Shutterstock/Mariia Tagirova
You may have learned about symmetry in school, perhaps being shown a snowflake’s six-fold symmetry and marveling at its appearance regardless of rotation. However, the concept of symmetry goes much deeper, as mathematicians will attest.
“Instead of being something visual, which is what I responded to as a child, it became something much more abstract and linguistic in nature,” says mathematician Marcus du Sautoy from the University of Oxford. “The understanding of symmetry I have now is so much deeper and stranger, and it gives me access to symmetries that are so much more exotic than anything you can see with your eyes.”
For mathematicians, symmetry refers to invariance, which means that something remains unchanged under a transformation like flipping or rotating. While this sounds simple, as du Sautoy explains, most symmetries go beyond what a casual observer would notice.
Consider antimatter, which occurs when positively charged particles become negative and vice versa. If no significant effects occur, then the system has charge symmetry. However, the laws of physics suggest that the early universe should have contained equal amounts of matter and antimatter, which would have annihilated each other. The fact that this didn’t happen indicates a lack of charge symmetry in the newborn universe, and understanding this is a major challenge in physics.
However, symmetries related to matter are not simply a list of things that remain unchanged. They can have complex relationships with each other.
