It will soon be half a century since the American astronomer Frank Drake first pointed a radio telescope at the star Tau Ceti in the hope of picking up an extraterrestrial broadcast, and we still haven't heard anything. So is there anyone out there?

Fifty years ago Frank Drake – then a young astronomer from Cornell University – began an experiment that would have profound implications for humanity's understanding of its place in the cosmos. He turned the newly constructed Green Bank radio telescope in West Virginia towards Tau Ceti, a nearby star that is similar to our own Sun.

His purpose was simple: he wanted to pick up transmissions from any alien civilisations that might be flourishing on planets in orbit round Tau Ceti.

Drake and other scientists had realised that for the previous 40 years our own increasingly powerful radar, radio and TV transmissions – of news programmes and I Love Lucy shows – had formed an expanding shell of electromagnetic radiation that was spreading across space. Picked up by alert aliens, these signals would tell them that Homo sapiens had arrived in their full intellectual and cultural glory.

And, of course, what was true for earthling transmissions would also be true for broadcasts made by aliens. We should be able to hear theirs just as they could listen to ours.

So Drake set up Project Ozma – named after the Land of Oz, a place where exotic beings lived – and in early April 1960 turned the Green Bank telescope towards Tau Ceti. It would be humanity's first attempt to pick up radio signals from intelligent beings beyond our solar system.

Green Bank was a state-of-the-art observatory, we should note, though it was relatively crudely equipped by today's standards. "The radio receiver used vacuum tubes, there was no computer and we only had an old reel-to-reel tape recorder to record any alien voices we might pick up," Drake recalls.

For half an hour the team listened to the noise of Tau Ceti – a persistent, meaningless hiss – before they switched stars, to Epsilon Eridani, another Sun-like neighbour that they had already selected to be their second target. This time they got a very different response: a series of regular, clearly artificial pulses boomed from the receiver's loudspeakers. The team had struck extraterrestrial gold almost at the first attempt, it seemed. "Could it be this easy?" Drake wondered.

Then a few control adjustments revealed the truth. The "transmissions" from Epsilon Eridani were in fact coming from a nearby military base. Despite continued efforts over the next two months to detect intelligent signals from the two stars, in various different wavelengths, Drake's team of young astronomers drew a complete blank.

Thus human beings' first search for intelligent aliens ended without finding a hint that there was anyone "out there". Scientists heard nothing then and, more to the point, we have heard nothing since then. Despite half a century of trying to eavesdrop on ET, by pointing telescopes of increasing power at thousands of stars, and by searching across millions of different radio frequencies, not a single signal has ever been picked up to suggest that somewhere in our galaxy there is a life form, other than ourselves, that possesses an IQ that ever rises above room temperature: not a snatch of an episode of the Archers of Arcturus, or even a snippet of news about climate change rows on Betelgeuse. All we have picked up is static. The rest is silence.

But why have we not heard from ET after half a century of searching? There are a lot of stars – and, by inference, lots of planets – out there, after all, and plenty of potential homes on which aliens could evolve. So why hasn't one had the courtesy to make itself known to us?

It is a good question, one that was originally posed by the Italian physicist and Nobel laureate Enrico Fermi, one of the founders of quantum physics. If intelligent life is common in the universe, we would have been contacted long ago, he argued. After all, Earth is relatively young in astronomical terms while alien civilisations elsewhere in the universe have had billions of years to rise, establish themselves and make themselves known to humanity. "So where are they?" asked Fermi.

This is Fermi's paradox and scientists – despite all their efforts – still struggle to resolve it. Much of their problem lies with the basic make-up of our galaxy, they complain. The Milky Way is an unremarkable group of stars, in a not very special part of the cosmos that contains 100bn stars, a promising enough number if seeking the odd intelligent alien, you might have thought. However, most of these stars are going to be too big, too short-lived, too hot or too cold to support planets that might sustain intelligent life, say astronomers.

Thus the hunt to find the homes of clever ETs becomes less of a steady systematic search and more of a hunt for a planetary needle in a galactic haystack. In fact, it is becoming clear that astronomers may have to search through the radio spectrums of millions of stars before we stumble on an artificial signal from an alien.

