A model to predict where photons will turn up

The spinning arrow of each photon explores the space, at the speed of light (light only knows this universal speed). See how to explore some of the space by choosing paths between source and detector. A single waypoint defines a simple path. The length of the path sets the trip duration and this fixes the rotation of the arrow.

Every path contributes an arrow, and the sum of these contributions predicts the brightness.

The photons are not fired off along particular trajectories, so there are no preferred paths. Photons explore all paths: but that's an impossibly time-consuming calculation to do for mere humans, so make a smart guess as to the important paths and calculate for these. Later, justify your guess by showing that calculating for additional paths makes not much difference and that your prediction from the few paths that you did try corresponds to what happens in the lived-in world.

Saying each photon explores all paths is attributing an essence to the photon – a character – that is a translation of the mathematics that you do to calculate where the photon is likely to end up. If you don't like this essential approach , you could just say you're manipulating a mathematical model, but that may demand a metaphysics that is too austere for younger learners.

The contributions from different paths may be more or less in step. Start with two paths. The more the contributions are in step, the greater the resultant. A greater resultant predicts a greater brightness. (To be precise, the brightness is proportional to the resultant squared).

Since it is only whether the arrows are in or out of step, you can choose to freeze the spinning, making the diagram simpler.

To explore all space you'd have to try all waypoints – and the photon does. But you can get a good idea what to expect by selecting fewer paths, and matching your selection to the particulars of the changes made to the space you're investigating. The selection of a few waypoints requires insight, experience and cunning – increasing the number should not affect the predictions about where will be bright by much. That way we can have a model which is fit for purpose – accurate and precise enough, but not too cumbersome (Calculating the contributions for all paths would take a very long time).

The result of all explorations of the many paths sets the brightness. See how this is done by varying the paths and seeing how the contributions set the resultant.