Fermi’s Paradox

Written on December 28, 2014. Written by .

Wikipedia describes Fermi’s Paradox as follows:

“The apparent size and age of the universe suggest that many technologically advanced extraterrestrial civilizations ought to exist. However, this hypothesis seems inconsistent with the lack of observational evidence to support it.”

Scientists estimate that out of the roughly 200 billion star systems in our Galaxy, there are roughly 40 billion potentially habitable planets in the “goldilocks zone” and 8.8 billion of them around sun-like stars, the rest belonging to red dwarfs [1]. This figure doesn’t even include all the smaller moons that could potentially support life. Even if the probability of life forming on any given planet is low, that is a lot of chances. It’s hard to guess how many of those planets have life and how many have intelligent life, but it would be clearly be unreasonable to confidently assume that extraterrestrial life does not exist in our galaxy. And given that there are at least a hundred billion galaxies in the observable universe, and many more beyond the observable universe, it seems quite likely that there are lots of worlds with intelligent life.

So why do we have no evidence of extraterrestrial life? Life outside our galaxy would be too hard to detect, but if there were life in our galaxy, it might be detectable. For example, it would only take 5-50 million years to colonize the galaxy using “slow” technologies that we already have access to. If an advanced civilization existed over 50 million years ago, it could have colonized every planet in the galaxy by now, including earth. But it’s not obvious that it would do that. In fact it seems more likely that it would not colonize the galaxy because expansion is costly an unnecessary. Humans expanded to cover most of the earth, but only because the population was growing and expanding provided easier access to resources. An advanced civilization might realize that population control is preferable to expansion because expansion out of the solar system would mean communication latency on the order of years, effectively disconnecting them from the internet of their home world.

If they were sufficiently advanced, it would probably be better to build more planets in their home system to keep the communication latency low. After consuming all the matter in their home system, they would then have to either stop growing, mine other systems for matter/energy, or expand. Again, the first two seem like better options than expansion. If they do start mining, it would certainly slow their growth because they still have to obey the laws of physics. But eventually they would reach a point where the energy cost of mining is greater than the total energy in the matter they are mining, discounted for the time it takes. Getting $2 in exchange for $1 is only a good deal if you get the $2 in the near future; if it takes 20 years then you could have done better with other investments. At this point, mining would stop if they are acting rationally, so they might stagnate from a growth perspective, while still improving their home system internally. Perhaps this would result in a Dyson sphere or Matrioshka brain where the civilization could live in a virtual reality, making physical expansion unnecessary.

Expansion of humans over the surface of the earth is not a good analogy for expansion of advanced civilizations across the galaxy because advanced civilizations will likely care more about communications and be able to utilize space more effectively with computers.

But if a highly advanced civilization existed, wouldn’t it want to at least send out probes to explore the galaxy? It seems prudent to know what other life exists to make sure that it doesn’t come to destroy you. It would also make sense to make the probes stealthy because if one gets captured it would take a very long time to replace it. There could be a tiny probe in our solar system monitoring radio broadcasts and forwarding them to its home system using perfectly targeted beams like a laser. The probe itself wouldn’t make contact with us or it would risk being captured.

But once the extraterrestrials got the message, they might make contact with us. But even if they did, it might be a while before we hear from them. The earth has only been broadcasting radio waves for about 100 years. And those radio waves rapidly lose their strength the further they travel. The Arecibo radio telescope would only be able to detect such radio broadcasts if they were within 0.3 light years and the nearest star is 4.2 light years away [1]. Beyond that, the signal would get lost in the noise. However, if there was already a probe here, then it could forward the signal directionally to avoid this issue. Assuming that the probe was present, there would have been enough time for a round-trip to a star up to 50 light years away. But there are only about 2000 stars within 50 light years [2], which is just 0.000001% of the stars in the galaxy. It is quite likely that any extraterrestrial civilizations haven’t heard about us yet because we are so new as a technological civilization.

And for the same reasons as above, we will probably have a hard time detecting any signals that they create, unless they are aimed directly at us. Even if they were trying to make contact (and it’s not clear that they would want to), it would seem like a big waste of energy to send beams to every star system in the galaxy too frequently. We certainly aren’t doing it, Earth has only sent a few interstellar messages and they were short in duration [3]. Assuming a message did get beamed directly to earth, there is a very high probability that we would miss it [4].

Overall, it’s not too surprising that we don’t yet have evidence for extraterrestrial intelligence; the vast scale of the galaxy, the speed of light, and lack of alignment with incentives make it difficult. 

[1] http://www.nbcnews.com/science/space/8-8-billion-habitable-earth-size-planets-exist-milky-way-f8C11529186

[2] http://www.atlasoftheuniverse.com/50lys.html

[3] http://en.wikipedia.org/wiki/List_of_interstellar_radio_messages

[4] http://www.setileague.org/askdr/howmuch.htm

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