Alaric Sanders
About Me
Outreach Talk: Dividing the Indivisible
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Transcript
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Slides
Transcript
The story centres around the idea of chopping a magnet in half - separating a dipole into a pair of disconnected monopoles, "all north" and "all south" elements of a magnet. This is the start of a surprisingly deep idea, not just about magnetism, but about the nature of electricity, quantum mechanics, and indeed it will lead us to question the very notion of "fundamental" in physics.
Firstly - what is a magnet?
I want you to do a thought experiment with me: Take an ordinary fridge magnet, and saw it in half, with the intent of separating the north end from the south end. You can't: if you look very closely under the saw blade, you see quickly that the big magnet is made up of many little magnets all facing the same way, these we call "spins". The little magnets / spins are atoms (
ατομος
) in both the modern and the ancient Greek sense - they are
indivisible
, i.e. the North and South are inextricably linked. For that reason, you always get two smaller magnets when you cut the big magnets. Clearly, we need to employ more trickery to pull a magnetic monopole out of the hat.
We need to think a little harder about magnetism to pull this off. First, nomenclature - a
monopole
has only one pole, it is all north or all south. It has no "direction", only a charge. However, the only difference between a dipole and two monopoles close together is nomenclature. In this sense, to get a monopole, you need a dipole whose end you are in some sense free to move.
A sketch of Dirac's idea, to essentially 'hack' Maxwell electromagnetism, is the following. Start with a dipole, then stack one on top of the other. The North and South parts cancel, effectively "moving" the North pole by one magnets' length.
The idea: if you can somehow "forget" about the long-magnet joining the two, then you merely have two free magnetic monopoles.
But how do we forget about the intermediate magnet? One way is by looking at a rock - specifically this rock, Dysprosium Titanate, which is a spin ice - more on the name later. This is a magnetic material, made up of little magnets / spins, arranged in a rather special way.
The spins still act like the magnets you're used to - North repels North and attracts South. All the magnets in the tetrahedron on the lower left want to be arranged North-To-South, but in fact, there's a problem - you can only make at most 4 of the 6 pairs of spins happy (tick) at a time. This is called "frustration" (the spins want to line up nicely, but can't), and is a very active field of modern quantum research. The point is that the spins are forced into follwoing this rule - 2 in, 2 out, called the "Ice Rule".
A side note on why it's called "Ice" - a very old paper (1933!) was thinking about water ice - remember from high school chemistry that H2O has slightly positive Hydrogen, and slightly negative Oxygen. It wants to line up + to -, forming the structure you see on the right - visualising the electric dipole moments, you get a 2 in, 2 out ice rule. The spin ices came much later (~1990), taking their name from this.
Starting from a 2 in, 2 out ice state, it's natural to ask what happend when you add some energy. Flipping a spin, we create these two coloured tetrahedra, red and blue, which are even worse than 2 in 2 out - they have, respectively, 3 cross-bonds (i.e. North-to North or South-to-South repulsions), making them higher in energy than the 2 cross-bond ice state on the left.
However, onece I pay that energy cost to make the two coloured tetrahedra, I find a surprise - when I flip a spin part of the red tetrahedron, the total number of X bonds stays the same: I didn't have to use any energy to do it!
Looking at the red tetrahedron, you'll notice that the red has three North poles sticking out and only one south. That doesn't look right - squinting our eyes, that's a net 3-1 = 2 North charges on the tetrahedron, which was meant to be forbidden: it seems like we really have an "all north" magnet!
Crucially, they _emerged_ from a deeper, more fundamental theory.
What you’re seeing here is a computer simulation of monopoles moving in time (at low temperature). Every so often, the computer randomly flips a spin, making the monopoles ‘hop’ in random directions. (see [here](/2022-03-22-diamondrender/, change 'System Size' to 3 and click 'Simulate" on Classical Spin Ice") you see the tetrahedra moving around randomly. Notice that we don't really need to focus on the details of which spins are pointing up or down - from a zoomed-out point of view, it's just monopoles diffusing through space.
Finally, I just want to signpost the similarities between the spin-flip / North-South monopole pair creatio nevent I yapped about earlier, and the real world. In space, a high energy gamma ray can split into an electron/antielectron pair; here, an entropic spin-flip can drive the creation of a North-antinorth pair.
These 3-out / 3-in tetrahedra are really acting like particles, and in condensed matter, anything that smells vaguely like a particle is called a particle. In this case, being made of spins, it's called a "Spinon".
To summarise: Starting from spins in a crystal interacting with simple rules, we found complex and surprising behaviour. Quasiparticles emerged naturally out of this system, manifesting as effective magnetic monopoles, which move at random in the bulk of the crystal.
Finally - this discussion has been classical, but I want to stress that my work is fully quantum-mechanical instead. When you make things quantum, things start to look even more like the real-life theory of electricity and magetism (QED) - emergent quasi-photons, and even an emergent "dual-magnetic-monopole", which you can ask me about later.
As a final, pholosophical note -you might say, "Alright I’ve just written down some effective theory, this says nothing about the universe." We have this situation, where real QED is responsible for real magnets, and the real magnets make my funny fake QED.
That's true to an extent, but I’d counter that by asking - "How real do you believe electrons to be?" If a simple model of spins can make the rich physics of QED, then perhaps we should view QED as the shadow, and not the light.
[remaining slides are supplementary]