Re: adapting to an open universe

Nick Bostrom (bostrom@ndirect.co.uk)
Sun, 18 Jan 1998 17:05:21 +0000

Hal Finney <hal@rain.org> wrote:

> It may be that the universe expansion is worse than I thought.
> Consider that the computer must, as time goes on, be composed more
> and more of empty space, since the density of space is decreasing
> (exponentially?). We must signal from one side to the other by sending
> something that takes energy, whether gravitational radiation, photons,
> or particles. Suppose we send a particle. The problem may be that if we
> give the particle too small an initial speed, that it never gets there.
> It loses ground due to the universe expanding out from under it, and at
> some point it actually starts to go backwards.

I had a similar thought the other day.

I started out with the following idea. Suppose we construct probes
that fly out in all directions, and when they reach a lump of matter,
they use some of the energy it contains to shoot fragments back to
origo (Earth). Some fragments have to fly in the opposite direction
to conserve total momentum, but there should be a constant fraction
of the energy in a lump of matter that we can send back to origo at a
certain speed.

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.

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.

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.

________________________________________________
Nick Bostrom
http://www.hedweb.com/nickb