Talk:Action (physics)

Critique of section Action_(physics)#Abbreviated_action_(functional)

The following critique was left the section Abbreviated_action_(functional) in Dec. 2023:

1. Add citations.
2. Define $\mathbf {p}$ and $\mathbf {q}$.
3. Reorder discussion so that the definition of abbreviated action comes before the discussion.
4. Justify why this is called abbreviated action and the difference from non-abbreviated action.

Johnjbarton (talk) 17:02, 6 December 2023 (UTC)

Making these fixes is much harder than one might expect. Different source give different definitions of abbreviated action, all of which are mathematically equivalent. But the sources I'ves seen that use the most common and transparent form, as given in the section do not call it "abbreviated action". I can add a reference but it amounts to synthesis because I am applying the math.

Since the source barely agree on the formula and not at all on the name (if they use one at all), I have found no source on why is it called "abbreviated action". On the other hand no source explains "action" has its name or "Hamilton" had his name for that matter. Names don't need to have a justification. Johnjbarton (talk) 17:53, 6 December 2023 (UTC)

Hi Johnjbarton, thanks for looking into this and the improvements you've already made. If there are sources that provide the formulation currently given in the section, but don't call it abbreviated action, then perhaps don't call the section "abbreviated action"? (Is there another name for it?) We could mention the other formulations at the end of the section and the fact that those other sources call it "abbreviated action".

I agree that names don't need justification, but in this case, the similarity between the names "action" and "abbreviated action" prompts one to wonder why they are both called "actions" and what makes them different. It's clear that at some point some author thought they were somehow "abbreviating" actions in this definition. The-erinaceous-one (talk) 08:25, 7 December 2023 (UTC)

The problem is "it", not the name. Authoritative sources call this action "abbreviated action", but the use a formula with $p_{i}{\dot {q}}_{i}dt$ rather than $p_{i}q_{i}$. Mathematically these are the same. I suppose I should just go ahead.

I believe "abbreviated" comes from $S=W-Et$, as in "shortened" by $Et$. I'll be on the look out for a ref. Johnjbarton (talk) 17:52, 7 December 2023 (UTC)

Validity of claim “ Action is quantized: the smallest value ( ℏ / 2 \hbar /2) is limited by Planck's constant.[1]”

This seems to frankly be nonsense. The claim is unsourced and not expanded upon in the citation.

Action and angular momentum share a unit, and the projections of angular momentum measurements are quantized into intervals of n times hbar/2 . This does not mean that action is also quantized in the same way. They are two separate concepts. As action isn’t even really an observable in QM (broad strokes, potential edge case definition issues to that statement) I think the claim that is measurable is extremely out of place here.

While not really citations, the following links provide relevant discussion.

Mark John Fernee’s answer here https://www.quora.com/The-Planck-constant-is-the-smallest-possible-amount-of-action-What-is-action-and-why-is-it-so-central-in-quantum-mechanics

Arnold Neumaier’s answer here https://physics.stackexchange.com/questions/348092/in-what-sense-if-any-is-action-a-physical-observable#:~:text=Numerous%20physicists%20finish%20their%20university,over%20a%20lapse%20of%20time.

I recommend the removal of the statement.

In case anyone is wondering why I said action isn’t really observable, here is a relevant discussion. https://www.physicsforums.com/threads/is-action-truly-an-observable-in-physics.436955/ My view is that it is at the very least not a simple operator on a hilbert space, please don’t push me to hard on that. (Path dependent, non local in time, etc.) Zach7898 (talk) 22:50, 30 January 2024 (UTC)

The reference (Lorenzo J Curtis) says

• The ‘mechanical action’ (orbital angular momentum) is quantized in multiples of 2(¯h/2), and is associated with the ‘parity’ or handedness of an atomic state.

So I infer that this source considers angular momentum representative of action rather than a merely sharing its unit. That would cover the "observable issue".

Also we need to explain why Planck called his constant "quantum of action" if it is not quantized.

