... can someone explain to me why the following thought experiment does not give the object a speed greater than 3*10^8 m/s. Imagine that the experiment takes place in a very large vacuum. A very long toy train is moving at 100 m/s on a track from rocket propusion. On the top of this train, there is another smaller train that starts to run on a track on the top of the larger train. The smaller train now has a speed of 100 m/s relative to the larger train and 200 m/s relative to a still observer. Then, a smaller train does the same thing on the second train. There are 3*10^6 + 1 trains that are all on the backs of another doing 100m/s. Exactly what happens when the 300000th train fires up its rocket relative to a still observer? If possible, what happens when the 300001th train's rocket fires?