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

Hi Luca,

an interesting application of Tarski's notion of semantically closed languages on QM's formalism! With regards to Wigner's Friend:

"If an outside observer wants to make a measurement on a closed system, which is not compatible with the relative measurable quantities within that system, then the dynamics within that system is not unitary and not invariant under the symmetry any more" (p.4).

I'd only ask from whose perspective are we making these determinations? Is it the case that from the Friend's perspective it is Wigner who is in a closed system with respect to the Friend's lab and vice versa? Does the asymmetry then cut both ways in which case the application of QM laws is semantically closed both for Wigner's perspective and his Friend's?

To me this sounds like it leans towards a relational or relative-state interpretation. What do you think?

Also it looks like the scoring functionality is still down here so I'll have to wait to give you a rating.

Cheers,

Malcolm

Je suis, nous sommes Wigner!

"In a way, yes, the relational point of view...Separability from the rest of the world is condition under which the formulation of laws and definition of concepts is possible."

So your own personal ontology is, very generally speaking, a 'relational objective realism'? And you claim that we can save the objectivity of a relational interpretation of QM by physically closing the system?

Now a relational interpretation is a natural language mode of interpretation so it will be semantically closed which means in my terms, it is fundamentally incommensurable with the mathematical languages of QM formalism, but also more or less closed with certain other natural language ways of interpreting QM such as objective collapse theories. Different sub-cultures can express very different meanings using the same language... and here we are trying to communicate globally in English!

Yet these natural language ontologies together are (semantically closed) quantum foundational ways of thinking about how we might apply the (semantically open) QM formalism to any quantum system. Your particular natural language interpretive strategy guides how you think about the calculations ... or depending on your ontology so goes your maths ... or as Lbar's computer says in my essay "quantum foundations do not compute"!

"Wigner's friend has only a mixed state being an entangled subsystem of the whole. In that sense Wigner's view is more objective."

So my question remains, from what physical (formal mathematical) and ontological (natural language) perspective can this statement be true? From the Friend's perspective they do not experience themselves as a mixed quantum state entangled with the whole ... unless you're just describing one's normal experience from a Many Worlds perspective! In which case the same goes for your objectively privileged Wigner and they are now both on the same footing as entangled subsystems of the wave function of the universe (ontology alert!--no matter how hard I swim against it I keep drifting back towards wave function realism).

Otherwise, the Friend's alleged entanglement only makes sense from Wigner's perspective but you would then need to justify that observer bias--why should we privilege Wigner over the Friend? What semantically closed natural language ontology is driving this interpretation?

Hi Luca,

Thanks for an interesting paper!

As I mentioend in my reply to you, as I see a number of similarities between some of what you say here and what I've said elsewhere. One thing that I'm a little confused by, though, has to do with what you say regarding separability of a quantum system and its enviroment. You write that your "interpretation protects the subjective view from contradictions by not allowing unwarranted outside interventions. It makes the subjective loss of the phase information objective and thus avoiding contradictions. Contrary to decoherence I ask the system to be separated from its environment in order for a measurement being well defined."

Do you mean to imply that when a system isn't isolated from its environment that it can't be said to have been 'measured'? If this is the case, then do you think there are different types of physical interactions in the world, some of which are measurements and some of which aren't?

Best,

Mike

Dear Luca Valeri,

From what I understood ( and there is a decent amount of technicality that eluded me), I found your proposition of symmetries, objects, and laws only taken together are unitary and well defined a nuanced and rich concept.

It is truly an interesting way of addressing the measurement problem ( in so far as a layman and serious enthusiast understands) and an interesting avenue for Incompleteness Theorem(s) to enter the picture!

Best Wishes,

Raiyan Reza

Dear Luca Valeri,

You are most welcome!

It was a pleasure reading your ideas.

I intend to try to take QM or Physics related classes but that depends on my credit space ( Education background: A CS major here, switched from Physics due to financial obligations).

If not, I will try to self learn as much as possible! I had saved a copy of your essay and hope to re-read it when I posses a more in depth knowledge of QM and related topic.

