I look at the abstracts of new papers on the quant-ph archive every day. This is a type of paper which, based on the abstract, I would almost certainly not bother to look at. Namely, it proposes to explain where quantum theory comes from, in terms which obviously seem like they will not be enough. I read the promise in the title and abstract and think, "Where is the uncertainty principle going to come from - the minimum combined uncertainty for complementary observables? How will the use of complex numbers arise?"
I did scroll through the paper and notice lots of rigorous-looking probability formalism. I was particularly waiting to see how complex numbers entered the picture. They show up a little after equation 47, when two real-valued functions are combined into one complex-valued function... I also noticed that the authors were talking about "Fisher information". This was unsurprising, there are other people who want to "derive physics from Fisher information", so clearly this paper is part of that dubious trend.
At a guess - without having worked through the paper - I would say that the authors' main sin will turn out to be, that they do not do anything at all like deriving quantum theory - that instead their framework is something much, much looser and less specific - but then they give their article a title implying that they can derive the whole of QM from their loose framework. Not only do they thereby falsely create the impression that they have answered a basic question about reality, but their fake answer is a bland one, thereby dulling further interest, and it is presented with an appearance of rigor, making it look authoritative. I would also expect that, when they get to the stage of trying to derive actual QM, they have to compound their major sin with the minor one of handwaving in support of a preordained conclusion - that they will have to do something like join their two real-valued functions together, in a way which is really motivated only by their knowing what QM looks like, but for which they will have to invent some independent excuse, since they are supposedly deriving QM.
All the foregoing may be regarded as a type of prediction. They are the dodgy misrepresentations I would expect to find happening in the paper, if I actually sat down and scrutinized it in detail. I really don't want to do that since time is precious, but I also didn't want to let this post go unremarked. Is it too much to hope that some coalition of Less Wrong readers, knowing about both probability and physics, will have the time and the will to look more closely, and identify specific leaps of logic, and just what is actually going on in the paper? It may also be worth looking for existing criticisms of the "physics from Fisher information" school of thought - maybe someone out there has already written the ideal explanation of its shortcomings.
I wonder if you would apply the same criticism to so-called "derivations" of quantum theory from information theoretic principles, specifically those which work within the environment of general probabilistic theories. For example:
http://arxiv.org/abs/1011.6451 ; http://arxiv.org/abs/1004.1483 ; http://arxiv.org/abs/quantph/0101012
The above links, despite having perhaps overly strong titles, are fairly clear about what assumptions are made, and what is derived. These assumptions are more than simply uncertainty and robust reproducibility: e.g. on...
The paper: http://www.sciencedirect.com/science/article/pii/S000349161400102X
Authors: Hans De Raedt, Mikhail I. Katsnelson, Kristel Michielsen
Abstract
It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the observed events are robust with respect to small changes in the conditions under which the experiments are carried out.