And there are other reasons why our galaxy is not alive with the sound of extraterrestrial twitter (see box on the Drake equation above). Alien life may be commonplace but rarely evolves into complex beings, for example. Planets may support life – but only the single-cell, plankton type that coat their oceans and rocks. In other words, all aliens are scum. "And let's face it, pond scum doesn't qualify as intelligent life," says Seth Shostak, chief astronomer for the Search for Extraterrestrial Intelligence (Seti), the US group dedicated to the hunt for aliens.

Indeed, it may be that the circumstances that led to the creation of life here are so unusual as to make us, and other earthly creatures, a unique galactic experiment, an argument put forward by US astronomers Peter D Ward and Donald Brownlee in Rare Earth: Why Complex Life Is Uncommon in the Universe (Copernicus).

Earth, from their perspective, turns out to be prime galactic real estate. First, our sun is a highly stable star and is unaffected by wild fluctuations in radiation output. Such afflictions affect many other stars and would destroy evolving life forms. Similarly our solar system is situated in a safe suburban part of the galaxy, the astronomical equivalent of Cheltenham. It is therefore undisturbed by close neighbouring stars that could dislodge the swathes of comets believed to hover at the edges of most solar systems and cause them to crash into our planet. For good measure, our world is further blessed in having a relatively large moon which helped stabilise Earth's rotation, preventing wild swings in our seasons and climate.

In other words, the primitive slime that evolved on Earth four billion years ago was blessed with privileged conditions that allowed it, eventually, to evolve, about 250,000 years ago, into the only intelligent creatures known to science, ourselves. Humanity may therefore be viewed as the outcome of the biggest accumulator bet in the universe. 'Earth is a charmed place," says Brownlee. "We know of no other body that is even remotely like it."

Or it could be that extraterrestrial civilisations are 10 a penny in our galaxy but doomed from the start. Aliens may simply be like us: just smart enough to invent technology but not clever enough to control it. Thus they may be snuffing themselves out round the galaxy almost as fast as they develop technology, an argument put forward by the evolutionary expert Stephen Jay Gould. "Perhaps any society that could build a technology for such interplanetary travel must first pass through a period of potential destruction where technological capacity outstrips social or moral restraint. Perhaps, no, or very few, societies can ever emerge intact from such a crucial episode."

Such arguments get short shrift from other astronomers, however. Scientists, led by Drake, Shostak, the late Carl Sagan and others, have argued that absence of evidence is very different from evidence of alien absence. For a start, says Shostak, alien hunting has been stymied – until recently – by a lack of equipment and resources. Governments have consistently refused to fund Seti programmes and so its practitioners have had to borrow time on astronomical radio telescopes, usually for only a few days at a time. At best, they have been able to look at a few promising stars over a range of a few radio frequencies. "It's like trying to do medical research when you have to go next door to borrow a microscope for a couple of hours at most," adds Shostak.

However, Seti scientists are now building their own telescopes, a classic example being the Allen Array, funded through a $11.5m donation from Paul Allen, co-founder – with Bill Gates – of Microsoft. To date, 42 radio telescopes, each with a six-metre diameter, have been erected at a site north-east of San Francisco. When the project is complete, a total of 350 dishes will transform earthlings' hunt for aliens.

"When we do get a signal – and I am betting it will happen before 2025 – we will follow its source very carefully across the sky, as the Earth rotates," says Shostak. "Then we will ask other observatories to check it out, and if they back us we will simply announce the existence of a message from ET. There will be no message to the president and no interference from Men in Black.

"As to the nature of the alien that is sending the signal, I am pretty sure they will resemble us in one way. Computers will run devices like the Allen Array and I strongly suspect the first contact will come from one of their computers talking to one of ours."

However, the biology of aliens themselves is virtually unguessable, most astronomers agree. ET could be of almost any size or shape you could imagine, though most scientists believe he or she is likely to be a carbon-based being like ourselves, from a world, like ours, that is rich in water, the matrix of life. Indeed, there are some scientists who maintain that the similarities between us and them may turn out to be too close for comfort.

