Coulomb's law

About a year ago, I discovered a very interesting short video by Richard Feynman responding to the question of what happens when we hold two magnets next to one another. His answer was brilliant.

Recently, I came across a video from the 50s where a physicist is conducting experiments trying to explain electrostatics and, more precisely, Coulomb's force. What is very interesting is that he doesn't merely present facts, but also argues, from various points of view, trying to convince the listener that the force must depend on the distance r between two charges as a linear function of 1/r² (and linearly on each charge). The argument, especially towards the end, is not dissimilar from that of a mathematician who is trying to explain Potential Theory and Laplace's equation. In the end (skip to 17'22'' if you wish), we realize, with a bit of thinking, that a lot of the things we see in the experiment are merely outcomes of geometry and the fact that we live in a 3 dimensional space (this is an experimental observation that works well!) where distances obey the Pythagorean theorem.

I found out that the physicist is Eric Rogers. The video was intended to be for secondary schools. These days, one can find students of electrical engineering who do not understand electrostatics, students of mathematics who do not understand what potential theory has to do with physics, and educators (they are called pedagogues--and, as I have explained, they form a modern type of plague) who insist that education is independent of the discipline. Not that there aren't universities that teach properly and students who understand a lot, but this species (those who strive to understand and, hence, to explain) is becoming rarer and rarer.

What does "why" mean?

The following short clip shows Richard Feynman answering the question why two magnets attract or repel one another. The person asking the question is trying to understand why he has this feeling when he holds two magnets close to one another.

Feynman answers the question by not answering it! It is brilliant. He says that in order to answer the question he must know what the truth basis of the person asking it is. He digresses giving a number of interesting examples. He says that a first-order answer, such as "it's due to the magnetic force", may satisfy the person who asked but may not be an answer at all. A second why may follow, and a third, and so on. (Does the guy know what a magnetic force is? Is this not just a reduction of the problem to another problem?) A basis for truth must be known before the question can be answered. Feynman points out that the `magnetic force' (whatever this is) is intimately related to the `electric force' (whatever this is) and that the two are, essentially the same. (A consequence of a happy marriage of Electromagnetism and Relativity. In fact, the latter was borne because of the first.) But, Feynman continues, when the guy asking the question rests his arm on the chair he doesn't ask (or even think that he could ask!) why the arm doesn't go inside the chair. Ultimately, it's an electric force keeping the arm where it is, but it does not seem as `unnatural' as a magnet. They are, however, the same kind of forces. So, he concludes, he can't answer his question, because, clearly, the person asking has no basis for understanding it.

Watch the video and read some more comments below.



As an electrical engineer and mathematician, I find these things quite natural. This is due to the things I learned in the university and to the work I did. I am also puzzled as to how to explain certain concepts to people who want to know but who have no time or desire for a bit deeper studies. One can give `popular' answers, but over-popularizing is always--to some degree--cheating.

You may (correctly) argue that I shouldn't expect a lay person to study relativity before he or she can understand the answer. No. But I would expect an academic  to have the scientific curiosity (and integrity) to learn further.

Another thing that comes to mind when listening to Feynman's `explanation' is the word `pedagogy'. For several years now, universities (especially in certain parts of Europe) keep getting infested  by a new species of people who claim to have answers to all `pedagogical questions'. In fact, they are so sure of themselves, that they have convinced universities that they should train others on the matter. And yet, they themselves cannot answer simple, pedagogical, questions. The example above is perfect. One would expect that a lecturer in Physics ought to be know what Feynman is talking about, including the meaning of `why'. Traditionally, teachers learn these things by `doing' teaching, by practice. Now, if the species of pedagogues wants to train a teacher in physics, then one would expect that the pedagogue would be in position to teach what Feynman has in mind. Alas, this never happens. Pedagogical courses are, by and large, void of content. I've seen young guys and gals suffer in the UK by the pedagogical training they receive. I've been to pedagogical courses in Sweden with absolutely no content. Hours of wasted time, Nobody has ever gone to a pedagogical class watching, for instance, a Feynman lecture. Why, in order that this happen, the pedagogues themselves must be in a position to understand what Feynman is talking about, from a pedagogical point of view. Unfortunately, pedagogical classes teachers seem to have no qualifications other than dissemination of bureaucracy. (Example: they train teachers how to fill in forms. It's absurd and obscene.)