I agree that these two lines of reasoning are weak, but so are the online discussions.

I don't think this claim merits the intro however. I will replace it with a claim about quantum effects appearing when action compares to hbar. Johnjbarton (talk) 00:04, 31 January 2024 (UTC)

ok I did that much. Johnjbarton (talk) 00:10, 31 January 2024 (UTC)

Seems like a reasonable change to me. It should at least help avoid some misunderstanding in the intro. But I honestly don't think the Lorenzo source is great, its pretty much the only paper I can find that makes that kind of statement so definitively, and it has only been cited by one other. On page 1268, he also says these properties are applied on elementary particles. The statement, "The smallest possible action is $\hbar/2$; larger action values must be integer multiples of this quantum." makes no such distinction, and honestly, I think even with this distinction, there is problems associated with quantized action as it would relate to linear momentums.

Even accepting that the author has intrinsically linked action and angular momentum, the language will confuse others, and cause people to fail on separating the two concepts. Looking around at a bunch of amateur science blogs, it seems to already have. Honestly, I think the aforementioned sentence does more damage than good just by its very inclusion, and should be removed.

Unfortunately I can't ask Planck what he meant, he himself may have had a misunderstanding. The field was moving incredibly quickly at the time, and some theories even postulated quantized action. Perhaps in hindsight, he may have referred to it differently.

I would love to hear others opinions as well.

TL;DR I have personally never seen any widely used interpretation of modern QM that has quantized action, which is what the Lorenzo source implies. I think it's inclusion in the article is problematic, and causes more trouble than it is worth. Zach7898 (talk) 22:35, 29 July 2024 (UTC)

"Unfortunately I can't ask Planck what he meant," Please see his Nobel lecture. Johnjbarton (talk) 22:45, 29 July 2024 (UTC)

I've read it. Unfortunately I can't ask Planck "to expand on exactly" what he meant by "quantum of action. Or if he believed in quantized action at the time, or if he would change his wording in hindsight." I don't think that statement invalidates the rest of what I said though, which is that I believe it is incorrect to say that the smallest possible action is hbar/2. It may be a fine enough statement in the context of the bohr model, or even PURE atomic transitions, but QM has come a long way since then, and I can't find a widely sourced recently modern paper or source which makes such a strong claim, that THE SMALLEST possible value of the action integral must be hbar/2. Zach7898 (talk) 14:41, 30 July 2024 (UTC)

That's pretty much how they quantized things back in the days. Then they also added ½ (so harm. osc. quantization would work, I assume). Ponor (talk) 15:10, 30 July 2024 (UTC)

Yep. But that's not how things are quantized in modern times as far as I know, and the path dependence of the action integral leaves me worried about such explicit statements about action, especially considering more complex systems. It also seems that it will cause people to confuse "action" with angular momentum. (Which, for atomic systems, can be pretty explicitly linked. As they were in the old quantum theories, but those were generally LIMITED to atoms.) But nowadays, I guess I'd say quantization is a result of commutation relations and just the general form of the shrodinger equation. Generally quantized action isn't really a common thing anymore, especially as explicit multiples of the spin projection value of particles. (Which is where hbar/2 comes from as far as I can currently tell.) Zach7898 (talk) 15:21, 30 July 2024 (UTC)

It can be mentioned, somewhere in passing, (+linked to Old quantum theory) as it is part of the old quantization rule. Schiff mentions it: "This rule is applicable to Hamiltontan systems in which the coordinates are cyclic variables, and states that the integral of each canonical momentum with respect to its coordinate over a cycle of its motion must be an integral multiple of h. The rule was applied with considerable success to the computation of the fine structure of hydrogen, the spectra of diatomic molecules, and other problems." Gasiorowics says: "a more general statement by Sommerfeld and Wilson... was of no help in treating problems other than those associated with atomic levels of hydrogen". The only time I used it was in a high school physics competition, they asked us to quantize the motion of a particle bouncing between two walls. I would see it applied to some toy models in condensed matter phys. every now and then. Just saying; I haven't read the article (yet). Ponor (talk) 15:38, 30 July 2024 (UTC)

Schiff https://physicsgg.me/wp-content/uploads/2021/01/schiff-l.i.-quantum-mechanics-mgh-1949t417s.pdf

Gasiorowics http://sampa.if.usp.br/~suaide/MecQuantica1/Quantum%20Physics%20-%20Stephen%20Gasiorowicz.pdf

Were these your sources, could you maybe give the page numbers or sections?

