added pointer to:

- Garth Warner:
*Lagrangian Mechanics*, EPrint Collection, University of Washington (2009) [hdl:1773/4606, pdf]

Not sure what happened here – possibly a copy-and-paste glitch given that Kibble & Berkshire is and has been the first item of the list of references in the entry.

I have hyperlinked the DOI for Valter’s book – which looks like a great book:

- Valter Moretti,
*Analytical Mechanics*–*Classical, Lagrangian and Hamiltonian Mechanics, Stability Theory, Special Relativity*, Springer (2023) [doi:10.1007/978-3-031-27612-5]

56

added pointer to:

- Tom W. B. Kibble, Frank Berkshire,
Classical mechanics, McGraw-Hill (1966, 1973, 2004) [pdf, Wikipedia entry]Valter Moretti

No you didn’t. You badly linked your own textbook.

]]>added pointer to:

- Tom W. B. Kibble, Frank Berkshire,
*Classical mechanics*, McGraw-Hill (1966, 1973, 2004) [pdf, Wikipedia entry]

Valter Moretti

]]>added pointer to:

- Tom W. B. Kibble, Frank Berkshire,
*Classical mechanics*, McGraw-Hill (1966, 1973, 2004) [pdf, Wikipedia entry]

So perhaps mechanics is mechanics in the narrowest sense —the mechanics of point particles

I do not know which of the historical figures in mechanics – Archimedes, Newton, Lagrange etc. would put point particles separate at least from rigid bodies, vibrating rods and few other simple mechanical continua. But logically this is true nowdays: we can start with discrete, even finite discrete system of point particles and go on with abstracting, taking limiting procedures and so on.

]]>what is mechanics?

Oh, I see. That’s interesting. It wasn’t clear to me that this is now the question (I wasn’t following your exchange with Zoran).

I’ll try to come back to this a little later.

]]>There is a real question here, which ought to be easy to answer but has not been: what is mechanics?

I thought once that I knew the answer, but I was wrong. I looked up the answer on Wikipedia, and that was wrong (and also inconsistent). Nobody else has given an answer.

]]>When supplied with a list you object.

No, I have not been supplied with a list.

I supplied a definition that I learnt; you and Urs objected. Urs gave a definition; you objected. I have been told certain things about the list to which I objected, such as that statistical mechanics and classical optics don’t belong on the list, while field theory does.

But where is the list?

Here is a new idea, which I kind of like:

some theories tries to evolve from starting with mechanics of point particles and taking various generalizations toward quantum fields and so on

So perhaps mechanics is mechanics in the narrowest sense —the mechanics of point particles— and various generalisations thereof? So potentially all of physics, but only to the extent that it is a generalistion of the mechanics of point particles? Then membership on the list would be a matter of degree, with neither statistical mechanics nor field theory being mechanics par excellence, but both close and high up on the list?

I could buy that, but is that what you’re saying?

]]>I have not been following this discussion. I wish similar energy would be invested into getting genuine content into the $n$Lab.

But if the question is still whether the entries classical physics and classical mechanics should be separate:

I think they should. The former lists stuff like thermodynamics which should not be the direct content of an entry on mechanics.

(Incidentally, much of thermodynamics has not even be fully rigorously been derived from mechanics. I once heard a talk by Jürg Fröhlich who had worked on the mathematical foundations of thermodynamics, and I was surprised to hear how comparatively little has been turned into theorems, and how comparatively hard that has already been. )

]]>A delimitation of a subject is a conventional list of topics covered. As such it does not need to be defended, but remembered. When supplied with a list you object. But most of people orient by such lists including many potential users. For mechanics as for algebra there are several meaningful generalities possible. Neither of them is by the definition “all physical reality”, but some theories tries to evolve from starting with mechanics of point particles and taking various generalizations toward quantum fields and so on to believe that at the end that process of the generalization does include all physical laws. This is a meaningful thing, as it can be something of completely different nature complementary to that line of generalization.

]]>Zoran, you write:

Toby, we do not know if all physics can be reduced to mechanics

At this point *I have no idea whatsoever what this would mean*!

When I say physics = mechanics, it is *not* to suggest that all physics can be *reduced* to mechanics, but rather that all physics already *is* mechanics, since nobody has suggested any other meaning of the term ‘mechanics’ (that hasn’t been shown to conflict with established usage).

