Talk:Correspondence principle

Criticism to the correspondence principle

In this book [1] we are told how Einstein, Heisenberg and Pauli dismissed the correspondence principle, specially after the creation of matrix mechanics. This article sees the principle in a positive way, what's up with that? ReyHahn (talk) 00:06, 7 March 2024 (UTC)

I think we should be a bit cautious with

• Beller, M. (1999). Quantum dialogue: The making of a revolution. University of Chicago Press.

From the reviews on [2]

• '...an excellent, though controversial, book."
• "Of course, one may not agree with all the conclusions. "

And one in Science by Daniel Greenberger

• " I think Beller is guilty of trying to force the worst possible conclusions out of very slight and ambiguous evidence."

Johnjbarton (talk) 03:17, 12 March 2024 (UTC)

Oh I see, there are three different correspondence principles: Bohr's, the naive one, and the generalized principle used here. This article should be reworked to include that. See [3].--ReyHahn (talk) 00:15, 7 March 2024 (UTC)

I think you are on the right track. As I understand it, the principle worked ok in the Old quantum era, but fell out when two level quantum spin projection showed no continuum limit.

I think there is an important issue: the Bohr era intended the principle to be a form of boundary condition to fix values in theories. As I understand it, all the later uses were more like interpretation analysis, trying to show that certain quantum parameters relate to certain classical parameters when comparing extreme values. The "principle" part only really applies to the former. On this count most of the article is off base, esp. the generalized bit. Johnjbarton (talk) 16:56, 7 March 2024 (UTC)

So far I think the article should start stating the generalized principle which is the important one and what most people care for. Then the modern quantum mechanics principle with all its caveats. And finally Bohr's old quantum theory one as an undercover history section. Nobody should go through Bohr first to get the overall idea. What do you think of the examples?--ReyHahn (talk) 21:38, 7 March 2024 (UTC)

Sorry, but I disagree. The section here on generalized principle is just an unreferenced rehash of classical limit. It is not related to the correspondence principle.

If we look at Pais Inward Bound pg 247 he describes the Balmer formula with n>>1 as used by Bohr to determine the Rydberg constant. Pais: "This correspondence has predictive power; it determines R.". On 498 he discusses Heisenberg's work on QFT for S matrix theory and describes the principle as "what long distance aspects of the theory would survive a change of it short distance properties".

I know that Messiah v1 has a chapter on Correspondence principle, but I don't have with me just now. I can find a ref on how spin messed with the Correspondence principle.

It looks like the current article follows https://plato.stanford.edu/entries/bohr-correspondence/ which has lot of references. My synopsis would be: despite some early success, Bohr's correspondence principle did not pan out. A lot of historians have tried to make it into something, but the physics does not back it up. I suppose we could report on specific references that mutate the concept into something about the classical limit. Johnjbarton (talk) 22:35, 7 March 2024 (UTC)

Part of the current article was just me trying to make it look more like the Standford entry. If I am reading you right do you prefer to start the article with Bohr's account? I think Bohr's version is very old quantum like and no longer useful. A modern version was reworked after new quantum theory but it is far from being perfect.--ReyHahn (talk) 02:32, 8 March 2024 (UTC)

Bohr invented and famously used the Correspondence principle; he literally wrote the book on it. Later other folks came along, could not figure out Bohr so they took up a similar idea and called it "Correspondence principle". Bohr's work should be judged by what it said, not by mis-alignment with an idea of the same name that came along later.

My reading of the "Generalized Correspondence Principle" section of the Stanford work is that there are two different things: Bohr's Correspondence Principle and the classical limit correspondence. I think the article could reflect this rather than pick one. (But if one must be picked it has to Bohr's). Failures of each are instructive FWIW.

The Stanford article actually has Bohr's reaction to the generalize form:

• When Rosenfeld off-handedly suggested to Bohr that the correspondence principle was about the asymptotic agreement of quantum and classical predictions, Bohr emphatically protested and replied, “It is not the correspondence argument. The requirement that the quantum theory should go over to the classical description for low modes of frequency, is not at all a principle. It is an obvious requirement for the theory” (Rosenfeld 1973, p. 690).

