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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
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Dec
13
awarded  Informed