All the best with your research, work and this contest!

Best Wishes,

Raiyan Reza

Dear Luca,

Very enjoyeable essay! I liked how you explained difficult concepts like the classification of the wavefunctions by spin and mass in terms of representations of the Poincaré symmetry, made by Wigner and Bargmann, the role (or absence of such a role) of the observer in various interpretations, decoherence, the measurement problem etc. I like this statement "the objects themselves can never be known. Only the relations these objects have with each other shows as properties of the objects" :). I also agree with "the applicability of the basic concepts, that define a physical theory and describe the laws, might depend on the environment and hence the laws themselves might depend on contingencies". This can be interpreted in two ways: that the laws really change, or that our formulations change. For example, does the spontaneous symmetry breaking with the Higgs mechanism represent a change of constants considered before as ... constant, like the particle masses and coupling constants, or this just represent that they depend on the state, and the state transition is not changing the fundamental laws, only the laws we used to think as fundamental? (edit: I see that toward the end of your essay you wrote "The richer theory might emerge from the poorer one by symmetry breaking.")

I liked the mention of the WAY theorem. I'd just want to make the observation that, if the Hamiltonian doesn't change and the symmetry breaking happens just at the level of the system (as in Higgs mechanism), the constraints imposed by the WAY theorem don't change. Because the theorem takes conservation laws as an indication of unitary evolution, which has to be true during the pre-measurement phase, when the system is supposed, e.g. in von Neumann's formulation, to branch into a superposition corresponding to different outcomes. So the symmetry of the system has no relevance, because the theorem uses mean values of the conserved quantities to check unitarity, and not eigenvalues. For these constraints to change in time, the Hamiltonian itself has to change, and I understand that this is a thing that you want to propose.

Another thing I liked was the mention of Poincaré's "Science et l'Hypothèse", which, together with "Science et méthode", were among my favorites when I started to be interested in physics as a kid. However, I never agreed with him that there's actually no difference in what geometry you choose. Take his representation of hyperbolic geometry in the Poincaré disk. If you take the disk with the Euclidean metric, you'll have to admit that the objects deform as they move. If you take the hyperbolic metric, they are rigid w.r.t. the hyperbolic geometry. So, in such a world, you'll have these two theories, one in which the objects are not rigid, but they deform as they move in a conspirational way, that makes them behave "as if" they are rigid w.r.t. a hyperbolic metric which is just a construction. The other one in which these "coincidences" of zero probability are explained by the symmetry of the hyperbolic geometry, which makes them have probability 1. Klein's insights in his Erlangen program are really genius, and the entire physics, from relativity to quantum mechanics and Wigner's classification and gauge theory, is indebted to these ideas. We can keep an open mind that maybe these "coincidences" can be explained in a different way than because of the symmetries of the geometry, but this is not the same as saying that they are undistinguishable. I think this idea made Poincaré miss the opportunity to become the main author of the theory of relativity and Minkowski spacetime. But, even if it is more in the spirit of Occam's razor to pick the theory which requires less conspirational fine tuning to explain the "coincidences", Poincaré's observation is important, in the sense that it is always possible that a better explanation, with completely different rules, will explain the same data with fewer hypotheses and adjustments to explain the apparent symmetries.

I like the way you take various ideas and make them converged to your proposal of semantically closed theory, which makes sense. I wish you success in the contest!

Cheers,

Cristi

Dear Luca,

After reading your thoughtful essay I am wondering:

Can you take the actual development of physical theories since the time of Galileo and Newton, and arrange them the way you prescribe...[poorer to richer] and `predict' what should come next? At least in outline? i.e. is your construct predictable / unpredictable?

I am not sure if computability can also be addressed in this framework? Are richer theories better at computing?

I appreciate your original line of thinking. All the best,

Tejinder

Dear Luca,

I learned a lot of things from prosaic style of your essay. You mentioned

Since in physics we are not used to imagine the laws and basic concept as something that could change, I shall briefly give two examples from totally different areas, where the changing of the laws is much easier to imagine.

