Are we alone in the Universe?



Updated: December 26, 2006

September 2009, update: Two of my readers have informed me that I have an error in my calculations. In fact, I have overestimated the number of planets with life + civilization level like ours by a whole order of magnitude. This means the distance to nearest populated star system (planet) is even greater by (10)1/3 or roughly ~2.15x. Many thanks to Nanda and Bram!


Let's assume for a moment that millions of attention-seekers have had it right. UFOs that we see are in fact intelligent alien life forms, come to visit our home planet. The question is, how likely are these encounters, regardless of their peculiar nature? I've decided to make a hugely simplified calculation that will help quantify the probability of meeting aliens.

Ages

First, here's a table of ages that will help us understand my calculations. For the sake of simplicity, I have rounded the space age to a century. In other words, the calculations assume that we've been able to send communications and people into space for 100 years already.

Universe
15·109 years
Earth
5·109 years

Human race
2·106 years

Civilization
1·104 years

Space technology
1·102 years

Assumptions

I'm going to be generous. Very generous. I'll assume that our Galaxy has had life forms in it from the very moment of its conception, which I'll even out with the life span of the Universe, even though it is much less. I'll assume that every solar system has had, at one point or another, developed the perfect conditions for existence of carbon-based life forms on one of its planets. I'll neglect the fact that life on Earth took about 5 billion years to formulate into an advanced civilization that we claim to be. In other words, I'll assume that every solar system developed instantly, which means that even planets that are much younger than Earth will be included into the count.

I'll assume that every civilization will enjoy 10,000 (104) years of advanced technologies; just for comparison, we are less than 1% into that count, having had radio for barely a century and having flown to space the first time only about 50 years ago. Do you really think we will still be around year 12006? Or even year 3006? This means that every one of 100·109 stars in our Galaxy has been, is or will have been a host to intelligent, advanced life. Sounds like a lot.

Mathematics

Galaxy
It's very lonely and cold out there

OK, so all of our stars have had planets with life on them. But that does not mean all of them are having them right now. If we look back at our table of age, we can easily find the fraction of time that we've been around, sending signals into space, is just a tiny number, only 6.67·10-9. This means that if the length of the Universe is one meter, we've just claimed a few nanometers. Even if we assume that each civilization will have the full 10,000 years of hi-tech without destroying itself, our reach is still a feeble 0.6 microns.

If I evenly distribute 100 billion lifeforms (equal to the number of stars in the Milky Way), each lasting 10,000 years, this means that at any given time, there will be about 65,000 (6.5·105) human-like planets in our Galaxy, sending radio communications and spaceships in search of other civilizations. Again, this sounds like a lot.

But is it?

Let's look at our Galaxy. It's about 100,000 (105) light years wide and 15,000 (1.5·104) light years thick, except the core, which is about 40,000 light years across (1.5·105). To make the calculations simpler, let's say our Galaxy has a cuboid shape. In that case, the volume of our galaxy is:

105 x 105 x 1.5·104 = 1.5·1014 LY3

Assuming uniform distribution of stellar matter, this means that each solar system occupies a small cube of its own. The volume of this cube for each solar system is:

1.5·1014 / 100·109 = 1.5·103 LY3

In other words, the average distance from one star to the next is:

(1.5·103)1/3 = 11 LY

The approximation is not that far from the truth. Now, not all of these stars have life on it - and more importantly, intelligent, advanced life. Only about 65,000 stars will have planets with civilizations capable of any sort of communications with us, during the lifetime our existence as a space-age race. This makes the effective volume of each "inhabited" solar system much larger. In fact:

1.5·1014 / 6.5·105 = 2.3·108 LY3

In other words, the minimal distance from Earth to a civilized planet, in any which direction is:

(2.3·108)1/3 = 610 LY

What's the meaning of this calculation?

We have sent communications into the space, hoping that other intelligent life forms will be able to discover our transmission and respond to it. But we are going to have to spend quite a lot of time waiting. Even if our Galaxy is teeming with life, it's going to take about 1,200 years, on average, for such an inter-stellar message to reach the recepients and return to sender, by which time many generations of life will have gone by.

On Earth, we should expect a reply to our s-mail around 3200 CE, which is a long, long way ahead. To make things worse, we will not be able to do much with such a reply. Today, our finest spaceships travel at an embarressing fraction of the speed of light. Even if we were dead-sure about our intergallatic neighbors and wanted to visit them, we would be sorely limited in the speed at which we could conduct our voyage. Even at 10% the speed of light, we would probably arrive too late for any warm welcome and defitely get back to a planet long wasted, because the designated 10,000 years would have gone by.

Another question that pops to my mind is the tiny issue of human life span? Sending a spaceship on a 1,000-year mission will require quite a dedication from its crew. And lots of breeding. And while the first generation of astronauts might be well-trained and loyal, there's little hope that their children, let alone grandchildren, will be adept for the difficult task.

Think of your own offspring. You wanted them to be lawyers, but all they wanna do is play music. That's life. Go figure. Now, how do you expect to control some 20 generations, in cold recesses of space, growing up in a spaceship, far from the human's natural habitat? That spaceship would be DOA. What about fuel? Or supplies? How do you expect to feed a spaceship for 1,000 years? These same limitations also apply to our carbon-based neighbors. They would too have to face insurmountable challenges of maintaining the mission ideal across centuries, building a spaceship that will last a bit longer than what we have today (Challenger, Discovery etc.), and providing sufficient stores to make it all work.

UFO fans will start talking about super technologies and such. While such ideas may be nice for a book, they still need to comply with basic physics rules, which, in most cases, they do not. Tamponium is a nice name for cold-fusion fuel, but we have yet to see one such reactor working. Phase Space, My Space, all lovely concepts - except MySpace. But they do not help us solve the tiny problem called "speed of light."

Now, the real problem ...

I have assumed that every solar system in our Galaxy is suitable for life. Which is utter nonsense. The conditions have to be perfect for life to be created, and continue to be perfect for several billion years to allow primitive lifeforms to evolve into Internet users. What's the chance of that happening? One in a million? One in a billion?

Although it is impossible to make an accurate calculation, I am quite convinced that we are the only life form in the Galaxy. Which probably makes the hundreds and thousands of stories about alien visits here nothing more than a wild dream. Next time you gaze up at the stars, remember how lucky we are. Or not. Depends on how you look at it.

Cheers.

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