- Mar 31, 2009
# Can fractals make sense of the quantum world?

QUANTUM theory just seems too weird to believe. Particles can be in more than one place at a time. They don't exist until you measure them. Spookier still, they can even stay in touch when they are separated by great distances.

Einstein thought this was all a bit much, believing it to be evidence of major problems with the theory, as many critics still suspect today. Quantum enthusiasts point to the theory's extraordinary success in explaining the behaviour of atoms, electrons and other quantum systems. They insist we have to accept the theory as it is, however strange it may seem.

But what if there were a way to reconcile these two opposing views, by showing how quantum theory might emerge from a deeper level of non-weird physics?

If you listen to physicist Tim Palmer, it begins to sound plausible. What has been missing, he argues, are some key ideas from an area of science that most quantum physicists have ignored: the science of fractals, those intricate patterns found in everything from fractured surfaces to oceanic flows (see What is a fractal?).

Take the mathematics of fractals into account, says Palmer, and the long-standing puzzles of quantum theory may be much easier to understand. They might even dissolve away.

It is an argument that is drawing attention from physicists around the world. "His approach is very interesting and refreshingly different," says physicist Robert Spekkens of the Perimeter Institute for Theoretical Physics in Waterloo, Canada. "He's not just trying to reinterpret the usual quantum formalism, but actually to derive it from something deeper."

That Palmer is making this argument may seem a little odd, given that he is a climate scientist working at the European Centre for Medium-Range Weather Forecasting in Reading, UK. It makes more sense when you learn that Palmer studied general relativity at the University of Oxford, working under the same PhD adviser as Stephen Hawking.

So while Palmer has spent the last 20 years establishing a reputation as a leading mathematical climatologist, he has also continued to explore the mysteries of his first interest, quantum theory (see "Quantum ambitions").

"It has taken 20 years of thinking," says Palmer, "but I do think that most of the paradoxes of quantum theory may well have a simple and comprehensible resolution."

Arguments over quantum theory have raged since the 1920s, starting with a series of famous exchanges between Einstein and the Danish physicist Niels Bohr.

Bohr and his supporters believed that the theory's successful description of atoms and radiation meant you should abandon old philosophical concepts, such as the idea that objects have definite properties even when no one is there to measure them.

Einstein and his followers countered that such radicalism was wildly premature. They argued that much of the quantum weirdness was nothing more than a lack of adequate knowledge. Find a quantum system's "hidden variables", Einstein suspected, and quantum theory might make common sense, a view that quantum enthusiasts thought was ultra conservative and out of touch. The argument rages to this day.

### Fractals unite

Palmer believes his work shows it is possible that Einstein and Bohr may have been emphasising different aspects of the same subtle physics. "My hypothesis is motivated by two concepts that wouldn't have been known to the founding fathers of quantum theory," he says: black holes and fractals.

Palmer's ideas begin with gravity. The force that makes apples fall and holds planets in their orbit is also the only fundamental physical process capable of destroying information. It works like this: the hot gas and plasma making up a star contain an enormous amount of information locked in the atomic states of a huge number of particles. If the star collapses under its own gravity to form a black hole, most of the atoms are sucked in, resulting in almost all of that detailed information vanishing. Instead, the black hole can be described completely using just three quantities - its mass, angular momentum and electric charge.

Many physicists accept this view, but Palmer thinks they haven't pursued its implications far enough. As a system loses information, the number of states you need to describe it diminishes. Wait long enough and you will find that the system reaches a point where no more states can be lost. In mathematical terms, this special subset of states is known as an invariant set. Once a state lies in this subset, it stays in it forever.

A simple way of thinking about it is to imagine a swinging pendulum that slows down due to friction before eventually coming to a complete standstill. Here the invariant set is the one that describes the pendulum at rest.

Because black holes destroy information, Palmer suggests that the universe has an invariant set too, though it is far more complicated than the pendulum.