The Heisenberg uncertainty principle $\Delta x \Delta \nu \geq \frac{c}{4\pi},$ seems to be the foundation of all quantum mechanics. However, as far as I'm aware, this uncertainty arises (at least in part) from estimation and measurement limitations associated with the Fourier Transform (Gabor limit looks like $\Delta x \Delta \nu \geq \frac{1}{4\pi}$ ). I would interpret this as a limitation to what we can actually probe from the quantum world, and how we percieve it. However, there are quantum phenomena that appear to arise from an intrinsic notion of uncertainty, like quantum tunneling, election-proton stability within an atom, etc.. I'm wondering first if my view holds to one of the more subjectivity centered interpretations of QM, and if so, how to interpret quantum-tunneling and atomic stability in that view. Second, are there other details or views that would help me align to a more Copenhagian interpretation here?
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The uncertainty principle isn't a statement about waves we send out to probe a system. It's a statement about the waves that make up that system. – Connor Behan Sep 30 '22 at 22:01
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How do you make a distinction between the two? – Davey Sep 30 '22 at 22:25
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Found an answer here. The Fourier transform fits the mathematics, but it is not the "true" reason for the uncertainty, which is derived from the canonical commutation relation.
Davey
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1https://physics.stackexchange.com/questions/720811/confusion-regarding-heisenberg-uncertainty-principle
I posted a question a while ago about the uncertainty principle, you might be interested in the discussion we had. I've gained some new insights about this over the time period that has passed, let me know if you would like me to give my take.
– Abhijeet Vats Oct 02 '22 at 00:58