Tom Roberts <tjroberts@Lucent.com> wrote in message news:<3F70B8FD.7030106@Lucent.com>...
>On 9/22/2003 8:40 AM, Ken S. Tucker wrote:
>
>> diag(1,1,1,1) permits *oblique* coordinate systems 
>> that are *nonorthognal* and Lorentz compatible.
>
>Review what "metric" means, and you will realize that ANY AND EVERY
>coordinate system in which the metric is diag(1,1,1,1) has orthogonal
>coordinates. 

Tom, I agree a metric equivalent to diag(1,1,1,1), is
certainly orthogonal, I said the metric has diag(1,1,1,1) 
set obliquely. For example, (you'll probably enjoy this),
the determinant in 2D  t,x  of the metric is,

g_uv = | 1   -v |  = 1-v^2
       | -v   1 |

the diagonal is (1,1) yet this produces the Lorentz transform
and is non-orthogonal.

ds^2 = g_00 dt^2 + 2*g_01 dt dx + g_11 dx^2

     = dt^2 -2*v dt dx + dx^2,   now set v=dx/dt,

     = dt^2 -2 dx^2  + dx^2 = dt^2 - dx^2 which is the LT.