Beyond the standard glosses of QM (the realistic clock interpretation)

[LuisPe]

I have a more concrete question.

My motivation for the work we've done is that I see a very basic and problematic problem in QM (apart from all this thing of merging it with GR, and QFT problems): the measurement problem. Schrodingers cat and all that. Decoherence is not a fundamental answer.

My question is in what sense do you find it necessary to deny the existence of timeless hilbert spaces? Is it sort of a philosophical argument because you do not like making that assumption, or do see something wrong in QM that makes you look in this direction?

 

[LukeD]

Luis Pedro,

After reading through some of Gambini & Pullin's work, I have some questions.

What kind of scope does this have? In particular, what does it mean to measure time with a clock, and what sorts of things do I necessarily need a clock for? Do I need clocks to determine if 2 events separated in space are simultaneous? (something tells me I do) If that's the case, am I using a clock whenever I declare that 2 events are happening at the same time? But I usually just say that they take place at the same "ideal time" t. Can I no longer get away with that?

Or am I only using a clock when I make an interaction with my system at some time as measured by my watch?

To calculate the effects of a real clock, we still have to use the ideal time t. The entire theory is still formulated in terms of an ideal time. If I turn off GR, it's ok because I can still measure time as accurately as I please, so I can say that t exists in non-relativistic Quantum Mechanics. However, in the case of GR, where I use space-time separation, this is an idealization that does not exist at all (since time cannot be measured arbitrarily accurately), so I am uncomfortable with using the ideal space-time separation in calculations.
Can the theory be formulated without needing to make reference to an ideal time?
the FAQ seems to indicate that the ideal time drops out in the end. Does this mean it's unnecessary?

 

[Fra]

I think the questions we now start to discuss are good ones, so I probably will complement my answers later when I've formulated the better answers, but here are some quick ones.

Now, by observer you mean an environment then?

Yes it could be, but more often it's just a part of the environment, not necessarily the entire environment.

Also, conceptually I think of physical law as a tool used by each observer, to interact with its environment. In this abstaction I flip the notions, the "environment" is "the system under observation", and the observer is what "interfaces" to the environment.

But the key in my view, is that one must account for the action of the observer on the system, as well as the backreaction from the system on the observer.

I don't have all answers here, but to flesh it out a bit as part my starting point I picture that each observer, at each moment in time to to speak, has what I call a system of microstructures which defines or constraints the state space in complexity, and a this structure also has a state, corresponding to the "information state". I picture a entropic action that induces a natural flow on this state space, thus the structure of the statespace encodes the hamiltonian. Once the statespace is set, the hamiltonian flow is basically an entropic flow.

Hilbert spaces and QM state vectors would be a special case, that I expect to be derived from this deeper picture. But I have not been ablt to do so yet, but I'm somehow convinced it's possible.

Just to be sure, are thinking in the Schrodinger picture?

Since I'm picturing a reconstruction, where QM structure eventually would be emergent or induced, it may be confusing to borrow all the usual notions from QM. In the writing I made abover, the schrodinger picture was probably closest, but otoh I don't think it makes any difference to my point if we have a space of evolving state vectors, or we have a space of evolving operators.

So you propose that one cannot fully know what is the hilbert space of some system, and that it might also change in time, ie evolve. I am having a hard time picturing it in some concrete example (probably because I am sort of used to thinking in the ortodox way, the one that is the basis of our work). For instance, say I consider some spin interacting with a bunch of other spins. There I believe there is no problem with assuming that the state space is known.

This is all subtle I guess. First, my own preferred phrasings would not be to say that the hilbert space "evolves IN TIME", it would be rather silly, it's rather that the evolution of the hilbert space, as quantified by a kind of information divergence, IS a kind of time. An incomplete analogy, think about how we used the expansion of our universe to somehow "define" cosmological time. I'm thinking similarly, but in a differeny way.

