Re: Interval


"Curt" <curt2@xxxxxxxxxxxx> wrote in message
news:NY%Oe.4055$Rh5.2958@xxxxxxxxxxxxxxxxxxxxxxx
> Bilge said:
>
> ........ What it means is
> that rotations in any plane are just like rotations in any other
> plane.
>
> Since a rotation by \pi changes the direction
> you are facing, this would have to apply to rotations that
> allowed you to change directions in time, just by turning around.
> That is clearly different that what we observe. The metric
> with ---- has the same problem.""
>
> Essentially, you are saying that "time's arrow" prevents rotations in a
> space-time (eg (x-t) plane) plane from being the same as those in a purely
> space plane
> eg (x-z) plane?
>
>
>
> "The metric --++ is degenerate. A degeneracy implies that more than
> one eigenvector corresponds to the same eigenvalue. In this case,
> the eigenvalues are associated with directions in space, so that the
> spacetime isn't really four dimensional. That rules out both --++
> and every other combination of two + and two - signs."
>
> The way I would reason it is that if we had --++ (or ++--) then that would
> mean that one of the spacial dimensions is "special" in some way, which
> would be ridiculous, intuitively.
>
> eigenvectors. I had never heard of these. A quick look on the internet has
> yeilded definitions which I can't really grasp. I think I can get the
> basic idea. Eigenvectors are vectors that, after some transformation,
> preserve their direction (basically right?).

Eigenvectors and eigenvalues are concepts from a branch of mathematics
called linear algebra. See
http://joshua.smcvt.edu/linearalgebra/
I fully concur with PD's recommendations

Thanks
Bill

> Eigenvalues represent the factor by which the vector length has increased.
> So the metric with ++-- is degenerate. So this means, using the
> definitions I found, that after some rotation, there is more than one
> vector which has not changed direction ands some of these vectors share
> the same eigen value; they have increased in size by the same factor. I
> will think this over for a while...
>
>
> Thanks
>
>
>
>
>
>


.

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