The theorem we prove – that quantum states cannot be understood as merely lack of knowledge of an underlying deeper reality described by some as yet undiscovered deeper theory – assumes preparation independence. ...I guess the editors took the superdeterminism loophole too seriously. Or maybe they did not like being scooped by a preprint server.
We are in a similar position with Bell’s theorem, which I consider the most important insight into the nature of physical reality of the last century, an honour for which there are some serious competitors! That theorem relies on a presumed ability to make independent choices of measurements at separated locations. Denial of such is the “super-determinism” loophole, ...
The authors claim to be ruling out an "undiscovered deeper theory", but they really only rule out certain types of theories. Maybe the editor was fooled into thinking that their theorem was stronger than it really is.
I do not agree with the hype over Bell’s theorem or the above paper. Those theorems just affirm the understanding of quantum mechanics that has been the consensus since about 1930. They only get attention because they claim to say something about what "reality" is. Lumo is harsher:
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.My FQXi essay was written, in part, as a response to quantum confusions about reality shown by the attention given to the above paper. The authors and many others assume that "deeper reality" means a mathematical model of a certain type. There could be a deeper physical reality that is not so neatly modeled mathematically. That is what I argue in the essay. If you think that I have worthwhile points, please go online and give a rating to the essay, as that will help me get the attention of the judges. The contest submission period is now closing, and there is a period of public discussion about the essays. Dozens of essays have been submitted, and many have far-fetched ideas.
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.
Update: Lumo adds, in his rant against the above paper:
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.No, I am not a creationist. By "Shwoit fan", he means a critic of string theory.
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).