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I'm trying to understand the reason for Heisenberg's uncertainty principle which I read is a "fact of nature" rather than an experimental limitation. I found this thread in which the accepted answer talks about quantum objects as being wavepackets which seems to satisfy the criteria for HUP and how position and momentum can be related by Fourier transforms. However we can reach this result without even considering quantum objects as wave-packets from commutator relations between position and momentum. I'm aware of how to calculate the commutator of position and momentum from their definition in Schrodinger's equation. What I am seeking is the reason why they can't commute. The introductory textbooks (Griffith's: Introduction to Quantum mechanics and Arthur Beiser's: Modern physics) I've read so far don't seem to mention the reason why they don't commute and take it as an axiom. I would like some justification for it.

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Weezy
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    That the classical Poisson bracket between $x$ and $p$ becomes the non-zero commutator in the quantum theory is a postulate of quantum mechanics. So you are essentially asking Why quantum mechanics? – ACuriousMind Jul 13 '16 at 15:27
  • Thanks for the link. Although I don't understand Poisson bracketts yet the link has helpful answers @ACuriousMind. – Weezy Jul 13 '16 at 15:59
  • @ACuriousMind I don't agree this is a duplicate of the question you've linked. Rather this one link has my answer – Weezy Jul 17 '16 at 09:22
  • Ah, I see. Yes, if you want the specific link between non-commutativity and uncertainty, and not the reason why we believe in either of them, than that's a better duplicate. Do you want me to reopen your question - then it can be marked as duplicate of that one? – ACuriousMind Jul 17 '16 at 09:59
  • Yes that'd be a better duplicate. – Weezy Jul 17 '16 at 10:02

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