I've been a Fermi Paradox fanboy since a June 2000 Scientific American article roused my ire.
The essence of the puzzle is that while the galaxy is big, exponential growth and galactic time scales mean that critters like us ought to have filled it up by now.
I find it helpful to consider the ubiquity of bacteria ...
Bacteria: 10**-5 m
Human: 1 meter
Earth: 10**7 m - "mid" way between the Planck length and the universe.
Sun: 10**9 m
Milky way Galaxy: 10**21 m
So it takes at most 10**12 bacteria to stretch (directly) between any two points on the earth's surface.
Conversely it takes at most 10**14 earths to connect any two points in our galaxy.
So, within a an order of magnitude or two, a bacterium is to the earth as the earth is to the galaxy.
Over a mere 1-2 billion years bacteria have saturated the earth; common species are found everywhere. So how come the galaxy doesn't crawl with exponentially expanding aliens?
There have been lots of great theories, I won't review them here (see my old web page for examples). The most widely held explanation is that there is a Creator/Designer and She Wants Us Alone. This is more or less what you'll hear from most of the world's theists and from the Matrix crowd.
I prefer some other theories, though I do take the 'by design' answer seriously. Recently Charles Stross, who's explored the paradox in many of his science fiction novels and short stories, wrote a particularly strong summary of recent discussions ...
The Fermi Paradox [is]... ...a fascinating philosophical conundrum — and an important one: because it raises questions such as "how common are technological civilizations" and "how long do they survive", and that latter one strikes too close to home for comfort. (Hint: we live in a technological civilization, so its life expectancy is a matter that should be of pressing personal interest to us.)
Anyway, here are a couple of interesting papers on the subject, to whet your appetite for the 21st century rationalist version of those old-time mediaeval arguments about angels, pin-heads, and the fire limit for the dance hall built thereon:
First off the block is Nick Bostrom, with a paper in MIT Technology Review titled Where are they? in which he expounds Robin Hanson's idea of the Great Filter:The evolutionary path to life-forms capable of space colonization leads through a "Great Filter," which can be thought of as a probability barrier... The Great Filter must therefore be sufficiently powerful--which is to say, passing the critical points must be sufficiently improbable--that even with many billions of rolls of the dice, one ends up with nothing: no aliens, no spacecraft, no signals...The nature of the Great Filter is somewhat important. If it exists at all, there are two possibilities; it could lie in our past, or in our future. If it's in our past, if it's something like (for example) the evolution of multicellular life — that is, if unicellular organisms are ubiquitous but the leap to multicellularity is vanishingly rare — then we're past it, and it doesn't directly threaten us. But if the Great Filter lies between the development of language and tool using creatures and the development of interstellar communication technology, then conceivably we're charging head-first forwards a cliff: we're going to run into it, and then ... we won't be around to worry any more.
But the Great Filter argument isn't the only answer to the Fermi Paradox. More recently, Milan M. Ćirković has written a paper, Against the Empire ... an alternative "successful" model for a posthuman civilization exists in the form of the stable but non-expansive "city-state". Ćirković explores the implications of non-empire advanced civilizations for the Fermi paradox and proposes that such localized civilizations would actually be very difficult to detect with the tools at our disposal, and may be much more likely than aggressively expansionist civilizations.
Finally, for some extra fun, here's John Smart pinning a singularitarian twist on the donkey's tail with his paper Answering the Fermi Paradox: Exploring the Mechanisms of Universal Transcension:
I propose that humanity's descendants will not be colonizing outer space. As a careful look at cosmic history demonstrates, complex systems rapidly transition to inner space, and apparently soon thereafter to universal transcension...
A very nice summary, even it doesn't add anything novel.
My "SETI Fail" page independently reinvented the singularitarian Great Filter, but I soon learned my thought was far from novel. Among others the ubiquitous Mr. Smart told me he'd come up with this resolution in 1972!
Another explanation, btw, is that established powers, fearing rivals, routinely wipe out any civilization foolish enough to advertise itself. Few find this explanation persuasive, but it's pertinent to my next tangent.
Assume one were a cautious high tech entity that had survived the Great Filter in some far away galaxy. You have lots of power available, but you fear sending a signal a galactic neighbor could capture. Better, perhaps, to send a generous one-way message to another galaxy. The distances are so vast, and light is so slow, that there's no possibility of unwanted extra-galactic visitors. Communication between galaxies is a message to the far future, and thus "safe".
So I wondered, this morning, how one would send such a signal.
... That's the conclusion of a group of US astronomers who say that the galaxy is filled with photons that make communications channels noisy whereas neutrino comms would be relatively noise free. Photons are also easily scattered and the centre of the galaxy blocks them entirely. That means any civilisation advanced enough to have started to colonise the galaxy would have to rely on neutrino communications. And the astronomers reckon that the next generation of neutrino detectors should be sensitive enough to pick up ET's chatter...
So now we need only look for extra-galactic neutrino messages ...