Re: resolve to perpendicular components, because they are independent

"Ken S. Tucker" <dynamics@xxxxxxxxxxxx> wrote in message
news:1137871786.842707.317150@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
|
| FrediFizzx wrote:
| > "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
|
| Here's an interesting quicky...
|
| http://en.wikipedia.org/wiki/Fractional_calculus
|
| that demo's a departure from our usual "integer" thinking, we
| commonly apply to both calculus and so to dimensionality.
|
| Recall that when we integrate a line like "x" by
|
| $ x dx = x^2/2 == area
|
| we go from 1D "x" to 2D "x^2" , but what the link above shows
| is that integration (and differentiation) can be a continuous thing,
| and so can dimensionality.
|
| Is that where we're going?

Yep, I am really thinking that this is what she is talking about with
"warped" spacetime. Now what is that particular name you had for this?
Sheesh... I can't believe I forgot it!

FrediFizzx

http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps

http://www.vacuum-physics.com

.

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