It ranks among the most enduring mysteries of the cosmos. Physicists call it the Fermi paradox after the Italian Nobel laureate Enrico Fermi, who, in 1950, pointed out the glaring conflict between predictions that life was elsewhere in the universe - and the conspicuous lack of aliens who have come to visit.

Now a Danish researcher believes he may have solved the paradox. Extra-terrestrials have yet to find us because they haven't had enough time to look.

Using a computer simulation of our own galaxy, the Milky Way, Rasmus Bjork, a physicist at the Niels Bohr institute in Copenhagen, proposed that a single civilisation might build eight intergalactic probes and launch them on missions to search for life. Once on their way each probe would send out eight more mini-probes, which would head for the nearest stars and look for habitable planets.

Mr Bjork confined the probes to search only solar systems in what is called the "galactic habitable zone" of the Milky Way, where solar systems are close enough to the centre to have the right elements necessary to form rocky, life-sustaining planets, but are far enough out to avoid being struck by asteroids, seared by stars or frazzled by bursts of radiation.

He found that even if the alien ships could hurtle through space at a tenth of the speed of light, or 30,000km a second, - Nasa's current Cassini mission to Saturn is plodding along at 32km a second - it would take 10bn years, roughly half the age of the universe, to explore just 4% of the galaxy. His study is reported in New Scientist today.

Like humans, alien civilisations could shorten the time to find extra-terrestrials by picking up television and radio broadcasts that might leak from colonised planets. "Even then, unless they can develop an exotic form of transport that gets them across the galaxy in two weeks it's still going to take millions of years to find us," said Mr Bjork. "There are so many stars in the galaxy that probably life could exist elsewhere, but will we ever get in contact with them? Not in our lifetime," he added.