Semantically Closed Theories and the Unpredictable Evolution of the Laws of Physics by Luca Valeri

Dear Israel,

Thanks for your kind reply. Symmetry is so central in the conceptualisation of physics and in my opinion part of the conditions of the possibility to make science at all. And yet rarely it is used a foundational principle for the derivation of the structure of physics - beyond the practicality.

And the symmetry or asymmetry of time is the most difficult one. If time would not 'appear' asymmetric, there would be no need to do any physics. And yet it is difficult not to see explain the asymmetry as an epistemic notion of our course grained perception.

Sometime I think the problem time is the reverse one than the usually discussed. And the question is: How can one derive the time symmetric laws from the asymmetric phenomena and operationalization of actions.

Thanks for pointing me out Zeh's book.

Luca

Hi John,

Very good question! Thanks for asking it. By definition every quantity has do be defined and must be measurable within the theory. I would say as a first instance this can be decided formally within the theory. In the reconstruction in the essay you have a symmetry defining the basic quantities. Also the free evolution is defined. Then one needs an interaction, that correlates these quantities to another system or objects, which then serves transporting the information about the quantities of the first object to the other one. The interaction doing this is mostly defined by some gauge principles.

I would say, that quantum field theory, the standard model, are semantically closed theories, depending maybe on the Interpretation (relating to the measurment Problem). Except maybe for the time measurement, since time is entering the theory as external parameter and not as observable.

But also Newton classical mechanics might be a closed theory. Maxwell's theory also. Here I am not sure, if the length scales can be defined within the theory.

General relativity, I'm not sure if it is closable, because it needs rulers defined in another theory. It is questionable if a general covariant gheory can be a closed Theory, because no seaprable objects can be defined in it.

Now the question is: how do we know, this theory is realized? There are several problems here. One of them is connected to the Duhem-Quine thesis. In here to falsify theory trough observation needs always an auxiliary theory describing the measurement. Usually this theory is well established and no reason to doubt it. But for closed theories the observational theory is the same as the theory to be falsified. This looks really circular.

The objects and systems to be well defined must be separable from the rest. But this separability is only approximative. The rest can be modelled as external forces, that change the 'normal behaviour' of the system. But whether the theory has to be modified or the not normal behaviour explained by external forces might not be decidable from observation alone. See for instance dark matter vs. MOND.

Finally such a closed theory generated from symmetry and some principles is a big tautological construct. We might not expect to create some empirical theory from principles. So in order to give meaning to the concepts in the theory, the theory must contain Newtonian classical mechanics as limit, which is the language of our intuition.

Sorry. Long answer for a short question.

Luca

Dear Pavel and Dimitry,

Thanks a lot for your rating, your kind reply and the question.

I am not sure about Poincaré's hidden axioms. I have read about the hidden definitions. Although axiom and definition might be the same. But to return to your question: Yes, I think - and that was exactly the point of my essay - that it is possible to apply it to different foundations. In my approach it is the symmetry group defining the foundation - the basic concepts. One can imagine, that under different environmental conditions different symmetries are realized. For instance in free space or near black holes. Leading to different fundamental laws and objects.

The main difficulty is then on how to describe the change from one system to the other as objects do not maintain their identity and the fundamental laws and concepts change. I don't know, how one could do that.

I imagine the following situation: In free space objects and system are well defined. (The free space or vacuum itself is not defined independently of the laws or symmetries. It is itself as the objects of the theory an emergent thing.) If there is an external force like gravity, the identity of the objects and the free laws can be maintained and the force is treated as an external disturbance. This is a good and well defined approximation as long the back reaction of the system is small enough. But when gravitational forces are becoming to big, the approximation do not hold any more. We have to look for new symmetries, which create or define new separable objects and systems. These determine new foundational concepts and new laws.

Luca

Hi Ian,

Thanks for your reply. The question you raise is very interesting. In short I would say, that the standard model is semantically closed and General Relativity is not. GR needs the laws of optics for the definition of the Geodesic, or QM (atomic spectra) for a length scale. There are indications, that general covariant theories are not semantically closable.

On a mesoscopic, emergent level there might be Newtonian mechanics, chemistry, biology that are semantically closed.

I want to stress 3 points, that are connected to the question:

1. The meaning of physical concepts are defined by possible physical operations and hence the meaning depends on the laws they ought to describe. So there is something inherently circular in these theories. But this might be merely a self consistency requirement.

2. There is a unity between the formal system and the physical system as the concepts are not defined independently.

3. The separability condition as condition for the definability of concepts is always only realized as an approximation. Insofar semantically closed theories are never strictly realized. If separability is broken the environment can be modelled as external system with external forces (gravitation for instance) or heat bath (decoherence). If the back reaction of the system is too strong or the influence of external disturbance is too strong, one needs to find another separable systems, ie. symmetries within the system, that describe separable subsystems.

Finally the main point, I want to make, is that under different environmental conditions (low gravity vs. black holes) one might have different semantically closed theories describing these systems and there might not exist a unified theory describing both.

And another point is that semantically closed system might change. Such a change is not describable within one theory and is maybe untheorizable (as Daniel Sudarsky writes in his essay). I belief this opens new ways to talk about consciousness and free will.

Luca

Hi Ian,

why should SR not be closed or closable? SR basically means, that you have the Poincaré group as symmetry group. The irreducible representation define what a free particle is - given by the Casimir operators of the group: mass and spin. Then by gauche principles the interaction is derived. In QFT you have even, that particles are only defined as free particles, because the interaction changes the vacuum (which also depends on the particle definition) and would lead to different inequivalent representations in fock space ...

So the Poincaré group defines, when a system is free and separable from the environment etc. It defines the observables (except maybe for time, which is really difficult!).

The difficulty in general relativity is, that you do not have a global invariant symmetry group and cannot define invariant separable objects. That might be the cause, why it is not renormalizeable.

Luca