Proof that everything sounds better with the word "quantum" in front.https://cloudblogs.microsoft.com/quantum/2019/02/28/announcing-the-microsoft-quantum-network/ …
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... classical approximations. But what's interesting (and a priori not obvious) is that this kludge actually is pretty nice mathematically! E.g. the map from Poisson bracket to Lie bracket.
I suppose that's not so surprising, given that we have an extraordinarily beautiful (but ultimately wrong) approximation to the world in classical mechanics, and another extraordinarily beautiful (and maybe correct?) theory of the world in quantum mechanics.
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To the extent the approximation is a good one, I guess it's not so surprising that the deep objects in one theory might sometimes have some interesting and rich correspondence to deep objects in the other.
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Yes, I agree it's a big mystery why classical and quantum mechanics should be so tightly and beautifully entwined, if QM is "true" and CM is "just an approximation". That's something I've been working on lately: http://math.ucr.edu/home/baez/gq/ pic.twitter.com/xd2bR39Sg5
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