I've listened to many interviews and lectures of Alain Connes, in which he says something which goes roughly as follows

"Every non-commutative algebra has its own time (evolution of), by which I mean a one-parameter group."

I find this statement somewhat mysterious and intriguing at the same time.

Question. What is the precise statement of this result and how to can this proven explicitly even for a simple scenario like the von Neumann algebra of $2 \times 2$ matrices over $\mathbb C$ ?

Disclaimer. I have essentially no knowledge of non-comutative geometry, etc. I'd appreciate a very simple construction / proof; nothing too fancy. Thanks.

I've listened to many interviews and lectures of Alain Connes, in which he says something which goes roughly as follows

"Every non-commutative algebra has its own time (evolution of), by which I mean a one-parameter group."

I find this statement somewhat mysterious and intriguing at the same time.

Question. What is the precise statement of this result and how to can this proven explicitly even for a simple scenario like, say, the von Neumann algebra $M_2(\mathbb C)$ of $2 \times 2$ complex matrices ?

Disclaimer. I have essentially no knowledge of non-comutative geometry, etc. I'd appreciate a very simple construction / proof; nothing too fancy. Thanks.