental. One obvious example is the mass of an elementary particle like the electron. In some sense that is what was done when we chose the mass of the nucleus of carbon 12. Modern physicists would not choose this as a standard because we feel that we will calculate it in some future Theory of Everything. In fact, the hope is that the future theory will contain only the constants c , the speed of light, ~ , Planck’s constant divided by 2 π , and G , Newton’s constant in the gravitational force. These form an independent set that contain a length, mass, and a time. As indicated above, we already use c . With the increase in the precision with which we....
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 Spring '07
 Anderson
 Physics, Special Relativity, Harry, Sally

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