The example you take, is the type of example where indeed the timeless statespaces make the MOST sense! This is also what Smolin called the case of "subsystems" which is the typical scenario for most particle physics experiments, which after all is WHERE QM as we know it, is confirmed.

The opposite to the "subsystem" scenario, is the "cosmological scenario".

To elaborate: The subsystem scenariou really corresponds in my use of the word, with the entire environment of the observed system (say a system of interacting spin-systems) IS "the observer".

In a particle physics lab, with decectors etc, I think it's fair to say that loosely speaking the ENTIRE environment of the collision domain, is under our control, and here it's fair to think of the ENTIRE environment of the localized events as "the observer". Also the environment is MASSIVE in complexity(and energy) relative to the system. In this example, the usualy logic works very well (but not perfect, but I could expand on that another time since it's a more subtle thing which will only confuse things here). Here I picture that repetivity experiments, and storing large time histories of experimental sequences including preparations in the environment (laboratory) are actually possible, here one can also infer effectively stable "timeless" state spaces. So QM works fine.

But, if we now consider the flip situation, that we sciencetist are the ones stuck inside a some small detector and are making our "observations" not towards a subsytem but out towards our cosmological horizon, into effectively an "open system", then our possibilities to infer, hold and store, histories of experiments are limited simply by _complexity_ or an information bound. For this kind of situation, the inference of a timelss state space of the environemtn just doesn't make any sense to me. As smoling puts it a bit provocative in this talk bout evolving law, it's a "fallacy" to apply the logic of subsystems to the cosomological situation. And I agree with him.

So, I am basically consider that the physical law, and theory itself, LIVES or is encoded, in the microstructure of the observer - in the above examples it's either encoded in the lab-environment, which is relative to the microscopic particles "infinite", or in the other scenario, which we can also call the "inside perspective" corresponding to how the subatomic particles "see" physical law, they must encode the laws themselves! And of course, this is a different situation, but I also think thta this is the reason why the interactions are bound to be unified as we consider less and less (complex) "observers" (read subatomic fragments) which is what happens in High energy experiments and we try to break matter into smaller fragments, then the interactions between the fragments are bound to have simpler and simpler "logic".

This is something I think we need to systemize and take seriously, and it's a natural part in the intrinsic model to me.

About event spaces, I distinguish between expected, and unexpected events. To any observer, the expected evolution in the knowns event space is always "information preserving" (to use a more neutral notion) for obvious reasons, but the undecidability makes it impossible to predict the full evolution. Now my exploit is that I think this will have observable effects to a second observer. The system will have an action, that reveals that it can not predict everything! This is a key exploit, and how I envision that the hamiltonian or action eventually follows and evolves along with the state spaces.

anothre thing is that I've come to the conclusion that the state spaces is rather more like a system of state spaces, that corresponds to "memory compartments" having different compression codings, and that THIS eventually is the origin of non-commuative structures, and QM. But there is a lot of work left here. I have reasonable ideas on all this but progress is snail-speed.

More later, let me know if any of this makes sense to you.

/Fredrik

 

[Fra]

I have a more concrete question.

My motivation for the work we've done is that I see a very basic and problematic problem in QM (apart from all this thing of merging it with GR, and QFT problems): the measurement problem. Schrodingers cat and all that. Decoherence is not a fundamental answer.

I also find motivation in issue with QM as it stands, in the sense of there beeing things that doesn't quite make sense even prior to trying to mix it with GR. I don't find decoherence a satisfactory solution either. But I suspect my issues with it, may be slightly different than yours.

In short: to me the "solution" to the "measurement problem" is to account for the action of the observer on the system, and the backreaction from the system. But I do not mean it in the silly sense of just picturing a new system with the old system + "apparatous". That doesn't solve the problem, it IMO misses the crucial point, by repeating the same flawed logic once more trying to hide it.

