I know that is not really what your comment is about, but symmetries, conserved quantities and Noether’s theorem are some of the neatest bits of fundamental physics.
Basically you observe that stuff stays the same if you move around (not true on earth, but like, in space, generally speaking). The physics is invariant under translation. That’s what we call a symmetry.
Now Emmy Noether came up with a relationship and formulae that connects each such fundamental symmetry with a conserved quantity. For translation the quantity turns out to be momentum. Conservation of momentum is one of the most fundamental building blocks of classical mechanics. And we can derive that it is in fact conserved from something as simple as a symmetry.
And it doesn’t stop there: next in line: invariance under rotation: angular momentum conservation, which is equally important as momentum conservation. If angular momentum wasn’t conserved, our universe would look entirely different.
Ages later people figured out that this symmetry business goes way deeper than initially thought. These U(1), SU(2) and SU(3) from the posted link are notation for other, less intuitive, symmetries. Here they don’t apply to space itself anymore but to quantum fields. With that and Noethers theorem (and some admittedly kind of involved maths) you can derive theories describing all electromagnetic and nuclear interactions.
So basically, these symmetries are effectively at the heart of the world (and physics) and I think that’s amazing.
Basically you observe that stuff stays the same if you move around (not true on earth, but like, in space, generally speaking). The physics is invariant under translation. That’s what we call a symmetry.
Now Emmy Noether came up with a relationship and formulae that connects each such fundamental symmetry with a conserved quantity. For translation the quantity turns out to be momentum. Conservation of momentum is one of the most fundamental building blocks of classical mechanics. And we can derive that it is in fact conserved from something as simple as a symmetry.
And it doesn’t stop there: next in line: invariance under rotation: angular momentum conservation, which is equally important as momentum conservation. If angular momentum wasn’t conserved, our universe would look entirely different.
Ages later people figured out that this symmetry business goes way deeper than initially thought. These U(1), SU(2) and SU(3) from the posted link are notation for other, less intuitive, symmetries. Here they don’t apply to space itself anymore but to quantum fields. With that and Noethers theorem (and some admittedly kind of involved maths) you can derive theories describing all electromagnetic and nuclear interactions.
So basically, these symmetries are effectively at the heart of the world (and physics) and I think that’s amazing.