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Unformatted text preview: 1 PHY3221 Detweiler Lecture #1 Relativity Time Dilation Some Taylor expansions: I had intended to go over these Taylor expansions again in class. They are useful for the homework. 1 1- x = 1 + x + O ( x 2 ) , 1- x = 1- 1 2 x + O ( x 2 ) , 1 1- x = 1 + 1 2 x + O ( x 2 ) The mathematical notation O ( x 2 ) represents something that is smaller than some number times x 2 , when x is very small. Then, x 2 will usually be comparable to the error in these approximations. In this class, when x is very small, you are allowed to just use 1 / (1- x ) 1 + x 1- x 1- 1 2 x 1 / 1- x 1 + 1 2 x. Try them out on your calculator for x = 10 1 , 10 2 , 10 3 , 10 4 and 10 5 to see how the approximation improves while x decreases. See if the error is comparable to x 2 . Details of Time Dilation Definition A thought experiment : is an experiment that we can imagine doing, but which would not be possible under reasonable circumstances. Thought experiments allow us to test our understanding and to sharpen our physical intuition. Formulating a thought experiment is particularly useful when the laws of physics, as understood, appear superficially to be paradoxical, self-contradictory or inconsistent. Definition An Event : is a particular place at a particular time. Something might happen at that place and at that time, such as the snap of my fingers, or a firecracker going off....
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