Symmetry Summary

What comes to mind when you hear (or read) the word symmetry?

If you’re like most folks, you’re thinking about something like the Taj Mahal, a structure known throughout the entire world for its beauty.

Taj Mahal has bilateral symmetry, meaning that if you draw a vertical line down the middle, you will see an identical picture on the left as you see on the right.

Astute readers may be thinking that’s not quite right, and you’re onto something: it’s not identical, exactly, but it’s a mirror image. Taj Mahal takes full advantage of this architecture by adding in a second form of bilateral symmetry, but this time it’s horizontal instead of vertical.

That’s because the pond is placed perfectly in front of the structure, so that if you stand at the right place, you get this wonderful doubling from left to right, and from top to bottom, all at once. The vertical mirroring imitates and complements the horizontal mirroring, giving us a wonderful feeling of things being in balance.

Balance is a useful way to describe what symmetry really is. If you do something to one thing, you have to balance it out if you’re going to have symmetry by doing that same thing to something else. If you want bilateral symmetry, you have to do the same thing to the right as you do to the left, or to the top as to the bottom.

I think this is the easiest type of symmetry to understand, largely because we humans are (mostly) bilaterally symmetrical. It’s not just us, either—most animals have this feature as well, and we see it everywhere in nature.

I take it back: radial symmetry might be even easier for us to grasp. If you take a long look at the night sky, you’ll notice that it pretty much looks the same in all directions, no matter where you are. Sure, there are some features here and there that catch your eye, but the further out you tend to zoom from everything, the more similar everything looks.

Astronomers say that the universe is homogeneous and isotropic. The homogeneity component means everything is made up of the same stuff overall, and the isotropic component means you can look in any direction and see the same makeup of stuff. The universe has radial symmetry, meaning it’s basically the same over there as over here.

A sphere or a circle also has this type of symmetry: you can rotate it from the center as little or as much as you’d like, and that shape will look exactly the same as before the rotation.

Things get really interesting when you start thinking more abstractly. What if there are other things in nature that are symmetric, but not along visual lines, like radial and bilateral symmetry? Could there be other types?

You bet. One type of symmetry you’re probably already familiar with is temporal symmetry, or something that is the same if you run it backwards in time. A musical crescendo is like this, where a part of a song starts out quietly, then builds up noise in the middle, then gets quiet again, often ending in the same place where it began.

Palindromes are like this, too. “Madam, I’m Adam” reads the same from back to front as it does the other way around.

The more abstract the thinking about symmetry gets, the more useful it can be in the world of cutting-edge physics. Murray Gell-Mann was awarded the Nobel prize for using abstract thinking about symmetry in a unique way.

This is where a concept from math comes in very handy. It’s the idea that you can use an idea as a metaphor and kind of run with it, applying the same sort of idea to a completely different situation.

Gell-Mann’s idea was to use symmetry in this way, where instead of everything on the left being the same as everything on the right, there’s a sort of symmetry among different particles. Here’s how that all happened.

Back during the turn of the 20th century, the existence of atoms was assumed to be true, but it took a paper from Einstein to seal the deal. Soon thereafter, the picture got very complicated very quickly, as physicists realized there was a dense and massive nucleus at the center of every atom, and electrons somehow orbiting that nucleus.

Then, things got even more messy. The nucleus itself was made up of protons and neutrons, and those particles were, in turn, made up of quarks (a term Gell-Mann himself coined).

Physicists had, by now, observed lots of different types of fundamental particles. Who ordered that?!?, they asked, as slew after slew of unexpected particles were discovered. Murray Gell-Mann tried to make sense of it all.

He did this by categorizing particles based on observed properties like spin, charge, and strangeness. You don’t need to know what all those attributes are to get the idea: some of them shared tantalizingly similar characteristics.

This was a new kind of symmetry, stretching the boundary of what might fit within that classical definition beyond its breaking point. Gell-Mann had come up with an analogy that was incredibly useful in predicting future particles.

By looking at existing particles scientists already knew about, they could predict the existence of never-before-seen particles by using symmetry.

The universe seems to use a few ideas over and over again. Symmetry is one of those multi-purpose tools that physicists can use to unlock new secrets time after time.