In November 2011, a group of three physicists/mathematicians wrote the 3,635th paper suggesting that there had to be something wrong about the foundations of modern physics as redesigned by the founding fathers of quantum mechanics. Or at least this is how the paper was interpreted by some journalists.
None of these 3,635 papers has ever offered any successful description of experiments by an alternative theory that isn't equivalent to proper quantum mechanics and most of these papers contain statements that are manifestly false. Everyone knows that this whole anti-quantum program has been a giant waste of time and a miserable failure but people keep on writing similar garbage because the human stupidity and bigotry knows no limits.
If you read the paper by Pusey, Barrett, and Rudolph, it is self-evident in pretty much every sentence that they always assume that the world is a manifestation of a fundamentally classical system of laws. Even though physicists have known that the laws of physics in this Universe fundamentally differ from the very framework of classical physics for more than 85 years, these folks view the possibility of a non-classical essence of the world as a taboo. It can't even be thought about. A heresy. These folks are typical cultists, religious nuts.
In practice, they only think about several classes of hypothetical classical descriptions; non-classical candidates aren't allowed. In essence, these crackpots assume that the state of the world is fundamentally described either by an "ontic" state (from a Greek world related to the existence of things) – a pompous would-be philosophical term for a point in a phase space – or an "epistemic" state – a fancy word for a probability distribution on a phase space.
These nuts are sometimes capable of finding arguments that one of the scenarios is incompatible with the reality – everyone can do it easily because both scenarios are obviously incompatible with reality – but they incorrectly assume that any evidence against one of these two classical models shows that the other model is right.
But it doesn't because both of them are wrong. The world isn't described by any "ontic" state; and it isn't exactly described by an "epistemic" probability distribution on a phase space, either. It is described by a theory – quantum mechanics – that cleverly generalizes the second possibility.
The statement that there is no "ontic" state underlying the world is nothing else than the statement that the world doesn't follow the laws of classical physics. Nature can't objectively be in any "right point" of a "right phase space" now because phase spaces are fuzzy and one can't determine all the coordinates simultaneously; that's called the uncertainty principle.
Concerning the second wrong possibility, conventional probability distributions on the phase spaces look more general but they are still classical. In fact, if you say that an object may be described by a probability distribution on an ordinary classical phase space and nothing else, then you are implying that the probabilistic nature is purely due to one's personal ignorance about the "actual" point of the phase space that Nature chose. All observations will be compatible with the assumption that at every moment, Nature was objectively occupying a particular point of the phase space and all predictions fundamentally boil down to this assumption. The usage of probability distributions in classical statistical physics is purely about our ignorance (or lack of interest) about the detailed microstate but in principle, this state could be isolated.
However, quantum mechanics says that it ain't the case. Even in principle, there can't be any objective state of the system. The wave function is closely related to probability distributions – probability distributions may be "rather easily" calculated from bilinear expressions in the wave function – but the wave function isn't a classical probability distribution exactly. It has extra phases that are very important for almost all predictions yet totally unknown in classical physics; and due to the complementarity, its dependence on the position (or another observable) automatically encodes its dependence on the momentum (the complementary observable to the first one). Of course, the phases \(\psi(x)\) are critical for any reconstruction of \(\tilde\psi(p)\).
So Nature isn't a classical model with a simple phase space parameterized by the observables we know and routinely measure; Nature isn't a classical model with a more complicated phase space that also contains additional "hidden variables"; Nature isn't a classical model whose phase space emulates the numbers in the wave function; and Nature isn't a classical model based on a probability distribution on a classical phase space that would be in one-to-one correspondence with the complex-number-based quantum entities.
To summarize, Nature isn't any of these things. Nature isn't classical. Nature is a wonderfully new and clever beast, a quantum mechanical system. Its quantum rules can't be squeezed into any of these classical straitjackets indefinitely advocated by the infinitely stubborn anti-quantum cranks. That's why the evidence against either of these classical pictures isn't evidence in favor of any of the classical alternatives.
In their misguided "competition" between various wrong classical models, the winner was a "truly bad guy" which was maximally different from quantum mechanics, and the people therefore insanely concluded (in the very title!) that the quantum state cannot be interpreted statistically. Just to be fair, the same Barrett and Rudolph together with two new co-authors also wrote a paper called The quantum state can be interpreted statistically. What a diversity. The first, "cannot" paper was later renamed to a neutral title, On the reality of the quantum state. Depending on the paper and the version you read, the same authors can answer the key question positively, negatively, or neutrally.
