Talk:Classical limit

Untitled

I think that this should also include something about the classical limit in statistical mechanics e.g. regaining the classical distribution function of the ideal gas from the Fermi-Dirac distribution function in the dilute limit (i.e. classical limit). Hence, I don't think this should be merged with correspondence principle; or at least, should have a disambiguation page that distinguishes between classical limit (quantum mechanics) and classical limit (statistical mechanics).

This Wiki entry suggests that the limit hbar goes to zero recovers classical mechanics.

This is not actually true.

The Planck constant is a dimensional parameter. For any rescaling of the units the entire quantum mechanical theory is still present. To say that one theory goes over into the other theory is mathematically false. This fact was demonstrated by K.R.W. Jones in 1991 and was the subject of the Wiki post The Classical Schroedinger Equation which was subsequently deleted.

I suggest that this post be appropriately edited to highlight that discovery. — Preceding unsigned comment added by 202.146.6.240 (talk) 22:50, 8 October 2013 (UTC)

You may well be misreading the clear statements provided. Deformation parameters are in dimensionless ratios, and that includes ħ/S, so the classical limit is approached in a quantifiable sense for large action systems. Please read up on introductory QM articles (e.g. Correspondence_principle#The_quantum_harmonic_oscillator ), and the phase space formulation which might exemplify the systematics of the process more explicitly. You cannot make mathematical statements on something as poorly defined as misconstrued straw-man "suggestions". This talk page, however, is not a newsgroup discussion forum. Please seek an appropriate venue. Cuzkatzimhut (talk) 11:19, 9 October 2013 (UTC)

Discussion on proposed merger??

I'm not sure what the merger proposal is about, but, on the face of it, I see no reason why that article there , Newtonian limit, is not fine in its logical autonomy. The classical limit of Moyal brackets to PBs here is a very different contraction than the Newtonian limit contraction of curved Geometry to flat space. I hope the proposer is not conflating all group contraction limits in physics and expect to see them under the same roof. Cuzkatzimhut (talk) 23:56, 8 May 2019 (UTC)

The term classical limit refers to taking the framework of either the quantum world or the world of relativity, to retrieve the classical (see Newtonian) behaviour. In the quantum world, this is usually when h → 0, and in relativity this is when v/c → 0 (or in weak gravitational fields). There are different types of classical limits, but they are nonetheless all classical limits. If a decently-done merger, the relativity section of this article would be expanded with the content found in the current version of Newtonian limit. I accept the usage of 'Newtonian limit' is usually applied to the relativity side of things, but there are plenty of examples from the quantum world (e.g. [1], [2], [3], etc...). Headbomb {t · c · p · b} 00:03, 9 May 2019 (UTC)

There is also a separate meaning, related to the Newtonian limits in fluid dynamics. This refers to limits where fluids behave as Newtonian fluids. This one isn't a type of classical limit, so the plan would be to disambiguate Newtonian limit to clarify its multiple meanings. One being classical limits, the other concerning various things called 'Newtonian' behaviour (off the top of my head, I know only of the fluid dynamics situation, but there could be others). There could be some Newtonian limits that apply to finite element analysis or whatever else Newton touched. Headbomb {t · c · p · b} 00:32, 9 May 2019 (UTC)

If anything, I should think WP should contrast, not conflate completely different concepts and processes confusingly characterized by the same term "Newtonian". It is clear the Bricman et al. books and refs should have never abused the term "Newtonian", when they only mean "classical mechanics", in contrast to quantum mechanics; this is precisely the bad pompous terminology routinely confusing readers. The clueless reader would google their way into here, and be further confused, rather than have their confusions dispelled! If anything, the Newtonian limit article should have a disclaimer of sorts, contrasting the Minkowskian limit they are discussing with the vanishing/subdominant $\hbar$ considerations of these unfortunately worded books. So, my sense is that WP should try to alleviate the damage, rather than enhance it by throwing all pots on the fire implying non-existnt logical linkages... While it is true that GR and QM are all deformations of classical, "Newtonian" concepts, they go in such aggressively disparate directions, conceptually, that an emphatic effort should be put in contrasting them. As it stands, the final section here dramatizes the different directions that modern physics extended older, "classical" physics; but implying nonexistent, indeed, deprecated, conceptual unities in the different deformations is really not cool... Cuzkatzimhut (talk) 14:57, 9 May 2019 (UTC)

There is no conflation. Both are classical/Newtonian limits, and both refer to the same thing: finding the usual results of classical physics in the conditions where classical/newtonian physics apply. In the case of quantum mechanics, that's h → 0. In the case of SR, that's v/c → 0. In GR, that's flat spacetime + v/c → 0. Yes the starting points are different, but the landing place is the same. And getting to that landing place is the entire point of taking a classical/newtonian limit to begin with. Headbomb {t · c · p · b} 18:24, 9 May 2019 (UTC)

