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With conceptually straightforward I meant that the concepts are easy to pick up. For example, the paper you cite is entirely understandable for anyone with som

With conceptually straightforward I meant that the concepts are easy to pick up. For example, the paper you cite is entirely understandable for anyone with some training in hermitian QM. In contrast, good luck trying to understand elementary concepts like the spectrum of the hydrogen atom or interference of matter waves from unitary QM. Of course the field of quantum info has progressed enormously and has its own interesting challenges, for which hermitian QM is all but useless.

eigenket 3y ago
I think maybe we have some difference in how we're talking about things. Concepts like the spectrum of the hydrogen atom or interference phenomena aren't particularly difficult to understand conceptually: the Hamiltonian has some eigenvectors and eigenvalues, you use the Dirac equation and work them out. The "matter waves" interfere essentially in the same way that waves on the surface of a pond do. The things that you're calling conceptual understanding I guess must be different to this: maybe something like detailed calculations of the structure of the spectrum?
- prof-dr-ir 3y ago
  In my definition, someone cannot claim to know QM if they do not know (a) Heisenberg's uncertainty principle, (b) how to compute interference patterns or (c) how to compute the spectrum of hydrogen. Aaronson claims that QM "can be derived" (quote from the original comment) are followed by an introduction to some aspects of QM that leads to strictly none of these things. That is why I am unhappy with it, and I still do not see why I am "somewhat mistaken" (quote from you). In fact, I can go even further and say that (from a quick glance at least) in his whole book positions and momenta make no appearance, let alone the correspondence principle. (I do not even see hermitian operators!) Without them I just do not see any reasonable "derivation" of (or, more properly, argumentation for) what I call QM.
  - eigenket 3y ago
    Ah, I see. You've changed from talking about concepts and conceptual understanding to talking about computations. I completely agree with you that from the perspective of a quantum information theorist computing the spectrum of the hydrogen atom is a rather complicated thing. I disagree wholeheartedly that this is part of the essence of quantum mechanics. The hydrogen atom is one system, understanding conceptually that its behavior is governed by a self-adjoint operator and its spectrum is very relevant to the whole of quantum physics. Understanding exactly the details of the calculation I think are not. Especially because if you do the calculation within quantum mechanics without quantum field theory you will obtain a somewhat incorrect result anyway (you will miss interesting phenomena like Lamb shift). Similarly interference is an interesting phenomenon that one needs to understand to understand quantum mechanics, but understanding the specific calculation of how interference makes nice patterns in some example setup isn't particularly enlightening. I agree that the Heisenberg uncertainty principle is important, but it certainly be derived from Aaronson's point of view (e.g. the standard Robertson-Schrödinger inequality is easily obtained). As an aside, I also think that self-adjoint operators and the correspondence principle are a fairly terrible way to think about observables in quantum mechanics. An obvious fact is that every measurement of (for example) the position of a particle has some unavoidable experimental error (our apparatus only has finite resolution) so the thing we actually measure in reality is some fuzzy observable which can not be represented as a self-adjoint operator. A POVM is a much more natural candidate (as a physicist it is natural to assume that the thing you get by adding some classical noise to your measurement is still a measurement).
    - prof-dr-ir 3y ago
      > Ah, I see. You've changed from talking about concepts and conceptual understanding to talking about computations. No, or at least I did not mean to: I said "know how to compute", not "compute". One typically uses the Schrodinger equation to do so (although Pauli did not need it), but this starting point is nowhere to be found here. > I agree that the Heisenberg uncertainty principle is important, but it certainly be derived from Aaronson's point of view (e.g. the standard Robertson-Schrödinger inequality is easily obtained). Robertson-Schrödinger is fairly trivial, at least in Aaronson's finite-dimensional world. But you conveniently forgot how to "derive" the part of QM that actually gives you the value of the commutator sitting on the right-hand side. So will you just postulate it? That sounds pretty terrible pedagogically, and it might be better to provide at least some general discussion. And that discussion is exactly what I am advocating as a necessary ingredient in any self-respecting introduction to (let alone derivation of) QM. > I also think that self-adjoint operators and the correspondence principle are a fairly terrible way to think about observables in quantum mechanics. No teacher of QM should introduce POVMs before talking about positions and momenta.
- deleted 3y ago
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eigenket 3y ago

