# Re: adapting to an open universe

Hal Finney (hal@rain.org)
Sun, 18 Jan 1998 19:51:05 -0800

Nick Bostrom, <bostrom@ndirect.co.uk>, writes:
> As the colonization wave spreads, the frontier surface that they
> harvest matter from increases as the square of the radius of the
> colonization bubble. My idea was that even if the average density of
> the universe decreases over time as a result of expansion, this
> decrease might slow enough so that amount of matter that
> could be sent back to origo at any moment would diverge as t goes to
> infinity. This could allow an infinity of computations at origo.

One flaw with this plan, which is actually mentioned by Tipler, is that
there will be an infinite number of civilizations in the universe, each
with only a finite volume of space they can use. Now, maybe you could
assume that when different civilizations meet, they will combine their
resources and collect them together at one point. However, this would
have to go on an infinite number of times. Maybe this is not really any
worse though than Tipler's assumption that life throughout the universe
will cooperate an infinite number of times to keep the universe collapsing
the right way.

> I did some back of the envelope calculations. I think the expansion
> rate of the universe (if it is open) will asymptotically approach a
> constant (could anybody confirm this?). So the density of the
> universe would decrease as t^3, for large values of t, and the volume
> from of the space where we can have harvested a constant fraction of
> its matter content grows as t^3 (if the probes have constant speed
> ans since the volume of a sphere is proportional to R^3). So far,
> things look bright.

Parenthetically, it grows faster than t^3 because of the hyperbolic
geometry, but this should not be too significant.

> But then I thought of this problem. Suppose the probes travel with
> the speed v. Then there must be some distance d such that if the
> probes start at that distance, they will never return to origo. For
> if d is big enough, then by the time the probes have traveled 10% of
> the way, the remaining 90% will have grown larger than the original
> 100%, due to the expansion of space inbetween. So if that expansion
> rate settles down to a constant, then there must be a sphere centered
> around Earth such that nothing that is outside of that sphere can
> *ever* affect Earth, even if it travels with the speed of light.
> Hence the above proposal fails, unless somebody can point to some
> mistake in this reasoning.

I think this is right for normal velocities, but I'm not sure it
generalizes to the speed of light. I find a lot of references to
the behavior of light in a collapsing universe, how many times it can
circumnavigate during the collapse, but I will have to do more study to
figure out what happens in an expanding universe. My intuition though
is that the region of space which can affect the earth will grow without
bounds, and that there is no limit to how far a photon can travel in an
infinite universe.

Hal