Talk:Introduction to quantum mechanics

Ehrenfest's theorem

Copying conversation from my talk page, as it seems best to continue here:

"Hi MichaelMaggs I am a little confused by your comments concerning Ehrenfest's theorem and quantum mechanics, could you elaborate on why you believe it doesn't cure apparent quantum-classical paradoxes?

--Best Bosonichadron2 — Preceding undated comment added 20:58, 3 August 2022 (UTC)

It's not correct to say that "Many of these paradoxes can be cured", as that implies that QM is wrong in some way. Most of the so-called 'paradoxes' are in truth things that appear from a day-to-day perspective simply weird. We should be explaining to beginner readers that such weirdnesses are unavoidable and are real, no matter how counterintuitive they may at first appear. They are not things that can be explained away by Ehrenfest or any amount of classical analysis. If there are particular and specific examples of beginner missapprehensions that Ehrenfest's theorem can help dispel, by all means let's include them. But we do need a specific reliable source for that, not just a statement to that effect. MichaelMaggs (talk) 10:02, 4 August 2022 (UTC)

I respectfully disagree with your first sentence, because if we take the definition of paradox as Webster defines it (using 2a) and replace it in the sentence that I wrote originally:

"Many of these paradoxes can be cured using Ehrenfest's theorem, which shows that the average values obtained from quantum mechanics (e.g. position and momentum) obey classical laws."

with the definition paradox:

Many of these statements that seem contradictory can be cured using Ehrenfest's theorem, which shows that the average values obtained from quantum mechanics (e.g. position and momentum) obey classical laws.

The above sentence certainly does not make a value judgement on the correctness either of the two classical or quantum "statements" it simply says that there are apparent contradictions. But then goes on to say that many of them are not contradictions at all, because of Ehrenfest's theorem.

With paradoxes like

"How is it that Newton's laws are wrong at the atomic scale, but then perfectly correct when dealing with systems which are simply large collections of atoms?"

easily being cured by Ehrenfest's theorem. These questions being the most natural, obvious and fundamental a student might bring up, mention of Ehrenfest's Thm is extremely helpful if not absolutely necessary. As to the point of citations, the entire purpose of Ehrenfest's Thm is to answer questions/paradoxes like the above and therefore satisfy the correspondence principle. I could add a citation, but it would just be a copy of the citations which are already present in the main article on Ehrenfest's Theorem, which I linked to and is well-written, so I believe a citation would be inappropriate for that reason.

What are your thoughts? Bosonichadron2 (talk) 16:41, 4 August 2022 (UTC)

MichaelMaggs (talk) 12:02, 5 August 2022 (UTC)

The third paragraph, with Feynman's quote, is all that needs to be said in the lead. Ehrenfest's theorem is far too subtle and sophisticated to be included in the lead of this beginner's article. No beginner following that link would be able to glean anything useful from even the first sentence of the Ehrenfest's theorem lead. More useful to a beginner would be a non-technical explanation of the Correspondence principle, which is referred to lower down, but is not developed.

The assertion that Ehrenfest's theorem (which is technically quite specific) "cures statements that seem contradictory" seems far too broad, and a reliable source for the exact wording to be used really is essential if it is to be mentioned. The E th article discusses nothing about apparent or real contradictions, let alone that the theorem can be considered a 'cure'. Few if any physicists would maintain that contradictions can be cured without (at the very least) a solution to the measurement problem. MichaelMaggs (talk) 12:02, 5 August 2022 (UTC)

@MichaelMaggs

" The assertion that Ehrenfest's theorem (which is technically quite specific) "cures statements that seem contradictory" seems far too broad, and a reliable source for the exact wording to be used really is essential if it is to be mentioned. The E th article discusses nothing about apparent or real contradictions, let alone that the theorem can be considered a 'cure'. "

After reading the article again, I think this is a good point, I'll find a citation.

