When Stephen Hawking saves you a seat next to him at a conference dinner, you know you've arrived in theoretical physics. Anna Fazackerley meets Lisa Randall, whose ideas about extra dimensions have stunned her peers and whose book explaining them to a wider audience looks set to become a bestseller

It isn't easy to meet men when you are a theoretical physicist - even when you are a theoretical physicist who looks like a glossier version of Jodie Foster. "Some think it's pretty cool, though that may not last when they realise you also work really hard. Some just walk the other way," Lisa Randall, professor of physics at Harvard University, laughs. "Some you can have fun with when they don't realise you do physics and they talk condescendingly to you."

In fact, no matter whom Randall is talking to, telling them she is a physicist always provokes a reaction. People tell her it was their worst subject at school, or their best, or - most predictably - that she doesn't look like one. "It's like being a vegetarian," she says. "Everyone has to have an opinion."

If you don't know Randall, you soon will. She has written a book, Warped Passages , in which she aims to "unravel the universe's hidden dimensions", exploring old and new theories about unseen extra dimensions of space. When it is published later this month it will inevitably prompt comparisons with Stephen Hawking's publishing sensation A Brief History of Time , comparisons that will have a certain frisson because it is a beautiful young woman doing the big thinking. It will also, she hopes, turn a whole new group of people on to physics - helping them to comprehend the sort of huge and potentially intimidating ideas that they may have thought beyond their grasp.

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Randall tested the book on friends outside the field as she was writing it to gauge which analogies aided their understanding and, more important, where they got stuck.

"I'd like to think anyone who is interested could read it," she says. "I hope its appeal goes beyond geeky 14-year-old boys. I'd love to see more girls and women reading it."

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Explaining tough physics using fantastically twisted Alice in Wonderland stories and quotes from sources such as The Rocky Horror Show , Randall seems to have a flair for making her subject approachable. She talks very fast with the sort of palpable excitement that makes you want to understand things as she sees them. She is the theoretical physics equivalent of a favourite schoolteacher whom you didn't want to disappoint by not doing your homework.

She describes the theoretical model building that she does as "adventure travel through concepts and ideas". Her book takes us on one of these journeys, but she keeps stopping to recap key facts and check that the reader has not been left behind. At the outset she asks us to imagine that we are climbing upwards in a ski lift the day after a storm, looking at the untracked snow below. Once you get off, she says, the path might be steep and frightening and you might take a wrong turn but "no matter what, once you hit the snow it's going to be a great day".

Randall has negotiated some tremendous slopes. In the late 1990s she provided an answer to one of the chief mysteries of particle physics: why gravity is so much weaker than all other known forces. Or, as she puts it, why a tiny magnet can lift a paperclip when all the mass of Earth is pulling in the opposite direction. With her collaborator, Raman Sundrum, she showed that extra dimensions could provide a solution.

The possible existence of unseen extra dimensions was not a new concept: they had been discussed since 1919. But for three quarters of a century there had been an assumption that they had to be limited in size - either rolled up or confined within pairs of membrane-like entities known as branes - to explain why we had not spotted them. Randall and Sundrum challenged this assumption by demonstrating that an invisible fifth dimension could be infinite in size without a second brane to confine it.

The concept of something so huge escaping our perception was mind-boggling.

According to accepted theories it was not possible: surely an infinite fifth dimension in which the gravitational force would spread infinitely far would destabilise everything, including the solar system?

But Randall and Sundrum showed that spacetime could be so warped ("like reflections in a funhouse mirror") that a dimension could stretch endlessly yet remain hidden. And as a result of this warping the gravitational field could be contained in one small region near the brane. Gravity would be so concentrated that the bewildering size of an infinite dimension reaching beyond this region would be irrelevant.

The two papers Randall published with Sundrum in 1998 and 1999 are among the most cited in physics literature, yet this success did not come without an ego struggle. They were, after all, challenging canonical ideas.

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Both of them were certain their theory was a seriously big deal. But it took a while before physicists in their field agreed. "People thought either it was wrong or equivalent to an existing idea," she says. "It really took off when the people who do string theory, who we weren't competing with, realised what was going on."

Randall's non-physicist friends took less convincing that she was on to something. This was not because they had grasped the complicated ideas but because when she attended a big conference dinner Hawking had saved her a seat.

Nonetheless, hitting this intellectual brick wall must have been an infuriating anti-climax to her eureka moment, and in her book Randall strays from the theory to dwell on the initial reactions of colleagues.

