# B Against length contraction explanation of magnetism

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1. Nov 10, 2017

### Demystifier

I agree, but I wouldn't blame Purcell for that. I would blame Einstein himself, or more precisely the usual practice of teaching introductory special relativity in the form Einstein himself introduced it in 1905. It was Minkowski, not Einstein, who later introduced the 4-dimensional view of relativity, and Einstein even didn't like it in the beginning. (Later he accepted it in the formulation of his general relativity.) My point is, given that special relativity is presented to students in a non-covariant non-4-dimensional form, the ugly Purcell pedagogy of electrodynamics looks "more natural" than the elegant covariant formulation.

2. Nov 10, 2017

### vanhees71

I don't think one should blame Einstein, who used the mathematical machinery used at his time. E.g., although Heaviside had introduced the much more clear vector calculus obviously physicists still used to even write Maxwell's equations in components in a very cumbersome way, and this is what Einstein did in his famous paper. Minkowski, however, came with this mathematical analysis already in 1908, and since then textbook writers have had enough time to adopt it. There's no excuse for confusing students simply by being too lazy to write new text books and not just copying old ones! Purcell would have an impact in the better direction, had he not overdone the task to make things "pedagogical".

For me special relativity also has been an enigma, until I discovered Landau-Lifshitz vol. II at some time in my 4th semester, where we had to suffer a boring presentation of classical electrodynamics in the old-fashioned way starting from electrostatics in all detail, with the result that at the end of the semester the professor had barely touched magnetostatics and then was shocked himself that he hadn't ever talked about waves, let alone relativity ;-(. That's why together with some other nerdy theory addict students we studied Landau-Lifshitz vol. II on the side, which was much more fun than the traditional lecture presented to us.

3. Nov 14, 2017

### Demystifier

They had enough time, but the fact is that they didn't do it. My point is that Purcell is not the only guy who didn't do it. All introductory textbook writers, who include some introductory special relativity, are equally guilty.

Why is beginning relativity taught the way it is? I don't know. Perhaps because it is believed that 4-dimensional thinking is too difficult for most beginning students. After all, at the beginning it was too difficult even for Einstein.

Last edited: Nov 14, 2017
4. Nov 14, 2017

### Demystifier

Suppose that you must choose between the following two ways to teach electrodynamics:
1) Purcell way, which uses special relativity from the beginning, but in the old-fashioned non-covariant form.
2) Traditional historical semi-empirical way, in which Maxwell equations are obtained without using special relativity at all.
Which one would you choose?

5. Nov 14, 2017

### vanhees71

I'd never ever teach E&M like Purcell. Of course, maybe in Germany the strategy is a bit different. In our theory course you get an introduction to SR already in the 2nd semester (analytical mechanics). Then, in principle, you can teach electromagnetics, which is taught in the 3rd semester in the theory course, from the very beginning as a relativistic theory, and some of our professors do so. It, of course, also depends on the addressed audience. For people who haven't ever heard about electromagnetism before, you'd have to start in the traditional way and carefully explain the idea behind fields in the usual operational way first. Usually this is covered by the experimental course, where E&M usually is treated in the 2nd semester. Of course, in any case at the beginning should be introduced the full Maxwell equations as pioneered by Heinrich Hertz. I'd be sparse on history, but from time to time tell about the people after whom the phenomena/formulae are named :-)).

The best theory book on the traditional way, in my opinion, still is Sommerfeld's Lectures vol. III. Of course, I'd never use the pseudo-Euclidean $\mathrm{i}c t$ convention of the metric but substitute it with Minkowski. The best books using the relativistic approach are Landau+Lifshitz vol. II or the book by Melvin Schwartz.