Platinum is a silver-colored metal with a high melting point. If you heat it to 3825 °C, it will boil! If you carefully study platinum vapor, you can see spectral lines - different colors of light - as the electrons hop from one energy level to another.
Inside a platinum atom there's a nucleus. This too has different energy levels, shown in the middle picture. The energies here are huge: about 1 million electron volts. So, as the nucleus hops from one energy level to another, it emits gamma rays.
Physicists have come up with many theories that try to predict these energy levels. At left we see predictions of a theory called the SO(6) DS model. DS stands for 'dynamical symmetry' and SO(6) is a group of symmetries. The predictions are not *completely* wrong, but they're damned bad. At right are predictions of a more complicated theory called the SO(6) 'partial dynamical symmetry' model. They're better, though still flawed.
I'm studying these theories not because I care about the energy levels of platinum nuclei, but because it's incredibly cool that symmetry groups like SO(6) have anything to do with nuclear physics! Why? Because SO(6) is the group of rotations in 6-dimensional space!
What in the world does 6-dimensional space have to do with platinum nuclei? Here's what:
A platinum nucleus in its lowest energy level is shaped roughly like a kiwi fruit: an ellipsoid with all 3 axes of different length. In higher energy levels this ellipsoid is vibrating, constantly changing shape back and forth. It takes 6 numbers to describe an ellipsoid. So, we can describe the nucleus with a point in 6 dimensional space, which vibrates back and forth.
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