Is the word "beginner" defined anywhere? Bosonichadron2 (talk) 12:21, 5 August 2022 (UTC)

These "Introduction to..." articles are supposed to provide a non-technical overview of a subject for non-specialists, but with repeated edits there is a tendency for them to become more and more complex. Rather than "beginner" it would perhaps have been better to refer to the "non-specialist" or "non-physicist" reader. MichaelMaggs (talk) 12:39, 5 August 2022 (UTC)

Yes, "beginner" should not be used of someone with roughly a high school education who is curious about quantum mechanics and some of its specific topics. "Newcomer" also seems a bit judgmental. The legal definition "reasonable person" doesn't feel right. Is there such a thing as an "average person"? That would be my choice. Otherwise, I am fine with "non-physicist", except that many non-physicists may be fine with mathematics. In QM, as I've said, the truth can only be expressed fully in mathematics--that is the way that Nature actually works at the atomic scale; but WP articles ought not to include any mathematics in their lead or first few paragraphs, so as not to be off-putting. David Spector (talk) 15:40, 8 July 2023 (UTC)

Both mathematics and "Ehrenfest's theorem" are forms of jargon: specialized vocabulary expressing complex ideas quickly to those trained in the subject. To be successful an "introduction" needs to focus on those un-trained in the subject but nevertheless interested. For a complex fundamental topic like QM, I would expect 'interest' to grow out of a curiosity and thus exposure to scientific and technical ideas. We shouldn't have to explain "atoms" or "electrons" as general concepts for example, but neither should we expect such a reader to be excited about the constants in Planck's blackbody radiation formula. Johnjbarton (talk) 15:55, 8 July 2023 (UTC)

Problems with introduction

The introduction is way too long; it should be no more than 4 paragraphs (MOS:LEADLENGTH). The elementary explanation is good, but my feeling is that some of the more peripheral topics like superfluidity and Ehrenfest’s theorem could be moved to the body. --Chetvorno^TALK 18:08, 5 August 2022 (UTC)

Agreed. This is supposed to be an introductory article, and the lead, in particular, should concentrate on the basics. MichaelMaggs (talk) 22:07, 5 August 2022 (UTC)

My specific proposals:

1) Remove from the first paragraph: "This article describes.." through to the end of that paragraph. The historical content in the article can be grouped, making this material redundant with structure.

2) Move the entire paragraph "Light behaves in some aspects ..." to Applications

3) Remove the Ehrenfest content to a new section on connections to classical physics.

I'll move forward until someone yells. Johnjbarton (talk) 02:19, 28 June 2023 (UTC)

Ok down to two paragraphs. Lots of reorg. The Einstein material is still duplicated and the photon section is dubious, but the major character of the article is, IMO, in better shape.

Please check.

Resolved

Johnjbarton (talk) 17:25, 28 June 2023 (UTC)

Why are uncertainty principle, eigenstates, and Pauli exclusion under Copenhagen?

While historically these things emerged before alternative interpretations (except de Broglie/Bohm I guess), no modern treatment would make such an outline. Johnjbarton (talk) 02:28, 28 June 2023 (UTC)

I massively reorganized the article outline and added a few small sections to keep the flow.

Please check.

Resolved

Johnjbarton (talk) 17:26, 28 June 2023 (UTC)

Wave-particle duality section border-line incorrect :-(

The movie with the bouncy sound track is both incorrect and inconsistent. The first example, BBs through holes has a weird distribution: it should be sharp shadows of the slit, particles cant get around them. That's the point. The last example, observer, should identical to a single slit wave case, not the uniform dots shown. The simulated electron wave packets are dubious.

The single/double slit image is simply wave interference, no duality shown. Johnjbarton (talk) 16:59, 29 June 2023 (UTC)

Merge history -> History of quantum mechanics

Currently history takes more than 50% of this article; the history outweighs the article is supposedly summarizes.

To correct this imbalance and make room for new content here, I propose to merge the history with the main page. Then we can summarize the historical context for each concept selected for the introduction, linking the corresponding discussion in History of quantum mechanics.

I believe this will make both articles stronger. Johnjbarton (talk) 14:09, 7 July 2023 (UTC)

First of all, following the history of QM is how one is introduced to QM, at least in that article. It is not about redundancy, the history has a purpose. It is not simply extra content weighing down the article, Deleting the history in Intro to QM may be detrimental to that article. If you want to do some summarizing then that might best be suited for the History of QM article. If you want to do some copy editing in the Intro to QM that is fine. ----Steve Quinn (talk) 15:25, 8 July 2023 (UTC)

I agree that history is one path to learn QM, but only one and it has its pluses and minuses. Fortunately we don't have to choose: we can have both a history and a non-historical introduction. That is what we have been considering. Specifically we are proposing an almost non-mathematical introduction.

Before my merge, the History page was weak. It lacked adequate material, was disorganized, and had some small amount of incorrect material. By pulling from the Introduction the new page is (in my opinion) dramatically improved.

