In "The Strange Theory of Light and Matter" Richard Feynman uses a "stop-watch" to time the photon as it moves. For each photon path, the final direction of the hand is considered as a "vector", which is a rather strange step. Then all possible "vectors" are combined to end up with a "probability", which is is another stange step. All this appears as a simplified way to make the concepts of QED accessible to a non-expert audience like me. What are the more formal ways to describe this theory?