In modeling large-scale systems, wave equations are often useful approximations. So, while water at the quantum scale is made up of molecules that bounce around like billiard balls, in our swimming pool waves look perfectly smooth, and we can predict their behavior using wave theory.

A researcher at Cal Tech has applied this approximation to the modeling of very large astronomical objects: super-massive black holes and their entourage of stars and planetoids. In pursuing the mathematics, he discovered that the system behaves according to a wave equation that looks just like the equation that governs slowly-moving subatomic particles: Schrödinger’s equation.

But the equation alone does not generate “quantum” behavior in the objects described by the equation. That is generated by Fermi’s “exclusion” rules. In Fermi’s rules, the particles that make up stable matter all obey this rule: all particles of any one type (such as an electron) are indistinguishable, and therefore the equation describing the behavior of the system must be the same if any two particles are exchanged, with one exception: the amplitude of the wave changes sign.

Going back to our swimming pool, this is like saying that if we exchanged any two water molecules, the wave would turn into its mirror image: where there were peaks in the wave, now there would be troughs (and *visce-versa*).

I am absolutely certain that this makes as little sense in describing the behavior of supermassive black holes as it does in describing the behavior of pools of water.

That a working physicist could so casually misrepresent the nature of the system reflects the subtlety of quantum concepts, and the tempting ease with which those concepts are used to manipulate public fascination.

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