Unfortunately there is to my knowledge none that has published anything that is completely in the direction what I think needs to be done, but there are several peoples and programs that have fragments that point to this direction.
But the general direction I'm favouring is an inference perspective to physics, where the ultimate idea is that the laws of physics are nothing but natures own "rational infernece". Then this is combined by physical constraints on the inference system (hosted by the observing system).
Some ideas that at least RELATE to this (but which develops different later) you find here.
1) Ariel Caticha
http://www.albany.edu/physics/ariel_caticha.htm
His main idea is that the laws of nature are derivable from the rules of rational inference. Ie. that information about physical interactions between two systems in nature, can be understood as a rational inference on their behaviour. In his view rational inference = probability theory, and for the extension to non-commutative cases quantum theory.
How this relates to my view: the main idea that the laws of physical are "rational expectations" is right in line with I envision, but I think we Need to start the analysi much deeper. In particular to I reject the too naive usage of continuum based probability. I think we need to start at the discrete levels and not just jump into the limits. This is why the causal set program may have bigger potential. But the idea is that these programs might meed somewhere.
2) Lee Smolin (Roberto Unger angle)
Smolin is very scattered and writes about almost everything, but the part I like the most is his collaboration with R Unger (expert in social theory) where he argues that the idea of eternal and timless laws of physica is wrong. The laws of the universe are evolving. I won't repeat the argument here, but this is also in line with my thinking, and it merges well with the reconstruction of ratinal inference from discrete ordered and partitioned sets of sets. It ultimately means that the laws of physics are also the result of a rational inference. But I find that Smoling isn't radical enough, he doesn't go all the way.
3) Kevin Knuth
Foundations of Physical Law
http://knuthlab.rit.albany.edu/index.php/Program/Foundations
His idea is that natural law derives from ordering relations. The idea could be that order is naturally present in the chain of events that defines the observers knowledge. This is an abstract idea that aims to ultimatley infer the laws of nature, from ordering relations of set, combining them also with equivalence relations of sets. This is an abstract reasoning that takes place long before spacetime is defined.
This kind of research is important and may relate to what I have in mind. But what he does is very basic structures, I can not answer for what Knuth's vision of the more elaborated things are.
How this relates to my view: This reminds of some of basic structure I'm working with. The basic abstractions are sets of distinguishable events, as well as counter states, that represents memory structure (where information is encoded). Then I have sets of such sets, that are related by different encodings (fourier transform is just an example). This entire set is constrained by a complexity. A time history is ordered, but a reencoded history has a different order. This is why networks of order create complex sturcutres that can be interpreted as multidimensional. Then this entire set of sets is subjct to random walks as the networks of sets develop in different directions entirely depending on the data stream fed into it. But this research is so abstract that on first sight, I have to admit that it's hard to see how it connects to physics. This is why I thin that IF someone is working on this, and publish parts of it, it may be in mathematical papers.
4) String theory
While I do not like string theory as such, it may be interesting to associate to it since it's after all one of the main BTSM reasearch programs.
In string theory, the idea is to deduce the action of the system, from some form of string action, and different state of the string. But ultimately the origin of the string action is just a silyl association to the string as a mechanical litteral string, oscillating. Then you quantize etc.
My generic view is to infer the action of a system from the rational action of the system, where the rational action is what follows from a random system just subject to the acquired self-constraints (such as ordering and equivalence relations of historical events). No classical action is needed. Also the "quantum" should be emergent as the structure of the system evolves from a single set to several non-commuting sets.
It is possible that string theory, may be a continuum limit of a deeper theory (without strings or more specifically without continuum objects at all; just sets of sets with inter-relations). The idea is that all interrelations would be understood from rational inference (almost the same as entropic reasoning).
5) Rovelli's LQG is not at all what I have in mind. When I started to read his book, during some of the first parts it started to converge to a picture I had where the networks would correspond to the observers information state; and that we would consider interacting networks. This would have been interesting to me, it could also connect at some point to te more abstract causal set views... but I later learning this is NOT Rovelli's vision.
Rovelli's RQM paper contains grains of excellent thinking, but again I find that because he wants to be conservative, he does not fully acknowledge his "no absolute relations" mantra. Because at some point he claims that communication is govergned by QM, and this is exactly the point where I find his reasoning looses coherence. But this is also because rovelli wants to find a "good interpretation" of QM, without changing it! But the outcome is not a good compromise IMO.
See
http://arxiv.org/abs/quant-ph/9609002
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My starting point, is a set of sets, that can be though of as (in constrast to classical statmech) a set of interacting microstructures, with a complexity conservation constraint. The microstructurs are related by different data encoding algorithms. When this structure is subject to new data, the data favours reallocations in this structure that can be understood as en entropic flow. New microstructures can be branched off at any time is situation demands. So there is NO static state space. The state space is always chancing. This is why expected changes are only relative to current state space. This is also why it's unitary (in the instant state space); there is simply no way to EXPECT the unexecpted. So unitarity is simpled to understand. It's no conicidene, or not magic tricks is needed to secure it. This is like when you move in a curved space; your tangent space is still always linear. There is an analogy here. Except that the structure of the embedding curved environment is unpredictable from the inside view; this is whay it's a true random walk, one step at a time.
But the difficulties start when these systems are interacting, then a selection will take place as there is a mutual interaction causing an evolution where at some point there may be a nash type equlibrium where systems maintain status quo (or approximately so). The task is to mathematically identify these equilibrium points, and the hope is obviously that the equilibrium points will prove to have a structure exactly fitting the standard model + of course include gravity and provide a GUT.
So in this view, there are no classical hamiltonian or lagrangians that are manually "quantized"! All there is are the logic of rationality (effectively serving as a selecting mechanics) then the effective hamiltonians will correspond to equilibrium points in this "game". Quantum logic automatically emerges out of this scheme as rational inference applied not to a single microstructure, but to sets of them (where they are related by information recodings), and constrained by "information capacity conservation".
/Fredrik