Instead, in the schrödingers cat example, the ACTION of the observer, that finds the macroscopic object in superpostion, even though another observer (the apparatous) does not, is simply implying that the ACTION of the observer reflects this. There is not objectivity in the collapse IMO, but again that is not necessary. Instead the "deviation from objectivity" as some would interpret as an "inconsistency" to me implies physical interactions, acting in between the observers that doesn't see the same collapse, the effect produces backreactions on all observers serving to eventually equilibrate them, producing somehow at equilibrium an objective consensus. So in practice, the lack of objectivity, is transient only. Somehow in line with the short decoherence times etc. Here I see also connections to inertia, not too unlike penrose gravity-decoherence connection, it's just that I don't share his vision to find a objective collpase. Penrose tries to use gravity to show that there by consistency has to be an objective collapse in some sort of unclear sense. I think that the SUBJECTIVITY of the collapse, and the evolution of observers IMPLIES the gravitational interaction.

That's the vision - but the details are not on the table of course.

My issue with QM, though is that it is not a measurement theory designed or built from an intrinsic perspective. It's really constructed for the case where we study a subsystem which we can control, manipulate (prepare), and repeat. This is in my view, a special case. The logic valid for this special case, fails in my view when we consider the general case of not having controlled subsystems - cosmological open systems are here the opposite. So the structures of QM, IMO, simply does not match what seems to be forcing traits of an intrinsic measurement theory - that's my basic motivation.

/Fredrik

 

[Fra]

My question is in what sense do you find it necessary to deny the existence of timeless hilbert spaces? Is it sort of a philosophical argument because you do not like making that assumption, or do see something wrong in QM that makes you look in this direction?

As I've tried to elaborate above, "timeless hilbert spaces" or "state spaces" in general, are to me a non-physical realist constructs.

In my picture, the physical state space is related to the state history, so that in a sense the truncated, compressed(datawise) state history sort of "spans" that statespace. In this construct, this space is in general constantly evolving, and the statespace is "encoed" implictly in the microstate of the observer. So the evolving state spaces are just mirroring the evolution of observers.

So from a more abstract view of intrinsic inferece, the information of the state spacestructure and that it's immutable and timeless, is a proposition that is not "constructible" or "decidable".

I am not saying I think that statespaces always has to change and can not be stable, I'm just saying that a intrinsic inference can not deduce with certainty that it does not, and that in some cases it's obvious that it fails, for example when the complexity of the observer grows (increases it mass/energy) then the observable state space will grow.

Another way of seeing it is that I see a "timeless hilbert space" in the cases where it clearly makes decent sense, as an equilibrium condition.

But I think the real benefit of this is when one is trying to understand the action of matter, and the action of a subsystem. Here the "logic" could be that everything looks simple if we could glimpse into the intrinsic perspective, and see an interaction from the point of view of that subatomic observers themselves. And in this view, I think an understanding of the fact that the intrinsic observer "sees" an evolution fo the state space that is unpredictable is the key to understand the construction and unification of action of matter.

But this is admittedly very radical and feeds question, not yet answered. It's just that the questions are a bit different than the questions we get in the current framework.

So the starting point of a timeless state space, that is objective, is I think wrong for an intrinsic measurement theory. But it's still true that my arguments are philosophical. But then there is no good argument the timeless state space either, except it's apparent simplicity.

Part of Lee Smolin's and Roberto Unger's provocation is suggest that we are sometimes trapped by tradition to think in terms of this logic: state space, initial conditions, timeless laws. When in fact there are a range of arguments that gives reasons to dout this.

Instead, a more general scheme should explain WHY, in some cases, the evolving state spaces do reach a steady state? This I think is the better question, and the one I have chosen.

/Fredrik

 

[Fra]

So from a more abstract view of intrinsic inferece, the information of the state spacestructure and that it's immutable and timeless, is a proposition that is not "constructible" or "decidable", because decisions and constructions are themselves physical processes.

OTOH, to construct an axiomatic setting for this, in which can be formally prooved is a different story. Wether possible or not, I'd expect it could maybe be related indirectly to Gödels theorems, but to me the essence is intuitively clear enough to rule my world.

