If time dilation is REAL, we must define reality. Reality is only an appropriate idea within the frame under consideration. Therefore, the time dilation, being real in the moving frame will affect the VELOCITY in the moving frame, NOT the lengths. This gives the same predictions in science as length contraction but gives infinite speed in the moving frame coincident with the relative speed of "c". What better way to understand WHY "c" is the limit of relative speed.
There is still a contradiction here. Whilst space-time diagrams do explain these things clearly, the notion that red shift is observed from either frame is challanged by the proven relative time dilation of ONE frame relative to the other (eg 1971, Hafele & Keating). If time dilation were purely relative, then the clocks would end up the same time when re-entering the stationary frame, and they are not. Deduction, relative time dilation is also REAL!
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