For your highschool example (impressive highschool) that makes sense. You can pop out multiples of plancks constant quite easily with particle in the box.

Essentially, the question being asked here is,

1) Is action quantized? If not, how should Planck's wording of "Quantum of Action" be explained, preferably to a general audience.

2) Should the section "Planck's quantum of action" be changed.

For the first one, I think a bigger discussion may be necessary, but I honestly don't think Planck's specific wording should be taken as gospel either way.

For (2), I think it should be. Specifically, the statement that there is a smallest possible action value, and that it is equal to \hbar / 2, should be removed. I general, I think the Lorenzo source makes use of a lot of language that is ripe for misinterpretation, and just shouldn't be cited or used here, for the clarity of newcomers if nothing else. Zach7898 (talk) 16:09, 30 July 2024 (UTC)

Schiff p4, Gasiorowicz p19. I wouldn't put it as "action is quantized"; I'd say that sometime in the past they applied the rule(s) of int(p dq) being n or n+½ to solve some very specific problems, which worked, until it didn't. I think what Schiff says is better suited for "Planck's quantum of action" tbh. It's not some grand rule (as I understand it), but it was useful in some ways. "Quantum of action"... just an old (silly) name because of (idk) units or the int(p dq) rule. See also Planck_constant#Statistical_mechanics. Ponor (talk) 17:19, 30 July 2024 (UTC)

Thanks for the location of the statements!

I agree with pretty much everything you said. Zach7898 (talk) 18:02, 30 July 2024 (UTC)

I read the Lorenzo source. It's excellent on what it covers, which is an argument for action based physics to replace Newtonian mechanics in introductory physics. It is not a secondary source for the quantization of action. I deleted the sentenced that used the ref. Johnjbarton (talk) 17:52, 30 July 2024 (UTC)

That was my impression as well (I didn't get around to reading it completely), considering that spin as a concept was only mentioned once. It's probably too niche for this purpose.

I think that is a good way of relieving confusion. Thanks for the communication! Zach7898 (talk) 18:01, 30 July 2024 (UTC)

I deleted one more sentence in the Planck section. It was mangled, off-topic, and not directly supported by the ref. I moved the ref to a new sentence which directly relates to the ref. Johnjbarton (talk) 18:03, 30 July 2024 (UTC)

Returning the general topic of "is action quantized?", after recent deletes our treatment has two flaws of omission: 1) Planck's arguments were based on statistical physics, both his original Planck's law work and his Nobel comments. This is not an old-quantum theory thing, but a fundamental aspect of observed physics. (The same kinds of arguments were used by Einstein and used as the main arguments for atoms and molecules until mid-20th century). However I don't know of a source showing how action relates to statistical physics. 2) Planck's constant is very commonly referred to as the smallest sensible length, which is equivalent to a quantum argument. I don't know if any source connects this to action but it may be a good place to look. Johnjbarton (talk) 18:13, 30 July 2024 (UTC)

Unfortunately I don't know of a great source either. I'd say that it seems like modern uses of action as the path integral of langrangian don't seem to make any constraints that would enforce quantized solutions for GENERAL systems/subsystems, which makes me think that modern QM does not consider action to be generally quantized, but I can't find a great source for that claim. Zach7898 (talk) 20:12, 30 July 2024 (UTC)

In the statistical case, maybe the term "quantum of action" refers to changes in action as in radiation, not to action as a functional dependence being quantized. So the action resulting from each path integral is not quantized, but rather the least action we find has a value that can only change by quanta. Anyway I'll keep looking. Johnjbarton (talk) 22:05, 30 July 2024 (UTC)

Not a big deal, but a very modern reference to 'quantum of action', again unexplained:

• Kiefer, Claus, Quantum Gravity, 3rd edn, International Series of Monographs on Physics (Oxford, 2012; online edn, Oxford Academic, 24 May 2012), https://doi-org.wikipedialibrary.idm.oclc.org/10.1093/acprof:oso/9780199585205.001.0001, accessed 20 July 2024.