"in physics we are not used to imagine" is this true in history of science? Around 16 centuries before Newton, the theory in physics, the imagination is important to create the laws of physics. Also, our building-up process of laws of physics, we often use the gendanken experiment such as quantum eraser. Is this different from the imagination?

Best wishes,

Yutaka

Dear Luca,

A really clear and interesting essay despite the many ideas that it references. It's a pleasure to read it.

I'm not sure that Poincare was right to say that Newtons first law is merely a definition. Personally speaking, I think that good definitions can be hard to come by, it's not always easy.

I like 'parts have meaning only in the context of the whole.

The whole builds a web of connections, of meaning. No meaning can be assigned to the part without the others.'

It's one reason why I've come to dislike the term fundamental particle. Surely it's more fundamental for there to be a world for the particle to be in? I guess I'm not that happy with reductionism.

I also like 'there are difficulties in comparing two different theories as there might not exist a correspondence between the different concepts'. The same is true for translating poetry. It's not that we're translating propositional content here.

'Von Weizsacker describes the expansion of the universe as a crystallization process from a simple homogeneous low entropy state into complex structures.' Have you come across Aristotle's notion of an evolving organism? I think once I would have dismissed this but now I quite rather like it.

My own essay originally referred to Wigner friend experiment and his notion of consciousness causing collapse. I had to excise because of the 25k character limit. I've looked through Wigners essay but he doesn't address one of the most obvious questions which is what happens to the universe when there aren't anybody to observe it. Of course Rovellis relationalism gets around this by making interaction synonymous with measurement. Personally I feel part of the reason for Wigners interest in posing an interpretation in this way was the great interest in Indian philosophy then. For example I know that Schrodinger was in later life was much interested in Vedanta. Perhaps this might mean that the world has, in some sense, a mental quality.

Warm Regards

Mozibur Ullah

Dear Valeri. I learnt quite a lot from your essay.i was particularly interested in treating observer as object who participates in the universe.rated You accordingly. can cognitive Bias be a source of the science we partake?please take your time to read my take here .https://fqxi.org/community/forum/topic/3525.Thanks.Wish you all the best in the contest.

Dear Luca,

your essay touches on many interesting notions, and sketches some intriguing arguments. Indeed, it's so rich that I unfortunately found myself a bit lost, in places, and could not always follow the thread of argumentation you present. Perhaps it's owed to the contest's length constraints---which lord knows I've had my own struggles with---but I felt perhaps you might've chosen to focus more on one smaller aspect of your imaginative tapestry, to better bring it into view.

Your notion of 'semantically closed theory' of course immediately evokes Heisenberg's 'closed theories'---as you later note yourself. However, I think you're right in drawing the dividing line between your concepts: Heisenberg's notion is essentially a syntactic one, where the change of any of its elements threatens inconsistency, hence making closed theories perfectly rigid frameworks, and theory-change an often revolutionary process.

You want to include not just the theories' framework, but also the meat, so to speak---not just the axioms, but also, the model they apply to, and bake that into a 'closed' edifice. You mention Gödelian difficulties for such an undertaking, but I think that another source of difficulty is more dangerous here: in general, due to Tarski's undefinability theorem, theories can't formalize their own semantics, and hence, there's a sort of 'gap' between the formal structures and the things they apply to. So, is your proposal that a theory, as it's usually understood (i. e. as just the formal, structural part) is simply not complete, but must include that which the theory is supposed to be about, or do you claim there's a unity here---that each theory brings its domain of applicability with itself?

I also appreciated the reference to von Weizsäcker. I think perhaps his notion of the 'Kreisgang' ('moving in circles', maybe) might be appropriate: you liken the semantically closed theory to something that comes back to its initial assumptions, but to von Weizsäcker, that wouldn't necessarily be a damaging notion---he thought that, coming back to our initial notions means we can obtain a refined understanding of them, cast them into a new light, and that, in fact, all knowledge generation is just coming back to the same principles at higher levels of appreciation.

Anyway, I wish you the best of luck in the contest!

Cheers

Jochen