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TLS signed “A. Einstein,” one page, 8.5 x 11, The Institute for Advanced Study letterhead, January 28, 1952. Letter to Sgt. Lionel H. Silva of the Granite City Engineer Depot in Illinois, responding to an inquiry about special relativity. In full: "The question is treated in every book about special relativity. In this theory the composition of relative velocities is not following the formula u = u1 + u2, but the formula u = u1 + u2 / 1 + u1u2/c2, where c is the velocity of light. If you put in this formula u1 = u2 = c it follows u = c." In fine condition, with some faint marginal stains. Accompanied by the original mailing envelope.
In this simple but outstanding letter, Einstein offers a comparison between the non-relativistic (classical) and relativistic 'velocity addition' formulas. Suppose a train is traveling south with velocity u1. You’re on the train, and you walk from the back of your car to the front with velocity u2 (relative to the train.) Then, the classical velocity addition formula says that you are traveling south relative to the ground with velocity u = u1 + u2. But if either u1 or u2 is very fast—an appreciable fraction of the speed of light, c—then that formula no longer holds, and the relativistic version (Einstein’s second equation) must be used. Here u1 + u2 is divided by the term 1 + u1 u2/c2. The relativistic velocity addition formula is an important result of special relativity, making this a very desirable Einstein letter.
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