IT'S ILLOGICAL, CAPTAIN

It is hardly Shakespeare, but the phrase "Beam me up, Scotty!" has earned itself a lasting place in the English language. The question is, will our distant descendants in the 24th century - while waiting for transporter beams to flash them to their galactic cruisers - look upon it as prophetic? Or will an Earth-bound future populace smile at the quaint naivete of their primitive ancestors?

This is no trivial question. Star Trek's influence spans a generation, and has intruded into university lecture halls. A recent study by the Particle Physics and Astronomy Research Council found that more than a quarter of physics undergraduates were inspired to enter the field by science fiction, and some seven per cent specifically cited Star Trek (the BBC's long-running science and technology programme, Tomorrow's World, rated just 2.5 per cent.)

But is Star Trek encouraging them to boldly go in search of scientific truth, or filling their heads with technobabble nonsense? "Anything that encourages scientific studies is good," argues Professor Frank Close, fellow in Public Understanding of Physics for the Institute of Physics. Professor Lawrence Krauss, a physicist at Case Western Reserve University, agrees, and has written The Physics of Star Trek in an effort to link the four television series and five films with the real world of science.

His book, or more precisely its foreword, caused a stir when it was first published in the US. In it, Stephen Hawking, Cambridge's leading theoretical physicist and former Star Trek guest star, suggested that both faster- than-light space flight and time travel might be possible in the future. "One of the consequences of rapid interstellar travel would be that one could also travel back in time," he said. "Today's science fiction is often tomorrow's science fact." Often, but not always.

Krauss believes that Star Trek inspires not only students, but the designers of modern technology. Flip-open mobile phones probably would not look the way they do if it were not for the programme's "communicators." The point is illustrated in an exhibition currently touring Britain's science museums, in which the fictional and real mobile phone technologies are shown side-by side. The display has been a huge hit, attracting 50,000 people a month. A spokeswoman for the Museum of Science and Industry in Manchester said: "It's our biggest exhibit ever."

Much of the jargon used in the shows is drawn from real physics, and sometimes leaps ahead of it - an early episode referred to a "black star" shortly before the invention of the term black hole. "They go off the deep end a lot but they start with things that are at the forefront of modern physics," says Krauss.

But at other times, the script writers have leant more towards fiction than science. "Beaming up" would defy the laws of quantum physics and release the energy of several atom bombs if it were possible. Warp drives (for travelling faster than light) and time travel are slightly less improbable - at least no one has found a definitive physical law banning them. Anti- matter engines, which would in principle be far more powerful than a nuclear reactor, fail mainly due to economics rather than physics. Holodecks (where crew members can live out their fantasies) may one day be a reality, though less realistic than those envisioned on Star Trek.

Transporters, the devices used to beam the crew from planet to starship, are the best example of the script writers' poetic licence being stretched too far. "Probably no single piece of science fiction technology aboard the Enterprise is so utterly implausible," says Krauss. Perhaps that is why most science-fiction writers have shunned transporters in favour of other plot devices.

They were necessary because Gene Roddenberry - who came up with the idea of Star Trek - designed an Enterprise that, because of its awkward aerodynamics, was obviously not up to flying through an atmosphere. Another way was needed to get the crew to planetary surfaces. His solution, transporters, could work in one of two ways - either by transmitting only a digital pattern representing a person, and reassembling that person from particles available at the receiving end, or by sending the original matter as well. Even if the beams transmit only a pattern, at least three virtually insurmountable problems crop up.

First, the transporter would have to "read" everything about that person on a sub-atomic level, and the laws of quantum mechanics - notably the Heisenberg uncertainty principle - decree that this is impossible. If you know where an electron or proton is now, you cannot say where it is going and vice versa. Furthermore - though it seems counter-intuitive to non-physicists - the theory says that the mere act of looking at the particle in question will change its state.

Second, you would have to get rid of the original body, and dematerialising it - turning it into pure energy - would be messier than one might think. According to Albert Einstein's equation E=MC2, dematerialising just one smallish person would release the equivalent of 1,000 one-megaton atomic bombs. Collecting material at the far end of the beam from which to reconstruct a body would be no mean feat either.

Finally, there's the sheer volume of data. The information for a single human being would fill a stack of present-day hard-disks reaching a third of the way from the Earth to the centre of the galaxy - "five years' travel in the Enterprise at warp nine," Krauss notes drily. Even assuming recent dramatic advances in computer storage technology continue uninterrupted for four centuries, this would be an overwhelming task.

Keeping the matter and transmitting it along with the data would create other formidable problems. Breaking a human down into quarks (the building blocks from which protons, neutrons and electrons are made) would involve heating them to 1,000bn degrees Centigrade, a million times the temperature at the centre of the Sun. Even if you only went part way, leaving the matter in the form of atoms, it would have to be accelerated to near light speed in order to keep up with digital pattern, and that would require 10 times as much energy as breaking it down into quarks.

Krauss says the idea for his book began as a joke over lunch with his publisher. But it had its roots in science conferences around the world. Lots of physicists are fans, and many of them enjoy nothing more than debating whether things like transporters can be made to work. One of their favourite topics is the warp drive.

Warp drive, the second fundamental technology that has been with Star Trek since the very first episode, is more feasible than transporters. Einstein's theory of relativity says nothing can move faster than light and at sub-light speeds, getting to alien worlds and far-flung human colonies would take decades or centuries. Worse, the theory says that time would slow down for crews as their velocity got close to the speed of light. After a quick jaunt to Earth's nearest interstellar neighbours, lasting a decade or two ship time, the travellers would return to find centuries had passed on Earth.

