Time travel, designer babies, climate change... teenagers find these subjects so intriguing that they are giving their own time to organise discussion groups outside lessons.

DR CONRAD Taylor is looking nervous. He's a psychologist from Bradford University, working in all sorts of cool areas like artificial intelligence. He's like no lecturer I ever had, with his edgy gelled haircut and silver thumb ring.

He speaks plain English. That helps. He's well experienced in talking to first year students, but his audience this afternoon is a little trickier than that, though undoubtedly enthusiastic. He isn't allowed the crutch of Power Point presentation or other audio-visuals. It's just him, facing 70 secondary school students and a few teachers.

The venue is an accoustically-challenging conservatory tearoom at the Eureka! children's science museum in Halifax.

He talks for 15 minutes on the theme of Truth: Science's Holy Grail? He's only allowed 15 minutes to explore and wrap this one up.

His discourse roves over flat earth theory, how 17th century scientists were convinced that all swans were white, string theory, the difference between science and philosophy, concluding with the provocative thought that we can never be sure of a real scientific truth – theories may be proven at a certain moment, but that "truth" almost never stands the tests of time and later investigation.

There's a break and a rush for the tea and buns. Students talk in small groups about questions raised by the talk. Dr Taylor then faces a barrage of friendly fire. How much of science is culturally driven? What's the point in establishing facts, if the facts never really prove anything? Where is science going? One of the students wants to know about how scientists make moral judgments.

The man at the centre of it all has some answers, and unapologetically can't provide others so readily. It must be an intense experience for him, as he has surrendered control of where the lines of inquiry are going. The students seem to love it.

This, in a nutshell, is a Café Scientifique. It's an informal discussion of science or technology that is about opening up areas previously colonised by boffins and rather closed off from the non-scientist community. Many of the students here are studying science for GCSE or beyond, but some are not. They are just interested – and like an argument.

These teenagers are all involved in organising Cafés Scientifiques in their schools around the North of England. In the UK, 40 schools have so far bought into the idea of taking science out of the classroom to any pupil in any year.

The organisers have come to Eureka! to talk about how they set up and market their cafés within school, what makes a good subject, (a small committee of students runs each school's cafés and chooses topics) and exchange ideas with other schools where things may be done differently.

Adult organisers assigned to area of the country (paid for by the Wellcome Trust, which has given £178,000 in sponsorship) find the scientists to speak to schools, and start each school off by running a "taster" café to demonstrate the model.

After it's up and running, students run their own show, and can take it where they want. At Urmston Grammar School in Manchester, where the café has been a regular feature of school life for 18 months, the enterprising committee found their Holy Grail of healthy audiences lay in sponsorship from Starbucks, who send along two members of staff to serve up free coffee and biscuits.

Tom Thorp and Rachel Stansfield, both in the upper sixth at UGS, say it doesn't really matter why people turn up at first – whether it's simply for the free fodder or because they want to add some added interest to their university application. What matters is that they find it lively enough to come back.

"Before we set up the café, there wasn't really a place to debate anything at school," says Tom, who is taking arts A-levels and wants to become a professional musician. "I got involved in the committee because I'm particularly interested in the ethical side of science and new technologies, and I love an argument."

Rachel is taking a mixture of arts and sciences, and hopes to go to medical school in Liverpool this autumn. "A-levels are about sticking to what examiners want, with no time to widen discussion out to general debate, or what science means to everyday life. The café has given us that extra dimension, and within the café no-one's view is any more valid than anyone else's, whatever year they are in.

"We also get to question a practising scientist and speak to them as equals. What the café has brought is the idea that science is not about being a geek, and it isn't just something that goes on in a classroom."

Cafés at the school have hosted 80 students, but the average attendance is about 40. Popular topics have been cloning, stem cell research and alternative energy. "Sooner or later, I try to steer everything towards alternative energy...." says Tom, with a little laugh.

Duncan Dallas, the former head of science programmes at Yorkshire Television, founded the adult version of Café Scientifique in the UK in 1998, along the lines of the café philosophique started by Marc Sautet in France. Dallas thought science, rather than philosophy, would be a better bet over here. The gatherings attract mixed audiences and generally involve wine.

After its beginning in a cafe in Leeds 7, CS sprang up all over Britain, also sponsored by Wellcome, and there's now a federation of them across the world. There's even a world conference, to be held this year in Leeds. Clearly, there is a thirst to understand science among the general population.

"The junior cafés are not run by staff, and are about science not just being a body of facts that you learn, but debatable and changing all the time," says Dallas. "So far, almost all the junior cafés have been keen to talk about global warming, but some other really fun subjects like the science of colour, code-breaking, emotions and rockets have been suggested. When I was at school, I'd have loved something like this."

At Eureka! students are chewing the fat over the criteria for a good café. They agree that a subject has to be current, relevant to the lives of the audience, controversial, not too technical, and easily grasped.

But they seem open to an element of the unknown, a surprise. Invisibility was a quirky topic that proved a winner recently. A few boys in the group suggested addiction to electronic war games, and another chipped in with biological warfare. Was there a gender difference in subjects proposed? "Well, these are very boysy, aren't they?" said one girl. She couldn't think of the "girlie" equivalents except perhaps "the usefulness of diets". A general tag of "obesity" might be more generally appealing was the consensus.

The fledgling Café Scientifique at Morley High School in south Leeds has just had its lunchtime taster session, on The Reproductive Revolution. Future cafés will be organised by a group of Year 10s (14-15 year-olds), David Harper, Adam Austin, Rosie Raistrick and Emma Bickerdyke.

David got involved because he loves science. Adam is looking forward to discussing topics like the universe and time travel, and thinks involvement in the café will look good on his CV.

"I felt it would broaden my horizons," said Rosie. "I'd like to discuss stuff like genetics. The café takes you beyond what you're taught, really."

Emma said a group of 20 attended the first session, and the committee now had to get more students interested. "One of the attractions is that there is no other place where you can discuss anything with other years at school. I would only argue with someone in Year 13 in the café, not outside it."