I think maybe we have some difference in how we're talking about things. Concepts like the spectrum of the hydrogen atom or interference phenomena aren't particularly difficult to understand conceptually: the Hamiltonian has some eigenvectors and eigenvalues, you use the Dirac equation and work them out. The "matter waves" interfere essentially in the same way that waves on the surface of a pond do. The things that you're calling conceptual understanding I guess must be different to this: maybe something like detailed calculations of the structure of the spectrum?

prof-dr-ir 3y ago
In my definition, someone cannot claim to know QM if they do not know (a) Heisenberg's uncertainty principle, (b) how to compute interference patterns or (c) how to compute the spectrum of hydrogen. Aaronson claims that QM "can be derived" (quote from the original comment) are followed by an introduction to some aspects of QM that leads to strictly none of these things. That is why I am unhappy with it, and I still do not see why I am "somewhat mistaken" (quote from you). In fact, I can go even further and say that (from a quick glance at least) in his whole book positions and momenta make no appearance, let alone the correspondence principle. (I do not even see hermitian operators!) Without them I just do not see any reasonable "derivation" of (or, more properly, argumentation for) what I call QM.
- eigenket 3y ago
  Ah, I see. You've changed from talking about concepts and conceptual understanding to talking about computations. I completely agree with you that from the perspective of a quantum information theorist computing the spectrum of the hydrogen atom is a rather complicated thing. I disagree wholeheartedly that this is part of the essence of quantum mechanics. The hydrogen atom is one system, understanding conceptually that its behavior is governed by a self-adjoint operator and its spectrum is very relevant to the whole of quantum physics. Understanding exactly the details of the calculation I think are not. Especially because if you do the calculation within quantum mechanics without quantum field theory you will obtain a somewhat incorrect result anyway (you will miss interesting phenomena like Lamb shift). Similarly interference is an interesting phenomenon that one needs to understand to understand quantum mechanics, but understanding the specific calculation of how interference makes nice patterns in some example setup isn't particularly enlightening. I agree that the Heisenberg uncertainty principle is important, but it certainly be derived from Aaronson's point of view (e.g. the standard Robertson-Schrödinger inequality is easily obtained). As an aside, I also think that self-adjoint operators and the correspondence principle are a fairly terrible way to think about observables in quantum mechanics. An obvious fact is that every measurement of (for example) the position of a particle has some unavoidable experimental error (our apparatus only has finite resolution) so the thing we actually measure in reality is some fuzzy observable which can not be represented as a self-adjoint operator. A POVM is a much more natural candidate (as a physicist it is natural to assume that the thing you get by adding some classical noise to your measurement is still a measurement).
  - prof-dr-ir 3y ago
    > Ah, I see. You've changed from talking about concepts and conceptual understanding to talking about computations. No, or at least I did not mean to: I said "know how to compute", not "compute". One typically uses the Schrodinger equation to do so (although Pauli did not need it), but this starting point is nowhere to be found here. > I agree that the Heisenberg uncertainty principle is important, but it certainly be derived from Aaronson's point of view (e.g. the standard Robertson-Schrödinger inequality is easily obtained). Robertson-Schrödinger is fairly trivial, at least in Aaronson's finite-dimensional world. But you conveniently forgot how to "derive" the part of QM that actually gives you the value of the commutator sitting on the right-hand side. So will you just postulate it? That sounds pretty terrible pedagogically, and it might be better to provide at least some general discussion. And that discussion is exactly what I am advocating as a necessary ingredient in any self-respecting introduction to (let alone derivation of) QM. > I also think that self-adjoint operators and the correspondence principle are a fairly terrible way to think about observables in quantum mechanics. No teacher of QM should introduce POVMs before talking about positions and momenta.
deleted 3y ago
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