Specifically, what

means is that the time of light transit along both arms of the interferometer instrument is "equalized" by the factor
because time

will be reduced by the same factor as is the longitudinal arm

is also shortened by the same ratio
.
That is, the shorter is the longitudinal arm for light transit, therefore shortened will be the transversal transit time in the longitudinal component by time dilation!!
And in order, therefore, to maintain a universal constant speed of light in any light sphere in any direction by Einstein's special relativity proposition, longitudinal length contraction must be invoked!
And, hence, time dilation is inverse to Lorentz length contraction!


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