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PHYS195 NotesChapter10

PHYS195 NotesChapter10 - Chapter 10 The Sp ecial Theory of...

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Chapter 10 The Special Theory of Relativity 10.1 Pre-History of concepts about light 10.2 Pursuit of a special frame 10.3 Galilean Invariance Almost anyone who has sat quietly waiting to depart from a bus depot or a dock and has had the bus or boat gently start to leave has had the experience of feeling that it is the depot or dock that has moved away. This simple physiological phenomena has its basis in a very general physical law that was first articulated by Galileo and thus is called Galilean Invariance. It is one of the most striking and far reaching of all of the laws of physics. It is impossible to over emphasize its importance; it is the basis of our understanding of space-time and motion. The simplest statement of the law is that there is no experiment that can be performed that can measure a uniform velocity. Since we can only know what can be measured, we can never know how fast we are moving. There is no speedometer on the starship Enterprise. Stated this boldly, the idea is very counter to our experience. This is because what we generally observe as a velocity is not a velocity in space but is our velocity relative to the earth. Relative velocities are detectable. We note the amount of street that passes below our car or feel the flow of the air that moves over our face and infer a speed but we do not know how fast the earth is moving and thus do not know what our absolute velocity is. We 241
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242 CHAPTER 10. THE SPECIAL THEORY OF RELATIVITY do know that the earth moves around the sun and thus can determine our velocity relative to the sun. We know that the sun is moving in our galaxy and even that our galaxy is moving relative to other nearby galaxies and thus can know our velocity relative to the local cluster of galaxies. With the recent advances in astronomical detection, we are able to note our velocity relative to the place that we occupied in the early universe, our motion relative a background microwave radiation that is a detectable relic of the early universe, but again we cannot know whether that place had a velocity. The inability to detect velocity is one of the most mysterious and counter intuitive concepts that has ever been articulated. Consider a remote and empty part of the universe, no stars or galaxies nearby. Here there are no discernible forces and a released body moves in a straight line with a con- stant velocity. This is one of Newton’s Laws and was his way of articulating Galilean Invariance. Although when we start to work on General Relativity, we will have to revisit these issues, let us assume that this empty region is space. We envision this as that stable structure that Descartes and New- ton needed as a background against which motion took place. In this day and age, it is generally easy to convince someone that this space obeys the Copernican Principle; it is not centered on some special place like the earth.
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