# Re: Re: Re: Re: Evidence: Open vs. Closed Universe

27 Nov 1997 11:15:47 +0100

> In a message dated 11/26/97 7:10:01 PM, you wrote:
>
> >Nononono! A closed universe doesn't have a boundary, but its total
> >volume is finite.>>
>
> Mental masturbation.

It appears to me like you do not know or understand anything about
general relativity, instead preferring to propose neotech as the
solution at any opportunity.

Here is some basic cosmology, equations quickly cut and pasted from a
Freeman Dyson paper:

Closed universes are represented by the metric

ds^2 = R^2 [dpsi^2 - dchi^2 - sin^2 chi dOmega^2],

where chi is a space coordinate moving with matter, psi is a kind of
time coordinate related to physical time t by

t = T_0 (psi - sin psi),

and R is the "radius" of the universe (perhaps better seen as a scale
factor) given by

R = c T_0 (1 - cos psi).

(it will recollapse at time 2 pi T_0)

The spatial geometry of a closed universe is at a given time
equivalent to a three-sphere (S^3): it is bounded, the integral of the
volume of space exists and is finite and it has no "edges" (if you
move straight forward in any direction you will eventually end up
where you started).

I don't see why people have any problems with this. :-)

[While I'm at it, and cutting and pasting equations from Dyson, the
metric of an open universe is

ds^2 = R^2 [dpsi^2 - dchi^2 - sinh^2 chi dOmega^2],

where

t = T_0 (sinh psi - psi),

R = c T_0 (cosh psi - 1),

and 0 < psi < infinity 0 < chi < infinity. This universe lasts forever
and has infinite volume.]

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Anders Sandberg                                      Towards Ascension!