Is The Fermi Paradox Really A Paradox?

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Photo from WIkimedia Commons, by Colby Gutierrez-Kraybill.

Apropos of a bit in Wait But Why? About why there are (apparently) no other intelligent beings that we can see in the universe, there were a couple of things I wanted to check out. One was the average distance between civilizations. That is, about how far away the nearest group of aliens ought to be. The other was thinking through whether we’d even notice they were there.

Now a caveat: I am not an expert on extraterrestrials, or even astronomy. I am a guy who took some physics, and knows a little math, and who has had the occasional back-and-forth about this in other corners of the Internet. If there’s an expert out there who can tell me why I am way off, please let me know.

So, on the first point there are a couple of ways to approach it. One is to look at the number of planets that the Kepler mission discovered around other stars.

The Planetary Habitability Laboratory has one way of looking at it – they took the number of stars with anything like an “Earth like” planet around it in the solar neighborhood. A lot of those stars won’t be like the sun at all; they will be reddish dwarf stars. Such stars are nearly impossible to see with the naked eye, and they are much less massive than the sun. They can be, however, more stable in the sense that they live a lot longer.

That said, let’s take their estimate as a given. Up to 160 habitable worlds within about 33.6 light years sounds pretty good. So how far away from each other would they be?

Assuming a 33.6 light year radius, that works out to a sphere of about 159,000 cubic light years. We divide that by 160. So each planet is in a sphere of roughly 993 cubic light years, which we can round up to 1,000, or a cube 10 light years on a side. If we were more exact about the volume of a sphere we’d get a radius of about 6.1 light years, so let’s take an average and call it 7.5 to 8 light years on average. That’s about twice the distance to Alpha Centauri, and it’s close enough that radio communication is actually feasible, since the time lag isn’t so long – a message would take about 15 years to get a response.

But now we get to a harder problem. Why isn’t there anyone there? And that means looking not only at how many planets there are but how many are habitable and how many actually develop life.

There are no other examples of life except Earth (so far). We can, though, extrapolate a bit. Mars is dry and cold now, but it might have been wetter and warmer in the distant past. Jupiter’s moon Europa has possibilities, too. So let’s assume that any system with a habitable planet has more than one, call it two. That means 320 habitable worlds in the neighborhood, which also sounds good.

Not every planet will develop life. That’s the major bottleneck, as it were, to finding intelligent beings. There’s a lot of theories about such bottlenecks and why they might or might not occur, and I’ll get into those later. But for now, let’s stick to the numbers we have. Life developed on Earth pretty quickly, as these things go, within a billion or so years – the earliest evidence is 3.5 billion years back at least. That sounds like a long time but it is only a small percentage of the time Earth has been around, about 4.5 billion years.

So looking at our own planet at least it looks like life takes hold as soon as it can. There’s some scientific controversy about the exact mechanism, but the short answer is that whatever drives life to happen, it didn’t wait long – basically as soon as water was a liquid and the temperature dropped enough that organic molecules would hold together, you had life.

But now we get to the kind of life that we think of as resembling us. That took a lot longer. From 3.5 to 1.5 billion years ago (give or take 200 million years), there wasn’t anything on the planet that even had a cell nucleus. Colonies of single-celled organisms seem to have appeared about 2.1 billion years ago, but multicellular life that has specialized cells doesn’t appear until 600 million years ago or thereabouts (the Ediacaran fauna). Now, granted, multicelled animals probably existed before then, since we  only know about the ones that leave fossils. Even so, that means in the history of the planet, while there was biomass around, most of the time it’s been algal mats and bacteria. Multicellular life has only been around for some 15-20% of the planet’s history.

That may mean the leap from single-celled to multicellular life isn’t one that happens very often. It might mean that most planets that are near the mass of the Earth and in the habitable zone have life but the most intelligent creature is a lichen.

So let’s come up with a reasonable estimate for how often life gets to be multi-cellular. Assuming our number of habitable planets in a given system averages to two, we’ll assume that half develop life and half of those make the jump past algal mats and germs. That gets us 80 planets in the 33.6 light year radius we started with.

Once past that point, though, you need to develop intelligence, and you need to develop tools, and you need a way to communicate over interstellar distances (or at least be visible).

