SneerClub

Aaronson goes on:

Look, obviously the physicists had their reasons for teaching quantum mechanics that way, and it works great for a certain kind of student. But the “historical” approach also has disadvantages, which in the quantum information age are becoming increasingly apparent. For example, I’ve had experts in quantum field theory – people who’ve spent years calculating path integrals of mind-boggling complexity – ask me to explain the Bell inequality to them, or other simple conceptual things like Grover’s algorithm. I felt as if Andrew Wiles had asked me to explain the Pythagorean Theorem.

And then, did anyone clap?

This is a false analogy. I don't think it's a surprise, I am not convinced that it's an actual problem, and if it is, I don't think Aaronson makes any progress to a solution.

The Pythagorean theorem is part of the common heritage of all mathematics education. Moreover, it's the direct ancestor to the problem that Wiles famously solved. It's going to be within his wheelhouse. But a quantum field theorist who's been deep into that corner of physics might well not have had to think about Bell inequalities since they were in school. It's like asking an expert on the voyages of Zheng He about how Charlemagne became Holy Roman Emperor. There are multiple aspects of Bell inequalities that someone from a different specialization could want "explained", even if they remember the gist. First, there are plenty of questions about how to get a clean Bell test in the laboratory. How does one handle noise, how do we avoid subtly flawed statistics, what are these "loopholes" that experimentalists keep trying to close by doing better and better tests, etc. Aaronson has nothing to say about this, because he's not an experiment guy. And again, that's entirely fair; some of us are best as theorists. Second, there are more conceptual (dare I say "philosophical"?) questions about what exactly are the assumptions that go into deriving Bell-type inequalities, how to divide those assumptions up, and what the violation of those inequalities in nature says about the physical world. Relatedly, there are questions about who proved what and when, what specifically Bell said in each of his papers, who built on his work and why, etc. Aaronson says very little about all of this. Nothing leaps out at me as wrong, but it's rather "101". The third broad category of questions are about mathematical specifics. What particular combination of variables appears in which inequality, what are the bounds that combination is supposed to satisfy, etc. The expressions that appear in these formulae tend to look like rabbits pulled out of a hat. Sometimes there are minus signs and factors of root-2 and such floating around, and it's hard to remember where exactly they go. Even people who know the import of Bell's theorem could well ask to have it "explained", i.e., to have some account given of where all those arbitrary-looking bits came from. I don't think Aaronson does particularly well on this front. He pulls a rabbit out of his hat (a two-player game with Alice and Bob trying to take the XOR of two bits), he quotes a number with a root-2 in it, and he refers to some other lecture notes for the details, which include lots of fractional multiples of pi and which themselves leave some of the details to the interested reader.

Aaronson leads into this rather unsatisfying discussion thusly:

So what is Bell’s Inequality? Well, if you look for an answer in almost any popular book or website, you’ll find page after page about entangled photon sources, Stern–Gerlach apparatuses, etc., all of it helpfully illustrated with detailed experimental diagrams. This is necessary, of course, since if you took all the complications away, people might actually grasp the conceptual point!

However, since I’m not a member of the Physics Popularizers’ Guild, I’m now going to break that profession’s time-honored bylaws, and just tell you the conceptual point directly.

The tone strikes me, personally, as smarmy. But there's also an organizational issue. After saying he'll "just tell you the conceptual point directly", he then goes through the XOR rigmarole, which takes more than a page, before he gets to "the conceptual point" (that quantum mechanics is inconsistent with local hidden variables). It's less direct than advertised, for sure. I have not systematically surveyed pop-science explanations of Bell's theorem prior to 2013, but the "page after page of entangled photon sources..." rings false to me.