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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
So, even though there is no “cause and effect” the fact remains that per Special Relativity the relationship of L’(x) and L(x) can be defined as: L’(x)= L(x)*gamma*1/gamma= L(x) Substitution of actual values for their variables bares this out and serves as proof of validity.
With that, L’(x) and L’(y) are lengths with no particular attributes specific to either within the frame that is in relative motion because “there is no contraction nor dilation within the frame that measurement takes place in”.Previously stated: relative to the rest frame K, time in the moving frame is dilated by the factor 1/gamma. But relative to the rest frame K, length perpendicular the direction of motion L’(y) in the moving frame K’ is NOT contracted by the factor gamma. Then following the same logic used for L’(x) it follows that:L’(y)= L(y)*1/gamma= L(y)That, however, only holds true if v equals zero in which case gamma=1. That is the only case that L’(y)= L(y) as prescribed by Special Relativity.Thank you,ButchBy the way, you have probably heard that neutrinos at CERN have very likely exceeded the speed of light. That is consistent to the prediction I made in my post The Special Relativity Discovery MMXI.0 on the BAUTforum and directly relates to this thread.
In other words the null result of Michelson Morley was attributed to the affects of length contraction in the direction of motion and time dilation in the frame effectively canceling each other to yield a net result of no change of length in the direction of motion.My point is that if time dilation in a frame affects length in the direction of motion it must also affect length perpendicular to the direction of motion in the same manner unless there is a good reason that it doesn't.Thank you, Butch