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About length contraction Moving bodies are short
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How can we measure the length of a moving body?
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If (x 1 ;t) and (x 2 ;t) are the space-time coordinates of such events, then the length of the body is given by = |x 2 – x 1 | = x What’s the relationship with the length of the body according to a reference frame in which the body is at rest (this length being called “proper length”).
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A simple answer can be found by applying Lorentz’s transformation to the coordinates of the two events. From:x’ = (x – V t)we get: x’ = ( x – V t). As t = 0 and x =, we finally get: where a contraction along the direction of motion is found, being > 1.
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Another way to get this result
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What’s the relationship with the body’s length according to a reference frame in which the body is at rest?
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t’ is related to t 0 by the time dilation law t’ = t 0 So, again, we get:
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