Re: poly: eschatology

Nick Bostrom writes:
> But in the case of the open universe, if we project backward in
> time in the same simple mental model, then we seem to come to a
> point in time, about 15 billion years ago, where the whole infinite
> space with the infinite number of stars just pops up instantaneously
> all over the place so to speak. That surely can't be the right way to
> think about it? But what can we say about the spatial extention of
> our universe 15 billion years ago if it's open?

Keeping in mind the caveats I mentioned in my earlier message, an open
universe is infinite in extent. Activity since the big bang imposes
a scale factor on the universe; density has dropped, but the overall
size of the universe has remained infinite.

At the very moment of the big bang, the single instant t=0, I don't
think general relativity tells us what the size of the universe would be.
In the context of strict relativity, we have an infinite size times a zero
scale factor, and infinity times zero produces an indeterminate result.
Could be infinity, could be zero, or could be some arbitrary finite number.

But general relativity breaks down at that point anyway; we need to
incorporate QM. Presumably we don't actually reach a point of infinite
density, but QM factors intervene before then. Given that the mass of
the universe is infinite, I would imagine that it will turn out that the
spatial extent of the universe is so as well (assuming these concepts
remain well defined in the intensely quantum system we are talking about).

The Big Bang in all models happens "everywhere at once". My biggest
gripe with misconceptions of the BB is that people think they can stand
outside and watch it explode, like a spectacularly vivid supernova.
Popularizations of the BB often show it in these terms. A more correct
model is one in which there is no depiction of conditions before the
Big Bang, the universe starts out (nearly) infinitely hot and dense
everywhere, and immediately begins to cool and thin.

Hal
Received on Mon Jan 12 17:56:25 1998