This page, the Introduction, had a large amount of history (over half the content) providing no real hint of "introducing" QM. The material was not selected nor presented to introduce QM but rather was focused on encyclopedic history. That is, it was perfect for the History page!

Despite that approach, the Introduction page had numerous links claiming that the Main page was the History page. It claimed that the Introduction content was a summary. Now that we have a stronger History page, this Introduction page can legitimately summarize the History page. That would be the next step for the Introduction.

If you are interested in the History of QM I encourage you to help us improve the History of quantum mechanics page. It's a bit scruffy and certainly could use more content.

I hope this clarifies my point of view and I hope it also reflects, at least approximately, the views of @David spector and @XOR'easter. Johnjbarton (talk) 15:24, 8 July 2023 (UTC)

Well, it could be that editors have added extraneous 'history' content over time. I haven't looked at this article in awhile. It sounds like you have a good plan. I didn't notice that this page claimed to summarize the main History page. I'll have a look at the History of QM page. I would like input from the other editors that you pinged and hear their take on the matter. ---Steve Quinn (talk) 15:50, 8 July 2023 (UTC)

I haven't looked at the history issue due to lack of time. I agree that following the historical development of QM is an excellent way to learn about QM, but definitely roundabout, especially as QM history is littered with mistakes, such as a demand for local realism or the belief that atomic energy states are quantized because only so many waves can fit on a string that is constrained not to move at both ends, or the belief that hidden variables can explain everything without invoking nonlocality.

Because of such mistakes, because of the eternal misunderstanding of Feynman's remark, and because it is indirect, I would mildly oppose including much history outside of the main History of QM article. Let's just directly describe QM, okay? And let's definitely try to avoid too much talk about the mysterious named terms (axioms) that got codified around 1927 and haven't budged much since.

David Spector (talk) 16:03, 8 July 2023 (UTC)

Thanks very much for your responses. Your arguments are very convincing. So, keep up the good work. And all of you are doing a great job. This was probably a change that needed to happen awhile ago. I don't have a problem with any of this. ---Steve Quinn (talk) 21:25, 8 July 2023 (UTC)

Support the merger. In its current state this article mainly just reprises History of quantum mechanics. In general, I agree with David Spector that a minimum of history should be included here. We desperately need a real introduction to QM. I think there should be a simple section on the math - wavefunctions, bra-ket notation, Born rule, etc. As Feynman pointed out in his Lectures, the elementary math of QM is not difficult. --Chetvorno^TALK 22:00, 8 July 2023 (UTC)

Please see Talk:Introduction_to_quantum_mechanics#Draft_replacement_for_History_section_ready_for_review below; my replacement for the history in this Introduction article is ready for review. The only major question outstanding is whether to shrink the blackbody discussion to a sentence. Johnjbarton (talk) 02:34, 14 July 2023 (UTC)

The theory of relativity?

The lead paragraph mentions the theory of relativity. The word relativity is ambiguous and this paragraph suggests that there is only one such theory. There are at least two such theories: special relativity, which deals with causation and the constancy of the speed of light in a vacuum as measured in any inertial frame of reference (a frame of reference that is not being accelerated by any force), and general relativity, which deals with the physics of acceleration, especially that caused by gravity. The subject matter of these two theories is clearly, from these brief definitions, quite different. The equations that embody these two theories are different. In fact, the time differences caused by these two theories, which must be corrected by the Global Positioning System for it to function with adequate accuracy, are of different magnitudes. David Spector (talk) 22:09, 10 July 2023 (UTC)

@David spector I would support removing mention of relatively altogether in the lead. Johnjbarton (talk) 22:27, 10 July 2023 (UTC)

I see references in papers and on the Web often to "relativity" and it really annoys me, because I can't always tell which theory is being referenced. The relationship between QM and these two theories is important, yet not fully understood in physics today. David Spector (talk) 22:45, 10 July 2023 (UTC)

The ambiguous mention of “the theory of relativity” in the lead of this article on quantum mechanics is minor, perhaps even trivial. In the lead it is blue linked to the Wikipedia article, and the title of that article includes the singular “theory”. The article then proceeds to resolve the ambiguity and explain the subject.

