It is what can generate a bit (part 1)
It takes two to tango (part 2)
So now the cat is out of the bag. The paper deriving quantum mechanics from physical principles is now public and on the archive http://arxiv.org/abs/1407.7610 and I'll wait for about a month to collect feedback before submitting it for publication. Please don't be afraid to ask any questions, no matter how silly they may seem. Also, if you like the paper and/or this blog please vote for the paper on Scirate: https://scirate.com/?range=3 In the meantime I am going to explain what is going on under the mathematical cover, and what is the physical intuition.
The paper is based on two pillars: information and composite systems. Today I'll cover the information side. John Wheeler asked: "to describe how information is fundamental to the physics", how it comes from bit. In his book: "Our Mathematical Universe" Max Tegmark proposed this idea that reality is nothing but mathematics. While this got a less than cordial reception in the academic and philosophical circles, something along the lines of "not even wrong but we want to be polite because we like his grant money from FQXi", I think on one hand the cold welcome is not deserved but the on the other hand the idea is not fully baked. Let me explain.
The bad reception was due to the distinction between object and language used to describe the object. This is certainly a very serious objection, but consider this: if the laws of nature are relational, objective existence independent of everything is certainly an illusion. Sure, there may be different (mathematical) languages expressing the same thing, but ultimately reality is made only out of relative relationships. To the extent that mathematics is about relationships, and reality is about relationships, reality is mathematical, and I am a Platonist just like Tegmark. The "unreasonable" effectiveness of math explained Wigner.
On the other hand Tegmark's idea is not fully baked because it is only an entertaining interpretation devoid of consequences, a parlor trick good to sell a book. "Show me the money", show what is the consequence of this idea! There are none because we do not need to know how we are like mathematical theorems, but the other way around: what is the distinction between the abstract world of math and concrete reality? Sticks and stones may break my bones, but when is the last time you saw on TV that "Person X was injured by Pythagoras' theorem"?
So here is the first principle I want to discuss: ``it is what can generate a bit''. In other words, positivity. There are three composability solutions in the QM reconstruction paper: elliptic, parabolic, and hyperbolic. We know that elliptic composition corresponds to quantum mechanics, and parabolic composition leads to classical mechanics, but what is this hyperbolic composition. What if this is something physical as well? But before I packed my bags to go collect my Nobel prize on predicting a brand new physics more Earth shattering than the Higgs' boson, I wanted to understand why this may be unphysical (quantum and classical mechanics are ubiquitous and we can expect the same thing on the hyperbolic case as well if it were physical).
The answer was that in the hyperbolic case one cannot define an "objective reality" for which one can make predictions which can be tested against experiments. Why? Because in this case you cannot eliminate negative probabilities. Objective physical reality demands to be able to generate information. If you cannot do that, you are not an "it", but just another abstract mathematical relationship of no ontological value.
Ontology = ability to generate information
There are many papers attempting to distinguish classical from quantum information. Similarly there are many attempts to derive Born's rule. This is all misguided because of counterexamples. Born's rule and quantum information is not as universal as people think. They only form a particular very important flavor in the quantum garden.
Figuring out the complete classification of quantum information is a big open problem and a prerequisite first step. Finding a natural physical principle distinguishing quantum from classical mechanics is an impossible task just like finding an explanation for why there is a maximum speed limit in the universe. A maximum speed limit cannot have a dynamic explanation, because it has a kinematic origin. The elliptic composability class cannot have a parabolic explanation either. Sure, there are equivalent descriptions, like: existence of quantum superposition, existence of continuous transformations between pure states, but are those formulations really intuitive? Different quantum mechanics interpretations can provide intuitive explanations for this only at the expanse of sweeping the dirt under the rug for other things. Different quantum interpretations means different dirt and different rugs.
In special theory of relativity one first needs to give up the attempt to understand the maximum speed and give up concepts of aether. In quantum mechanics one first needs to give up the attempt to explain quantum superposition. Quantum superposition, quantum correlations, elliptic composability class are primitive concepts. Causal explanations of quantum correlations, are not only silly, but impossible due to Bell's theorem.