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I was reading Gödel's incompleteness theorem and Heisenbers's uncertainty principle. I found some similarities although one is based on a physical phenomenon and the other is mathematical.

Q: Are they interrelated? Can one interpret the incompleteness and inconsistency of Gödel as uncertainty as well?

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    I'd say there is a big difference, since Heisenberg is more about how our intuition of the real world breaks down when deal at the smallest levels.2012-09-06

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Heisenberg's uncertainty principle can be given a precise mathematical formulation that, as far as I can tell, has nothing to do (mathematically) with the incompleteness theorem.

One version is a statement about how spread out a function on $\mathbb{R}$ can be relative to how spread out its Fourier transform can be; roughly speaking, a function and its Fourier transform cannot simultaneously be localized (physically the function can be interpreted as describing the position of some particle and its Fourier transform can be interpreted as describing its momentum, but the mathematical statement is independent of this interpretation). A more general version is a statement about the variances of noncommuting random variables. In this form it is essentially an application of the Cauchy-Schwarz inequality.

If there are similarities to the incompleteness theorem, they are philosophical, not mathematical.

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    have a look at the latest answer.2015-03-14