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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