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It is said that the classical world emerges from the quantum world, but would it be more reasonable to say that the classical explanation is the limit of the quantum one, whilst the quantum explanation is the extrapolated limit of the classical one?

Extrapolated classically because the sun isn't guaranteed to rise tomorrow in a quantum world. Extrapolated quantumly, at the very least, because of the quantum Zeno effect.

In short, can the relationship of the quantum and the classical be described as dependently originated, in line with pratītyasamutpāda?

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  • $\begingroup$ Voting to close this question as it isn't clear what you are asking. Moreover, your question seems to be very concerned with concepts from mysticism which is not a part of mainstream physics. $\endgroup$
    – user87745
    Commented Mar 19, 2019 at 17:22
  • $\begingroup$ "concepts from mysticism" Care to explain? $\endgroup$
    – Gert
    Commented Mar 19, 2019 at 18:17
  • $\begingroup$ @Gert The notion of "pratītyasamutpāda", on which the OP anchored their question via summarizing the question in the last line in relation to that notion, is what I refer to when I say "concepts from mysticism". It is a notion arising from and discussed mainly in Buddhism: en.wikipedia.org/wiki/Prat%C4%ABtyasamutp%C4%81da. Also, I am sure you are more aware than me of this but kindly tag a user if you are addressing them on someone else's post--otherwise they don't get notified. $\endgroup$
    – user87745
    Commented Mar 19, 2019 at 18:23
  • $\begingroup$ See also Correspondence Principle: "QM is necessary for the description of nature on the atomic scale, but Newton's laws do fine for baseballs. Somewhere along the continuum from quantum to classical, the two descriptions must merge. Starting from the quantum end and noting that energies depend upon some quantum number, one would anticipate that for high enough quantum numbers, the quantum treatment should merge with the classical. This idea of the merging of the quantum and classical is called the "correspondence principle"" hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc6.html#c1 $\endgroup$
    – Gert
    Commented Mar 19, 2019 at 19:38
  • $\begingroup$ @DvijMankad: Hi. Sorry, I didn't see that bit, my bad. Have you actually voted? $\endgroup$
    – Gert
    Commented Mar 19, 2019 at 20:39

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No, Quantum Mechanics cannot be extrapolated from Classical Mechanics. There is no classical equation that predicts quantum effects.

On the other hand, in quantum mechanics we have more fundamental Ehrenfest's Theorem

$$ \bigg\langle \frac{d\hat{p}}{dt} \bigg\rangle = - \bigg\langle\frac{\partial V}{\partial x} \bigg\rangle $$

which indeed predicts Newton's second laws in the classical limit.

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