If Wikipedia has a problem on this matter, that problem is embedded in the article on the theory of relativity, and that is where it should be fixed. The lead to this article on quantum mechanics appears fine to me. Dolphin (t) 00:09, 11 July 2023 (UTC)

Independent of the importance of relativity to QM the topic does not belong in the introduction to the Introduction unless the subject dominates the article, which it does not. This article is about one revolution and has enough to do on that topic. So I boldly fixed this. Please check. Johnjbarton (talk) 00:45, 11 July 2023 (UTC)

I'm glad it's gone, thanks. David Spector (talk) 01:07, 11 July 2023 (UTC)

Draft replacement for History section ready for review

I am proposing a shorter, more focused history section for this Introduction. Personally I would be ok with no history but I know others want one and I think we should focus our energy on getting a good Introduction rather than debating whether history is part of it.

My draft aims for these goals:

• no math, intro level.
• short, beyond summary short.
• accurate.
• cover only phenomena likely to be discussed in Introduction.
• emphasize "quantum/quanta" not particle-wave.

I anticipate we will use the photoelectric effect, photo-absorption, and Stern-Gerlach in the new Introduction, but not blackbody. Nevertheless I don't think we can have a history without blackbody. Thus I put a bit more text in to blackbody radiation to satisfy the "intro" requirement.

I left 'photon' to the end for accuracy and for 'quanta'.

DRAFT: User:Johnjbarton/sandbox/introduction_to_quantum_mechanics#Quantization_of_matter

Please review this draft only for "scope" or similar overall-ness. If it seems like we are likely to agree on the character of a replacement, I will add sufficient references and ask for a second detailed review. Johnjbarton (talk) 18:52, 11 July 2023 (UTC)

John, I'm not following at all why black-body radiation should be in a summary or an introduction to QM, historical or not. The classical Maxwell–Boltzmann distribution of particle velocities does a fine job of explaining temperature. The leap from that to describing the distribution of black-body radiation involves using a model of bound harmonic oscillators and thus mathematics to a great extent. I don't see the value of including it in a summary or an introduction, especially if mathematics is not to be included. I do agree with the first concept being the photoelectric effect, although the Millikan/Fletcher oil drop experiment showed quantization as the number of free electrons on the surface of each droplet, without any of the further strangeness of QM, in around 1900. I would leave out black-body radiation from any readable introduction to QM. David Spector (talk) 19:39, 11 July 2023 (UTC)

All QM histories I have read start with Planck. I believe this is because the main participants of the day viewed Planck's blackbody paper as the key starter event. Planck -- a deeply old-school physicist -- was "forced" in to using quanta by the experimental data, much the way the rest of QM unfolded. Einstein's paper photoelectric effect paper was primarily aimed at Planck's blackbody work. The statistical analysis was used again and again esp. by Einstein (eg Bose-Einstein statistics).

However I am not against removing the text I wrote, condensing it to a single sentence.

(The Millikan/Fletcher oil drop experiment was completed in 1909.) Johnjbarton (talk) 23:04, 11 July 2023 (UTC)

I'm looking forward to seeing your draft, thanks. David Spector (talk) David Spector (talk) 19:41, 11 July 2023 (UTC)

I put the link above, thanks. Johnjbarton (talk) 23:04, 11 July 2023 (UTC)

I have replaced the two history sections with my draft. Please review the new page content.

Resolved

Johnjbarton (talk) 16:51, 16 July 2023 (UTC)

References on teaching QM

There are a quite a number of educational studies and surveys targeting better QM instruction for non-expert students. For example there are even meta-reviews.

I think reading through these and applying their insights would be helpful.

I wonder: should we create a "Teaching Quantum Mechanics" page that summarizes these articles and some of the key findings? Johnjbarton (talk) 15:09, 12 July 2023 (UTC)

I'm sure some WP editors would reply that an article on good teaching methodology for topic X is off-topic for any article about X, but I disagree. Since so many have difficulty learning QM from scratch (which is clear from the comments on QM articles on YouTube), an article discussing how to teach/how to learn QM would be an excellent idea. It could summarize how QM popularizers like Don Lincoln teach QM. There could be a number of steps in which the experimental evidence is reviewed (including descriptions of the lab equipment used), followed by steps for learning the basic mathematics needed to understand the theory, followed by the ontology, the general way in which Nature works in tiny scales. I would, please, leave out the historical development, since the order in which concepts were discovered is likely not the best order in which to learn about QM. David Spector (talk) 16:06, 12 July 2023 (UTC)

I was thinking of a completely separate page, to avoid the off-topic/meta discussion issues.

