One line that particularly stuck with me is:
"Dragging a modern-day student through all this may be a historically realistic approach to the subject matter, but it also ensures the historically realistic outcome of total bewilderment. Talking to aspiring young physicists about 'wave/particle duality' is like starting chemistry students on the Four Elements."
In Physics sometimes and approximated theory / model is useful, in spite it is incorrect.
The problem is that the Schrödinger / Heisenberg quantum states of a particle are a lie. If you have an electron, it doesn't follow the Schrödinger / Heisenberg equation. It can emit a photon an reabsorb it a little time after. This is not part of that equation and has a very easy to measure effect that is the Lambs Shift http://en.wikipedia.org/wiki/Lamb_shift#Lamb_shift_in_the_hy... .
And the electron can even do more crazy things, but they are luckily more difficult to measure. This is the reason to use Quantum field theory.
* If you are only going to buy a lens to put in front of your photodetector, then probably the wave/particle duality is a good enough approximation (in spite that it doesn't make sense).
* If you are doing quantum-chemistry then use the Schrödinger equation (in spite that it doesn't work for strong electric fields and is not compatible with special relativity).
* If you work near a big particle accelerator you should try at lest to use the standard model (in spite that renormalization doesn't make sense).
* And I hope that you never have to use string theory to explain and experiment.
It's nothing like the quantum physics sequence. Yudkowsky starts out making up numbers from nowhere and asserts things for purely philosophical reasons, whereas Aaronson actually has proofs (albeit left to the reader).
Sure, the numbers in "Quantum Explanations" are made up, but (1) the experiments are real, and (2) everything besides the numbers is accurate (as far as I know). Plus, the goal of the sequence was never to actually explain quantum physics. It was to explain why a realist perspective (the wave function is all there is, and the math says it doesn't collapse, so it really doesn't) is by far the most probably correct, despite the fact that it makes no new prediction compared to previous interpretations. That, plus answering some philosophical question with physics.
Aaronson's explanation definitely is a step in the right direction. I still have a quibble however: he keeps mentioning "probability" as an analogy to amplitude. That confuses his explanation in my opinion. I'd rather have a straight explanation of QM math, then an explanation about its similarities with probability theory. And the mixed state paragraph seems to conflate subjective probability and actual distribution of amplitude. Ick.
When Yudkowsky says configuration space in that sequence, he doesn't mean a separable Hilbert space, because he doesn't believe (for philosophical reasons) that that's the correct setting for QM.
But… Of course it's not the correct setting for QM. Before even talking about Turing computability and infinite set atheism (which rule out a continuous, infinite configuration space), configuration space is folded on itself around the identity axis.
Unless you think (a,b) is not the same configuration as (b,a), even though their amplitudes would add up before we have access to their square at the experimental level? Evidence towards "its the same configuration" looks quite overwhelming.
Or, could a "permutable" space, where (here with 2 dimensions) (x,y)=(y,x) for all x and y, be a Hilbert space as well?
Overall, I'm not sure what you're talking about. Can you be more explicit, or provide some links?
I don't know how you expect me to respond to this.
> Before even talking about Turing computability and infinite set atheism (which rule out a continuous, infinite configuration space), configuration space is folded on itself around the identity axis.
Infinite set atheism is basically Yudkowsky's reason for denying Hilbert space, so I don't know why we should talk before it.
Read the comments on "The Quantum Arena" -- Yudkowsky didn't even know whether the thing he was railing against as an uncountably infinite set was indeed infinite! (Presumably he has updated by now.)
> Unless you think (a,b) is not the same configuration as (b,a)
Well, it depends on the situation. I assume you're talking about the configuration space of the position of two indistinguishable particles, in which case of course I think they're the same configuration (that's what 'indistinguishable' means) and you're just beating down a straw man. If wavefunctions in general are members of a Hilbert space, then so are symmetric wavefunctions.
> Overall, I'm not sure what you're talking about. Can you be more explicit, or provide some links?
All of the wavefunctions for two particles described within are elements of L^2(R^2); the subset of physically realizable wavefunctions forms a subspace which is also a Hilbert space (answering your question about "permutable" spaces).
Well… I agree. But then again, I don't think he really was trying to teach it. The way I see it, he just lifted confusions you would have if you start to really learn QM.
One line that particularly stuck with me is: "Dragging a modern-day student through all this may be a historically realistic approach to the subject matter, but it also ensures the historically realistic outcome of total bewilderment. Talking to aspiring young physicists about 'wave/particle duality' is like starting chemistry students on the Four Elements."