re T.N. Palmer, Invariant Set Hypothesis (2008.12.05)
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What has been missing, [Palmer] 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."
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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.
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.
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