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In almost every derivation of a quantum theory (quantum mechanics or quantum field theory), we start with a classical theory using classical equations and quantize it (by imposing certain constraints on commutation relations, etc).

My question is, isn't the entire process of starting with a classical theory (which is less fundamental) and deriving a quantum theory (which is presumably more fundamental) backwards? Why should we expect the correct fundamental quantum theory that describes our universe to be derivable from a less fundamental (averaged over, approximation) classical theory?

David Santo Pietro
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  • Yes, you are correct. There are quantum theories for which no classical limit exists or multiple classical limits exist, etc. –  Mar 28 '19 at 17:55
  • Related: https://physics.stackexchange.com/q/3500/2451 , https://physics.stackexchange.com/q/245300/2451 and links therein. – Qmechanic Mar 28 '19 at 17:59
  • OK but my real question is, if this is the case, why would we expect a more fundamental theory to be derivable from a less fundamental theory? – David Santo Pietro Mar 28 '19 at 19:46
  • We don't derive it, we guess it. We hope to be able to guess correctly by using the guidance of experimental evidence. That's how all science works. – knzhou Mar 28 '19 at 20:20
  • Existing attempts to derive quantum physics from axioms supposed to be more obvious or simple all seem to ring a bit hollow. The use of classical physics to provide pointers is much more fruitful in practice. We don't derive quantum from classical, but rather we get insightful hints and suggestions. – Andrew Steane Mar 28 '19 at 20:31
  • Saying that this is how we've made progress so far "rings hollow" to me. You could say the same to a bunch of monkeys who were trying to reach the moon and said they'd made the most progress by climbing higher and higher trees. It doesn't mean that approach will ever actually accomplish the task. – David Santo Pietro Mar 28 '19 at 20:34

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