Talk:Action (physics)

Symbol ${\mathcal {S}}$ ?? Same as Entropy ???

I am extremely surprised : ${\mathcal {S}}$ is the symbol of the Entropy. Could any one confirm that this symbol is also used for the Action ? With good references ? Thank you.
Valp (talk) 12:28, 20 April 2021 (UTC)

There are many more distinct physical concepts than there are symbols, so overloading of symbols is unavoidable. Get used to it. JRSpriggs (talk) 02:09, 21 April 2021 (UTC)

Entropy is usually written with a roman S not a cursive S. If it makes you happier, you can always use H for entropy, the way they do in probability-land. All you have to do is to pretend you don't know what a Hamiltonian is. 172.58.187.109 (talk) 01:00, 16 August 2021 (UTC)

Reorganization/clean up needed

The article has a hodge-podge of duplicated topics; the Introduction was about Hamilton's principle.

I wrote a new introduction focused just on action and added a section on quantum of action. I moved the older introduction down into the TOC where the Hamilton principle was discussed. Still a mess.

One high priority is a section enumerating the many different names for least-action-like principles. Simply using them as heading is confusing. Johnjbarton (talk) 03:16, 5 November 2023 (UTC)

I tried adding a section listing the variational principles, but now I will try a reorg that moves all of the principles as subsections. Johnjbarton (talk) 15:21, 5 November 2023 (UTC)

The new org is in place:

• introduction
• history
• definitions
• action principles

Still need some clean up and additions. Johnjbarton (talk) 16:08, 5 November 2023 (UTC)

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)