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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]

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]

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]

In Applications > General Relativity the action R (the scalar curvature) is attributed to Hilbert. It is now generally accepted that this view is wrong: that Hilbert did not reach this form for the action until after Einstein had published it. This new understanding arose from study of the time-stamped page proofs of Hilberts original submission and his final submission prior to publication. This examination was first described in Leo Corry, Jürgen Renn, John Stachel: "Belated Decision in the Hilbert-Einstein Priority Dispute", SCIENCE, Vol. 278, 14 November 1997. It has since been studied and supported by other historians of science and studying the same and related archival material. FinnLS (talk) 17:16, 19 March 2026 (UTC)[reply]

The article already uses "Einstein-Hilbert". The Corry/Renn/Stachel article is not about the history of action principles, but is related to General relativity priority dispute. Johnjbarton (talk) 17:53, 19 March 2026 (UTC)[reply]