Re: Theory of Relativity


Spoonfed wrote:
> Ken S. Tucker wrote:
> > As prefaced in my post, a reasonable familiarity
> > with tensors is required. I use covariant "A_u",
> > and contravariant "A^u" notation, also the summation
> > convention, association, and the Absolute derivative,
> > as is standard, and well founded by mathematicians.
>
> Well I'm up to page 83 of Introduction to Vector and Tensor Analysis,
> by Robert Wrede, although I'm planning to reread 65 through 83
tomorrow
> (where the concepts of covariant and contravariant are introduced).
I
> was frustrated with it at first, since I found it impossible to skip
> through it.

Sorry, I don't have that book. Learning Tensors by oneself
is difficult (I had the benefit of Profs), for even a good
math student. It would be good if could speak to a local prof
for 15 minutes a week, just to get by some the sticklers.

I'm rather poor at math, but I did come to appreciate the
diff between covariant and contravariant tensors in GR, for
example, g^00 = 1/g_00 (approximately) and g^11=1/g_11,
where x1 is parallel to radius.
So the g-field makes spacetime go like g_00 == g^11 and
g^00 == g_11 so what remains is g_00 g^00 == g_11 g^11
which is neat.

> There's no way to look up mathematical conventions and
> semantics in the index. For instance, lower-case letters are from
the
> original matrix, upper case letters are cofactors. a_i^k is a
rotation
> matrix. b_i^k is something else, and X, unfortunately seems to have
a
> different version of a very vague definition every time it comes up.
>
> Eventually, I'll get immersed in it and be even harder to understand.
> ;)

Well, there's lots of people in this group who would like to
help, but doing through ascii is difficult, but try it and see.
Ken

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