Let us pass on to the second revolution in physical thought of the present century - the quantum theory. This is a theory of atomic phenomena based on a mechanics of an essentially different type from Newton's. The difference may be expressed concisely, but in a rather abstract way, by saying that dynamical variables in quantum mechanics are subject to an algebra in which the commutative axiom of multiplication does not hold. Apart from this, there is an extremely close formal analogy between quantum mechanics and the old mechanics. In fact, it is remarkable how adaptable the old mechanics is to the generalization of non-commutative algebra. All the elegant features of the old mechanics can be carried over to the new mechanics, where they reappear with an enhanced beauty.
https://www.damtp.cam.ac.uk/events/strings02/dirac/speach.html
Time is non comutative with singular direction. The arrow of time. Unless you are an Einstein type nutcase who think time flows backwards.
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