E.G. The object sending out the light wave can not be traleving away
from us at a speed higher than the speed of light no matter of how
far away it is! Therefor the light will allways reach us.
> From: Nick Bostrom <firstname.lastname@example.org>
> To: email@example.com
> Date: Sun, 18 Jan 1998 17:05:21 +0000
> Subject: Re: adapting to an open universe
> Reply-to: firstname.lastname@example.org
> Hal Finney <email@example.com> 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
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