A Ensembles in quantum field theory

[Peter Morgan]

Is this somehow related to the Epstein-Glaser approach (as used in Scharff's book "finite quantum electrodynamics"?

I think only rather loosely, insofar as they use an extra test function to modify the dynamics. They still aspire to work with the Wightman axioms unchanged, so that there is only a linear dependence on the test functions that we use to describe the apparatus. Epstein-Glaser is generally not taken to successfully solve or evade "The Renormalization Problem" (if one accepts that there is such a thing).

Another thing is that this hierarchy of resolution is a gift for physicists, given the historical development of science, i.e., they could deal with pretty classical physics first, before they discovered that underlying this "effective model of the world" there's need for a more abstract and less familiar "quantum model of the world", which however leads to the conclusion that the "classical description" is valid only as an "effective theory" for coarse-grained macroscopic observables.

The relationship between classical and quantum mechanics is the subject of my recent post, "The collapse of a quantum state as a joint probability construction" (which links to an article in JPhysA 2022). I can't tell whether you've seen that? One premiss: CM has been straw-manned. By steel-manning CM so it has a noncommutative measurement algebra, we can ensure its measurement theory is the same as that of QM. CM₊, as I call that extended CM, has the same measurement theory as QM and is as empirically effective, but it nonetheless is different so we can learn something about QM from CM₊.
We can work with either CM₊ or QM models, as we like, according to this, but of course this is not (and cannot be) a naïve return to CM. By analogy with the idea of Schrödinger and Heisenberg pictures, we can introduce the idea of a "super-Heisenberg" picture that puts the unitary dynamics and the "collapse" dynamics into the measurement algebra, with the quantum state unchanging. This also makes contact with the idea of Quantum Non-Demolition measurement and Quantum-Mechanics–free subsystems in an article by Mankei Tsang and Carlton Caves in PhysRevX 2012. Another perspective is that Generalized Probability Theory is classically much more natural than has been recognized: a book by George Boole in 1854 (which I discovered only through a paper by Abramsky in 2020, which cites a paper by Pitowsky in BJPS 1994: why is this not widely known?!?) effectively lays out why it is necessary for classical theory to go beyond an uncomplicated probability theory (if probability theory can ever be called uncomplicated).
We can, in other words, think significantly more classically if we are sophisticated enough. Of course many people see this and run away from the crazy person, but not everyone.

Field quantization, ironically, was rejected by the physics community as "overdoing it".

I can totally sympathize with this as an empiricist, because field theories introduce so many degrees of freedom that we could not possibly determine the initial state by experiment. My feeling, however, is that although we can't measure everything everywhere and everywhen, we can imagine measuring to finite but arbitrary accuracy within some limited region of the parameter space, and that seems to me enough to introduce field theories as an ideal limit of arbitrary accuracy. That's effectively what you say in this quote...

In this sense the fact that Nature doesn't need to be explained by a "theory of everything" but in steps of "ever finer resolution" (or observing at "ever higher energies") is a gift for model building, and it's pretty sure that also all our currently used QFTs (including the Standard Model on the yet most "fundamental" level but also the effective theories needed to describe hadrons like (unitarized) chiral perturbation theory) are indeed "effective theories" as well.

I'm totally on board with the idea that our current theories are "effective theories". [Have you seen the YouTube channel All Things EFT?] Indeed, I think the construction I offer in 2109.04412 allows the construction so many manifestly Poincaré invariant theories so easily that to me it makes the effectiveness of any given theory significantly more transparent.

 

[Fra]

In this sense the fact that Nature doesn't need to be explained by a "theory of everything" but in steps of "ever finer resolution" (or observing at "ever higher energies") is a gift for model building

As I see it, it's not a "gift" nor "lucky coincidence", I think it's more that "effective theories" is all an inside agent can construct, it's likely the "best inference" given a certain perspective or energy scale and information processing capacity etc. And that any "ultimate" one fixed theory of everything, that is independent of the context (agent/observer) is not inferrable. Ie. an effective theory is the best inference of a predictive model of the admittedly incomplete observable parts of the universe, that the context(agent/observer) can handle/encode.

But I think that even if you embrace effective theory in this sense (which I also do), I think the question that still begs for an answer is how any two such contexts (encoding two difference effective theories of the same universe) interact. Ie. what is the physics of the interacting agents. If you keeping thinking the agents are humans then this is no longer physics, it's social interaction theory somehow, and not physics. But if we see that agents can be physical systems, then the questions seems relevant.

This is the key question, that I think is not treated satsifactory in the current standard models and paradigm. And this question is clearly related to the deeper questions such as unification of all known interactions in a conceptually coherent way.

So even if we are fine with "effective theories", it seems irrational to think that the kind of "theory space" where all these theories has no structure or logic or having no physics content, such as thinking this is just a problem of "human science". I can imagine Karl Popper or similar thinkers would suggest that this is not a question for science, but I just can't get myself to accept that. It's just that the answer we seek probably is not a "naive" fixed TOE cast in the same "form" as the effective theories, this is why I think another paradigm for thinking about theory and dynamics is required but I see this perfectly consistent with the effective theory view, at any energy scale. And the basic criteria of falsification/corroboration, is instead complemented by a higher order traits such as fitess or flexibility of revision, after taking a "falsification hit". A bad theory living in a nonflexible theory spacve will be falsified and die. A good theory should learn from it's genereate an improved offspring, and if the offspring was randomly generated from big bang on each occasion, no progress would likely ever take place. So falsification events are not problems, I seem as just natural bumps in evolution....

Some of these questions has also existed in the trouble of string theory landscapes etc, but it seems, without much progress, but this question would not end even if string theory does. I think the answer to how two agents encoding different effective theories would interact physically, is the flip side of the same coin where you have a duality between two seemingly different theories. This seems abstract and it's a challenge to see what relevant this has to the physical world, and this difficulty is I think because we are analysing all this in a given outdated paradigm of "physical theory".

/Fredrik