A regular description of the paradox involves a train travelling through a tunnel which is fitted with doors at either end which can be raised and lowered. In their respective rest frames the length of the train is measured, by an observer on board, at 500 metres and the length of the tunnel is measured, by a ground-based observer, at 300 metres.
Ground Observer measures the train travelling at such speed that gamma = 2 and therefore measures the train length, due to contraction, as 250 metres and concludes that the train will fit in the tunnel. He activates a control which causes the gates at either end to simultaneously close and instantly open again while the train is inside the tunnel and the train passes through.
Train Observer measures the tunnel approaching at such speed that gamma = 2 and measures the tunnel length as 150 metres. He, therefore, concludes that the train can not fit within the tunnel but, nevertheless, it passes safely through, despite the fact that he observes the doors closing and opening again.
The solution given is that while Ground Observer measured the doors closing and opening as being simultaneous events, Train Observer did not, and measured them as occurring at different times. The Theory of Special Relativity asserts that both observers are equally entitled to claim the correctness of their individual perspectives.
Now, to my question. Imagine that the experiment is set up so that there is a single hook above the tunnel, aligned to its midpoint. The two doors are suspended from this hook by cables of identical length as measured by laying them side by side upon the ground or on the train. When the control is activated the hook releases both cables in one instant. Would not this mean that the two doors must objectively close simultaneously giving preference to the reference frame of Ground Observer in contradiction to the first postulate of Special Relativity?