The Cambridge University palaeontologist Simon Conway Morris says the process of biological convergence – which produces similar species from organisms from very different evolutionary origins – makes it likely that aliens will be very similar to us, not just in design but in attitude and behaviour. "Extraterrestrials… won't be splodges of glue… they could be disturbingly like us, and that might not be a good thing – we don't have a great record," Conway Morris says.

And you know what he means. Humans have wiped out countless species on Earth, including the Neanderthals. Aliens could be just as bad, if not worse. So if ET does phone in, it may be best not to pick up the receiver, it is suggested.

On the other hand, the sheer scale of the universe offers us protection. Proxima Centauri, the nearest star to our Sun, is four light years away. That means that a photon from it – travelling at 186,000 miles per second, the speed of light – takes four years to reach us (a distance of around 23 million million miles). Suppose then we find intelligent life on a reasonably close star – say one that is 50 light years distant. That means conversations will proceed at a stately rate of a century an interchange. We won't learn a lot that way. On the other hand, we will have a lot of notice if our new neighbours start taking an unhealthy interest in us.

In fact, it is not what aliens will say or do that will be the really important part of their discovery, say Seti scientists. The mere fact of their existence will be the bombshell, a point stressed by Prof Paul Davies, a British cosmologist now based at Arizona State University and author of the forthcoming book on life in the universe The Eerie Silence (Allen Lane). "It would surely be the greatest discovery of all time, greater than those of Newton, Darwin or Einstein put together," he says. "The knowledge that we are not alone would affect people's psyche, and totally transform our world view. The mere fact alone would be disruptive."

For a start, the discovery that there is someone more advanced than us out there would tell us that self-destruction is not Homo sapiens's inevitable fate. And then there are the religious implications, adds Davies. "I think the discovery of a civilisation, particularly one that is found to be cooperative and non-aggressive, would have a devastating effect on earthly religions, particularly those with a Christian basis. After all, Jesus is supposed to be God's only begotten son, sent specifically to save one planet and one species."

If we find civilisations that are far more advanced technologically and ethically than us, this will pose a serious problem for Christianity, adds Davies. "By our standards, they would be saints. So why should we be saved by Christ but not them?" Hence his prediction that there will be bad days ahead for religion should we hear from ET, though we should note this thesis is disputed by theologians.

Professor Ted Peters, of the Pacific Lutheran Theology Seminary, in Berkeley, California, recently reported a survey that suggested that most religious people would have no problem accommodating their beliefs with the existence of advanced extraterrestrials. "Contact with extraterrestrial intelligence will, in fact, expand the existing Christian vision that all of creation is the gift of God," he insists.

Davies is unrepentant. "Few of those Christians who respond to these studies realise the theological minefield posed by the existence of intelligent aliens. They are just sweeping the problem under the carpet." Contact will ultimately prove corrosive and possibly fatal for most religions.

On the other hand, there are likely to be many benefits from studying Seti signals. Aliens could pass on all sorts of knowledge. "Besides learning all the physics we don't know, we might be taught the secret of immortality, or at least lessons in how to get along," says Shostak. Thus we have much more to gain than to lose from talking to aliens, he argues.

All we have to do is make contact, of course. And that remains the problem. Despite all our efforts for the past half century we have heard nothing. It is worrying to some scientists but only a minor difficulty for others, including Frank Drake. "I don't think the silence is eerie," he told a recent Royal Society meeting on the subject of Seti. "It is predictable." Dressed in neat black jacket and slacks, with carefully parted grey hair, he displayed a calm sense of certainty about our chances of finding intelligent life out there. "Fifty years ago I was naive in thinking we could find signals straight away. For all I knew there were radio broadcasts pouring from civilisations on every star. But that was really unreasonable.

"I now realise that it is going to be harder than that. There may be up to 10,000 civilisations in the galaxy but, given that the galaxy also contains 100bn stars, that means we will have to search around 10m stars before we have a realistic chance of finding one. That is certainly not going to happen in my lifetime. Nor might it happen in the next generation. But we will make contact one day. I am sure of that."