Talk:Classical mechanics

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@Quondum I'm puzzled by your {{dubious}} tag. The content is:

• The qualifier classical distinguishes this type of mechanics from physics developed after the revolutions in physics of the early 20th century, all of which revealed limitations in classical mechanics.

The stated reason for the dubious tag is: The term "classical mechanics" is used variously by different authors, both to include and exclude relativity, and should not be taken as defined by one author. The development of analytical and descriptive methods and tools as described next that do not change the underlying model of Newtonian mechanics, which is a clearer term.

The content is sourced and I don't think it is dubious. I agree that some authors may use the term more narrowly. For example, a source about physics in the early 1920s would likely focus on QM vs classical, while a book on relativity may call mechanics for v<<c "classical mechanics". Some authors may explicitly include relativistic effects in discussions of classical mechanics but in terms of a neutral point of view I think that is rare. A good example is Goldstein's "Classical Mechanics" which discusses relativity "on the side".

Your challenge seems to indicate you have another source with a different definition, perhaps a source that covers "classical mechanics" with relativity built in? If you don't wish to add content to match, please post that source and I'll take a shot at it.

In my view "Newtonian mechanics" is not a synonym for "classical mechanics" because sources distinguish different aspects of classical mechanics using "Newtonian" for particular formalisms and techniques. Thus Hamiltonian mechanics is classical mechanics but not Newtonian mechanics.

How can we address your concerns? Johnjbarton (talk) 15:17, 18 August 2025 (UTC)

This stackexchange answer says: In advanced physics circles, "classical mechanics" always means something very specific, and it doesn't mean "Newtonian". Classical means not quantum. My own experience is in line with this, with the caveat that I am not a trained physicist. Einstein's general relativity is typically called a classical theory. Sean M. Carroll uses it this way to my memory. Penrose refers to "The classical fields of Maxwell and Einstein" in The Road to Reality. I think this use is widespread enough that we would find many serious physicists cocking an eyebrow at this claim in the article.

"Classical mechanics" is a convenient label that authors use to make a distinction that they want to make. Defining it is IMO a dictionary function; I don't think its use as a classification is a topic in itself, and as such I don't think it really makes sense to have an article on it. OTOH, I have no inclination to try to persuade you of any of this. —Quondum 16:44, 18 August 2025 (UTC)

Classical Mechanics (3rd ed.) by Goldstein, Poole and Safko says, "In the past century the term 'classical mechanics' has come into wide use to denote this branch of physics [i.e. mechanics] in contradistinction to the newer physical theories, especially quantum mechanics. We shall follow this usage, interpreting the name to include the type of mechanics arising out of the special theory of relativity." On the other hand, undergraduate courses in "classical mechanics" explicitly exclude relativity, and the reader is likeliest to seek this meaning. In light of the concerns raised, it is justifiable to describe the semantics of the term "classical mechanics", but we need an article to describe Newtonian mechanics and the mechanical theories compatible with it such as Hamiltonian mechanics, and "classical mechanics" is the most well known term for such a topic. Chthe (talk) 18:22, 18 August 2025 (UTC)

"Hamiltonian mechanics" is not a theory, per se. If it is used to describe Newtonian mechanics, this does not stop it being the Newtonian theory ("Newtonian mechanics"). It is just a different formalism of the same theory. How would you describe Hamiltonian methods as they are applied to special relativity, general relativity, and quantum mechanics? Surely these are using the same formalism, but with a different underlying theory ("mechanics")? —Quondum 18:39, 18 August 2025 (UTC)

Perhaps Newtonian mechanics#Relation to other formulations of classical physics will help? In your paragraph you use "Newtonian mechanics" in the way I would use "classical mechanics". Thus I would say "If it is used to describe classical mechanics...", meaning physical phenomena in the classical regime of relative velocities and sizes. Newtonian and Hamiltonian are equivalents, different treatments of classical mechanics.

Hamiltonian methods as applied to quantum phenomena is (non-relativistic) quantum mechanics, see Hamiltonian_mechanics#Generalization_to_quantum_mechanics_through_Poisson_bracket. The connection is also discussed in Hamilton's optico-mechanical analogy.

Broadly speaking relativity does not mix well with "mechanics". Mechanics typically uses "time" as a parameter, a point of view that relativity explicit rejects. That is why theories like Modified Newtonian Dynamics and Bohmian mechanics struggle with relativity. Field theories that work within a geometry that incorporates time (eg spacetime), like general relativity or quantum field theory, are more successful. I don't know that Hamiltonian methods in general relativity have had success. Johnjbarton (talk) 19:15, 18 August 2025 (UTC)

This article is about "classical mechanics". The "mechanics" part means models addressing the motion of bodies. The qualifier "classical" is used in other ways, say "classical field". So general relativity is a classical field theory even though it includes special relativity. So the case of fields, its always "classical" vs "quantum". Thus sources like Carroll and Penrose are fine, but they are about a different topic.

I'm sorry that physicists are not completely uniform in how they use this term, but as a modifier of "mechanics", "classical mechanics" does not generally include relativity. Johnjbarton (talk) 18:50, 18 August 2025 (UTC)

Agree with Quondum. Classical mechanics work exactly as advertised in special relativity, and general relativity is undisputably a classical field theory, despite being much more difficult. Tito Omburo (talk) 21:37, 18 August 2025 (UTC)

I seem to have run into an issue of how the article should present this. Perhaps we should instead just start with a contextualizer, rather than assuming who the reader is? An article hatnote, or a footnote to the first use of "classical mechanics", saying in effect that in more advanced contexts this often includes essentially all non-quantum approaches? My main issue is that many readers will sit with some dissonance without this framing. —Quondum 21:48, 18 August 2025 (UTC)

Let me take a guess based on the several mentions of general relativity above: your concern is related to classical field theory eg general relativity being confused with classical mechanics? If so then perhaps we need to include a section in the article connecting field theories with mechanics (via gradients and potentials). Then we can include a summary sentence in the intro. Would that help?

General relativity is a classical field theory and there is a lot of connection between classical field theory and classical mechanics esp around the use of the Lagrangian. But the common name of the subject of this article, mechanics in the classical limit, is "classical mechanics". I have never seen a source include general relativity as a formulation of classical mechanics. Have you? These are both non-quantum approaches but this common feature does not some how make them the same.

I can provide more sources for "classical mechanics" if that would help. Johnjbarton (talk) 22:27, 18 August 2025 (UTC)

I suppose my issue revolves around "classical" being used with such a different meaning in easily confused contexts ("classical mechanics" vs. "classical physics" in the same Wikipedia). At this point, I'm not going to pursue this; I find just communication the issue to other editors too much. I've removed the ^{[dubious – discuss]} tag. —Quondum 12:43, 19 August 2025 (UTC)

Thanks. While you may not be satisfied, your comments lead me to make edits and add references which I hope improved this article. Johnjbarton (talk) 17:48, 19 August 2025 (UTC)