A solution
Last time I said:
You have a magic box with two buttons on it labeled C and D. The box is filled with an unknown number of particles flying around at random. When you push button C, a single new particle magically appears inside the box; when you push D, a single particle magically vanishes from the box.
I say there’s a subtle breakage of symmetry in how these two buttons operate. Can you spot it?
Note: it’s deeper than the fact that the two buttons are “opposite” in the sense of one creating and the other destroying a particle.
intothecontinuum said “uhm… C increases entropy while D decreases entropy?”
That is true, but it’s sort of another way to say the two buttons are opposite or inverse operations. I regard inverse operations as symmetric in a sense (they are like reflections of each other). The truth is though, these buttons are not exact inverses of each other!
There are at least two ways to notice symmetry breaking. The more concrete one is this: when the box is empty, pushing C followed by D leaves you with an empty box again, while pushing in the opposite order leaves one particle in the box! For true inverse operations, the order you apply them never matters.
Another subtle difference between C and D is that there’s only one way to add a new particle to the box, but there are n ways to remove a particle from the box, where n is the number of particles currently in the box. In other words, D involves making a choice.
These two buttons are more commonly known as the Creation and Annihilation Operators in quantum mechanics. I don’t know much about QM, but Prof. John Baez has a wonderful series of articles explaining how certain graphs describing random processes (called stochastic Petri nets) can be analyzed with quantum-theoretic ideas.
