system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5 what is gauge theory and why is it important?
gpt
If we’re both driving, saying that you’re standing still and I’m moving away from you is equivalent to saying that I’m standing still and you’re moving away from me, or that the earth is standing still and we’re both moving relative to that (for more or less obvious reasons, that’s the version we always use).

All of those are accurate descriptions of the same situation, and we can describe how to convert one description into another description through what is called a group of symmetries. Gauge theories are mathematical models that have this sort of symmetry. For example the traditional Newtonian mechanics taught in school is one particular case of a gauge theory.

The reason this is important is that in some cases you have a description where you can’t measure things directly (e.g. you can’t measure density directly), but you know how to translate between that and an equivalent description where you can measure things (you can weigh an object and measure its volume). In this particular example it’s mostly a mathematical trick, but in electromagnetism and related fields these transformations are somewhat fundamental to our understanding of things.