Einstein informs the gullible world that the Lorentz transformation entails the ASYMMETRICAL time dilation on the rotating disk:

Albert Einstein: "An observer who is sitting eccentrically on the disc K' is sensible of a force which acts outwards in a radial direction... [...] The observer performs experiments on his circular disc with clocks and measuring-rods. In doing so, it is his intention to arrive at exact definitions for the signification of time- and space-data with reference to the circular disc K', these definitions being based on his observations. What will be his experience in this enterprise? To start with, he places one of two identically constructed clocks at the centre of the circular disc, and the other on the edge of the disc, so that they are at rest relative to it. We now ask ourselves whether both clocks go at the same rate from the standpoint of the non-rotating Galileian reference-body K. As judged from this body, the clock at the centre of the disc has no velocity, whereas the clock at the edge of the disc is in motion relative to K in consequence of the rotation. According to a result obtained in Section XII, it follows that the latter clock goes at a rate permanently slower than that of the clock at the centre of the circular disc, i.e. as observed from K." http://www.bartleby.com/173/23.html

Einstein refers to Section XII but this Section does not contain any results explaining why the (inertial) clock at the center of the rotating disc should run faster than the (non-inertial) clock placed on the edge of the disc. Rather, the results in Section XII are all based on the Lorentz transformation which predicts SYMMETRICAL time dilation for two INERTIAL clocks: either inertial clock (more precisely, the observer in this clock's system) sees the other inertial clock running SLOW by a factor of 1/gamma = sqrt(1-(v/c)^2).

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