So far technological intelligence has developed only once on Earth – that is, in primates. We could argue all day about how smart dolphins are, but they don’t build radio telescopes, so any intelligent sea life out there probably won’t be visible. (Water is an excellent shield for high-frequency transmissions, so even if they built radios they wouldn’t be transmitting in a band we could hear). The fact that only one lineage out of thousands got to tool-making does not bode well.

What are the odds then? One percent? Ten percent? Going by a number-of-species argument (remember that millions of species have come and gone) it would be less than one percent, and even counting by whole families (in the zoological sense). So let’s assume one percent make it to a technical civilization, which is probably high.

Now we’ve reduced the number of planets in the neighborhood with intelligent life to about 0.8.Which is about what we observe. There’s just us – or rather, we’re the only ones anyone else could see with a radio telescope. If the percentage is 0.5 percent, then the nearest civilization will be (on average) 60 light years away or more.

This is important when thinking about how we might detect other civilizations. The most powerful signals we ever sent out – and those were not omnidirectional – were those from early-warning radar during the Cold War. An alien civilization might pick those up if they happened to be in the beam, but even that is only out to tens of light years – call it 100 at the outside. If the ETs are more than a few tens of light years distant then we’d never see them at all even if we happened to be right in the beam.

Aliens using AM or even low-frequency FM radio wouldn’t be heard (and neither would we), because AM signals don’t penetrate the ionosphere. To get an interstellar signal you need to at least be in the UHF television range. (Any planet with life in the first place is pretty likely to have an ionosphere, because gases in the atmosphere get ionized by solar radiation).

A paper by John Billingham and James Benford on the ArXiv (link here) outlines the difficulty of hearing “leakage” transmissions, which is what we are talking about. They note that the Square Kilometer Array can pick up anything within about 650 light years by looking at how much energy it produces against the background — but deciphering of the signal itself is much harder, because it is still faint. Their paper focused on the costs of building a radio telescope that could pick up other civilizations, but the main point is that absent some technology and physics we haven’t heard about, while aliens who happened to point a radio telescope in our direction might figure out  something is there, “I Love Lucy” reruns wouldn’t be visible.

There’s also an old graph from the SETI projects from NASA here. Look at the effective power of the transmitters and the sensitivity of the sky searches (the vertical lines). What it shows is that if you used the biggest radio telescope in the world — Arecibo, which is some 300 meters across — as a radar array you could be detected within 1000 light years, if an observer were looking right at it. Otherwise, more than 30 or so light years out you’d never see the transmission. UHF TV wouldn’t be heard at all, even by an Arecibo-sized receiver staring right at the relevant star.

What about more advanced aliens? That might actually be an even bigger problem. Digital signals are fast becoming the way we communicate – the old loud radar and RF transmissions are becoming passé. We have used radio for about 100 years, and that means anyone listening for us has to hit that window. The same applies in reverse.

This gets into something else about finding alien life forms: the issue of time. Picture an alien civilization that is situated 200 light years away. They do exactly what we did, and invent radio. They broadcast, and 100 years later they invent the Internet.

If they invented radio 300 years before we did, in say, 1600, the first signals we could hear would arrive around 1830 or 1840. (Assuming it took them 30 years to hit a golden age of radio, like we did). That means our window to hear them would have ended in about 1950 – if we even knew to listen. After that, no dice. The digital signals would be almost impossible to pick out from the background, even if they were loud enough.

Think now about the idea that the distances aliens are likely to be will be random and the galaxy is very, very big. For us to pick up an equivalent civilization they would have to be precisely placed in a sphere of about 200 light years. The whole galaxy is thousands of times that size. A civilization too close hasn’t invented radio yet (or not far enough in the past for us to hear). Too far and we missed them.

Now, I want to be clear: this is not to say that there is no intelligent life. I am offering a set of reasons why even if there were people living right nearby they would be very, very hard to see. There could be a half-dozen civilizations within 100 light years, and unless they did some major stellar engineering project like a Dyson sphere or beamed a signal right at us, we might never know.

Maybe a better way to phrase the Fermi paradox is to ask not why we don’t see anyone, but how we can improve the detection methods to see them at all. That may be a bigger project than lots of people realize — but I think it’s certainly worth doing.

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One Response to Is The Fermi Paradox Really A Paradox?

  1. Pingback: Fermi Paradox Part III: Why Aren’t They Here? | Traveler's Tales

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