Symmetries and Physics
Physics is about symmetries. But the question arises, how much is it about symmetries, and how much is it about **something else**?
Look at mechanics. You have Newton's first (inertia) second (F=ma) and third (action/reaction) laws to get physics off the ground, but in the end, forces are just a way of keeping track of conservation of momentum, and conservation of momentum is just (via. Noether's theorem) a way of stating a symmetry of our descriptions. The universe doesn't care where we are or how we are oriented. It doesn't care how we define our axes. Take whatever Copernican revolution tells you: the earth as NOT the center of the universe, and raise it to the n'th power. There is no center of the universe, there's no center of anything. The complete, perfect lack of a center, or even the notion of a center, is what makes all of it WORK. That the secret that makes all of mechanics tick. So all that is a symmetry. Momentum is conserved, because everybody knows this is nowhere.
Or look at conservation of energy: Energy is the mirror, the mathematical dual of time. The energy operator is, mathematically and metaphorically, the generator of time. Conservation of energy is deeply entwined with the fact that for the universe there is no NOW. Nothing really cares where t=0 is. So, via a subtle chain of reasoning that took hundreds of years to understand, the total energy of an isolated system can't change. Energy is conserved, because everybody knows now is no-when.
Through quantum mechanics and general relativity and the whole project of rounding out the standard model, it is all driven by symmetry. But is that all it is? It seems only a **negative** way to build a theory: the theory of reality can't depend on this, or that. It can't depend on where we are in time, and where we are in space, and how we color our quarks or the phase of the wave function. Okay, fine, reality isn't keeping track of when now is or where here is. What is reality doing then? We have spent the last three hundred years discovering what physics cannot be like. So what can it be like? Is there any **positive** notion of what the world is doing.
Of course there's synthetic, descriptive notions: atoms exist, volcanoes exist, stars exist etc. and here's how they work. But that's material science, or geoscience or astronomy. I'm not really sure that stuff is physics as I understand it. And it might be the nature of how the physics has drawn its borders (or how I personally have drawn its borders) that this science, in claiming for itself the most general descriptors of nature, can only be negative in its conclusions. So it must be about symmetries, because that's the only way to use the power of nowhere.
