Magnets & Relativity

Posted by jns on 27 May 2009

This^* is Scottish physicist James Clerk Maxwell (1831–1879). He did significant work in several fields (including statistical physics and thermodynamics, in which I used to research) but his fame is associated with his electromagnetic theory. Electromagnetism combined the phenomena of electricity and magnetism into one, unified field theory. Unified field theories are still all the rage. It was a monumental achievement, but there was also a hidden bonus in the equations. We’ll get to that.

He published his equations in the second volume of his A Treatise on Electricity & Magnetism, in 1873. I think we should look at them because they’re pretty; I suspect they’re even kind of pretty regardless of whether the math symbols convey significant meaning to you. There are four (which you may not see in Bloglines, which doesn’t render tables properly for me):

	;
	;

I don’t want to explain much detail at all because it’s not necessary for what we’re talking about, but there are a few fun things to point out. The E is the electric field; the B is the magnetic field.

The two equations on the top say that electric fields are caused by electric charges, but magnetic fields don’t have “magnetic charges” (aka “magnetic monopoles”) as their source. The top right equation gets changed if a magnetic monopole is ever found.

The two equations on the bottom say that electric fields can be caused by magnetic fields that vary in time; likewise, magnetic fields can be caused by electric fields that vary in time. These are the equations that unify electricity and magnetism since, as you can easily see, the behavior of each depends on the other.

There’s one more equation to look at. A few simple manipulations with some of the equations above lead to this result:

This equation has the form of a wave equation, so called because propagating waves are solutions to the equation. Maxwell obtained this result and then made a key identification. Just from its form the mathematician can see that the waves that solve this equation travel with a speed given by , which is related to the product of the physical constants and that appeared in the earlier equations.

The values of these were known at the time and Maxwell made the thrilling discovery that this speed

was remarkably close to the measured value of the speed of light. He concluded that light was a propagating electromagnetic wave. He was right.

That’s fine for the electromagnetism part. What’s the relationship with relativity? Let’s keep it simple and suggestive. You know from the popular lore that Einstein came up with the ideas of special relativity from thinking about traveling at the speed of light, and that the speed of light (in vacuum) is a “universal speed limit”. Only light — electromagnetic waves or photons depending on how your experiment is measuring it/them — travels at the speed of light.^†

In fact, Einstein’s relativity paper (published as “Zur Elektrodynamik bewegter Körper”, in Annalen der Physik. 17:891, 1905) was titled “On the Electrodynamics of Moving Bodies”. (Read an English version here; there are no equations at the start, so read the beginning and be surprised how familiar it sounds.) That’s suggestive, don’t you think?

Speaking of special relativity, you’ve no doubt heard of the idea of an “inertial reference frame”, a concept that is central to special relativity. But, what exactly is an “inertial reference frame”?

I’m so glad you asked, since that was half the point of this post anyway. You surely realized by this time that Maxwell was partly a pretext. For our entertainment and enlightenment today we have educational films.

First, a quick introduction to the “PSSC Physics” course. From the MIT Archives:

In 1956 a group of university physics professors and high school physics teachers, led by MIT’s Jerrold Zacharias and Francis Friedman, formed the Physical Science Study Committee (PSSC) to consider ways of reforming the teaching of introductory courses in physics. Educators had come to realize that textbooks in physics did little to stimulate students’ interest in the subject, failed to teach them to think like physicists, and afforded few opportunities for them to approach problems in the way that a physicist should. In 1957, after the Soviet Union successfully orbited Sputnik , fear spread in the United States that American schools lagged dangerously behind in science. As one response to the perceived Soviet threat the U.S. government increased National Science Foundation funding in support of PSSC objectives.

The result was a textbook and a host of supplemental materials, including a series of films. In a discussion I was reading on the Phys-L mailing list recently, the PSSC course was discussed and my attention was drawn to two PSSC films that are available from the Internet Archive: “Frames of Reference” (1960) and “Magnet Laboratory” (1959). (Use these links if the embedded players below don’t render properly.) Both are very instructive and highly entertaining. Each lasts about 25 minutes.

Let’s look first at the film on magnets; it’s quite a hoot. First, the background: when I was turning into a physicist I knew some people who went to work at the “Francis Bitter National Magnet Lab” (as it was known at the time) at MIT. This was the place for high-field magnet work.

Well, this film is filmed there when it was just Francis Bitter’s magnet lab, and we’re given demonstrations by Bitter himself, along with a colleague, not to mention a tech who runs a huge electrical generation and is called either “Beans” or “Beams”–I couldn’t quite make it out. These guys have a lot of fun doing their demonstrations.

At one point in the film we hear the phone ringing. Beans calls out: “EB [?], you’re wanted on the telephone.” Bitter replies, without losing the momentum on his current demonstration, “Well, tell ‘em to call me back later, I’m busy.” Evidently multiple takes were not in the plan.

This is great stuff for people who like big machinery and big electricity and big magnets. Watch copper rods smoke while they put an incredible 5,000 amps of current through them. I laughed when Bitter started a demonstration: “All right, Beans, let’s have a little juice here. Let’s start gently. Let’s have about a thousand amps to begin with.” Watch as they melt and then almost ignite one of their experiments. It evidently happened often enough, because they have a fire extinguisher handy.

This next film on “Frames of Reference” is a little less dramatic, but the presenters perform some lovely simple but clever and illustrative experiments, demonstrations that would almost certainly be done today with computer animations so it’s wonderful to see them done with real physical objects. After they make clear what inertial frames of reference are they take a look at non-inertial frames and really clarify some issues about the fictitious “centrifugal force” that appears in rotating frames.

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^* The photograph comes from the collection of the James Clerk Maxwell foundation.

^† Duh.