From: Hal Finney <hal@rain.org>

Date: Sun Jan 11 1998 - 09:57:10 PST

Date: Sun Jan 11 1998 - 09:57:10 PST

As I understand it, the possibilites are these:

Curvature Global 3D Geometry Ultimate Mass

Topology Fate Density

---------------------------------------------------------------

Positive Closed Elliptic Collapse > Critical

Zero Open Euclidean Expand = Critical

Negative Open Hyperbolic Expand < Critical

The recent measurements suggest that the expansion is decelerating so

slowly that the universe will expand forever, and that we must be in

the third row.

I'm not sure about my characterization of the 3D geometry as being related

to the spatial curvature, but I think it is right. I have listed the

classical non-euclidean geometries. In elliptic geometry there are no

parallel lines; all lines intersect. For the 3D case we would say that

all planes intersect. That is a property of a spatially closed universe.

In hyperbolic geometry there are an infinite number of lines through a

given point parallel to a given line (say "planes" for the 3D case).

The sum of the angles in a triangle is respectivelly greater than, equal to,

or less than 180 degrees for the three rows.

The critical density is about 10^-29 g / cm^3 from one reference I found.

The articles about the recent discoveries were garbled by the press, but

it sounded like they calculated that the actual density is less than

20% of this. If so, that is actually pretty consistent with previous

attempts to measure mass directly, which even counting the dark matter

showed only about 10% of the critical density.

Unless there are some ad hoc topology wraparounds, the zero and negative

curvature universes are infinite in spatial extent, with an infinite

number of stars, unlike the closed universe.

Amusingly, I was browsing a book at the bookstore yesterday called

"Before the Big Bang", by Sternglass. He turns out to be a crackpot

(anybody know a non-pejorative term for this?) who has his own theory

of atomic structure and the universe. I checked to see how his theory

would have fit the recent discoveries. Turns out that he believes there

is no significant deceleration of the expansion, because he says the

universe formed from a spinning super-atom which split and split into

smaller sub-atoms until we have what we see today. It is still rotating,

so that the centrifugal force balances the gravitational pull. He has

a note added late about the recent discovery of apparent anisotropy in

the universe as being consistent with his theories, and presumably the

recent measurements showing lack of deceleration are as well.

I don't have a clear picture of what the attraction was

of a closed universe despite the lack of physical evidence

for it. I found some excerpts from a sci.physics posting at

http://www.seanet.com/~ksbrown/closed1.htm which discussed some

issues, but they didn't seem very convincing.

As David Brin mentioned, Frank Tipler's "Omega Point" theory predicted

that the universe would be closed. Tipler argued that this was the only

way that life could avoid the heat death of the universe. Freeman Dyson

had suggested that life could last forever in an open universe, but Tipler

calculated that it would be doomed to fall into an infinite regress.

Maybe these recent discoveries will force people to find a way to escape

Tipler's negative conclusions.

Hal

Received on Sun Jan 11 18:11:04 1998

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