All right guys. I am on the second chapter of Cox book Why E=mc^2 and I am interested in their explanation of observer standing on the train station being passed by a train. But I think they are complicating the thing by vector compounding in 2 directions. So I have the simpler picture ^^^ I'll explain this. Let's imagine an observer is standing on the rails and the train is rushing towards him. Now observer fires a beam of light towards ticking clock. The axiom here is: the speed of light is constant. Therefore if we consider Newtonian mechanics we see the speed of train and the light are c+v2, so blue dashed line would be correct according to Newton. So the clock would tick sooner. But hey the light speed is a constant, so it can not be compounded with train speed. It is simply c=3e8m/s. That means light is later on the train's clock. And this is Einstein's thought experiment, meaning the clock on this train MUST tick SLOWER from the point of view of this observer. That's it guys.

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