Beard of the Week LXXX: Magnets & Relativity

This week's beard* belongs to 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 $c_0$, which is related to the product of the physical constants $\mu_0$ and $\epsilon_0$ that appeared in the earlier equations.

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

$c_0 = \frac{1}{\sqrt{\mu_0\epsilon_0}}$

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.

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

† Duh.

Posted on May 27, 2009 at 21.41 by jns · Permalink
In: All, Beard of the Week, It's Only Rocket Science

2 Responses

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  1. Written by chris
    on Thursday, 28 May 2009 at 23.09
    Permalink

    Those were charming – I was especially amused by "Beans", who, single name and technician duties and all, seemed decidedly Igor-esque.

    and yes, popping breakers and smoking copper (and undoubtedly lethal electrical current running through those copper straps not very far away from their arms) added to the mad-scientist air. Was this the film with one of the background people smoking a pipe?

    The "very sensitive balance" above their humongo-powerful magnets is a Gouy (pronounced "gooey") balance. We had one of those at Scarborough College (part of UofT) when i was an undergraduate (71-75) – an electromechanical balance (where you dialled the weights on and off, and read milligrams and tenths of milligrams on an optical scale) mounted on a counter-top high counter. There was a perspex tube [to shield from wind/drafts] below the balance table, and inside was a thread attached to a fine chain, in turn attached to the bottom of the balance pan. There was a small (pencil eraser-holder size) cradle at the end of the thread, which was about 20-25cm above ground level. There was an electromagnet that rolled along rails in the floor – it had two poles about 4cm apart, and large discs beyond that about the size of an LP record (30cm diameter) and maybe 15cm thick. There was cooling water ran through hoses through the magnet, and the drain hose ran into the safety shower drain. The idea [this was a synthetic inorganic chemistry lab] was to make transition metal complexes and pack them into a small glass tube that hung from the cradle, on the thread. You'd weigh the sample, and then apply the magnetic forces. Paramagnetic materials (unpaired electrons!), attracted to the magnetic field, would become apparently heavier with the magnet in place, and diamagnetic materials were repelled by the field, and became apparently lighter. Fancy calculations including the acceleration due to gravity, and taking into account the diamagnetism of the sample tube itself (weigh an empty tube with/without magnet), and an equation we really didn't understand with all sorts of ill-reproduced hand-written Greek letters (coz typewriters couldn't do them), let you calculate the number of unpaired electrons in the complex.

    Did you notice that the frame-of-reference film was from the University of Toronto (my employer for the last 27 years)? I recognised the name of Donald Ivey – the guy who's hanging upside down at the beginning. There are libraries named after him just steps from my work venue. If you google on "donald ivey university toronto" you'll find this film, as well as information on both the scientists. This one for instance – which also mentions your magnets film:

    http://philosophyofscienceportal.blogspot.com/2008/10/hume-and-iveys-pssc-filmframes-of.html

    We will now have a chorus of It's a small world after all. The Hume/Ivey film was 1960, not long before Scarborough College was founded: it opened to students in September 1964 (so was p€lanning for several years before that). Following the success of films like these ones, the idea to teach via audio-visuals was much to the fore. Scarborough College had TV monitors in all the big lecture theatres, with the idea of teaching thataway. It wasn't very satisfactory at the time -partially because the technology was clunky (TV tape was very expensive, and difficult to edit). Lab demonstrations happened too – we saw a few in my labs, but the lab instructors weren't as important as the professoriate, so they didn't tape them, and the demos were live every time, repeated for every lab section. By the time I came along ten years after the film, we had very few taped lectures – which aren't as good as viva voce lectures, coz there's only one-way communication, and the audience could be watching TV (or chatting) at home. So when I teach now using audio and video, I'm there present to take cues from my student audience – but it started 49yr ago with this fillum.

    an unexpected trip down memory lane.

  2. Written by jns
    on Friday, 29 May 2009 at 21.47
    Permalink

    I think I'll have to write a story with an incidental character in it named "Beans".

    Thanks for the stories & background, Chris. I think I notice the U Toronto name but then failed to make the mental connection to your institution. Perhaps I was distracted by the guy hanging upside down or the dry-ice puck making its fanciful loop. I'll have to watch again, but Francis Bitter may have been smoking a pipe; I know the guy who appeared first in "Frames of Reference" (and ended up being upside down) was seen to be smoking a pipe, but I doubt that it was lit.

    Televisions in classrooms: at that time didn't educational theorists tend towards progressive ideas so that swiftly adopting new technology, like TV, was desirable? Certainly these film let us know that, although television as an educational tool may be neutral, there are times when it provides a way to experience things that one otherwise would never get to experience. Let's have a few thousand amps!

    Oh, now that I look at your link above, I see they confirm that it was "Beans" Bardo turning up the juice.

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