I am missing something here. Topology is a field of mathematics that studies the properties of objects that do not change under continuous deformations. So before asking why can Earth be treated as a topological something - one should specify what topology he is looking at, that is what continuous deformations of Earth he is talking about.
So - what continuous deformations of Earth are you talking about?
Well, the description of a topological insulator does use a tiny bit of topology.
So when you cut a topological insulator in half to expose the non-conducting inside, that exposed surface becomes conducting again.
So… I remain puzzled ((
It’s similar to the layman view of an atom as a miniature solar system. There are some similarities, but also very significant differences and not all knowledge is transferable from one to the other.
It is not particularly surprising that we would find new solutions to Navier-Stokes equation applied at the level of a whole planet, these things are very complex and far from completely understood.
> Then why can the earth can be treated as a topoligical insulator and what implications does this have?
That’s jumping to conclusions a bit. Again, they have found similarities in atmospheric flows and magnetic currents in topological insulators. It does not mean that the Earth is one, or that all properties of topological insulators also applies to the Earth.
> Or maybe even to the earths core?
There is bound to be some similarities, as with any fluid flow (assuming we’re not talking about the solid inner core). There are also significant differences in things like viscosity, compressibility, etc. So yeah, that’s a possibility, but as in the atmosphere, that would not make the outer core a particularly quantum object.
I think this is the wrong way of looking at this, quantum physics does not really have anything to do with this. Both systems, the oceans and topological insulators, share some of their structure and dynamics which means that the same mathematical models can be used to describe some aspects of both systems.
Large groups of people or animals can, to a certain extend, be described with fluid dynamics equations as they have some common structure, i.e. being composed of many particles interacting with each other locally. But the link is not from fluids to groups of people or the other way around, the link is a similar structure underlying both systems which makes mathematical models transferable between the two.
Underlying is the question though, why does this equation apply to the earths wheather? There seem to be parallels in the quantum and "macro" model, like windings of electron and wheather currents. Maybe the right view to modeling the earth is about dynamics as much as it is about topoligical phenomenons. After all, topology is used for solving gravitational problems, too.
Then why can the earth can be treated as a topoligical insulator and what implications does this have? Can we learn something from it that can be applied to other wheather phenomenons? Or maybe even to the earths core?