Fortunately for captains Kirk and Picard, relativity provides a loophole. Just as time is not fixed, neither is space. Large gravitational fields can bend our four-dimensional universe much the way a heavy ball-bearing would distort the two-dimensional world of a sheet of elastic. It would, to borrow the jargon, warp space-time and bring distant stars much closer together.

When Star Trek was first conceived, this was just speculation, but Miguel Alcubierre - a physicist working in Wales - recently used the equations of general relativity to prove that warp drive is, in principle, possible. The big advantage of his calculations, from the point of view of future spacefarers, is not just that they would arrive quickly, but that their speed relative to their local surroundings would be low. This means they will have aged at the same rate as someone at their destination or home port.

Such warping of space-time has implications for a wide range of technologies used on the Enterprise. Deflector shields, tractor beams, inertial dampers (which allow the ship to accelerate without creating crushing G-forces), and the artificial gravity that lets characters walk around the ship, would all be possible. What a shame there's a catch. Bending space-time in this way is dependent on there being enough mass to create huge gravitational fields. Even the Sun's gravity at its surface is only strong enough to bend light by one 1,000th of a degree. Bouncing an incoming phaser beam off at right-angles would therefore imply a gravitational field 90,000 times more powerful. Bending space-time enough to allow a starship to move quickly between stars would take even more.

What is more, the equation which says you can use large amounts of matter to curve space-time is not a one-way street. The implication is that if you could bend the Universe, the very act would create a large mass.

Extremely large masses are the stock in trade of Stephen Hawking. The theoretical work that made him famous was on black holes, stars which have run out of fuel and have collapsed under their own weight until they take up zero volume. His conclusion that time travel might be possible is also linked to this work.

If two black holes were to "join" they would form a wormhole, like the one in the Star Trek series Deep Space Nine. It can be envisioned by going back to the two-dimensional sheet of rubber, folding it once, and poking a thin tube through each of the layers from opposite sides and feeling around until they meet up.

In theory it would be possible to travel through such a wormhole in the real, four-dimensional universe to another point in space-time. In practice, the immense gravitational force of each of the black holes would pinch off the connection long before one could get through. The only way to keep it open would be to thread the wormhole with enough exotic material - a substance that gravitationally repels other matter - to keep it open. Hawking has suggested that such matter does exist around black holes.

Whether time travel will ever be realised is hotly debated. The theory likely to answer the question, which would combine gravity and quantum physics, has yet to be worked out. Some physicists, including Professor Krauss, argue that the paradoxes that would arise - for example, if you were able to go back in time and kill one of your grandparents before you were born - imply that there is some, as yet undiscovered, law forbidding it. But he also notes that similar, common-sense assumptions about physics have been proven wrong in the past.

So is there any Star Trek technology that physicist fans can point to as a real possibility? Perhaps the holodeck, introduced in the second series, Next Generation, is the most likely to see the light of day. In the series, crew members could instruct the ship's computer to create a tailor-made virtual reality featuring their favourite people, places and things. In reality holograms have become commonplace on credit cards and even some countries' bank notes. The idea that a sufficiently powerful computer could fill a deck of the Enterprise with a three-dimensional virtual reality is a reasonable extension of today's technology.

But the holodeck also has solid matter, which creates more problems. Professor Krauss suggests that this technology, and the replicators that produce food and drink for the crew, are based on transporters. If transporters can reconstruct people from a stored digital pattern, surely a cheaper version of the device can reproduce innumerable copies of a bad cup of coffee from a single template. But if that is the case, they would suffer from the same objections about the amount of energy required.

Discussions of energy bring us back to the anti-matter engines that power the Enterprise. While the idea of anti-matter engines is plausible, their practical applications may in fact be limited to laboratory curiosities. Anti-matter and matter were created in almost equal amounts during the Big Bang at the start of the Universe. The two types of matter promptly collided with each other, leaving a background radiation which has been detected by instruments like the Cosmic Background Explorer (COBE) satellite. A slight imbalance - one part in 10 billion - resulted in all the matter in the universe today. Cosmic ray measurements also indicate that there are no significant reserves of anti-matter for the corporate descendants of BP, Shell and Exxon to exploit.

Anti-matter can be created, however. Large particle accelerators, such as Europe's CERN and America's Fermilab, have been producing anti-electrons (called positrons because they carry a positive electrical charge) for 60 years. Anti-protons have been around for almost as long. Earlier this year, nine atoms of anti-hydrogen were created when positrons spontaneously began to orbit anti-protons.

Anti-hydrogen is a difficult substance to deal with, however. Its electrically charged components can be contained by magnetic fields, but the neutral atoms are free to move until they bump into ordinary matter resulting in mutual annihilation. It is this type of anti-matter, unfortunately, that the Star Trek writers decided to use as the Enterprise's fuel.

The script writers were right in thinking that such collisions were the most efficient way to create energy. The problem is that making the anti- matter in the first place uses at least a million times as much energy as will eventually be released. Professor Krauss calculates that, using present technology, Fermilab could make 10m to 20m antiprotons for a dollar. That may sound like a lot, but when that dollar's-worth of anti-protons collide with ordinary protons, they would release only about one 1,000th of a joule. He goes on to put this into perspective. "It would cost at the present time more than the annual budget of the US government to light up your living room in this way."

While this may be discouraging for fans who find their dreams of the future being shattered by the laws they learn in university physics (or economics) classes, it is unlikely to deter the fanatics at home. As with all good science fiction, Star Trek succeeds not because of its science, but because of the interactions between individuals and cultures that imaginary technology makes possible - at least on screen.

! 'The Physics of Star Trek', by Lawrence Krauss, Harper Collins/Basic Books, pounds 12.99.