/Fredrik

 

[LuisPe]

Hi everyone. First of all, I’m sorry I took soooo long to continue the discussion, I’ve been quite busy.About Luke’s questions.

We are thinking in quantum mechanical terms. So, of course, in real life one does not need a clock ALL the time (for instance when checking if the ball is green or blue). But, when thinking about QM, predictions always have to be checked by expected values of observables. One observation says nothing given the probabilistic nature, predictions are about expected values of observables given some initial state for the system.
So, if one needs to check expected values, one needs to repeat the experiment many times, with the exact same conditions. In particular, the time of duration of the experiment needs to be the same. So that is the intuitive idea of why one needs to express QM in terms of real time, as measured by a realistic clock.

Yes, the theory is formulated with the ideal time t, but observable things are expressed in terms of real time T. The ideal time is sort of in the background, somehow dictating how the evolution goes (schroedinger ec)

I like your idea of “turning off” GR. But I do not think that if you do this you could measure time with arbitrary accuracy. As we have presented it so far, limit in measuring time comes from GR, but in my opinion purely quantum clocks, without GR, also have inescapable uncertainties.

Im not sure if I have answered all your doubts, please let me know if its unclear… I did not quite understand your comment “I am uncomfortable with using the ideal space-time separation in calculations”, please explain it a little bit if you can.About Fredrik’s comments.

Ok, so there are lots of ideas to discuss here. I`ve been reading a little of your other posts on your ideas, somewhere else in the forum.
I think I understand a bit more of how your reasoning goes, but I don’t quite share your views. I see that since your preoccupation is somehow about the mathematical foundations of QM, and that since we don’t quite attack the problems that you mention, our theory is probably not satisfactory to you. I guess that there are many many views on this subject, and that these sort of discussions are going to be around for long time. But hopefully arguing about the problems will get us closer to some sort of understanding.

But the key in my view, is that one must account for the action of the observer on the system, as well as the backreaction from the system on the observer.
/Fredrik

I agree with this if by observer you mean environment. Actually, I believe every backaction should be considered, but not necessarily the real observer, since I am thinking of a human-observer free theory (meaning that the act of human observation is of no relevance).

About event spaces, I distinguish between expected, and unexpected events. To any observer, the expected evolution in the knowns event space is always "information preserving" (to use a more neutral notion) for obvious reasons, but the undecidability makes it impossible to predict the full evolution. Now my exploit is that I think this will have observable effects to a second observer. The system will have an action, that reveals that it can not predict everything! This is a key exploit, and how I envision that the hamiltonian or action eventually follows and evolves along with the state spaces.
/Fredrik

I agree that it cannot predict everything, but due to the probabilistic nature of qm, not because of undecidability. Undecidability means that the predictions of qm with collapse or without collapse are the same, but not that there is some further cause of unpredictability.

In short: to me the "solution" to the "measurement problem" is to account for the action of the observer on the system, and the backreaction from the system. But I do not mean it in the silly sense of just picturing a new system with the old system + "apparatous". That doesn't solve the problem, it IMO misses the crucial point, by repeating the same flawed logic once more trying to hide it.
/Fredrik

By observer here you are thinking of environment?There are many more ideas you comment which I find interesting, but I still have to assimilate them, hehe. And then come back with an answer...Regards,
Luis Pedro

 

[Fra]

Thanks for your comments Luis.

But the key in my view, is that one must account for the action of the observer on the system, as well as the backreaction from the system on the observer.
/Fredrik

I agree with this if by observer you mean environment. Actually, I believe every backaction should be considered, but not necessarily the real observer, since I am thinking of a human-observer free theory (meaning that the act of human observation is of no relevance).

If you see only two options here, where option1 is that observer = human observation; and option2 is the environment of the system (under observation), then surely option 2 would be more closely to what i mean.

But I have a feeling that I wasn't able to communicate the main point in post#33, or maybe you just don't share my view. But the point is that there is no "external view" of the observer or the environment, and "the observer" is more regularly only a FRACTION of the environment, not the entire environment.

