(no subject)

[meanfreepath]

So I guess I've been inadvertently lying for the last two years or so every time I've told someone in the Physics Clinic that quantities like magnetic field B or torque are vectors. But what else do you tell people in introductory physics?

Until today I really did believe that B was a vector. But having finally managed to work out a long E/M problem on the transformation properties of vectors vs. pseudovectors (aka axial vectors), and having shown that curls transform like pseudovectors, I stand corrected. For while pseudovectors transform like vectors under some orthogonal transformations, such as rotations, they don't transform like vectors under reflections or switching from right to left-handed coordinates.

Comments

[eclectic-boy.livejournal.com]

A-ha! I always knew there was somethin' fishy about them 'just put the arrow this way, even though things are moving in a completely different plane' quantities! ...time to go look up 'pseudovector' and get a little educated.

[meanfreepath.livejournal.com]

The discussion in Arfken & Weber's Mathematical Methods for Physicists has the relevant material scattered through the chapters on vectors and tensors, but overall is fairly lucid.

Or try:

Mathworld (http://mathworld.wolfram.com/Pseudovector.html) (although Arfken is cited)
or
Wikipedia (http://en.wikipedia.org/wiki/Pseudovector) (this article cites Arfken too, so perhaps your best bet is to look there).

[rose_garden.livejournal.com]

It's fun to hear your thoughts about Jackson. Pseudovectors didn't surprise me at all--it just seemed like a natural result of defining vectors more rigorously and in a way more useful for physics.

But I still like the mathematical definition of a vector: anything that satisfies all those axioms. I'm assuming that pseudovectors do in fact fall under the umbrella of mathematical vectors, but I'm not checking the definitions at the moment.

[jedibl.livejournal.com]

Yeah, I was a little surprised by that also. But that doesn't stop me from telling intro students that B (and even I) is a vector, even though a little bit of me cringes when I do so.