Maxwell’s Treatise on Electricity and Magnetism: The Central Argument by Howard J. Fisher

My rating: 4 of 5 stars


Most good books lend themselves to be read on many levels. One can read them superficially, merely for momentary pleasure, or study them deeply, working your way slowly through their contents. For the most part, I try to chart a middle path through these two extremes, doing my best to understand what I’m reading—at least on a basic level—without getting bogged down in academic study.

However, some books simply do not lend themselves to that approach, and this is one of them. One can skim over the mathematical proofs in, say, Newton’s Principia and still get a fairly good idea of what the book is about. But in Maxwell’s magnum opus, the math is what does the talking. Indeed, by the midway point I was so desperate—feeling guilty, lazy, and stupid for understanding so little of what I was reading—that I decided to turn to an old ally, Kahn Academy. There, I went through all of the videos on electricity and magnetism, and learned a great deal. (The last time I had any formal instruction on the subject was in my sophomore year of high school, and I doubt I understand much back then.)

But I found, when I picked up the book again, that even this Hail Mary would not save me from the perdition of Maxwell’s writing. Indeed, as I had already bought the heavily annotated student’s edition (with copious notes by Howard J. Fisher), it seemed that I had used up all of my lifelines, and simply had to content myself with only the most superficial reading of this important book.

What follows, then, is probably as valuable as a review of Hamlet by somebody with an elementary level of English. Here I goes.

Now, as I mentioned, the version I picked up is meant for students. Thus, it is heavily abridged and, often, so full of explanatory footnotes that the original text is crowded out.

For what it’s worth, even if you do have the mathematical and scientific chops to handle Maxwell’s tome, I would recommend either this version or something similar. The original is famous for being rather unfocused and overlong. After all, this book was not meant to be Maxwell’s Origin of Species—a text devoted to propounding a radical new theory. Maxwell had already set forth his most revolutionary insights—most notably in the paper “A Dynamical Theory of the Electromagnetic Field,” in 1865—several years before this book was published. Instead, this was meant as a kind of definitive textbook on the subject, to be studied by university students, telegram technicians, and other specialists. Thus, there are long sections in which he rehashed old theories which would be of limited interest to any modern reader.

This edition attempts to pare down the original, leaving only what Fisher considers to be the “central argument”—that is, the material leading directly to Maxwell’s signature breakthroughs. These would be, first, his four famous eponymous equations and, second, the electromagnetic theory of light.

Regarding the former, as you may know, Maxwell did not actually formulate his equations in the form which modern students encounter them. It was one of Maxwell’s followers, Oliver Heaviside, who put the equations into their definitive form. Instead, Maxwell puts forward twelve equations, which use the now-defunct quaternion notation rather than vector calculus. This makes Maxwell’s presentation seem rather foreign, even to those less ignorant than myself. What is more, Maxwell has a liking for using Gothic letters as symbols in his equations, which gives them a doubly strange appearance.

More generally, I think even a mathematically literate reader will have some trouble following significant portions of this book, if only because Maxwell’s mathematical language seems clunky and dated. In my version, for example, Fisher is continually translating Maxwell’s operations into more familiar forms (which, admittedly, I still did not follow).

As I had recently made my way through an (abridged) version of Faraday’s epochal Experimental Researches in Electricity, I was most interested in the sections in which Maxwell reflects on his predecessor’s work. He is extremely laudatory of the English physicist and is quite generous in giving credit for developing this new way of examining electricity.

And, indeed, if I have any way of understanding Maxwell, it is only through the lens of Faraday. At first glance, the devoted experimentalist with no mathematical schooling seems to have little in common with the visionary theorist who prefers numbers to words. And yet, as I’m sure Maxwell would agree, they were bound together by a new vision of the cosmos. In a nutshell, and said very imprecisely, I think their insight was to see energy rather than matter as fundamental.

In the Newtonian view that preceded Maxwell, the world was composed of matter—indeed, even light was supposed to be made up of little corpuscles. This matter traveled in straight lines and attracted other matter in straight lines. This Newtonian view was embodied in, say, Ampère’s earlier theory of electromagnetism.

And yet this view always sat uncomfortably with Faraday, who instead saw the curving lines of the magnetic field as the fundamental reality, rather than one piece of matter attracting another via “action at a distance.” Indeed, Faraday’s brilliant experiment involving the shifting of light via a magnet got him tantalizingly close to the central insight of Maxwell’s life: the unification of light with electromagnetic radiation.

Faraday is one fount of Maxwell’s inspiration. Yet if Maxwell has a mathematical predecessor, it is Joseph-Louis Lagrange, whose work comprises a culminating chapter in this book. Lagrange arguably developed the math that Faraday had been striving toward from another direction. For in Lagrangian mechanics, rather than thinking of forces being exerted by physical objects, one thinks of the energies in the system—the object in question merely following the path of least resistance through the fields of energy around it.

It was Maxwell’s great insight to see how the work of Faraday and Lagrange—among many, many other brilliant scientists—fit together to form one complete account of electricity and magnetism. It is a theory in which fields of energy take precedence over particles, indeed in which the world around us is filled with vibrations in luminiferous ether. And while some parts of Maxwell’s theory (notably the ether) have not survived to the present day, his basic insight was so sound and so significant that, as Richard Feynman said, his discovery constitutes one of the major turning points in human history. You certainly wouldn’t be reading this review without it. Thus, Maxwell’s name stands beside Newton’s and Einstein’s as one of the greatest physicists of all time—even if his book is completely opaque to people like me.



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