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The following are for lengths as judged from within the moving frame.The traditional formulas for time dilation and length contraction for X’ and Y’:Equation for length contraction of length in the direction of motion:L’=L*(sqrt (1- v2/c2)) - For these purposes L’=X’ and L=X therefore X’=X*(sqrt (1- v2/c2))
Judged from frame K’ which is in relative motion, L’(x) is not observed to be contracted because time in the frame is dilated by 1/gamma, the reciprocal of the contraction factor.
Imatfaal,You are absolutely correct when you say that you cannot tell that you are in relative motion to something by measurement in your own frame. However, Einstein and Lorentz were in agreement that in the Michelson Morley experiment length in the direction of motion relative to the sun was contracted by the factor gamma. But time dilation within the inertial frame of the experiment was responsible for the “null” result.Or in mathematical terms as judged in the moving frame: L’(x)= L(x)*gamma*1/gamma=L(x) where gamma is the length contraction factor and 1/gamma is the time dilation factor and being reciprocal to each other they cancel to exhibit zero net change. Butch