We were asked to describe the “physics” of Maxwell’s Equations in my MIT optics class. It was an unusual kind of homework question so I decided to give it some thought. To zeroth order, one could simply separately interpret each equation: “Charges source electric fields; there are no magnetic monopoles; magnetic and electric fields are coupled (E generates M and M generates E).”
But it’s not quite right, and I would learn nothing in writing down this “interpretation” for credit. To consider each equation separately and then talk about their mysterious connectedness, though that is the way we are taught to do it in school, is like marveling at each face of a cube and noting with interest that they are all equal area. Historically, this was the progression of our understanding of electromagnetism, but besides an appreciation for the process of discovery, what is gained by sticking to a chronological exposition? There is in fact a non-zero movement going on in physics to reform the E&M curriculum. Basic ideas of symmetry can be understood at even the layman level. Students should be primed from the very beginning for the ideas in modern physics, and not be deprived of a more coherent interpretation if there is one available.
Anyways, so I was thinking about all this. And for too long really because I ended up not having any time to write the damn thing so I turned in something scrambled together that I was very unhappy with but nevertheless should give me some credit for the assignment. But this mailing list I joined, I decided to make some good use of it. I had joined it for the sake of motivation. Lack of an audience is a major cause for all my little unfinished projects, for my lack of blog updates, etc. I’d like to think that I could generate real value. But it’s hard writing into an abyss.
So this piece, when I finished it up, I had a bunch of ex-MIT students in mind. So it’s not really layman. But probably everyone who reads my blog has taken some form of introductory physics. It actually is quite technical at some points, but that’s kind of for me and for those who want to follow the math, but you can really skip that and just read the physical explanations and I think you won’t be missing out on much.
I’ll happily take edits.