Re: GR -> Black Holes Can't Form... Take 2

From: FrediFizzx (fredifizzx_at_hotmail.com)
Date: 02/24/05 

Date: Wed, 23 Feb 2005 22:04:06 -0800

"Tom Roberts" <tjroberts@lucent.com> wrote in message
news:cvie6l$5oq@netnews.proxy.lucent.com...
| FrediFizzx wrote:
| > "Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
| > news:1109060845.272121.176720@f14g2000cwb.googlegroups.com...
| > | a quote
| > | from Dover's PoR, pg 77, Minkowski writes,
| > |
| > | "Hence we may give to the time axis whatever
| > | direction we choose toward the upper half of
| > | the world t>0. Now what has the requirement of
| > | orthogonality in space to do with this perfect
| > | freedom of the time axis in an upward direction?".
| > |
| > | Lovely words, very meaningful to me.
| > |
| > | Minkowski provides a picture in FIG.1 (pg.78),
| > | wherein x' and t' are nonothogonal.
|
| You have a devastating unacknowledged PUN on the word "orthogonal" here.
|
| That paper is in the context of SR and Minkowski coordinates, so x' and t'
are
| indeed orthogonal in the usual sense: g_t'x' = 0. But because the paper on
which
| the drawing is made is inherently Euclidean, the x' and t' axis ON THE
PAGE are
| not AT RIGHT ANGLES. While this latter property is also called
"orthogonal", it
| is a completely different sense than the former. It is the former property
that
| is important in SR.
|
|
| > | That does indeed have something to do with
| > | relativity.
|
| Not really. One must keep separate the concepts of "orthogonal in
Minkowski
| spacetime" and "orthogonal in a Euclidean space".
|
|
| > Wow! I just looked that up. Seems like you are right. Time can be
like a
| > loose cannon.
|
| Only when you confuse Euclidean notions with Minkowski meanings.
|
|
| > Is this something like if we are at a point in 3D space, I
| > can point my finger in an infinite number of directions; space is really
| > infinite dimensional with respects to that?
|
| No. Your usage of "dimensional" here is completely incorrect.

So what? You don't think there is an infinite number of non-orthogonal
coordinate systems for "3D" space?

FrediFizzx

Relevant Pages

  • Re: GR -> Black Holes Cant Form... Take 2
    ... | the drawing is made is inherently Euclidean, the x' and t' axis ON THE ... |> can point my finger in an infinite number of directions; ... FrediFizzx ...
    (sci.physics)
  • Re: resolve to perpendicular components, because they are independent
    ... FrediFizzx wrote: ... It's well known "orthogonality" is ... > | If your intrinsic dimensionality differs from an integer, ... I wonder if that would apply to what Lisa Randall is calling ...
    (sci.physics)
  • Re: GR -> Black Holes Cant Form... Take 2
    ... > | orthogonality in space to do with this perfect ... It is the former property that ... One must keep separate the concepts of "orthogonal in Minkowski ... spacetime" and "orthogonal in a Euclidean space". ...
    (sci.physics.relativity)
  • Re: GR -> Black Holes Cant Form... Take 2
    ... > | orthogonality in space to do with this perfect ... It is the former property that ... One must keep separate the concepts of "orthogonal in Minkowski ... spacetime" and "orthogonal in a Euclidean space". ...
    (sci.physics)