Our best theory of nature has imaginary numbers at its heart. Making quantum physics more real conjures up a monstrous entity pulling the universe's strings
Leader: "The u-bit may be omniscient, but it's no God particle"
IF YOU'VE ever tried counting yourself to sleep, it's unlikely you did it using the square roots of sheep. The square root of a sheep is not something that seems to make much sense. You could, in theory, perform all sorts of arithmetical operations with them: add them, subtract them, multiply them. But it is hard to see why you would want to.
All the odder, then, that this is exactly what physicists do to make sense of reality. Except not with sheep. Their basic numerical building block is a similarly nonsensical concept: the square root of minus 1.
This is not a "real" number you can count and measure stuff with. You can't work out whether it's divisible by 2, or less than 10. Yet it is there, everywhere, in the mathematics of our most successful – and supremely bamboozling – theory of the world: quantum theory.
This is a problem, says respected theoretical physicist Bill Wootters of Williams College in Williamstown, Massachusetts – a problem that might be preventing us getting to grips with quantum theory's mysteries. And he has a solution, albeit one with a price. We can make quantum mechanics work with real numbers, but only if we propose the existence of an entity that makes even Wootters blanch: a universal "bit" of information that interacts with everything else in reality, dictating its quantum behaviour.
What form this "u-bit" might take physically, or where it resides, no one can yet tell. But if it exists, its meddling could not only bring a new understanding of quantum theory, but also explain why super-powerful quantum computers can never be made to work. It would be a truly revolutionary insight. Is it for real?
The square root of minus 1, also known as the imaginary unit, i, has been lurking in mathematics since the 16th century at least, when it popped up as geometers were solving equations such as those with an x2 or x3 term in them. Since then, the imaginary unit and its offspring, two-dimensional "complex" numbers incorporating both real and imaginary elements, have wormed their way into many parts of mathematics, despite their lack of an obvious connection to the numbers we conventionally use to describe things around us (see "Complex stuff"). In geometry they appear in trigonometric equations, and in physics they provide a neat way to describe rotations and oscillations. Electrical engineers use them routinely in designing alternating-current circuits, and they are handy for describing light and sound waves, too.
But things suddenly got a lot more convoluted with the advent of quantum theory. "Complex numbers had been used in physics before quantum mechanics, but always as a kind of algebraic trick to make the math easier," says Benjamin Schumacher of Kenyon College in Gambier, Ohio.
Quantum complications
Not so in quantum mechanics. This theory evolved a century ago from a hotchpotch of ideas about the subatomic world. Central to it is the idea that microscopic matter has characteristics of both a particle and a wave at the same time. This is the root of the theory's infamous assaults on our intuition. It's what allows, for example, a seemingly localised particle to be in two places at once.
And it turns out that two-dimensional complex numbers are exactly what you need to describe this fuzzy, smeared world. Within quantum theory, things like electrons and photons are represented by "wave functions
Hidden complexity
The odd thing is, though, we never see all that quantum complexity directly. The quantum weirdness locked up in the wave function "collapses" into a single real number when you attempt to measure something: a particle is always found at a single location, for example, or moving with a certain speed. Mathematically, the first thing you do when comparing a quantum prediction with reality is an operation akin to squaring the wave function, allowing you to get rid of all the i's and arrive at a real-number probability. If there is more than one way for a thing to end up with, say, a particular location, you add up all the complex number representations for each different way, and then square the sum.
- Subscribe to New Scientist and you'll get:
- New Scientist magazine delivered every week
- Unlimited access to all New Scientist online content -
a benefit only available to subscribers - Great savings from the normal price
- Subscribe now!
If you would like to reuse any content from New Scientist, either in print or online, please contact the syndication department first for permission. New Scientist does not own rights to photos, but there are a variety of licensing options available for use of articles and graphics we own the copyright to.
