A 20m long train at rest moves with 0.9c towards a 10m long tunnel at rest. According to an observer at rest with the tunnel, the train appears only 9m long while the tunnel is 10m long. When the train enters the tunnel, the front and rear door of the tunnel close for an instance, then open and the train continues its journey. This makes sense as the train is only 9m long and can fit in a 10m long tunnel with both doors closed at the same time. According to an observer on the train, however, the tunnel is moving at 0.9c towards the train and appears around 4m long, while the train is 20m long. Nonetheless, the reality of the observer in rest with the tunnel agrees with the reality of the observer in rest with the train. How is it possible that the 20 m train fits in the 4m tunnel with both doors closing? Draw adequate graphs for BOTH observers, provide a detailed explanation of the events taking place, label times as , distances as , and velocities as with appropriate indexes and proper mathematical inequalities (<, >, =, )