[ExI] Expansion of the Universe

[Anders Sandberg]

On 2012-12-31 01:53, Tomaz Kristan wrote:
> I am not so sure about the laser part. Probes can do the same. They are
> a bit slower, but non the less. They can chop an escaping galaxy in half
> and send one half to us.

The galaxy has to obey the rocket equation. Let's try to bring home M87, 
53.5 Mly away. Let's give ourselves 100 billion years to do it (beyond 
that, and the expansion will likely win). The necessary delta v is 
0.000535 lightyears per year, or 160,000 m/s. (this is on the same scale 
as normal galaxy velocities, actually)

Let's use the non-relativistic case (this is definitely slow enough). 
DeltaV = v_e log(m_initial / m_end) where v_e is the effective exhaust 
velocity and m_initial the initial mass and m_end the final mass. For a 
given delta V and v_e the mass ratio is exp(Delta V / v_e). If you use 
antimatter rocketry v_e is around 100,000,000 m/s. So we get a mass 
ratio of 2.72 - we will waste 2/3 of the galaxy as reaction mass.

But wait, there is worse! We probably want to *stop* the galaxy as it 
arrives, so we need to remove an equal amount of delta v. That means the 
mass ratio squares, and we loose 8/9 of the galaxy mass.

Still, antimatter propelled galaxies are a bit... messy. What if we use 
it as a photon rocket? Highest possible v_e, a different equation, 
http://en.wikipedia.org/wiki/Photon_rocket
We can use Spike's reflecting Dyson shells to do it. I get a mass ratio 
of sqrt[(1 + Delta v / c) / (1 - (Delta V/c)]. In our case it is 
1.000533 (no stop) and 1.001 (stop). Quite acceptable!

(However, I have not calculated whether the luminosity is enough to get 
the deltaV - we might have to boost some of the star luminosity, 
especiallysince we have a dark matter halo to drag along)

Generally, I suspect we can merge together local superclusters is way. 
Hydra-Centaurus is about 150-200 Mly away. So if we want to bring it 
over in 100 billion years we need 3-4 times the delta V. The mass ratio 
is still pretty decent.

Beyond a certain range the requirements go *way* up, because you will 
have to move against the expansion. Already Hydra-Centaurus has a 
redshift around z=1.012, so we have to overcome a 0.012 c velocity - 
much bigger than the above speeds (but still nonrelativistic). Plugging 
that in the photon rocket stopping mass ratio becomes 1.024 - not too 
bad. But at z=1 (8.4 Gly) the ratio is 4, z=3 (11 Gly) it is 9, z=4 (12 
Gly) it is 16 (neat pattern - see the equations for why). At the far 
distances you need to take ongoing expansion into account, which I don't 
feel a need for today (I have a new year's party to prepare).

Let's just conclude that moving galaxies is not too impossible if you 
let them take their time. However, it will be *very* visible and we can 
be fairly certain we are not seeing anybody doing it in our past light 
cone... or maybe the Great Attractor is actually our local dark-matter 
powered supercivilization?


-- 
Anders Sandberg
Future of Humanity Institute
Oxford University