Talk:Action principles

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Merge proposal

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

The result of this discussion was merge

I propose to merge stationary action principle into this article, action principles.

The terminology of action principles is inconsistent between sources. This issue is discussed in History_of_variational_principles_in_physics#action_principle_names. For the purpose of the merge, the important part is that "stationary action principle" is not universal or maybe even commonly used. The name "action principles" encompasses all of the names.

The content in stationary action principle is contained in action principles. Summaries of the various articles in wikipedia about action are included in action principles. Consequently redirecting stationary action principle to action principles should be an improvement. Johnjbarton (talk) 18:36, 22 May 2024 (UTC)[reply]

Merge: in textbooks, the use of "stationary action principle" vs "minimal action principles" is not always consistent, while "action principles" is.--ReyHahn (talk) 10:38, 23 May 2024 (UTC)[reply]

Comment ~~weak-don't~~. The article on action principles is already quite long, and provides a good general overview. Long articles contribute to reader fatigue and glazed-over eyes as one hunts for the desired info. Meanwhile, stationary action principle could be greatly expanded, in a variety of ways. One way is to include/expand a discussion of the principle of stationary phase, which is not uncommonly used in a variety of settings where the action occurs. Another reason, perhaps generally unknown to readers coming from a physics background, is that the definition of a geodesic in Riemannian geometry (and in pseudo-Riemannian, i.e. general relativity) is given as the stationary (often minimum) of the action. This is how math books define it; less clear how physics books do it. Lumping geodesics into action principles seems extreme. Finally, there's some obscure but neat stuff: turns out that inside of black holes, there is a (recently-discovered, i.e. about 10 years ago) surface that maximizes the action (I forget the buzzwords) This is in contrast to ordinary space, where, say, the volume of the inside of a sphere is defined as that quantity that minimizes the action. (The canonical example is from the theory of minimal surfaces: take a circular metal ring of radius r and dip it into soapy water, and you get a minimal surface of area pi r^2. Waving it in the breeze makes it clear other areas are possible. What's being minimized? The surface tension. Grind through the math, turns out this is just the "energy", or the "action"; the conventional ~~Hamilton-Jacobi equations~~ Euler-Lagrange equations provide the solution. Same deal for black holes, except now its a maximum, because the minimum doesn't exist.) Keeping the article separate allows it to expand to cover fun things like soap bubbles. (For the truly geeky, the fun never stops: harmonic maps are defined by minimizing the action (making Laplace's eqn be zero). Such maps are sometimes called solitons.) Jamming all that into action principles would be overwhelming.

I don't know where I'm going with this. Wikipedia science appears to lack a clear policy the "explain it to a high-school student" vs. "explain it to a grad student/prof". Absent a clear policy, I suggest that action principles can be kept at the "high school level", while stationary action principle could be groomed into some "advanced explanation" article. I dunno. Something like that. 67.198.37.16 (talk) 01:52, 25 May 2024 (UTC)[reply]

Maybe I'm off base, but it seems to me another way to express your comment: action principles focuses on physics but there are many related and interesting mathematically-oriented topics as well but adding them here would not be wise. Is that correct?

Can you point to some books or reviews covering the math area which would use the term 'stationary action principle'. I'm not against repurposing the name and we could have a summary section here to relate the result. My main goal in proposing the merge is to reduce the confusion around the various names used in physics by routing them through this overview. Johnjbarton (talk) 02:49, 25 May 2024 (UTC)[reply]

Ah. OK. You are quite right; it's not called "stationary action principle" in math, and I'm rambling cause its late & I'm tired. Yes, route all of the different forms into one. 67.198.37.16 (talk) 03:07, 25 May 2024 (UTC)[reply]

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

How is shooting free throws related?

What is the purpose of this figure? 210.61.187.232 (talk) 11:04, 17 June 2024 (UTC)[reply]

Thanks, I added text to the caption reiterating the content in the adjacent paragraph. Johnjbarton (talk) 14:49, 17 June 2024 (UTC)[reply]

Suggestion

The example about elliptical orbits of planets shows that the minimum may not be uniquely attained (both paths have the same least action). Can you give an example of a saddle point in terms of action? (i.e., a critical point where some perturbation may increase the action and some other may decrease it) 210.61.187.232 (talk) 11:17, 17 June 2024 (UTC)[reply]

Misleading phrases relying on classical descriptions

In particular the section about paths opens by saying a single path is taken and others are not taken. This fits classical thought but is terribly misleading. In reality a photon traveling from point A to B doesn't take "one path" - it literally takes ALL possible paths simultaneously. We only observe the path(s) that emerge because of the constructive interference of their waves, while wildly different paths cancel out through destructive interference. But all paths genuinely contribute to the amplitude, so saying things are "non-existent" is misleading. We're talking about genuine physical superposition where multiple states coexist. The mathematics bears this out in the wavefunction which assigns amplitudes to every possible configuration, and they all contribute to physical phenomena like interference. And this can be seen experimentally! Example- https://www.nature.com/articles/s41566-023-01212-1 So yeah, I'll do some rewording of these sections to better match our current understanding. BluejayBlackburn (talk) 09:05, 26 May 2025 (UTC)[reply]

Thanks, I can see how the previous content is confusing. I was thinking of this first part as all classical and left the QM for later and in the path integral article.

I removed a sentence you added about simultaneous paths. The reference you linked makes the point about paths very carefully:

Conceptually, one can determine the unique trajectory of a classical object moving from an initial position to a final position, but in quantum mechanics, according to Heisenberg’s uncertainty principle, position and momentum cannot be simultaneously measured. Furthermore, any path connected with initial and final points is possible in quantum mechanics, so a unique trajectory like that in non-quantum physics does not exist. Feynman’s path integral formulation creates a bridge between the classical Lagrangian description of the physical world and the quantum one, reintroducing the classical concept of trajectory to quantum mechanics.

So the idea that all paths are actually taken simultaneously is only within Feynman's path integral formulation. Other formulations don't even have paths. I made some other minor changes. I would like to add a reference for your additions. Johnjbarton (talk) 16:03, 26 May 2025 (UTC)[reply]