Following the lecture on the Higg's Boson a couple of weeks ago, I've been working on trying to understand Noether's Theorem that shows that any symmetry in physics results in a conservation law. I was given a clue that I might need to look into some harder maths so I've been working on Lagrange and Hamilton's formulations of mechanics. I have an outline understanding. But here's a mere illustration of what we might mean by symmetry in space or translational symmetry. My class did an experiment this week mixing hydrochloric acid with sodium hydroxide to make sodium chloride and water.
I took photographs in different parts of the room but they all looked the same because it doesn't matter where in the space the experiment is done - you get the same results. Translation mathematically means moving something around in a given space. With the experiment, a translation to a different part of the room affected nothing. That's a symmetry - you get the same everywhere. Noether's Theorem shows that this is equivalent to saying that there is conservation of momentum. I almost understand some of the mathematics involved but will spare you at the moment in case I get it wrong.
