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Consider an observer S pushing a fork towards a material x-axis as seen in the figure below

According to this observer E and F cut x-axis simultaneously.

Now consider an observer S' moving along x-axis with a constant relativistic speed. It is very easy, using Lorentz transformation, to show that E and F will NOT cut x-axis simultaneously (according to S')

How is it possible that E and F will not cut x-axis simultaneously with respect to S' knowing that the none of the arms of the fork will undergo any length variation because they move perpendicular to the motion of S'?