Logan M
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 Apr 7 comment Heisenberg's uncertainty principle for mean deviation? Note that this is also true for the original derivation. $\hat A$ and $\hat B$, as you've defined them, are not linear operators. But they don't need to be for anything in the derivation of the uncertainty principle, and indeed they definitely can't be because uncertainties are not observables. Apr 7 comment Heisenberg's uncertainty principle for mean deviation? I don't think it's possible to find an "operator which squares to $\hat x- \bar x$", since $\hat x - \bar x$ is not itself a linear operator. In a given state $| \psi \rangle$ we have $(\hat x - \bar x) | \psi \rangle = (\hat x - \langle\psi | \hat x | \psi \rangle )|\psi\rangle$, which is not a linear expression in $| \psi \rangle$, and so (like $\Delta x$) it can't be a (linear) operator at all. To take a simpler example, consider $\hat S_z - \bar S_z$ for a spin-1/2 particle. This gives $0$ when acting on both $\hat S_z$ eigenstates, but not when acting on (say) an eigenstate of $\hat S_x$. Jan 27 awarded Popular Question Oct 13 awarded Nice Answer Sep 24 awarded Notable Question Sep 13 awarded Popular Question Aug 26 awarded Favorite Question Jul 12 awarded Yearling Apr 25 awarded Notable Question Feb 24 comment What is the difference between leptons and baryons? When cosmologists talk about "baryons", what they really mean (usually) is all standard model particles i.e. everything that isn't dark matter. For part of that source, they use that terminology, and the other part uses the more precise particle physics terminology in which a baryon is a composite state of 3 quarks. It's understandable that this would lead to confusion. Dec 17 answered How far can light go? Oct 17 comment Hopf Algebras in Quantum Groups The keyword to look for here is Tannaka-Krein duality (e.g. on nLab), a natural extension of Pontryagin duality. Perhaps someone else here is capable of giving some simple explanation of it, but I don't think I can do better than what's already on nLab or Wikipedia. Sep 24 awarded Autobiographer Jul 24 comment Is speed of light and sound rational or irrational in nature? I'm not sure in what sense a system with $c=\pi$ would have "very complicated and perhaps even inconsistent behavior under Lorentz transformations". A Lorentz transformation is simply a linear map on $\mathbb R^4$ preserving the quadratic form $(ct)^2-x^2-y^2-z^2$. Even leaving $c$ as a formal parameter, the theory is exactly what we teach in introductory courses. One can just as easily rescale $t$ such that $c=1$ or $c=\pi$ or any other positive real number; the same theorems in dimensional analysis ensure these are all equiconsistent. Jul 12 awarded Yearling Feb 21 comment How can stars make up 0.5% of whole universe? Minor terminology quibble: neutrinos aren't baryonic matter. They are, however, ordinary matter. Jan 14 awarded Enlightened Jan 14 awarded Nice Answer Dec 23 awarded Tumbleweed Dec 13 awarded Informed