Fractals: The Missing Link?

A scientist named Tim Palmer may have just reconciled the worlds of classical and quantum physics - which have until now seemed irreconcilable - using fractals.

Before launching into Palmer's theory, remember the idea that the geometry of the universe may create its properties has excited scientists for a number of years. For example, Garrett Lisi's E8 theory claiming that the physics of the universe stems from its shape (a 248-dimensional object) made quite a buzz.

Similarly, some physicists believe that the properties of gravity stem from the geometry of higher dimensions in which gravity is active. And years before, Einstein concluded that gravity was an effect of the space-time geometry through which objects fall.

Okay, back to Palmer. As New Scientist writes:

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....

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....

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....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....

Complex systems are affected by chaos, which means that their behaviour can be influenced greatly by tiny changes. According to mathematics, the invariant set of a chaotic system is a fractal.

Fractal invariant sets have unusual geometric properties. If you plotted one on a map it would trace out the same intricate structure as a coastline. Zoom in on it and you would find more and more detail, with the patterns looking similar to the original unzoomed image.

Gravity and mathematics alone, Palmer suggests, imply that the invariant set of the universe should have a similarly intricate structure, and that the universe is trapped forever in this subset of all possible states. This might help to explain why the universe at the quantum level seems so bizarre.

For example, it may point to a natural explanation for one of the biggest puzzles of quantum physics, what physicists refer to as its "contextuality". Quantum theory seems to insist that particles do not have any properties before they are measured. Instead, the very act of measurement brings their properties into being. Or, put another way, quantum systems have meaning only in the context of the particular experiments performed on them....

According to Palmer's hypothesis, the invariant set contains all the physically realistic states of the universe. So any state that isn't part of the invariant set cannot physically exist.

Suppose you ... measure the position of an electron. Then you ask what you would have found if you repeated the experiment, only this time measuring the electron's velocity instead.

According to Palmer, when you repeat the experiment you are testing a hypothetical universe that is identical to the real one except that the position-measuring equipment is replaced with velocity-measuring equipment.

This is where the fractal nature of the invariant set matters. Consider a place of interest you want to visit along a coastline. If you get the coordinates even slightly wrong you could end up in the sea rather than where you want to be. In the same way, if the hypothetical universe does not lie on the fractal, then that universe is not in the invariant set and so it cannot physically exist....

Just as our eyes cannot discern the smallest details in fractal patterns, quantum theory only sees "coarse grain approximations", as if it is looking through fuzzy spectacles....

[Palmer's] theory backs Einstein's view that quantum theory really is incomplete. It is, Palmer says, blind to the fractal structure of the invariant set. If it wasn't, it would see that the world is not only deterministic, but it never exhibits any spooky effects.

On the other hand, it also agrees with the view of Bohr and his followers: the properties of individual quantum systems are not independent of the entire world, especially the experiments we humans use to explore them. We are stuck with the disturbing fact that how we measure always influences what we find.

Palmer's theory has - tentatively - been able to explain some of the mysteries and oddities of quantum physics.

Whether or not Palmer is ultimately proven right, I believe that scientists will come to see that the geometry of the natural world plays a bigger part in explaining the observed physics than previously realized, and that we are in for some exciting discoveries in the years ahead.