Quantization, String Theory

Topic Summary: This is a continuation of the small amount of debate that @alanforr and I had in another thread, concerning whether or not quantization and string theory are bad.

Goal: Generally, I want to determine to what extent the ideas about physics prevalent in the string theory community (which I will define as anyone who regularly posts their papers on the hep-th arxiv) are bad. More specifically, I want to determine whether or not the centrality of quantization to the way that these physicists think about QFT (quantum field theory) is fundamentally in conflict with MWI (many worlds interpretation) or the lessons of quantum mechanics, as David Deutsch and Alan seem to think.

CF relevance: First, the topic relates to a lot of the epistemology ideas in DD’s books / papers, which are related to CF. Second, CF emphasizes the importance of goals, and since I am basically a string theorist, the verdict of this discussion relates closely to some of my central goals (it might relate closely to Alan’s goals too since he is a physicist). Third, if the discussion gets involved we could start explicitly using the paths forward or discussion trees methodologies.

Do you want unbounded criticism? (A criticism is a reason that an idea decisively fails at a goal. Criticism can be about anything relevant to goal success, including methods, meta, context or tangents. If you think a line of discussion isn’t worth focusing attention on, that is a disagreement with the person who posted it, which can be discussed.) Yes.


Okay, so:

I read some of this paper that Alan linked me, and I have some questions/concerns:

  1. The paper is quite technical, and it’s using a formalism that I’m not familiar with. A specific problem I have is that I don’t know of any examples of quantum theories that can be derived by using this “quantum principle of stationary action” (I’ve only encountered the classical principle of stationary action before). Deutsch doesn’t give any concrete examples in the paper. He cites some other papers which I assume do have more examples, and maybe you (Alan) could recommend one of them to me? (Keep in mind that there’s no references section in the paper you linked, so DD’s citations might be ambiguous; I haven’t checked).

  2. You (Alan) showed this paper to me earlier because (I presume) you think that if I had a correct understanding of what Deutsch meant by “fully quantum mechanical entity,” I would see that the criticisms of Deutsch’s view of quantization that I made here are invalid. Where in this paper do you think DD defines what a fully quantum mechanical entity is? I don’t think he does, but it’s not a searchable PDF so I’m not sure. Alternatively, could you maybe define the term yourself?

The quote I gave initially was [1, 2 Chapter 18]:

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. But the people who work on them only ever construct classical, single-universe theories. Why? Because they think that the quantum part of the theory necessarily has to be trivial. It is assumed that in order to discover the true quantum-dynamical equations of the world, you have to enact a certain ritual. First you have to invent a theory that you know to be false, using a traditional formalism and laws that were refuted a century ago. Then you subject this theory to a formal process known as quantization (which for these purposes includes renormalization). And that’s supposed to be your quantum theory: a classical ghost in a tacked-on quantum shell.

One of the papers cited is this Quantum theory of gravity. II. The manifestly covariant theory from by DeWitt, see especially Section 2. Another paper cited is The commutation laws of relativistic field theory by Peierls.

DeWitt 1965 is a book called “Dynamical Theory of Groups and Fields” by Bryce S DeWitt.

Section 1 and the first four paragraphs of Section 2 explain the problem that DD is addressing. The way I would state the problem is that a fully quantum mechanical theory would not include any quantities that are supposed to be measurable that are not represented by quantum observables, since all such quantities are actually quantum mechanical.

Those parts of the paper are parts that I read, and I believe I understood what Deutsch wrote. I don’t see how any of it is a refutation of this criticism of the things Deutsch said in his speech.

I think I agree with this.

What theories do you think include quantities that are supposed to be measurable but are not represented by quantum observables?

edit: I don’t think that classical fields are supposed to be measurable quantities in QFT, I think that they are a tool to get to the measurable quantities.

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?