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IlyaShpitser comments on The Inefficiency of Theoretical Discovery - Less Wrong Discussion
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Here's a test of hindsight bias:
QM violates Bell inequalities, but obeys Tsirelson inequalities (http://arxiv.org/pdf/1303.2849v1.pdf).
What does that mean? (Not a rhetorical question, I really don't know!)
In graphical model terms, Bell inequality violations mean there is no "hidden variable DAG model" underlying what we see. But maybe Tsirelson inequality points to some correct generalization of the "hidden variable DAG" concept to the quantum setting (???). To my knowledge, nobody knows what to make of this, although it doesn't take much math background to understand Tsirelson inequalities.
To be a little more precise, I can imagine an object that does not posit anything ontologically beyond the four variables related by the graph:
A -> B <-> C <- D
The distributions that live in this object will, in general, violate both Bell and Tsirelson inequalities. So this object is "not physical." I can also posit a hidden variable DAG (in other words I posit in addition to A,B,C,D another variable H):
A -> B <- H -> C <- D
This will obey Bell inequality. So this is "classically physical, but not physical."
The question is, what should I posit beyond A,B,C,D to violate Bell, but obey Tsirelson? Whatever it is, it cannot be a hidden variable H. But maybe I can posit something more complicated, or "weird"? But obvious in hindsight?
I am not familiar with using DAG in QM, sorry.
Just wanted to mention that you can trade the EPR-style non-locality for macroscopic many worlds. For all its failings, this approach pushes the strangeness of QM into a local event where the branches interact. In the EPR example, it is where you compare the measurement results from the two detectors. Thus it might be more productive to base any DAG model on an MWI picture, or at least on a setup where there are only a finite and small number of branches, not uncountably many of them, like in Schrodinger's cat or EPR, maybe something like this quantum bomb tester.
The "non-DAG jargon" question is: "what are the ontological implications of Tsirelson inequalities?"
My point is that this has the feel of one of those questions with an answer that will be very obvious (but only in hindsight).