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Special Relativity
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We can give a quick heuristic insight as to why this result leads to the paradoxes of relativity. What is speed anyway (our argument here is qualitative, so we are going to be a bit sloppy here) It is distance covered per unit time: v= x t
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The commonsense viewpoint, which is formalized mathematically in prerelativistic Newtonian physics, is that distances and times are xed thus, how could you possibly have a constant velocity that is the same for all observers That wouldn t make any sense. However, the theoretical result that the speed of light in vacuum is the same for all observers is an experimental fact con rmed many times over. If v is the constant speed of light seen by all observers regardless of their state of motion c= x t
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then distances and time intervals must be different for different observers. We will explore this in detail below. In many treatments of special relativity, you will see a detailed discussion of the Michelson-Morley experiment. In a nutshell, the idea was that waves need a medium to travel through, so physicists at the time made the completely reasonable assumption that there was a medium that lled all of space, called the luminiferous ether. It was thought that the ether provided the medium necessary for the propagation of electromagnetic waves. The Michelson-Morley experiment was designed to detect the motion of the earth with respect to the ether but it found nothing. This is one of the most famous null results in the history of experimental physics. This experiment is a crucial result in the history of physics, but the record seems to indicate that Einstein based his derivations on an acceptance of Maxwell s equations and what they tell us more so than on the MichelsonMorley experiment (in fact Einstein may not have even known very much, if anything, about the experiment at the time of his derivations). As a result, while the experiment is interesting and very important, we are going to skip it and move on to the theoretical framework of special relativity. Interestingly, other researchers, Lorentz, Fitzgerald, and Poincare, independently derived the Lorentz transformations in order to explain the null results of the Michelson-Morley experiment. The gist of these equations is that clocks slow down and the lengths of rigid bodies contract, making it impossible to construct an experimental apparatus of any kind to detect motion with respect to the ether.
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Special Relativity
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In addition to the arguments we have described here, Einstein used results that came out of Faraday s law and the studies of electromagnetic induction to come up with ideas about relative motion. We won t discuss those here, but the interested reader is encouraged to explore the references for details. The history of the discovery of the special theory of relativity is a good lesson in the way science works for it demonstrates the crucial interplay between theory and experiment. Careful experiments within the limits of technology available at the time led to Ampere s law and Faraday s law. Later, purely mathematical arguments and theoretical considerations were used to show that Ampere s law was only approximately correct and that electromagnetic waves travel through space at the speed of light. More theoretical considerations were put forward to explain how those waves traveled through space, and then the dramatic experimental result found by Michelson and Morley forced those ideas to be thrown away. Then Einstein came along and once again used mostly theoretical arguments to derive special relativity. The bottom line is this: Physics is a science that depends on two legs theory and experiment and it cannot stand on either alone. We now turn to a quick tour of the basics of special relativity, and begin with some de nitions.
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