Ask Ethan: How do symmetries work in physics? | by Ethan Siegel | Starts With A Bang! | Mar, 2024

We can imagine that there’s a mirror Universe to ours where the same rules apply. If the big red particle pictured above is a particle with an orientation with its momentum in one direction, and it decays (white indicators) through either the strong, electromagnetic, or weak interactions, producing ‘daughter’ particles when they do, that is the same as the mirror process of its antiparticle with its momentum reversed (i.e., moving backward in time). If the mirror reflection under all three (C, P, and T) symmetries behaves the same as the particle in our Universe, then CPT symmetry is conserved. (Credit: CERN, Kevin Moles)

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.

There are many letters of the alphabet that exhibit particular symmetries. Note that the capital letters shown here have one and only one line of symmetry; letters like “H”, “I”, “O” and “X” have more than one. This ‘mirror’ symmetry, known as Parity (or P-symmetry), has been verified to hold for all strong, electromagnetic, and gravitational interactions wherever tested. However, the weak interactions offered a possibility of Parity violation. The discovery and confirmation of this was worth the 1957 Nobel Prize in Physics. (Credit:

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…

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