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A story about quasiparticles on the beach

September 21, 2009

A great story in physics can change the way you see the world.  If physics is worth all the terrible effort (for some of us, anyway), it’s because once you’ve learned some part of it — really learned it — it changes the way you think about the universe around you.  Sometimes when I’m walking down a hallway, for example, I’ll think about how both my feet and the floor they’re pressing against are really 99.9999999% empty space, but still I don’t fall through because of mysteriously strong electrical forces and an even more mysterious Pauli Exclusion Principle.  Or I’ll imagine the compression and rarefraction of air molecules that comprises the music I’m listening to, and how those pressure waves get transduced via oscillating hairs in my ears into electrical signals that please my brain.  Or, if I’m feeling particularly outlandish, I’ll imagine my body as an entangled mass of oscillations and “defects” propagating through a boiling, bubbling quantum sea.

I’m sure there are easier ways to stimulate your imagination than through the intensely confusing study of physics, but for someone who was born short of creativity (I had little to zero tolerance for “pretend” games as a kid), these images can be quite awe-inspiring.

The subject of the last post, I think, constitutes a great story in physics.  I only recently realized how it changed the way I look at the world around me, when my wife and I went on vacation in the Caribbean.  (You might want to read the last post, by the way, or this one might sound like gibberish).

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A particularly pretty rock

We were walking on the beach one afternoon when my wife found this beautiful piece of coral for me:

rocky

There’s something aesthetically pleasing about this rock in general, I think.  It has a nice, regular pattern, of the sort that could be made into a carpet or a wallpaper.  Stare at it a little longer, though, and you’ll start to see clear “lattice lines” connecting the circular skeletal marks that once housed individual coral polyps, and regions where the marks form a surprisingly regular hexagonal lattice.

After a while I found myself tracing out the lines, and looking for the “quasiparticle” dislocations, like this one:

rocky-one_dislocation

And here’s a place where the dislocations came as a pair — a “lower energy excitation”:

rocky-paired_dislocations

Maybe this seems like a cute analogy — something I liked just because it reminded me of something else.  But there are very few true coincidences in physics, so if a piece of coral has the same sort of structure that a two-dimensional electron gas does, then they probably have some physics in common.

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I don’t actually know much about coral

But I know this much: the appearance of dislocations as “quasiparticles” only requires two things to be true of the individual objects that comprise the field

  1. Individuals must have an effective repulsion from each other
  2. Individuals must have an effective attraction to the landscape they sit on

These two facts are certainly true of coral polyps, who grow as clones of their neighbors on an ever-expanding skeleton.  Coral polyps repel each other because they must compete for nutrients.  A coral polyp survives by sifting nutritious material from the water that washes past it, so it has a large incentive to not overlap strongly with another polyp that would steal all its food.  Coral polyps have an effective attraction to the “bed” they sit on because it requires a finite amount of resources to build additional coral skeleton.  Even though polyps repel each other, it would be too expensive for the organism to keep them very separated, because growing that much extra bone requires a lot of food input.  So the coral tries to build up its polyps with a certain density while keeping them as far apart as possible.  That how you get a hexagonal lattice, with “dislocations” as imperfections.  I would imagine that the harder-pressed the coral is for survival, the more carefully it will build its lattice of polyps (like a low-temperature electron gas).  A coral that is thriving and has no scarcity of food, on the other hand, will probably have a very disordered lattice (like a high-temperature electron gas).

Of course coral polyps don’t shift about the way an electron gas does, so coral “quasiparticles” don’t actually attract or repel each other in real-time.  But still, the description of both coral and electrons has some common language, because the two systems share some common physics.

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PS

If you stare at the coral above for long enough, you’ll see that something weird is happening to the lattice lines near the middle of the rock: they get bent as they pass near the center.  This is a fairly serious defect that can’t be explained as a dislocation or any combination thereof (it’s actually called a “disclination”: a rotational shift of lattice lines).  It isn’t surprising that the center was also the place where the surface was the least flat.  There’s a sort of a gentle lump in the center of the coral, and this seems to encourage the formation of defects in the lattice.  There is a lesson here for electron gases as well: topological or electrostatic defects in the “bed” that the electron sit on can disrupt or destroy their order, even when there is very little thermal energy to jostle them around.

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3 Comments leave one →
  1. Andrew Dalton permalink
    September 22, 2009 6:58 pm

    My favorite self-ordering structures are the phyllotaxis spirals of plants. They can even exist in fractal form.

    This phenomenon has been reproduced in non-biological experiments, too. (PDF

  2. September 24, 2009 9:38 am

    Lovely post. I have no meaningful contribution to the discussion, just words of encouragement.

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