Maxwell and after

Visit Edinburgh on a sunny day, and you may come across this statue to a man who changed everything. He made seminal contributions to colour vision, orbital mathematics, colour photography, the kinetic theory of gases, control theory, thermodynamics and electromagnetism.

There was a particularly interesting shift between his 1862 and 1864 papers on electromagnetism. One which left his peers a little confused, perhaps because the explanatory basis was so different. He changed from elaborate mechanical models of electromagnetism (spinning cells) to an account based on relating quantities (building on Lagrange's work in mechanics), with no mechanistic underpinnings. This change of model was a crucial shift affecting how physics developed: arguably changing what physics by changing the nature of the explanations acceptable as fundamental.

As the presentation of much of the physics taught in schools bridges the 19th-20th century divide, and Maxwell is considered by many to be the 19th-century physicist who most influenced the shape of 20th-century physics this shift deserves pedagogic attention.

I think this change should affect how we introduce electric circuits, as circuits are well-suited to be being the prototype for thinking about all kinds of different systems-based explanations. In these, aim for an account being complete and intelligible without representing a necessary abstraction or simple smoothing-out of underlying casual mechanical processes. There are topics where reductionism is fruitful: electrical circuits is not one of them.

If you accept this point of view, then exploring different mechanical models of resistance in circuits is noise, not signal. For children, it’s a blast from the past(pre-1864); and not a route to the future.