Quantization, String Theory

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.

By the way, I did think that my discussion about cryptocurrency stuff with Max was extremely disorganized, and I saw the value of making the discussion tree there. I just don’t understand why it would be valuable in this discussion (yet). Please enlighten me!

A post was merged into an existing topic: Career, Physics and Goals (was: Artificial General Intelligence Speculations)

I think the discussion is badly organised. This is partly because I made some mistakes, like the one I pointed out in this post. I have produced a tree of the discussion as I see it as practice:

I can provide the original if anyone would like to amend it.


Okay. Thanks for making the tree. You and I had very different understandings of what the discussion tree looked like. I saw the top 4 branches as being finished threads, which is why I didn’t think it was a complicated discussion. I will go branch by branch (top to bottom) and explain.

My reply: I’m not clear on whether and why lmf thinks this is relevant to whether DD is right or wrong

I thought this branch of the discussion was finished, but I was going back through the conversation in an effort to explain why to you, and I realized that I misinterpreted something that DD said.

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.

I think DD and I have different views of what particles actually are. For DD, particles are supposed to be fully quantum mechanical, and so it is a problem for him that they aren’t this way in QFT. From my perspective, particles are almost definitionally not fully quantum mechanical: I guess I think the ‘fundamental’ entities of physics are fields and spacetime, not particles.

This explains why, on my view, me explaining that particles in QFT are only partially quantum mechanical was a refutation of DD’s claim that particles should be fully quantum mechanical. For me, particles basically are particles in QFT, so they are not fully quantum mechanical. At the time, I thought DD made a mistake that I have seen other physicists make, the mistake of not realizing that Feynman diagrams are an inherently quasi-classical thing.

Anyway, I don’t know if this disagreement about what particles are is relevant to whether DD is right or wrong, but it might be worth digging into it later. I think we should resolve the definitional issue before we move onto this, though.

Me: Yes. The Heisenberg algebra is only partially quantum mechanical. Why does that matter?

This branch is finished, because it doesn’t matter (to you). It did matter to me at the time, because I was trying to get a clearer understanding of what you actually meant by partially quantum mechanical. My initial guess was that a definition of partially quantum mechanical should not include the Heisenberg algebra, so you must have a mistaken definition, but I was wrong.

Me: Yes. The way spin-1/2 systems are usually arrived at is only partially quantum mechanical. Why does that matter?

This branch is finished, because it was also a thing that mattered to me at the time but shouldn’t matter to you. Just like the above branch where you talk about the Heisenberg algebra, my purpose in talking about the spin-1/2 system was to get a better grasp on your definition. My initial guess was that a definition of partially quantum mechanical should not include the spin 1/2 system, so you must have a mistaken definition, but I was wrong.

My understanding of Elliot’s position: CR sometimes criticisms ideas based on the methodology by which people arrived at them, and such criticisms can be correct.

This branch is finished, because I also agree that Elliot’s blog post shows why my original criticism (of it being anti-CR to criticize theories for how we came up with them) is insufficient.

I consider the bottom branch unresolved.

Let me approach this by criticizing the root of the tree (my bold):

Alan: DD’s view is that all quantum theories arrived at by quantisation are only partially quantum mechanical.

I assume that “arrived at” here actually means “have been arrived at,” rather than “could be arrived at.”

The latter interpretation wouldn’t make sense, because

Am I right?

edit: oops, I didn’t include the criticism that I implied I would include above. I won’t include it yet because I want to better understand what you mean first.

By the way, a third possibility for what you might mean also just occurred to me. I noticed that you said (my bold)

Me: Yes. The way spin-1/2 systems are usually arrived at is only partially quantum mechanical. Why does that matter?

In the root of the tree, do you maybe mean that DD’s view is that all quantum theories which are usually arrived at by quantisation are only partially quantum mechanical?

Even when a fully quantum mechanical theory is invented it will have a quasi-classical limit. So I don’t think it’s a problems if we derive particles from the quasi-classical limit of a fully quantum mechanical theory.

I think we have a disagreement about what constitutes a theory. I would say that a theory consists of an explanation as well as some way of making predictions like an equation of motion. If an equation of motion is part of a fully quantum mechanical theory then that whole package would be fully quantum mechanical. You can’t entirely cleanly separate the explanation and the equations but you might be able to arrive at the same equation in more than one way. For example, the Heisenberg algebra is currently part of the standard quantisation based way of getting quantum theories, but it might be derived as a continuous limit of a fully quantum mechanical theory in some regimes.

I don’t disagree with that.

Ohhh, I think I understand now. The way in which the quantum equations of motion (or whatever) were derived is part of the theory, because it’s an explanation of why we’re considering those equations of motion and not some other equations of motion. If quantization is part of that explanation, then the theory in question is only partially quantum mechanical.

I no longer think that this is an absurd definition.

I am still not convinced that it’s a problem that our theories are only partially quantum mechanical. Could you explain in simple terms why you think it’s bad?

(I was originally going to respond to Deutsch’s paragraph, but I disagree with several different things he says and I don’t know which one to focus on).

I think(?) I agree. I’m not sure towards which part of what I said you were directing this, and I’m not sure what goal this post was intended to accomplish.

Quantised theories start out with a classical theory and then apply a collection of rules of thumb called quantisation to come up with a quantum theory. Starting with a theory we know is false is bad. Also deriving theories by rules of thumb is bad cuz it makes the derivation harder to criticise. Also, quantisation doesn’t seem to have actually worked for coming up with a theory of quantum gravity.