Later, you speak of ‘mechanics in [the] traditional sense’. Even if this traditional sense is indefensible both theoretically (because it excludes field theories, perhaps) or linguistically (because it excludes things called ‘mechanics’, perhaps), can you explain what this is?

]]>Toby, we do not know if all physics can be reduced to mechanics, but the contemporary opinion is that quantum mechanics together with theory of measurement does comprise all the physics. Quantum mechanics without the theory of measurement has a problem. You know that the wave function has a collapse/reduction in the process of measurement. Nobody know how that happens, is this instanteneous etc. There are interpretations, like Copenhagen says that these questions are out of realm of physics, but not all agree. In any case, the Schroedinger equation, that is the formalism of QM does not explain such things.

On the other hand, while I did agree that statistical mechanics can be taken part of mechanics, it is less true that the classical statistical mechanics can be taken part of classical mechanics in the full strict sense. Usually one starts statistical mechanics (say Feynman’s book or Landau’s book) with quantum picture of counting states, and the classical mechanics is just a case when the general Gibbs distribution is in a limit of Boltzmann distribution. I am not saying that it is impossible to do without quantum picture but even Boltzmann statistics is normally introduced with quantum picture in mind.

I think I can resolve things in the entry once. But I can not be driven by the momentary activities of others, being too busy with different subjects and duties now to pay enough attention to present burst of activities about mechanics pages. Despite agreement with yuo on principal issues I think it is opportune for the $n$Lab to keep different content at classical physics and classical mechanics. Also physics is usually including phenomena, theory and experiment; and by mechanics one only means the mathematical laws of physics (or engineering mechanics which is practical subject which is much more limited). If one wants to have any depth about mechanics in traditional sense in classical mechanics it would not be opportune to have much on thermal physics and so on there. On the other hand, I think one should have less specific of theoretical mechanics on classical physics page.

]]>Toby, we do not know if all physics can be reduced to mechanics, but the contemporary opinion is that quantum mechanics together with theory of measurement does comprise all the physics. Quantum mechanics without the theory of measurement has a problem. You know that the wave function has a collapse/reduction in the process of measurement. Nobody know how that happens, is this instanteneous etc. There are interpretations, like Copenhagen says that these questions are out of realm of physics, but not all agree. In any case, the Schroedinger equation, that is the formalism of QM does not explain such things.

On the other hand, while I did agree that statistical mechanics can be taken part of mechanics, it is less true that the classical statistical mechanics can be taken part of classical mechanics in the full strict sense. Usually one starts statistical mechanics (say Feynman’s book or Landau’s book) with quantum picture of counting states, and the classical mechanics is just a case when the general Gibbs distribution is in a limit of Boltzmann distribution. I am not saying that it is impossible to do without quantum picture but even Boltzmann statistics is normally introduced with quantum picture in mind.

I think I can resolve things in the entry once. But I can not be driven by the momentary activities of others, being too busy with different subjects and duties now to pay enough attention to present burst of activities about mechanics pages.

]]>After reading #43, Zoran, I’m not sure that we disagree any more. You keep arguing against positions that I’ve abandoned, so I won’t repeat that I’ve abandoned them. But in writing ‘Statistical mechanics is in the same way a part of mechanics as chemistry of physics. I have no problem with putting statistical mechanics into mechanics in that sense and I did learn it that way.’, you also seem to be abandoning any attempt to say that statistical mechanics is not part of mechanics. So we are basically left with mechanics = physics.

In #41, you do write ‘Traditionally classical physics is not equating with classical mechanics as a subject.’. However, I think that we’ve proved this false. Or rather, there are several traditions, none of which agree. I suppose that everybody (except maybe Igor?) will agree that chemistry is not mechanics (although I would not now attempt to defend that), but everything else that’s been brought up *has* been considered mechanics by some traditions. So while some fields (such as statistical mechanics and continuum mechanics) have ‘mechanics’ in their names and others (such as thermodynamics and field theory) don’t, no other consistent distinction can be made.

I also agree with you that mechanics shouldn’t be identified with a particular formalism. (Incidentally, I was taught statistical mechanics through the Hamiltonian formalism! Of course, more was added on top of that.)

I like the idea of making classical mechanics and classical physics into overview pages that link to specific branches and formalisms, each on its own page. I just think that the former should redirect to the latter. I suppose that an alternative would be to discuss the various uses of the word ‘mechanics’ and what fields have been thought to be part or not part of classical mechanics, but the list of links on both pages would be duplicated, so we might as well have that discussion at classical physics.

