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1 CHAPTER 15 SPECIAL RELATIVITY 15.1. Introduction Why a chapter on relativity in a book on “classical mechanics”? A first excuse might be that the phrase “classical mechanics” is used by different authors to mean different things. To some, it means “pre-relativity”; to others it means “pre-quantum mechanics”. For the purposes of this chapter, then, I mean the latter, so that special relativity may fairly be included in “classical” mechanics. A second excuse is that, apart from one brief foray into an electromagnetic problem, this chapter deals only with mechanical, kinematic and dynamical problems, and therefore deals with only a rather restricted part of relativity that can be dealt with conveniently in a single chapter of classical mechanics rather than in a separate book. This is in fact a quite substantial restriction, because electromagnetic theory plays a major role in special relativity. It was in fact difficulties with electromagnetic theory that led Einstein to the special theory of relativity. Indeed, Einstein’s theory of relativity was introduced to the world in a paper with the title Zur Elektrodynamik bewegter Körper ( On the Electrodynamics of Moving Bodies ), Annalen der Physik , 17 , 891 (1905). The phrase “special” relativity deals with the transformations between reference frames that are moving with respect to each other at constant relative velocities. Reference frames that are accelerating or rotating or moving in any manner other than at constant speed in a straight line are included as part of general relativity and are not considered in this chapter. 15.2. The Speed of Light The speed of light is, by definition, exactly 2.997 924 58 % 10 8 m s - 1 , and is the same relative to all observers. This seemingly simple sentence invites several comments. First: Note that I have used the word “speed”. Some writers use the word “velocity” as if it were merely a more impressive and scientific-sounding synonym for “speed”. I trust that all readers of these notes know the difference and will use the word “speed” when they mean “speed”, and the word “velocity” when they mean “velocity – surely not an unreasonable demand. To say that the “velocity” of light is the same for all observers means that the direction of travel of light is the same relative to all observers. This is doubtless not at all what a writer who uses the word “velocity” intends to convey – but it is the literal (and of course quite erroneous) meaning of the assertion. Second: How can we possibly define the speed of light to have a certain exact value? Surely the speed of light is what we find it to be, and we are not free to define its value. But in fact we are allowed to do this, and the explanation, briefly, is as follows.
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2 Over the course of history, the metre has been defined in several different ways. At one time it was a specified fraction of the circumference of Earth. Later, it was the distance between two scratches on a bar of platinum-iridium alloy held in Paris.
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This note was uploaded on 10/25/2010 for the course MECHANIC Mechanic taught by Professor Monfered during the Fall '10 term at MIT.

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