However in the generalization I envision (where the current QM formalisms is just a special case) the clostest fit to the actual QM formalism will take place when we study a small subsystems in the sense that it's a FAIR assumption to say that the ENTIRE environment is THE observer.

So I'd say that, yes I mean environment = observer, but there is a more subtle point that I tried to make because the observer does not always make up ALL of the environment, just part of it. The real point is mroe than obvious if you stop thinking of particle/lab experiments and instead consider cosmological observations. Then the situation is flipped right? The "system" surrounds the "observer=environment" rather than the other way around. And in this case it turns out awkward to label it environment.

In short: to me the "solution" to the "measurement problem" is to account for the action of the observer on the system, and the backreaction from the system. But I do not mean it in the silly sense of just picturing a new system with the old system + "apparatous". That doesn't solve the problem, it IMO misses the crucial point, by repeating the same flawed logic once more trying to hide it.
/Fredrik

By observer here you are thinking of environment?

Yes, but with the same notes as above. The environment is in my view, NOT an infinite "information bath/sink" in the sense of Zureks decoherence. I am taking seriously that the observer is bounded, and is evolving in a generall unknown environment.

So a more correct view is IMO, that the observer "observes" it's own entire environment. And that regulra QM enters as special case where we focus on a small subsystem of the environment that is of very low complexity relative to the observer. (with complexity here, associate energy and mass).

Compare here complexity of any human laboratory frame, including preparations and setups and decectors with the complexity of an atom. But compare also the flip situation, where the atom is observering it's environment .ie. the laboratory. This picture we do nto have! And my conjecture is that this is why we do not yet fully understand the action of matter with a coherent unified picture. It's mainly a patcthwork of effective theories with plenty of unexplained parameters.

/Fredrik

 

[LukeD]

Hi Luis,
Thank you for the reply. It's quite alright that you've been busy.

I like your idea of “turning off” GR. But I do not think that if you do this you could measure time with arbitrary accuracy. As we have presented it so far, limit in measuring time comes from GR, but in my opinion purely quantum clocks, without GR, also have inescapable uncertainties.

Im not sure if I have answered all your doubts, please let me know if its unclear… I did not quite understand your comment “I am uncomfortable with using the ideal space-time separation in calculations”, please explain it a little bit if you can.

Maybe there are limits to how accurate we can measure time without GR, but with GR, there are certainly limits. What I mean is that in a full theory that incorporates GR, can we really say that the space-time separation exists at all since it cannot be measured precisely?
Your theory seems to be attempting to correct for the fact that ideal times cannot be measured (and cannot be used by real clocks to measure something), but it does so by referencing everything in terms of the ideal time. I am uncomfortable with this because I don't see any objective sense in which the ideal space-time separation actually exists (except that when 2 events occur at the same time and place, we have 0 separation).

I also don't see any way around this problem.. But it's a problem that almost begs to be solved.

 

[LuisPe]

Thanks for your comments Luis.

So I'd say that, yes I mean environment = observer, but there is a more subtle point that I tried to make because the observer does not always make up ALL of the environment, just part of it.

/Fredrik

I agree that it is usually only a part of the environment that interacts with the system. But then, i don't see how this is a problem. Maybe, what we call environment is a part of a bigger environment, the part interacting in a significant way with the system.

And then, you are putting the situation of human observers observing (ah, this language is complicated, hehe) the rest of the universe, right? In our opinion classicality of the rest of the universe we observe would not depend on observers. There could be fields interacting with the part of the universe we are concentrating, and that these fields are unobservable. Sort of like Kiefers ideas for the transition to classicality of the universe.
This is of course complicated, and not clear to me, but I am just pointing that the situation could still have a solution in our terms.

What I mean is that in a full theory that incorporates GR, can we really say that the space-time separation exists at all since it cannot be measured precisely?
separation).solved.