The first paper in which the authors assumed wrong foundations of physics brought nothing new to the subject; they just described another simple toy model dealing with quantum information and showed, much like dozens of previous papers, that the actual behavior of Nature is in conflict with some of the classical ideas (while they self-evidently fail to see that it is in conflict with any type of a classical picture of the world, so they may publish 500 additional "revolutionary papers" with no meaningful content in the future).
Back to the sociological issues
As soon as the preprint was sent to the arXiv – which is something that pretty much every person with a university affiliation may do – Nature allowed a journalist named Eugenie Samuel Scott to announce a revolution in physics, Quantum theorem shakes foundations. The correct title should have been "another crackpot paper was posted to the arXiv" and this title should have been written on a high school toilet, not in a well-known journal claiming to cover science.
At any rate, there had to be an editor who was responsible for this unjustified and – as the following months confirmed, unjustifiable – hype. The paper was sent to the very same journal Nature at about the same time and, when someone important enough wants it this way, peer review was just a formality. In a new Cosmic Variance article, Terry Rudolph, one of the three crackpots, pompously described how their paper was almost published in Nature.
Well, the original paper received mixed reviews. In some cases such as this one, Nature doesn't need papers with perfect ratings so the editor simply ignored the negative review. What could he or she have done if Nature supervised by the same editor had already approved a popular article on a new revolution in physics? However, some extra problems and opposition appeared so the crackpot paper was finally published only in a new and dramatically less influential subjournal, Nature Physics. What they should have done is to reject the paper and publish a correction of Eugenie Samuel Scott's outrageously idiotic "commercial" but we would probably expect too much integrity from the journal.
Rudolph's detailed stories about the journey of their crackpot paper help to reinforce the theory about the crackpots' obsession with the conventional journals. They're not Wittens so they haven't published 300+ papers or so. So every paper that manages to penetrate through the quality filters is a source of immense pride for these folks. This is true both for the institutionally unaffiliated crackpots as well as the institutionally affiliated ones. Lee Smolin is a good textbook example of the latter category. If his paper is rejected, he doesn't care. He just keeps on sending it to other journals. By chance, it is almost inevitable that it is ultimately accepted somewhere.
Of course, the record holders in the "number of submissions per paper" work outside the system. This behavior is unusually hypocritical especially for those of them who otherwise criticize the "establishment". But if they see any nonzero chance to be admitted as members, they would do everything you can think of to join! Still, if they want to use the number of papers published in serious enough journals as an argument to win over science connected with folks like Edward Witten, they still need to publish at least about 350 papers in similar journals. ;-)
Terry Rudolph may be less obsessed with journal publications than the most obsessed crackpot colleagues but he's still obsessed with this sociological criterion. What he doesn't want to show is that even according to the sociological criteria, the paper sucks. Nine months after these folks "shook the foundations of physics", using Eugenie Samuel Scott's modest words, the paper has eleven citations. (Maldacena's AdS/CFT paper has had 300 citations, usually very serious and nontrivial papers, after 9 months.)
The only paper in this list of 11 papers that has been cited itself is a paper by Hardy – which is also deeply confused, by the way. In this list of the other 10 dull, confused, and uncited papers, the most eye-catchy one is the last one, an essay written by hardcore creationist crackpot and a Shmoit fan Roger Schlafly: Nature has no faithful mathematical representation. Although the author is a complete nutcase, this paper is arguably the most sensible one (or least insane one) in the list of the 11 papers (although it brings nothing new, of course).
Hype may occasionally be useful but do we really have to regularly see hype about similar junk? In particular, quantum mechanics and its rules have been known since the 1920s. Many people received their Nobel prizes and Max Born got 1/2 of the 1954 physics Nobel prize "for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction" – for a key feature of the quantum world that was new for physicists who had worked within classical physics for a few centuries. So don't you think that if someone writes papers with titles such as "wave function cannot be interpreted statistically", directly contradicting the Nobel-prize-winning insights by Max Born and others, he or she or they should have some evidence? And some evidence that goes beyond their ability to offer a 765th proof that Nature isn't a classical system following certain old-fashioned and obviously wrong rules?
There is no known evidence against quantum mechanics and there is no known alternative framework that could match the same empirical data (and the double slit experiment is really pretty much enough as a test) so why do some people speak about a permanent revolution in a layer of science that hasn't changed since the 1920s?
These people are living in a completely different world, a world of pompous crackpots who are much more interested in their visibility than in the truth about Nature.
And that's the memo.