In the section "1.1.3 Relevant scales" Johnjbarton (talk) 01:54, 31 July 2024 (UTC)

This site has a diatribe on action quantization which ends with a long list of references

• https://www.motionmountain.net/actionquantum.html

I suspect a number of these references will give minimal insight, but the list is long and it does seem like there is a thing called "action quantization", eg Einstein–Brillouin–Keller action quantization. Johnjbarton (talk) 00:38, 1 August 2024 (UTC)

Sorry about delayed replies, work often distracts me for long periods of times.

I saw that motionmountain blog. The fallacies section is interesting, but, I sure wish they provided specific proofs or citations for each claim as opposed to a big section at the end for everything.

Generally, I don't have a problem with considering action as effectively quantized in SOME way, I can see it being quantized at the point of measurements for example. Change in action being h or hbar also makes more sense to me than hbar/2, as that is the gap between projections of spin for any particle, but it doesn't seem easily supported for larger systems. The citations from that source though are interesting. Zach7898 (talk) 16:01, 6 August 2024 (UTC)

" It must be stressed that the statement "action is quantized" refers to the measured values of the action. In quantum theory, this is a statement on the eigenvalues of the action operator. "

This statement from that site is fully reasonable. Again, I don't really know how it holds up for things like QFT, but uncertainty principle plays a lot in the edge cases I'm thinking of, which they say is addressed.

I am not personally familiar with action being treated as a Hermitian operator, but if it can be, then it's eigenvalues being multiples of hbar would work?

If these sources justify that statement well, I think it would be fine to include it in the article with the emphasis on measurement (and obviously, using hbar instead of hbar/2), but near the beginning of the article may be too much. This is obviously a deep hole and could turn into quite a tangent. Zach7898 (talk) 20:17, 6 August 2024 (UTC)

In a mechanical system

@Ldm1954 changed the first few words from "In physics" to "In a mechanical system". My first thought, and I suppose for many readers, a mechanical system is something like my HVAC system or maybe factory. As far as I know the vast majority of uses of "action (physics)" occur in the field of physics for the purpose of developing equations of motion from guesses of interaction potentials. I suppose one could argue that (physical) chemists or similar scientists also use "action (physics)", but I would argue they are borrowing a technique of physics for application in their area of work.

Maybe there is another way to word this "field-of-the-term" phrase? Johnjbarton (talk) 14:41, 21 July 2024 (UTC)

Please go ahead and edit. There are/were stacks of "In chemistry" and "In physics" starts to pages most of which are inappropriate. An alternative is "in science", although that is a bit clunky. For certain a mechanical engineer would object to the "In physics" for action. Ldm1954 (talk) 14:48, 21 July 2024 (UTC)

Ok but so far we don't have any content about the use of the term in mechanical engineering, so for now I'll just change it back. Johnjbarton (talk) 14:55, 21 July 2024 (UTC)

It is the same context, so I would prefer a more general term. Maybe "In physics and mechanical engineering"?

We have the same thing with Sh's misdefinitions of nonmetal (and material science). Maybe pedagogically we teach individual topics at times, but in the 21st century everyone follows the science (& money) as you know. It would of course by ludicrous to say that you can't write code because you don't have a degree in computer science...etc. Ldm1954 (talk) 15:00, 21 July 2024 (UTC)

"Symplectic action" listed at Redirects for discussion

The redirect Symplectic action has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 July 28 § Symplectic action until a consensus is reached. 1234qwer1234qwer4 13:39, 28 July 2024 (UTC)