Johnjbarton (talk) 03:08, 8 March 2024 (UTC)

Aside from Bohr's principle and generalized principle, I was under the impression that there is an additional modern one. In the Standford source it is under "modern literature". The correspondence principle should have died together with old quantum theory. What we have now are the semiclassical limit where we can recover some of the results of old quantum theory and the result of classical physics. I will try to read on it over the weekend. Cheers.--ReyHahn (talk) 08:45, 8 March 2024 (UTC)

Examples

I am still far from understanding Bohr's version, but are the examples given really examples of the correspondence principle? ReyHahn (talk) 09:49, 13 March 2024 (UTC)

Per our discussion under "How to continue" we are deleting the Examples. Johnjbarton (talk) 18:08, 19 March 2024 (UTC)

Classical limit

The article Classical limit is essentially a better version of this without all of Borh's problematic take. I wonder if it would be just better to merge correspondence principle there. If not what would be the best way to distinguish both?--ReyHahn (talk) 10:09, 13 March 2024 (UTC)

I would strong oppose merger. Bohr did not win a Nobel prize for a classical limit. In my opinion the correspondence principle can't possibly be considered exclusively a classical limit of quantum theory: during the height of its application there was no quantum theory. There was only the Bohr-Sommerfeld atom and a hypothesis of quantum radiation transitions. The correspondence principle was Bohr's attempt to provide a radiation theory. With the emergence of quantum mechanics and QED, the correspondence principle had no value.

• If not what would be the best way to distinguish both?

I would have a section in each article explaining that application of the correspondence principle sometimes results in relationships that were interpreted as asymptotic relationships between quantum and classical. Post 1926 this was the only use physics had for the correspondence principle so that use got more attention the remaining 100 years. Johnjbarton (talk) 15:55, 13 March 2024 (UTC)

I think it's a good idea to have an article called correspondence principle that is mostly about the history (Bohr and immediate reactions). The classical limit article should cover how full-fledged quantum theory is used today. XOR'easter (talk) 16:18, 13 March 2024 (UTC)

I think we should use Rosenfeld's report that Bohr was adamant about the principle not being a limit as a transition to a section on how many sources (most modern QM books) use the name for a $\hbar \rightarrow 0$ limit. Johnjbarton (talk) 22:56, 13 March 2024 (UTC)

Thanks for the input. I am still lost here, (1) do we need the correspondence principle in some form or another for modern quantum mechanics? or can this article be just a history article for Bohr's take? (2) aside from Bohr's account is there any other principle? Should we just throw out the limit description (quatum->classical) from this article? If the answer is no to the latter, then how we define it? --ReyHahn (talk) 11:04, 14 March 2024 (UTC)

There are, I believe, three topics that fit into an article called "correspondence principle". First, there is Bohr's view (and the attempts by historians to figure out exactly what his view was). Second, there is the different but well-established practice of using "correspondence principle" to mean an $\hbar \to 0$ kind of limit. Third, there is the "generalized" meaning, where people talk about one theory reducing to another. I would organize this article accordingly: one section, probably divided into subsections, about readings of Bohr; another, probably shorter, about asymptotic limits and with a {{main}} tag pointing to classical limit; and a third about the "generalized correspondence" notion, which would resemble the section we have now but condensed to be less textbook-ish. XOR'easter (talk) 14:38, 14 March 2024 (UTC)

Yes, that is what I was thinking. The generalized section needs much better references. I've never heard of it, but then again I thought it was "common sense" so someone must have written about it. Johnjbarton (talk) 16:09, 14 March 2024 (UTC)

I added a small section on classical limit. Needs to be merged with the one following it. My main goals were to connect to Ehrenfest and WKB. Johnjbarton (talk) 22:27, 14 March 2024 (UTC)

"while referring back to this link"

The current article says:

• Bohr introduced the term "correspondence principle" during a lecture in 1920, while referring back to this link between classical and quantum mechanics.

