If you bug physicists enough, they will admit that the standard model has some problems, like the Landau pole. However, there are toy QFTs in 2 spacial dimension that have models rigorous enough for mathematicians. That should be adequate for philosophical purposes.
I don’t think the Landau pole can be characterized as an actual problem. It was considered a problem for strong interactions, but we now know that quantum chronodynamics is asymptotically free, so it does not have a Landau pole. The Landau pole for quantum electrodynamics is at an energy scale much much higher than the Planck energy. We already know that we need new physics at the Planck scale, so the lack of asymptotic freedom in the Standard Model is not a real practical (or even conceptual) problem.
If you don’t like the question I’m answering, complain to Komponisto, not me.
I wasn’t complaining to anyone. And I don’t dislike the question. I was just adding some relevant information. Anyway, I did reply directly to komponisto as well. See the end of my long comment above.
But what would you count as a conceptual problem?
If we did not have independent evidence that QFT breaks down at the Planck scale (since gravity is not renormalizable), I might have considered the Landau pole a conceptual problem for QFT. But since it is only a problem in a domain where we already know QFT doesn’t work, I don’t see it that way.
I don’t think that’s the normal use of “conceptual problem.”
If physicists believe, as their verbiage seems to indicate, that QED is a real theory that is an approximation to reality, and they compute approximations to the numbers in QED, while QED is actually inconsistent, I would say that is an error and a paradigmatic example of a conceptual error.
What does it mean to interpret an inconsistent theory?
If you bug physicists enough, they will admit that the standard model has some problems, like the Landau pole. However, there are toy QFTs in 2 spacial dimension that have models rigorous enough for mathematicians. That should be adequate for philosophical purposes.
I don’t think the Landau pole can be characterized as an actual problem. It was considered a problem for strong interactions, but we now know that quantum chronodynamics is asymptotically free, so it does not have a Landau pole. The Landau pole for quantum electrodynamics is at an energy scale much much higher than the Planck energy. We already know that we need new physics at the Planck scale, so the lack of asymptotic freedom in the Standard Model is not a real practical (or even conceptual) problem.
The Landau pole for QED goes away when coupled with QCD, but I believe another one appears with the Higgs field.
If you don’t like the question I’m answering, complain to Komponisto, not me.
But what would you count as a conceptual problem?
I wasn’t complaining to anyone. And I don’t dislike the question. I was just adding some relevant information. Anyway, I did reply directly to komponisto as well. See the end of my long comment above.
If we did not have independent evidence that QFT breaks down at the Planck scale (since gravity is not renormalizable), I might have considered the Landau pole a conceptual problem for QFT. But since it is only a problem in a domain where we already know QFT doesn’t work, I don’t see it that way.
I don’t think that’s the normal use of “conceptual problem.”
If physicists believe, as their verbiage seems to indicate, that QED is a real theory that is an approximation to reality, and they compute approximations to the numbers in QED, while QED is actually inconsistent, I would say that is an error and a paradigmatic example of a conceptual error.
What does it mean to interpret an inconsistent theory?