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Message: <blockquote data-quote="heshi32" data-source="post: 6766022" data-attributes="member: 37192">Lorentz ContractionThis is a derivation of the Lorentz-contraction formula. We will go over the ideas in class, but the algebra is a bit gruesome. So, I'm putting that part here. Refer to Fig. 2.As with the time dilation example, imagine a pulse of light reflects from a mirror back to a receiver. Light will be the "yardstick" used to measure the length of an object in the lab and rocket frames. <img src="http://www.drphysics.com/syllabus/time/fig2.GIF" alt="" class="fr-fic fr-dii fr-draggable " style="" />Some notation:L' = length of stick in the "rocket"L = length of stick in the "lab"t1 = travel time of light pulse to the end of the stick (lab)t2 = travel time of light pulse back from the end of the stick (lab)t = t1+t2 = total travel time in the labt' = total travel time in the rocketv = speed of rocket in the lab frameIn the lab:L + v*t1 = c*t1L - v*t2 = c*t2t = t1 + t2 = (2L/c)/(1-v2/c2)In the rocket:2L' = c*t't' = 2L'/cWe know from the time dilation formula thatt' = t*√(1-v2/c2)So,2L'/c = (2L/c)/√(1-v2/c2)L' = L/√(1-v2/c2)L = L'*√(1-v2/c2)The stick appears shorter in the lab frame since √(1-v2/c2)<1.</blockquote>

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