Re: resolve to perpendicular components, because they are independent

"Ken S. Tucker" <dynamics@xxxxxxxxxxxx> wrote in message
news:1137804799.742330.45120@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
|
| FrediFizzx wrote:
| > "Ken S. Tucker" <dynamics@xxxxxxxxxxxx> wrote in message
| > news:1137800854.404588.75250@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| > |
| > | Timo Nieminen wrote:
| > | > On Fri, 20 Jan 2006, Ken S. Tucker wrote:
| > | >
| > | > > I find nonorthogonal axes easier than orthogonal,
| > | >
| > | > Then you must be some kind of bizarre freak of nature!!!
| > |
| > | Not really, as in Chess, solving problems in mathematical
| > | physics consists of keeping your options open, to be
| > | closed by physical principle, and certainly not by an aprior
| > | preceived convenience. It's well known "orthogonality" is
| > | at best an approximation in a g-field, but Reimann and his
| > | "gang" evolved quite a nice "tensor" analysis notation that
| > | is easier to use than clunky "ijk" unit vectors.
| > |
| > | > > indeed a Curl
| > | > > becomes A_u,v - A_v,u (== &A_u/&x^v - &A_v/&x^u), because
| > | > > manipulating equations in tensors is streamlined by notation.
| > | >
| > | > Can't you just do that with orthogonal metrics too? (Mixing
| > covariant and
| > | > contravariant is just a naughty little trick to hide the metric
| > tensor!)
| > |
| > | If your intrinsic dimensionality differs from an integer, i.e
| > | let n= intrinsic dimensionality =2.9, then how the heck do
| > | you expect to squeeze 3 orthogonals into that?
| >
| > Hmm... I wonder if that would apply to what Lisa Randall is calling
| > "Warped Passages"?
|
| LOL, ok, how about a link, Randall is super-pop, so
| I know you're not jokin...

"Discretizing Gravity in Warped Spacetime"
http://www.arxiv.org/abs/hep-th/0507102

I haven't read this yet but maybe it has something. I was mainly
referring to something she was saying in her new book (did you get it
yet? ;-) ). I didn't make the connection at the time I was reading it
until you brought this up (forgot what you call it) again.

FrediFizzx

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