responses

So, I'm reading over other people's thoughts before I go to class, and I thought I could respond to some of them! W00ts!

Michael mentions that "A question about 1.6 and partial derivatives: in 1.6 a partial derivative was defined, and shown to transform like a tensor. But if I'm remembering correctly, in G.R. we saw a different 'partial derivative' (the "box operator"?) that was developed specifically because the old "standard" partial derivative did NOT transform in a covariant fashion. Is this simply because of some extra consideration arising in a non-Euclidean space, or am I getting these two cases mixed up or confused in some sad way?"

I think the reason that we needed a 'new' gradient operator is because in GR (or even in the special-relativity treatment of E&M) we want our vectors to be invariant not just under the standard rotations that we know and love in 3-space, but also under Lorentz transforms (essentially, 'rotations' in 4-space). In special relativity, as applied to E&M, needed the "box" operator because we needed the minus sign on the t component to make the physics and math work out.

And on a miscellaneous note, in response to " In composing this blog, I've been wishing that I could use cut-and-paste in the "Compose" window, but it doesn't seem to work. Is this a bug or a feature? Or is it just a quirk of my browser (Safari)? Thanks for any insight or advice!"

It's probably a bug. In Firefox under Linux, I can copy/paste fine into the text box, but it does behave strangely in other respects and isn't just a text box, it's got all sorts of fancy javascript behind it... yep, according to http://help.blogger.com/bin/answer.py?hl=en&answer=42247 , Safari isn't fully supported yet. Perhaps, if you want to copy/paste, temporarily switch over to the "Edit HTML" mode first (that looks like it just gives a standard text box) instead of the default "Compose" mode?