Sure to go with a bang

Laser scanners, electronic gadgets, nuclear weapons - we owe it all to quantum mechanics. John C. Baez looks at highlights from the London applied maths conference

Like many others attending the 13th International Congress on Mathematical Physics at Imperial College, London, I could not resist going to see the play Copenhagen at the Duchess Theatre.

The main characters are Niels Bohr and Werner Heisenberg: two creators of quantum mechanics, and the best of friends until they were split asunder by the second world war. Bohr eventually fled Denmark to work on the Manhattan Project, while Heisenberg led the unsuccessful Nazi effort to build an atomic bomb.

A chilling moment near the end of this drama still sticks in my mind. All of a sudden, the actors froze, a deep rumble shook the room and a bright light enveloped everything. Of course, this represented the awesome power of the bomb. But having just spent the day at the ICMP, I could not help but think of another explosion that Bohr and Heisenberg helped set off - quantum mechanics itself. I am not just talking about all the technologies that rely on it: the transistors in all our electronic gadgetry, the lasers that scan every purchase at our local grocery store and, yes, nuclear weapons. I am also talking about how quantum mechanics continues to transform our thinking about the world. This may not be evident in most spheres of life, but here at Imperial, with about 750 coffee-swigging mathematicians and physicists roaming the hallways, it is practically inescapable.

Pop your head into the sessions on "quantum information and computation", for example. You will see professors with a wide variety of accents waving their hands and flipping rapidly through transparencies as their talks run overtime - what are they talking about?

Well, as Bohr and Heisenberg realised, whenever we measure something, we automatically make it impossible to measure something else. This sounds like a nuisance, but now people have figured out how to use it to send encoded messages in a way that defeats eavesdroppers.

The basic idea is simple: if anyone starts to listen in on our conversation, they instantly ruin the signal being transmitted, tipping us off. To work this trick, one has to send the signal one photon at a time down an optical fibre. This is not easy, but it has already been shown to work over distances of several kilometres, so start-up companies are already sprouting, hoping to make money out of it.

However, sending signals is a big business: there is a whole branch of mathematics devoted to doing it efficiently. If we start doing it by sneaky quantum-mechanical methods, all that maths needs to be updated. That is what "quantum information theory" is about.

What about "quantum computation"? Well, Bohr and Heisenberg also found that when you do not measure something, it remains indeterminate. The classic example is Schrodinger's imaginary experiment involving a cat that is both alive and dead until you actually look at it. Now people are using this idea to design "quantum computers": gadgets that do several computations simultaneously in a ghostly superposition, only merging again when you look at the answer at the end.

So far, only toy models have been built: it is hotly debated whether full-scale quantum computers will ever be practical. But that has not stopped people from figuring out how to program them. Peter Shor, who gave a plenary talk here at the ICMP, has shown how to get them to do certain calculations faster than any normal computer. If they are ever practical, quantum computers may be great at cracking codes, so governments worldwide are throwing money at this field.

If all this is not mindblowing enough, try the sessions on "quantum gravity", "string theory", and "noncommutative geometry". Newton saw that the apple falls from the tree due to the earth's gravitational force; Einstein showed that this force is really just the apple trying its best to move in a straight line through space and time, which unfortunately happen to be curved by the earth. When we throw quantum mechanics into the mix, things get even trickier: not only are space and time curved, the curvature must be a bit uncertain.

Alas, nobody knows quite how this works, so members of three contending schools of thought came to the ICMP to discuss their theories. The loop quantum gravity people believe that space is ultimately made of tiny quantum rubber bands (yes, I am simplifying things a bit). The followers of string theory also believe this, but they mean something completely different by it, and lately they have been giving their rubber bands extra dimensions. Finally, people who work on noncommutative geometry are doing their best to weave quantum theory right into the foundations of mathematics.

It is too soon to tell if any of these approaches is on the right track, but one thing is clear: the quantum explosion is not over yet.

John C. Baez, department of mathematics, University of California, Riverside, US.

More conference highlights overleaf