From: Philip Goetz (philgoetz@gmail.com)
Date: Thu Jan 04 2007 - 16:21:45 MST
Okay, I did some math, and it turns out to be highly UNLIKELY that ET
would find it worthwhile to travel to the stars!
Considering just the energy payoff, in order for it to be worthwhile
to gather the energy of a sun, it would have to be the case that the
energy investment, with interest, would be less than the energy
payoff.
Let
T = time taken to harvest sun's energy
S = energy of sun
L = energy invested at launch time
I = 1 + "interest rate", in same units as T
We must have
L(I^T) < S
in order for the sun-harvesting to be worthwhile.
Suppose that the star is 6 light-years away. This is a reasonable
supposition, because, although you can find stars closer than that,
they aren't distributed evenly throughout space, and rather soon
you're going to find yourself at the edge of your local cluster,
looking more than 6 light-years to the next star.
I find, from the Wikipedia entry on "Orders of magnitude (energy)",
that the theoretical total mass-energy of the sun is 1.8E47 J.
We will suppose that our high-tech ET can accelerate to the speed of
light instantaneously, and make the round-trip to the star and back in
12 years = 4380 days. We then have
L(I^4380) < 1.8E47 Joules
ln(L) + 4380ln(I) < ln(1.8) + 47ln(10)
We will suppose that ET is very energy-efficient, and can create and
launch a spaceship using 1 Joule of energy, so ln(L) = 0. We thus
have
ln(I) < [ln(1.8) + 47ln(10)] / 4380 = 0.0248423
I < 1.02515
Thus, even if ET is able to build an impossibly-perfect spaceship and
launch it with 1 J of energy, it is not worthwhile for ET to do so, to
gather the energy from a sun and bring it back, unless the "interest
rate" (on investments; in our society we would think of it as an
interest rate on money, but in ET's more advanced society they think
of it as an interest rate on energy) is less than 2.5% per day.
It seems to me more likely than not that the interest rate in a
post-human society would be more than 2.5% per day. This is simply
because moving from thinking based on the stochastic movements of
proteins in fluid and currents traveling at 3m/s, to thinking based on
the computer architectures we have today, would at first glance
suggest a subjective speedup factor of about a million, making an
interest rate of 10%/year in human society translate to an interest
rate of about 27,400%/day.
The only vulnerable point that I see to this argument is the
supposition that ET needs to bring the energy back to his starting
point. I'm assuming that ET at home does not feel especially
benevolent, and wants the benefit of that sun's energy for himself.
I'm also assuming that ET is part of a relatively large computational
entity, and that sending out an ET would amount to making a copy of ET
and putting it on a spaceship.
You might argue that ET would be altruistic enough to let the copy of
ET stay out by the sun and use its energy there. You might further
argue that we should then consider the travelling ET's subjective
time, which will be very small, since it will travel near the speed of
light.
I don't think that a stay-at-home ET would evaluate its return on
investment from the point of view of the travelling ET. I might
consider than an ET that planned to pull up stakes and travel itself,
might consider the time to be that experienced on the voyage.
- Phil
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