Well, I don't see a problem. We can't measure it precisely, but we can measure it approximately, and it works. Wouldnt this imply that it exists?
We are thinking something like this. We assume Newtonian time t exists, and that schroedinger evolution goes with this time. Then we see you cannot measure it precisely, ever. So its complicated, its out of our reach, but still, we express things in terms of real accesible time T, and things work out. So its not like a situation where you cannot get info on something, so you can't even say it exists. We can get approximate info.

Its not really that we are trying to "correct for the fact that ideal times cannot be measured", but rather we are adding this fact to the way QM is presented. We believe it is neccessary. And we are trying to see what we can get from there...

Please let me know if I understood your point correctly...

LP

 

[Fra]

So I'd say that, yes I mean environment = observer, but there is a more subtle point that I tried to make because the observer does not always make up ALL of the environment, just part of it.

I agree that it is usually only a part of the environment that interacts with the system. But then, i don't see how this is a problem. Maybe, what we call environment is a part of a bigger environment, the part interacting in a significant way with the system.

Here is one of the focal points where we disagree. If you don't see that as a problem, that I understand why you probably don't see what I suggested.

At this point for me, it's obvious why this is a problem. I'll try to think about how I can make the point clearer. More later...

And then, you are putting the situation of human observers observing (ah, this language is complicated, hehe) the rest of the universe, right? In our opinion classicality of the rest of the universe we observe would not depend on observers. There could be fields interacting with the part of the universe we are concentrating, and that these fields are unobservable. Sort of like Kiefers ideas for the transition to classicality of the universe.
This is of course complicated, and not clear to me, but I am just pointing that the situation could still have a solution in our terms.

I think the main reasons we think differently is that I've tried take deeply seriously the notion that ALL notions of states, statespaces and laws, should be subjcet to strict inference an evolution.

I have a feeling that you think that there is an observer independent structural realism at some level, this is why you say it's "observer independent".

I claim that NOTHING is striclty observer independent, instead I claim that the effective objective reality, and our environment, and space are EMERGENT as evolution and equilibriation of all the A PRIORI "independent" views.

The idea is that there is a action and backreation in between ALL observers = in between all parts of the universe, that causes a parallell evolution at all points, where the equilibrium corresponds to all of them reaching consensus in their mutual environment.

One of my first principles is that the "laws of nature" in the scientific sense, are not forcing constraints that nature has to obey, that are inferred (or maybe better: abducted) constraints from their own subjective/local interaction history that guides the own action.

So I claim that we must treat the laws of nature almost a bit like observables, where it makes no sense to talk about what the laws are unless they are the reuslt of a physical inference process.

This is to me, just to increase IMO the standards of the philosophy of science. And an impliciation of this, is that since each observer is their own "information processing agent" the laws of nature in the inferred sense are observer dependent AND the laws of nature in the effectively objective sense as we know it, are emergent as a result of a population of interacting observers and their mutual action/backreaction on each other.

Emergence of social laws are a good example of a "similar" mechanism, becuse social laws are not forcing. Social laws can, and ARE broken. But anyone breaking it received a backreaction from it's environment, putting pressure on this to not happen again.

If you combine this with the idea of rational action, that each observers simply acts "rationally", not per an objective measure, but per it's own measure, then we get an idea of a complex dynamical system where the laws of the dynamics are also constantly evolving.

The challange I see, is if this idea predicts (using the complexity scaling as a tool) some stable configuration and preferred sttructures, and if we can identify there the structure of the current laws and structure of matter.

This goes very well with the entropic dynamics ideas, since "rational action" is in essence a generalisation of the same thing. But the entropy measure is itself evolving, MORE than just evolving the prior distribution (which induces a relative entropy measure).

/Fredrik

 

[LuisPe]

I have a feeling that you think that there is an observer independent structural realism at some level, this is why you say it's "observer independent".

Exactly

I claim that NOTHING is striclty observer independent, instead I claim that the effective objective reality, and our environment, and space are EMERGENT as evolution and equilibriation of all the A PRIORI "independent" views.