The sentence has two references, a Physics Today article by Liboff which I don't have and Bohr's lecture which is available:

• https://www.gutenberg.org/files/47464/47464-pdf.pdf

The way I read Bohr's lecture he does not refer back to a link. Rather he says:

• "This peculiar relation suggests a general law for the occurrence of transitions between stationary states. Thus we shall assume that even when the quantum numbers are small the possibility of transition between two stationary states is connected with the presence of a certain harmonic component in the motion of the system."

Bohr does not view correspondence as an asymptotic limit to classical theory. Johnjbarton (talk) 23:15, 13 March 2024 (UTC)

I agree. I removed "this link". --ReyHahn (talk) 09:26, 14 March 2024 (UTC)

How to continue

The history section is fine now. But it is the following sections that bother me, what should we put there? How should we define the not-generalized principle? Are the examples useful? ReyHahn (talk) 18:12, 18 March 2024 (UTC)

• Can you say more about which "following sections" and what bothers you?
• I'm unclear on what you mean by "the not-generalized principle".
• Examples:
  • Since there is no one thing called the correspondence principle, a single section does not make sense. The example section are well written but what are they examples of? The two historic ones could go in the history section if we could find matching historical refs. The limit of large quantum numbers could go with the classical limit section. I would delete the one D example.

I would rename "Description and Modern analysis" to "Modern view", include some modern textbook discussion. This could be a place for the large q.n. example. Discussion should include h->0.

Does this help? Johnjbarton (talk) 02:14, 19 March 2024 (UTC)

• Following sections I mean specifically "Description and modern analysis" and "examples". Do we need a description section?
• That has been my question all along. What is the correspondence principle is we forget about Bohr?. Is it the classical limit? You seem to agree that we should not conflate the classical limit with the correspondence principle

For the examples part I would remove them. We could built them back from scratch from good sources and put them in the historical section.

I am proposing to remove the "Description and modern analysis" entirely. What is that about?--ReyHahn (talk) 16:59, 19 March 2024 (UTC)

Maybe, can the the generalized correspondence principle section be a section of modern view?--ReyHahn (talk) 17:42, 19 March 2024 (UTC)

As you can see I started. I'd like to add to the Modern view some content from textbooks. I'll make the other changes you suggested. Johnjbarton (talk) 18:07, 19 March 2024 (UTC)

Oh I left one dangling paragraph with a reference

• Jaeger, Gregg (September 2014). "What in the (quantum) world is macroscopic?". American Journal of Physics. 82 (9): 896–905. Bibcode:2014AmJPh..82..896J. doi:10.1119/1.4878358.

At first I thought the ref was off topic but the articles it cites seem to suggest otherwise. I don't have access to the article. Johnjbarton (talk) 18:11, 19 March 2024 (UTC)

I've made another round of changes, please review and decide where we are. I think the "generalized" is marginally notable but only because I've not personally encountered it. The ref here is from a book with a couple of articles by different authors discussing it, so it's not obviously below the bar. Johnjbarton (talk) 16:48, 20 March 2024 (UTC)

Generalized principle

I read through most of Post's paper that covered (among other things) the Generalized Correspondence principle. I summarized it and in so doing replaced most of the corresponding section.

The old content was unreferenced material classical limits; that is not what Post's Generalized principle is about. Rather it is about correspondences between new and old theories: that they will have common parts. It does overlap with classical limits, eg v<<c in relativity, but Post at least does not make a deal of this. The book that included Post's article had more articles using the Generalized principle (his students I guess). We might find more examples or more about the connection to classical limits. Johnjbarton (talk) 01:36, 20 March 2024 (UTC)

Thanks. Great work. I agree much more with the current article.--ReyHahn (talk) 18:07, 20 March 2024 (UTC)

Connection to Heisenberg "reinterpretation" paper and examples.

@ReyHahn Ok I found the source of the now-deleted Examples section as well as a connection to Heisenberg's paper ‘‘Quantum-theoretical re-interpretation of kinematic and mechanical relations,’’ Z. Phys. 33, 879–893 1925.

• Fedak, William A., and Jeffrey J. Prentis. "Quantum jumps and classical harmonics." American Journal of Physics 70.3 (2002): 332-344.

Johnjbarton (talk) 01:12, 22 March 2024 (UTC)