I wouldn’t call quantization a rule of thumb. I have a different view of it.

My view of quantization is that it refers to one of several different mathematical procedures, like geometric quantization, deformation quantization, or the Wilsonian effective field theory formalism. Each of these procedures is completely mathematically rigorous*, but each depends on some sort of arbitrary choice (respectively: choice of polarization, choice of how to define the higher order terms in the bracket, choice of renormalization scheme).

[…] cuz it makes the derivation harder to criticise.

Since quantization doesn’t give a unique quantum theory for a given classical theory (it depends on an arbitrary choice), I don’t see quantization as a “derivation” of the quantum theory.

I think I agree with a part of what you’re saying though, in that I agree that it would be preferable if these choices weren’t arbitrary – if there was an explanation of which choice was right and why.

My objection to this relates to my above comment. I don’t think we are “starting with” a theory we know is false, then “deriving” quantum theory from that.

* The last example requires some qualification, because there are some things that people call EFT that I don’t think can be made mathematically rigorous. However, contrary to popular belief, Feynman rules and perturbative renormalization can be made completely rigorous. (I have not read that entire book because it’s very difficult, but I have read probably like 25% of it over the years and I think it’s legit.)

Another thing to add is that the method most physicists will think of when they hear quantization is what I was calling “deformation quantization.” Physicists are often very hand-wavey about how they are defining their bracket. This is partially because they don’t have to make any choices as long as the polynomial they are trying to quantize is at most quadratic in p and q.

Edit: Actually, I disagree with the last paragraph, and I wish I could delete it without breaking the rules (blurred it instead). Physicists aren’t hand-wavey about the bracket, which is always a commutator. They are hand-wavey about the hat. E.g. what operator is \widehat{p^2q^3}?

I made my own discussion tree for this conversation Discussion trees - #5 by lmf

If the choice is arbitrary then you’re making it by some sort of unexplained standard - a rule of thumb. Also there’s the problem of how you choose the quantization method itself. Also quantization starts with one theory and applies a procedure to get another theory. It’s not clear to me why you would resist calling that a derivation.

Derivations are supposed to be deterministic. One can’t derive a quantum theory from a classical theory using quantization alone; one needs some extra data.

My dictionary defines rule of thumb as

a broadly accurate guide or principle, based on experience or practice rather than theory.

I think that’s more specific than just having an unexplained standard. It makes it sound like quantization is a hodgepodge collection of rules that, in our experience, just-so-happen to work. That might describe the attitudes of many physicists towards quantization (especially early ones), but it is not my attitude towards quantization.

More about this later. I have to think about how to articulate my view of quantization.

(the parts of my view that I haven’t already expressed in this thread ofc)

Okay, I thought about this some more.

I agree with you that the classical theory can’t be taken seriously as an explanation of how the quantum theory was obtained. Worse yet, any such ‘explanation’ would necessarily be incomplete, because it would rely implicitly on an unexplained choice of additional data. Even if the auxiliary quantization data is explained, I have only ever seen it explained by saying things like “this choice is more convenient mathematically,” or “this choice looks more natural,” and it is never (AFAIK) explained with reference to a physical principle. I think that this has been my view for a while, but thanks for compelling me to articulate it.

I guess I see quantization as a computational tool rather than seeing it as a physical explanation. When a theory has a quasi-classical limit, it makes things tractable to compute and understand. This is related to the general math fact that algebraic geometry [commutative rings of functions] is way easier than non-commutative geometry (which is probably ultimately because there are fewer things that can happen in a more constrained formalism). I think that studying commutative limits of noncommutative theories (and producing a set of noncommutative theories by quantization) will be around ~forever, so in that sense I think quantization is much more than just the parochial procedure that you and Deutsch criticize.

I don’t think that modern physicists really take quantization seriously as a physical explanation either, but you have helped me realize that they are probably inconsistent about it in some places. I have incomplete thoughts here, but there are a few things I want to look into now.

I’m also curious what sort of explanation Deutsch gives for whatever quantum EOM he uses, because the quantum theories I’m used to studying are somewhat unexplained. I will probably study those papers you linked.

I think this is kind of like how if we were in an alternate history, where GR was invented via a dumb procedure called ‘covariantization’, where you take a coordinate-dependent observable / EOM / whatever and you turn it into a generally covariant thing. This would have lots of the same problems as quantization, because

  • the coordinate-dependent theory is known to be false
  • there’s not a unique way to make a coordinate-dependent thing into a generally covariant thing
  • which way you choose to covariantize would be unexplained

However, even though it’s a bad physical explanation, something like covariantization still does exist mathematically in the real GR, and it could conceivably have valid uses (in fact, I find some things when I look up covariantization on a search engine).

In that alternate reality, there could also be a DD, who could say:

There’s a related and even worse spanner in the works of general relativity: observables are supposed to be fully coordinate-independent entities. But the people who work on GR only ever construct classical, coordinate-dependent theories. Why? Because they think that the generally covariant part of the theory necessarily has to be trivial. It is assumed that in order to discover the true 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 (working in a coordinate chart), using a traditional formalism and laws that were refuted a century ago. Then you subject this theory to a formal process known as covariantization. And that’s supposed to be your relativistic theory: a Galilean ghost in a tacked-on Einsteinian shell.

(the above paragraph [edit: I mean fake DD’s speech] is not intended as a serious criticism, I just thought my edits to DD’s speech were funny so I wanted to share it).