]]>@ Zoran: “What is far less consistent is your distinction between continuum mechanics and a field theory.”

That is *not* my distinction; that is Wikipedia’s. (I probably never should have brought that up; it’s just one place that I went to see if they’d worked out a consistent definition, and they really haven’t, although they seem to think that they have.)

At the moment, having seen that the distinction that I learnt is not generally accepted, I see *no* distinction between mechanics and physics. All of the various ways to specify mechanics as merely one branch of physics have proved arbitrary and not generally accepted.

The way that I learnt it, classical statistical physics, when applied to point particles and rigid bodies, is mechanics, but continuous phenomena are not. You learnt about the opposite.

No Toby, I agree that foundations of statistical mechanics are mechanics. It is just a subject which developed (due its specific differences from the rest) as an independent branch. You know that usual thing that chemistry is part of physics. But still if we extend $n$Lab to chemistry, I think that chemistry should then have a separate entry! Statistical mechanics is in the same way a part of mechanics as chemistry of physics. I have no problem with putting statistical mechanics into mechanics in that sense and I did learn it that way. A newcomer looking for statistical physics and its thermodynamical limit will likely not look under classical mechanics (the latter should have a link somewhere, and I think it has to statistical mechanics and classical statistical mechanics eventually).

When I said that statistical mechanics is not about a matter (I meant many body system) but ensemble my intention was to show that it is strictly speaking formally about a different object than say Hamiltonian mechanics is. I do not say that the difference is very big, but that without defining a new object of study (ensemble) and, in practice, taking new level of independent assumptions, we do not get into the subject. Btw, the expression “statistical mechanics” is not yet involved in the entry classical mechanics so this is yet not critcial when talking the content of that entry.

But excluding continuua like elasticity and vibrating rods from mechanics. Even the engineer mechanics books do not do that and every physics introduction to this starts with a discrete system and INFERs (that is takes as a special case) what happens when the spacing becomes very small (you can call it limit, but physicist may alternatively think of a very small distance between the actual particles).

]]>Urs and Toby: when I created these pages, I had in view, which I still back somewhat that the entries classical mechanics and classical physics are more of disambiguation pages or informal toc clusters *with explanation* for a future expansion of $n$Lab into the physics side; and that as widely used branch names should attract an outsider to the $n$Lab and direct toward what is our content we can provide and its relation to the outside world. That is why I prefer that particular formalisms be in depth developed on pages devoted to particular formalisms.

Toby, of course, statistical mechanics applies to physics, but the content of its models is formally not a concrete matter system, but an abstract ensemble. Statistical physics in practice depends also on many principles which are not provable from pure statistics of mechanical models in general (and most often not true in full generality) like detailed balance and ergodic hypothesis. These principles are getting more clarified in modern, more rigorous research in mathematical statistical mechanics, which is not accounted in these subtleties in most pratical applications of statistical mechanics. I have nothing against considering statistical mechanics part of mechanics, and it is sometimes considered that way, but as a subject it has enough peculiarities to be considered a different BRANCH of physics. What is far less consistent is your distinction between continuum mechanics and a field theory. There is no difference: continuum mechanics is a pretty standard example of a classical field theory. Stress-energy tensor, density (also things like magnetization in more elaborate examples) etc. of the matter in continuum **are classical fields per excellence** just like magnetic field strength, electric field strength in another example of Maxwell theory. Wikipedia usually tends to express the viewpoint of undergraduate textbooks, as far as physics is concerned, which exclude infinite systems from mechanics textbooks, except for (systems of) rigid bodies where there is a reduction of degrees of freedom due constraints.

Traditionally classical physics is not equating with classical mechanics as a subject. Of course, mechanics as a basic subject for all physics, through which variants, limits and slight generalizations in or out of proposed scope, is relevant for all the physics. I agree that at the fundamental level all physics is (quantum) mechanics, at least with what we know nowdays.

Urs: you could see that my explanations in previous entries HAVE a lot of content on aspects of variables and approximation used by various parts of physics. But I can not incorporate that in formal viewpoint which you obviously want (like mechanical systems is Poisson algebras). When I created entries classical mechanics and classical physics I was hoping to put some real physics inside. My education in physics is in condensed matter physics and similar subjects and not abstract novelties like string theory and sigma models where I am mostly illiterate.

]]>Hey Toby,

not sure how to resolve all this right now. If you feel the entries need to be re-arranged, I suppose I’ll be fine with it all.

