I'm just getting started on relativity. I watched this a couple of day ago - But I didn't like the way Lorentz Transformation was derived (the assumption about the nature of the final transformations, to be more specific). I tried reading Einstein's original paper for a better derivation but it was kind of hard for me (I'm not really very comfortable with differential equations). Then I found this - http://arxiv.org/pdf/physics/0606103v4.pdf Is the derivation in the paper correct? I'm only interested in movement along x-direction, not any arbitrary velocity. Basically, the derivation goes like this - 1) Consider a light clock with two mirrors facing each other a distance L0 apart. Each unit of time corresponds to a cycle of light pulse getting fired from the first mirror, getting reflected and returning. Time period of this clock in rest frame T0 = 2L0/c 2) Let's say the clock is moving with speed v in a direction parallel to the plane of the mirrors. Time period of the moving clock from rest frame is T = T0/p where p = sqrt(1 - v**2/c**2). 3) Consider another clock moving with same speed v but in a direction perpendicular to the plane of mirrors. Here, the paper makes an interesting claim - "because the observer moving with the clocks sees that the clocks tick at the same rate, so should the observer at rest". So the time period of the second clock too is T in the rest frame. Is this necessarily true? 4) The only way 3 can happen is if L (length of moving clock in rest frame) = L0 * p. 5) From here the paper derives the transformation using x = vt + x'/p and x/p = vt' + x' The claim in 3 seems reasonable to me because I can't find a reason to think that two phenomena which happen to take the same time in a moving frame should take different amounts of time in the rest frame. But I want someone more knowledgeable to confirm that my thinking is correct.