This is really a question about the logic that applies to quantum mechanics. It comes down to this. If you describe a system using a kind of algebra in which the various terms in the equations commute – crudely meaning (page 151) that the answers you get don’t depend on the order in which you perform the calculations – then what you see is classical behaviour. But if the algebra of your equations doesn’t commute – if the order matters – then you get a quantum-type theory. Remember that this is where the uncertainty principle comes from: the fact that in quantum mechanics some quantities do not
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