What I’d like to see most is more genuine content added to all the entries in question.

]]>Certainly there are “standard boundaries” and “historical groupings” that distinguish mechanics per se from the more general subject of physics. However, there are several competing ideas of what this distinction is! You learnt one, Urs learnt another, and I learnt yet a third. (The way that I learnt it, classical statistical physics, when applied to point particles and rigid bodies, *is* mechanics, but continuous phenomena are not. You learnt about the opposite. Urs seems to have learnt the most restrictive definition, although he wants to reject it in favour of yours, or something like that. Igor seems to advocate the most inclusive version, in which continuous and statistical physics are both mechanics.) Of course all of the differences between these fields are real, but where to draw the line is starting to seem very arbitrary.

I would like to see clear evidence that there *is* a consistent usage of terminology in modern physics, but right now I don’t believe that. *If* there is such a consistent terminology, then we may as well have a page on it. If, however, there is not, then we should have (in addition to classical physics) pages on specific ideas (such as physics that can be described using Poisson algebras, which is what classical mechanics is about right now). I suppose that we might still have a page linking to fields of classical physics that are *called* “mechanics” (including continuum and statistical mechanics), but we could just as easily put that (along with the other links) at classical physics.

For what it’s worth, Wikipedia mostly agrees with me; it includes continuum mechanics (such as hydrodynamics) but distinguishes this from field theory (which is not included), and it includes classical statistical mechanics. However, that may just confirm that my education in terminology stopped as a second-level undergraduate.

]]>I really don’t understand this claim that statistical mechanics is not about matter!

Classical statistical mechanics is a method for studying what appears (in the ignorance of quantum phenomena) to be the real world: a classical physical system made up a large number of point particles (and perhaps other things). In other words, it is about matter. It is not about statistical ensembles any more than classical mechanics is about Poisson manifolds. Although its methods are specialised, fundamentally it is simply the application of probability theory to deterministic physics.

Furthermore, all of physics is about matter (and energy/radiation, which is not fundamentally different). If it’s not about that, then it’s not physics!

So I remain in ignorance of the difference between mechanics and physics.

]]>I should also note that the formal similarities between mechanics and thermodynamics hold only for equilibrium thermodynamics. Non-equilibrium thermodynamics is quite different. Fundamental mechanics, statistical mechanics and thermodynamics are often viewed as different hierarchical levels of describing multiparticle systems. Their distinction is over all physical.

]]>Toby 34 on geometrical optics – You are right, the eikonal equation looks like it could be viewed as a classical field theory, but as such it is not a uniquely defined system. It is an asymptotic theory which suffers for example Stokes phenomenon – the asymptotic expansions are well defined only in certain sections of the space, and there are discontinuities (described by Stokes factors) when passing from a region to region. The Maxwell Equations are on the other hand linear, and as for the linear wave equations one does not have such phenomena; moreover the mechanics of continua is usually derived as a limit of a discrete model when the spacing goes to zero, what makes it close to discrete mechanical systems.

Toby 34 on statistical mechanics – Mechanics describes both point particles and extensive objects of **matter**. Statistical mechanics does not describe single instance of a matter but an abstract entity, a statistical ensemble of systems which have some physical parameters in common, but otherwise vary enormously in detail.

I agree with you that it is hard, if possible, to give an abstract definition of mechanics without a recourse to formalism. But the subject is defined rather historically, by studying classical mechanics of point particles and extensive bodies defined only in terms of basic (not specific for a kind of matter) kinematical and dynamical quantities like force/pressure, energy, mass, density. The further features like magnetization, charge etc. possessed by bulk are just ways of expressing the contributions to energy, but they require additional dimensions in the game. This is the point where one can usually stays within formally the same formalism but the same kind of laws are applicable. In addition to mass density one has charge density, magnetization density and so on. Well mas is nothing special it is an effective quantity anyway. There are differences between various discrete and continuum formalisms but one can be obtained from other in regular cases or by limiting procedure, so they are all interconnected. In hydrodynamics one has already a problem: while formally one can proceed the same way, physically, for compressible liquids, the thermodynamic variations are of importance.

So I agree, there are problems, but historically some similarities and correspondences between good cases of formalisms define subgroups of physical theories and some ready differences like between matter systems and statistical ensembles are taken as imortant in defining the standard boundaries of the field. I do not see a solution to your objections (and mine) but see rather, to some precision what the features of the historical groupings are.

]]>