tom.stoer said:
So it's at least logic that serves as a basis for you.
Sure, of course I kind of rely on some kind of logic in the general sense, but I thought that from the context the association to logic here was to ideas that mathematical consistency and deductive logic. Ie. that you can get to KNOW the certain laws by though along - no interaction. I beg to differ with that view.
The kind of logic I do rely on is loosely speaking inductive logic, not deductive logic. Clearly the traditional quantification of inductive reasoning is probability theory. Ariel and Jaynes makes this point strong. However, even the rules of inference themselves are not unique. Here I differ with them.
They formalise inductive reasoning, into probability theory and then use various bayesian or max entropy methods as the RULES of inference. But of course, the rule of inference is chosen and the isntant you choose the specific entropy measure. Similarly there are objections to bayes rule.
I am trying to generalise inductive reasoning, by suggesting that by taking the proper intrinsic view, other rules of inference other than bayesian and max ent method are possible, and bayesian and max end methods with a fixed entropy measure are NOT the optimal inferences. Sometimes they are of course, but it's not a general case.
I have hopes that quantum logic to mention one think should b4e satisfactory explain as a unique choice of optimal inference RULE in particular situations! But again, but understanding hte general case, I also expect to understand the generalisation of Quantum logic, which will help solve QG problems and unification.
So in a certain sense, I am looking for a mathematical reconstruction, but it is not possible to understand the motivation from a pure mathematical perspective. Also the ides suggested does contain self-referential elements, and the this self-interaction should amount to a kind of self-inference, a kind of self evolution.
I think a correspondence here in simple case would be that the schrödinger equation is really just the expected self-evolution, or the self-inference. The optimal inference when external feedback is taken into account is the collapse thing.
In this view there is as I see it no mystery with the collapse at all.
Given that I want to take this further than Ariel and Jayes, who basically reconstructs the same old continuum probability theory and use that as a basis for inference, one of my basic conjecture, is like theirs that the laws of physics ARE more or less the rules of rational inference. And the point is then tht the optimal inference is a matter of point of view, since the instrinsic view allows no external measures of optimality.
There are also the symmetry principles hidden here, symmetries are emergent as a result of interactions, and are not fundamental. Understanding the interactions here should in my expecation help explain why certain symmetries in the rules of rational inference are selected. And thus the symmetries of physical law.
I have understood that this is hard to convey. Having thought of this now for a new years I think the conceptual part is becoming pretty clear, but still I see that not many seem to connect, with a few exceptions. Probably because I do not know of any current papers that does exactly this. The related ideas are from smolins, evolving law, ariel caticha and ET jaynes, as well as some other. Olaf Dreyer has partly acknowledge the inside view.
I suppsed this will remain foggy until substantial progress is made.
Edit: I also associate time evolution with the inference processes. The relativity of time in relativity should be reproduced from the relativity of inference, as in the emergent symmetries. Note that both Jaynes and Olaf Dreyer belives that GR could be DERIVED from the proper reconstruction. I fully share this view, although I have a different view of the starting points. Instead of derive, I prefer to say emergent, and this emergence is a physical equilibration process.
/Fredrik