Quantization, String Theory

Thanks.

I will hold off on reading these for now, because I think that the bottleneck issue is the one in the above reply. Let me know if you disagree.

I now think I was wrong about that. From DD’s point of view a partially quantum mechanical theory is one in which you start from a classical theory and then apply a procedure called quantization to get a quantum theory.

I think that’s a reasonable definition.

Then I assume that a fully (partially) quantum mechanical entity is defined to be an entity that plays a significant role in a fully (partially) quantum mechanical theory?

If so, I think that definition is consistent with the implicit definition of the term I was using when I wrote this paragraph:

I don’t know exactly what a “fully quantum mechanical” entity is, but I don’t think that the particles in QFT count (nor do I think strings or branes count, but that’s a more complicated discussion). Particles arise when you try to write your path integral as an asymptotic series in ħ, so the assumption that quantum effects are small is built into the whole formalism of perturbative QFT.

Spelling it out explicitly:

  1. Perturbative QFT (=summing over Feynman diagrams) is not a fully quantum mechanical theory, because it is obtained by applying a procedure called quantization to a classical theory
  2. Particles in QFT are edges in Feynman diagrams
  3. Therefore, particles in QFT are not fully quantum mechanical entities

Do you agree with 3. now?

One problem that just occurred to me with this definition is that it’s too broad. Like, I could obtain the Heisenberg algebra by quantizing a classical theory. Does that mean that the Heisenberg algebra is only “partially quantum mechanical”? That seems wrong.

I’m not sure if I’m being nitpicky or if this is relevant.

Another example where the claim would seem weird to me is that even a spin-1/2 system can be obtained by quantizing a classical system (an electrically charged particle confined to a sphere in a uniform magnetic field or something like that, I’d have to look it up but I have definitely seen it before).

By the way, isn’t it anti-CR to criticize theories for how we came up with them?

Also, CR contradicts itself by criticizing theories for being developed in an ad hoc way, which is criticizing the method that created the theory rather than the content of the theory. Broadly, I think methods should be discussed and do matter – and that certain methods lead to flaws in the theories they create, so it is possible to comment on those flaws directly, but commenting only on the content and not the method is missing part of the picture.

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I didn’t say anything about what a fully quantum mechanical entity. I don’t think DD did so either. Perhaps you could explain why you consider this relevant.

All existing perturbative QFTs are only partially quantum mechanical since they were all arrived at by quantising a classical theory.

The algebra of the position and momentum observables of multiple systems in quantum theory is only partially quantum mechanical. Why do you think this is odd?

To the best of my knowledge spin-1/2 systems have all arisen in partially quantum mechanical theories such as QED. What do you think the problem is?

I agree with Elliot’s position that it can be rational to criticise the method used to create a theory. The context in this case is that decades of attempts to find a theory of quantum gravity have not succeeded yet. All of the resulting theories have been partially quantum mechanical and DD said their failure isn’t surprising because they are only partially quantum mechanical.

DD said, in your quote of him in the earlier thread (my bold)

There’s a related and even worse spanner in the works of elementary particle physics: particles (or fields, strings, or whatever) are supposed to be fully quantum-mechanical entities.

Then I said, in response to that (bold added):

I don’t know exactly what a “fully quantum mechanical” entity is, but I don’t think that the particles in QFT count (nor do I think strings or branes count, but that’s a more complicated discussion). Particles arise when you try to write your path integral as an asymptotic series in ħ, so the assumption that quantum effects are small is built into the whole formalism of perturbative QFT.

Then you said, in response to that

It seems odd to me that you say you don’t understand something and then continue to write without asking questions.

Yes, I agree. Also, I would argue that it’s more than just all existing perturbative QFTs. I would say that all possible perturbative QFTs are only partially quantum mechanical.

You’re right.

By a spin-1/2 system, I was thinking of something really simple: a 2 dimensional Hilbert space with a Hamiltonian H = - B \sigma_z. I claim that such a system can be obtained by quantizing a (weird) classical theory, even though it’s not normally studied that way.

I thought these examples were odd because they are the first and most elementary things that come to mind when I think of quantum mechanics, and yet they are not fully quantum mechanical by your definition, because they can be obtained via quantization.

By the way, are there any simple examples of quantum mechanical theories that you would consider to be fully quantum mechanical?

The only example of a fully quantum mechanical theory by DD’s standards that I am aware of is qubit field theory.

Okay. I also agree with the blog post.

My issue is that criticizing a theory for being partially quantum mechanical is criticizing it because it can be obtained through quantization. To me, this is analogous to criticizing an idea on the grounds that Kate could have said it, which would be a bad criticism.

That particular way of obtaining that Hamiltonian is not fully quantum mechanical, but I’m not aware of any reason why every theory with that Hamiltonian must be partially quantum mechanical. The Hamiltonian is a tool for understanding and criticising an explanation, it’s not equivalent to an explanation. Existing quantum theories are mostly not fully quantum mechanical so it’s not surprising that simple examples are partially quantum mechanical.

What would be an example of CR criticizing a theory for being developed in an ad hoc way?

Let me apply this:

to this:

Suppose that one day, a mathematician comes up with a trick that allows him to obtain qubit field theory by quantizing some sort of extremely convoluted classical theory. Would you really consider that to be a criticism of qubit field theory?

I think that whether or not it’s possible to obtain a theory through a bad method should be irrelevant to how we judge the theory.

You can search “ad hoc” in various Popper books. E.g. C&R:

(7) Closely related to this problem is the problem of the ad hoc character of a hypothesis, and of degrees of this ad hoc character (of ‘ad hocness ’, if I may so call it). One can show that the methodology of science (and the history of science also) becomes understandable in its details if we assume that the aim of science is to get explanatory theories which are as little ad hoc as possible: a ‘good’ theory is not ad hoc , while a ‘bad’ theory is.

Re the broader discussion, I saw errors, but I don’t think they really matter in the broader context that it’s too disorganized and is being done using preexisting (prior to CF) automatizations (about how to think and discuss) without any visible attempt to understand and practice (and move towards automatizing) a CF idea like trees. Errors are simply to be expected prior to automatizing better methods. I think that issue (the parts related to automatizations) is also too low level to begin with, and broader plans and goals at the forum and in life are important context for it.

Why do you think this discussion is disorganized? It seems to me like we have been focusing on a really specific issue, and that there aren’t very many moving parts in our conversation. I was initially trying to understand what Alan meant by a fully quantum mechanical theory. Now I think I have a better idea of what he meant, and I am criticizing Alan’s belief that the definition he gave is sensible.

edit: I guess that’s only a description of the conversation today. Yesterday I was trying to defend my claim that particles are not fully quantum mechanical entities according to Alan’s definition (which is how our conversation started). After I posted that defense, I came to the belief that his definition had problems, so I decided to focus on the definition. It still seems pretty organized to me.