Sure, connecting to "classical physics", as a generic rubric is the "point", but the devil is in the details. Both the origins and the destination points are really, really different. The 3 items you mentioned are conceptually so disparate and methodologically disjoint, that special care must be taken to firmly contrast them, and prevent specious "analogies" or "parallels", that I have watched students tying themselves into logical knots forever, imagining connections that are not only absent, but actually meaningless. If a responsible job were done in avoiding bogus connections, it might be a good idea. But I already registered my revulsion at the pompous misuse of "Newtonian" to impress the confusable... You may have already noticed the conceptual erosion wreaked by the Ehrenfest map insert section. The QM classical limit is a nasty, controversial subject thriving on systematic abuse of a terminology expressly designed for that very purpose... Let's cross fingers and hope for the best.Cuzkatzimhut (talk) 22:11, 9 May 2019 (UTC)

The origin is different. The destination is not. These are not analogies or parallels, those are example of the same broad concept: Finding the classical/newtonian behaviour from a non-classical/modern/post-newtonian theory. Your personal preference of restricting the use of "Newtonian" to the Einsteinian/non-Einsteinian dichotomy is not supported by sources. Headbomb {t · c · p · b} 22:25, 9 May 2019 (UTC)

Just so we are clear: calling Liouville’s theorem violations , which is what it is all about, post-Newtonian is indefensible ; calling that theorem Newtonian asks for trouble. I’ll keep my peace until the stuff emerges....Cuzkatzimhut (talk) 02:52, 10 May 2019 (UTC)

Most physicists I know seem to regard relativity, both special and general, as "classical". For example, it would be typical to say, "We believe that general relativity is the classical limit of an as-yet-unknown quantum theory of gravity." This leads me to incline against the merge. Of course, people can be sloppy with their terminology, but we should follow the example of the most careful. XOR'easter (talk) 15:01, 10 May 2019 (UTC)

I've never heard of even one that would consider SR/GR classical physics. The very term classical contracts modern physics, which is specifically anything that has elements of QM or SR/GR. There is classical EM, as a contrast to QED, however. Headbomb {t · c · p · b} 20:14, 11 May 2019 (UTC)

A Google Scholar search for "general relativity" "classical limit" finds in excess of 8,000 results. "Classical general relativity" finds over 8,600, of which the very first is "Classical general relativity derived from quantum gravity" (Boulware and Deser 1975). Zwiebach's First Course in String Theory speaks of classical gravitational waves. Carlo Rovelli's 2007 textbook on quantum gravity states, "The first conclusion of loop gravity is that ... a quantum theory that has GR as its classical limit appears to exist. In order to merge, both QM and classical GR have to be suitably formulated and interpreted. ... QM modifies the picture of the world of classical GR as well." Robert Wald's General Relativity (2010) says, "Hence, classical general relativity certainly should break down at or before the stage where it predicts spacetime curvatures of order $l_{\rm {P}}^{-2}$. Although the singularity theorems do not prove that the singularities of classical general relativity must involve unboundedly large curvature, the strongly suggest the occurrence in cosmology and gravitational collapse of conditions in which quantum or other effects which invalidate classical general relativity will play a dominant role." John C. Baez and Javier Muniain write, in their Gauge Fields, Knots and Gravity (1994), "By the same token, the reader should take with a grain of salt anything we write about quantum gravity (as opposed to, for example, the new variables in classical general relativity), since today's conventional wisdom could easily be overthrown tomorrow." Stephen Hawking wrote, "Classical general relativity is a very complete theory." And if electromagnetism can be classical, then special relativity is classical. XOR'easter (talk) 21:24, 11 May 2019 (UTC)

Yes, but in the context of classical limit, it's not referring to a limit to 'classical relativity', but to newtonian physics. Headbomb {t · c · p · b} 23:15, 11 May 2019 (UTC)

All of these regard general relativity as a classical limit. Rovelli says it explicitly: "a quantum theory that has GR as its classical limit". Or, quoting Boulware and Deser, "a quantum particle description of local (noncosmological) gravitational phenomena necessarily leads to a classical limit which is just a metric theory of gravity." Or, Perez and Rovelli: "Can we get stronger evidence that the model gives general relativity in the classical limit?" Or this paper making a proposal for "General relativity as classical limit of evolutionary quantum gravity". That's the thinking at work. Classical does not contrast with modern, but with quantum. XOR'easter (talk) 00:08, 12 May 2019 (UTC)

Yes, special and general relativity are considered both modern and classical. Modern in the sense that it is a newer development of physics, which coincided closely with the era of quantum mechanics. Classical in the sense of how to describe the fundamental aspect of the subject matter itself. There is a distinction in the field between classical things that describe continuum type properties vs. quantum that has discrete properties. Until there is a complete description of quantum gravity then there is only a classical description of general relativity Cosmojellyfish (talk) 18:37, 24 September 2019 (UTC)

I support the idea of keeping the page and demystifying how the terminology "Newtonian limit" is used. Cosmojellyfish (talk) 18:37, 24 September 2019 (UTC)

DittoCuzkatzimhut (talk) 14:55, 25 September 2019 (UTC)