I understand, I just don’t like it. I mean, I’d prefer the universe wasn’t this way.

So I claim that we must treat the laws of nature almost a bit like observables, where it makes no sense to talk about what the laws are unless they are the reuslt of a physical inference process.

Very interesting idea. I have another view of how things work, as you probably understand from all my comments, but I still find the idea very interesting.

Emergence of social laws are a good example of a "similar" mechanism, becuse social laws are not forcing. Social laws can, and ARE broken. But anyone breaking it received a backreaction from it's environment, putting pressure on this to not happen again.

Another great idea. I like the comparison, the way environment is considered


I think I now understand a looot more about your views. I do not share them, I think because I have a more naïve idea about the physical nature of the world. I would like it to be simple, jeje. I still find all these views you presented, particularly on this last post, very intriguing. It would seem hard to translate all these ideas into a physical theory, what do you think?

LP

 

[Fra]

Thanks Luis, I think we're reached a state of mutual understanding including the disagreement.

I certainly understand your position as well. In a certain way structural realism make somes things easier, but unfortunately I've come to the initially painful conclusion for myself that it doesn't make sense as it does not comply to what I think of as scientific inference ideal. A principle that I hold much deeper than the ontological desire for some structural realism.

It would seem hard to translate all these ideas into a physical theory, what do you think?

Hard yes, I have no illusions :)

The first part of this work, would actually be more like developing the new mathematics, which more or less is a reconstruction of probability theory, and inference models, from more realistic physical starting points (which to me for example means to not just build a mathematical theory of inference (this already exists) but to understand also the PHYSICS of inference, namely that inferences are physical processes, and thus the new mathematical theory must respect things like complexity constraints - which means reconstructing the continuum). Then that new framework would I think be more fit to pose the open questions so that the answers are easier to find.

Anyway, since this is hard and very few people work on it. I'm very interested to learn about everyone that ARE working on something that is related to this, because there are a few, but none do it exactly like I think it must be done.

Ariel Caticha, Lee Smolin and Roberto Unger are probably the ones closest to my vision, among those I'm aware of.

/Fredirk

 

[Fra]

It would seem hard to translate all these ideas into a physical theory, what do you think?

Although I do not underestimate any difficulties here, I still of course think it's quite possible.

Compare with how probability theory, and bayesian probability in particular can be seen as the result of the quest for a method for rating degrees of beliefs. E.T Jaynes in his book "probability theory - the logic of science" attempts to present there probability theory as the mathematical theory the extends and quantifies rational reasoning.

He shows that his view of things, leads to a mathematical formalism that is identical to the koglomorov probability theory.

This is the same principal idea I have, but I have several objections to his "derivation". I think it can be generalized, and along with it should be get a more general formalism that actually has to evolve. There seems to exist no fixed static formalism - or rather - ANY choice of "fixed axioms" would eventually be potentially unfit, and thus be unstable. Maximum consistenct is achieved when there is an evolution (this is the point where the inference idea "buds" with Roberto Ungers analogy).

It's almost like a set of rules for self evolving axiom systems, where one considers two interacting axiom systems.

Unllike Ariels extra assumptions ontop of normal probability theory (to go from "simple diffusion" to more general dynamics) I think that if you reconstruct this inference system, and do it right, and acknowledge the evolution, these extra assumptions are not necessary, the should (says my but feeling at least) follow more or less uniquely from the construction, as - not the only mathematically possible - but as the most FIT "constructable" actions.

For example, the non-commutative structurs of QM, should (again I hope/think) ultimately be shown to originate from the higher fitness of these more complex memory structures. The biggest problem is that since fitness is context/environment dependent, and the contex and environment is also evolving, so there is a strong self-interaction. But fortunately inertia constrains self-interaction. But to explain the inertia, also the generation of complexity enters this same reasoning.

So I think it's hard, but there are some decent guides as to where to seek for this.

/Fredrik