Symmetries aren’t just about folding or rotating a piece of paper, but have a profound array of applications when it comes to physics.
In our everyday lives, as well as at the level of fundamental physics, symmetries play an important role. Human bodies have an approximate bilateral symmetry, or symmetry down the middle, and we judge more symmetric faces to be more visually appealing. Some animals, like starfish, have multiple lines of symmetry, as well as a rotational symmetry, where you can spin it by a certain angle (or set of angles) and it appears identical to the original. But in physics, there are extra kinds of symmetries that we don’t encounter conventionally: not just reflections, rotations, and translations, but discrete and continuous symmetries that are wholly divorced from our intuition and experience.
Can we break them down in way that are understandable, even to a non-physicist? That’s the question of Shiloh Paul, who asks:
“I’m curious about the concept of ‘symmetries’ in physics. I still picture symmetry the grade school way — can you fold a piece of paper on top of itself? But when I try to understand symmetries in physics, which are apparently super fundamental, I struggle to even get the concept, much less all the mathematical support. Is there a “simple” way to understand what symmetries mean in terms of their importance to all of physics?”
There’s a lot to unpack and dive into, but let’s give it a try.
The familiar symmetries that you know, including:
- a folding symmetry (where you can find an “axis of symmetry” like the various letters shown above),
- a rotational symmetry (either continuously like a circle, or discretely like a starfish),
- or a translational symmetry (like moving either up-or-down an infinitely long line),
all apply to objects we encounter in the everyday world, and are examples of spatial symmetries. Physics absolutely has these symmetries as an…