I cooked up a page that provides some links to review of educators doing studies:

User:Johnjbarton/sandbox/teaching_quantum_mechanics

I'm pretty sure this is not what you are thinking but I think it's a start. Refs to secondary articles and everything ;-)

I already got many ideas from these reviews. I'm inclined to create it as a real page. Feedback? Johnjbarton (talk) 01:45, 13 July 2023 (UTC)

Wonderful! Your new article should be helpful for those new to QM. Don't forget to put some back links to it in good places in other articles.

I know I've found several interesting ways to learn QM over the years, different from each other, that at least helped my intuition about tiny physics. My memory is not good: there was an approach (from a public MIT course?) starting with a light source and three plane-polarizing filters, that eventually reached an explanation of the Pauli functions of QM, there were several different approaches to proving Bell's Theorem, that shows how unnatural Einstein's intuition about locality was, there was Don Lincoln's course (for "The Great Courses/Wondrium") that used mostly a simplified model of the Mach–Zehnder interferometer to describe basic QM effects involving beams of light, there are the various presentations in videos and in papers/books of David Bohm's deterministic interpretation of the double slit and Stern-Gerlach/spin experiments, and there were several different approaches to reasoning with matrices and operators that were perhaps more important than all the others. David Spector (talk) 11:13, 13 July 2023 (UTC)

I've proposed to put my draft up as a page: Wikipedia_talk:WikiProject_Physics#Proposal_to_create_and_adopt_"Teaching_quantum_mechanics"

Follow up there, one way or another.

Resolved

Johnjbarton (talk) 16:54, 16 July 2023 (UTC)

The Uncertainty Principle is not Part of Quantum Mechanics

I'm not sure why so many physicists have stated that Heisenberg's Uncertainty Principle (HUP) is a basic part of the strangeness of QM. It is not any such thing.

I would ask them, is the equivalent inverse precision principle due to Joseph Fourier (and others) between the amplitude and the frequency of an audio or electromagnetic signal also part of QM? Or can you physicists out there finally admit that the inverse precision of measurement of complementary variables is entirely due to the interdependence of the two variables, one of which is the derivative or the Fourier transform of the other?

The HUP is usually expressed as $\sigma _{x}\sigma _{p}\geq {\frac {\hbar }{2}}~~$. But this scales up without difficulty to the classical regime, in which complementary pairs of variables are not treated as a mystery, merely as the natural result of measurement: it takes one measurement in time to fix the position of a particle, but many such measurements in time reduces the accuracy. Inversely, it takes many measurements in time to measure velocity accurately, but measuring only once reduces the accuracy. David Spector (talk) 16:22, 13 July 2023 (UTC)

I think considerations like this might fit on Uncertainty principle but I don't think we should get into Fourier analysis on this page. Fourier analysis applies to other waves than quantum probability amplitude, so yes if you accept matter waves then uncertainty principle is not additional information. However, it is a consequence and not something you expect if you are, well, unsure about matter waves. Johnjbarton (talk) 17:06, 13 July 2023 (UTC)

You're right in the sense that the uncertainty principle is inherent in the properties of all wave-like systems. But it is an important aspect of QM (and is almost always taught as such) due to the matter wave nature of all quantum objects. What learners find 'weird' is that the Principle applies to things they'd always thought of as particles, not waves. So of course it is important to discuss it on this page. MichaelMaggs (talk) 17:22, 13 July 2023 (UTC)

@MichaelMaggs oh uncertainty yes, Fourier no. Johnjbarton (talk) 18:16, 13 July 2023 (UTC)

Absolutely. Agreed. MichaelMaggs (talk) 19:34, 13 July 2023 (UTC)

Matter waves really exist, but have nothing specifically to do with the HUP. Also, matter waves are not a complete description of matter. While position and momentum are included, mass is not. Gravity is not yet a part of QM, and it would be misleading to imply otherwise. Since matter waves are not yet complete (they do not account for mass/gravity), and since they are not a justification for HUP, they are irrelevant to the discussion of HUP.

These objections by John and Michael do not address the points I actually made. Nor do their points justify the continued inclusion of the HUP in this Introduction article. David Spector (talk) 17:57, 16 July 2023 (UTC)

It would be perverse not to discuss the uncertainty principle in an introductory page on QM. I can't see any statement on the page that misleadingly implies that gravity is part of QM, but I don't see that that has much relevance to whether the uncertainty principle should be discussed in any event. MichaelMaggs (talk) 18:08, 16 July 2023 (UTC)