The realist epistemic view and the PBR theorem
Continuing with the realist psi-epistemic view discussion, let me first discuss if this paradigm deserves the attention that it got over the years. When one wants to establish independence of axioms/postulates, toy theories are a standard tool. However the explanations provided by realist psi-epistemic paradigm are far short of what mature quantum interpretations like Bohmian, MWI, GRW, etc do. So I am very puzzled by the traction Spekkens' toy theory got in the foundation community. This reminds me of the famous Alan Greenspan phrase of "irrational exuberance". Personally I've never fallen in love with this paradigm because I think the most effective way to spend my limited time and attention are on well defined problems. I do not know of any example from history where a philosophical paradigm was able to make genuine scientific advances. After new theories of nature are worked out and proposed, a new paradigm is formed to explain it, but not the other way around. It is more likely that a paradigm without results reinforces biases and prejudices than produces genuine advance of knowledge.
Anyway, the realist psi-epistemic view has suffered a major blow from a recent theorem by Pusey, Barrett and Rudolf (the PBR theorem). To the people who were in love with the paradigm this was a big deal, to me however, it does not look important because I found the original paradigm uninteresting to begin with. So what does PBR shows? It all boils down to this picture:
In the psi-epistemic view, there is an overlap in the support of a hypothetical ontic states and a measurement simply reveals what it is hidden. So suppose there is this overlap between the red and green pure states that you see on the horizontal and vertical axis. By some clever quantum basis arguments, PBR shows that the black square cannot exist (see my prior post for the technical details) and so there must be no overlap to begin with, and so the realist epistemic point of view is invalid. But is realism who is at fault, or is the epistemic idea at fault? Here is where the PBR result generated a lot of controversy. The original title was poorly chosen: "The quantum state cannot be interpreted statistically" and it was later changed to "On the reality of the quantum state".
If I were to venture a guess, it looks to me that Pusey, Barrett, and Rudolpf were originally realist psi-epistemic themselves, and they were unwilling to give up realism. With their poorly chosen title they drew the ire of Lubos Motl. That and most of other immediate reactions were basically only knee jerk reactions. PBR theorem is valid and is subject of celebration for the realist ontic camp like the Bohmian camp, but it is considered irrelevant by people who do not buy into the realist interpretations of quantum mechanics.
And how about the realist psi-epistemic view? Unless it reinvents itself and produces a comprehensive interpretation of quantum mechanics, it is confined to the long list of failed ideas in physics like phogiston theory. The epistemic point of view lives on in new-Copenhagen interpretations and QBism, while the realist point of view lives on in Bohmian interpretation, but the combination seems to be doomed.