Physicists are eager to praise her now. Andy Parker, professor of physics at Cambridge University, remembers colleagues discussing the first paper and concluding: "This is the greatest idea for the past ten years." Alan Guth, professor of physics at the Massachusetts Institute of Technology, says that these two papers "transformed the way that theoretical physicists think about the under-lying structure of space".

Yet a new challenge to Randall's ideas looms. Extra dimensions have always been intangible. Theories about them are backed up by mathematics but no one has ever known for sure what is out there. Until now.

Before the end of the decade, the Large Hadron Collider, an international experiment based in Switzerland that will smash together extremely high-energy particles to simulate the Big Bang, could prove or disprove the theory. Randall finds this exhilarating rather than scary, arguing that part of the value of her theories has been about stretching people's imaginations. "We found ways that extra-dimensional space could be hidden that no one had recognised for 80 years. It would be doubly wonderful if it actually applied," she says. She adds with quiet confidence: "I don't think it will all turn out to be wrong. I think there is at least a grain of truth there."

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Yet all this is still a few years away. Having proposed the unsettling idea that we might be living in an isolated pocket - a "three-dimensional sinkhole" - inside a five-dimensional universe, Randall is pursuing new questions of equal magnitude. How did the universe get to the point it is at now? Why do we live in three dimensions?

"There's all this stuff left to do that no one is thinking about," she explains. "It's humbling in a way. There might be so much out there that we don't know anything about."

And now, having spent many months trying to make her book as comprehensible and digestible as possible, Randall has to persuade people - preferably non-physicists - to take it off the shelves and read it. This does make her nervous. "If I say to people, 'You'll be able to understand it', it doesn't mean they will believe me," she says.

But, when it comes to marketing the book, Randall does not have a problem.

Just as people were attracted to Hawking's book partly by his strange, almost prophet-like appearance, so Randall's book will grab their attention because people won't expect a physicist to look so glamorous. She is well aware that this is how publishing works and is refreshingly unfazed by it.

"One of the reasons I thought it was important to write this book was to get the message across that you don't have to look like a weirdo to do science," she says.

But she insists that the hefty volume is not mere academic lip gloss.

"Writing this I didn't cheat - I wrote the best book I possibly could," she says passionately. However, she is unflustered by the idea that in trying to convert the masses to theoretical physics she may alienate some of the more fusty academics in her field. "I'm a woman doing physics: someone is always going to be criticising something I'm doing," she retorts. "But hopefully people will realise there are some things that I do do well."

Lisa Randall will be speaking at the Cheltenham Science Festival on June 11.

A new dimension

Lorna Kerry's idea of a 'science' book was The Hitchhikers Guide to the Galaxy . Then she picked up Lisa Randall's Warped Passages

Warped Passages initially seemed quite a daunting prospect. My knowledge of physics is strictly GCSE, and the book opens a world of vaguely familiar terms that I was resigned to never understanding: special relativity, string theory, supersymmetry and the like. Randall provides access to that world in her discussion of extra dimensions, addressing possibilities that seem alien to the tangible world, yet more fascinating because of it.

Randall admits that some of the ideas she raises seem more science fiction than science fact. But anyone accusing her of straying into fantasy would be brought up sharp by the detailed grounding in physics she provides. In early chapters, she explains concepts such as quantum mechanics, which are vital to understand the theories on extra dimensions.

Randall's relaxed style and humour make even complex ideas accessible. Many of the theories go against the way that we see the world, and that is what makes them so hard to comprehend. Reading Warped Passages gives an insight into how people must have felt on discovering that the Earth was not flat.

A certain suspension of disbelief is required to accept the counterintuitive theories Randall discusses. I needed to reread certain sections of her book, but that is the nature of the intangible concepts that she explores.

Interspersed among the physics are analogies relating these ideas to our "commonsense" world. They often provide the moment of comprehension that is needed for fuller understanding.

The final chapters of Warped Passages get to the heart of the extra-dimension debate, and are the most engaging. Randall cannot provide definite conclusions about the existence of extra dimensions, but she opens up a whole spectrum of ideas that I would never have contemplated previously. Her enthusiasm should make it possible for even the novice to feel excited about technological developments and the possibility of one day proving the existence of extra dimensions.

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Lorna Kerry is studying English at Manchester University. Warped Passages is published this month by Allen Lane, ?20.00.