Why don't most physics programs study the primary sources? In other words: Why don't they include Newton's Principia, Lagrange's Analytical Mechanics, etc., in the curricula?


The reason is that this is too time-consuming. The old papers are very difficult to read, because they have suboptimal presentation. Newton's Principia is not written well for the purposes of teaching mechanics. It is designed to emulate Aristotle in scope and completeness (but with the advantage of being correct physics), and it is optimal for the goal it served historically, getting Aristotle out of physics. It's absurd latin and old-fasioned geometrical phrasing with Greek-style geometry is suboptimal for pedagogy and clarity. One needs to use coordinate geometry and vector components in a modern presentation, there is no advantage to the old style.

In order to assign the Principia, one needs a modern translation of all the ideas in it. This is not provided by any source. Such a translation would keep all the arguments, but rearrange the order and the phrasing to be in common language and using modern calculus and vector component notation. This is very simple to do for someone who knows any physics, and Chandrashekhar did something like this in his annotated Principia (this is a very nice and respectful presentation). But Chandrashekhar wasn't writing an introductory physics book, rather he was trying to place the Principia's monumental achievement in historical context, to let modern readers know exactly what Newton was doing.

But I think it is possible to assign the Principia as an elementary physics book, if the translation is authentic and modernized. It requires rewriting the whole thing from scratch, but without throwing away any of Newton's insights. These insights are mostly contained in the special problems he solves.

I tried to provide an example of how to do this for less difficult things. The oldest is Archimedes "The Method of Mechanical Theorems", and you can read the gloss on Wikipedia, under Archimedes' "The Method". Using modern calculus, you can explain what Archimedes is doing in two minutes, and you can see exactly why his paper is so laborious--- he didn't have an algebraic notation or a standardized way to talk about infinitesimals. One should do a similar thing for "on floating bodies", "the equilibrium of planes" (this is simple to do, since it is all center-of-mass results which are trivial with modern calculus), "on the sphere and cylinder" (also simple, but it requires summing the squares, which is simple with modern calculus of finite differences), and the other works. All physics comes from Archimedes originally, especially the concept of force and torque.

One of the ideas in "the method" is the observation that certain integrals involving boundaries which are curvilinear algebraic varieties end up being polynomials in certain plane slicings, and so give rational number integrals. The simplest example he gives is of two cylinders intersecting at right angles. The question of which figures enclose rational volumes has never been investigated again, as far as I know, although it is interesting. It is similar to the question of periods, but it is different because of the slicing freedom. If people are familiar with the method, maybe there is interesting mathematics left undiscovered here.

With Newton, people keep the statement of the three laws of motion (the least important part of the Principia) and throw away all the special problems Newton analyzes. This is exactly the opposite of what they should be doing. One can state Newton's laws today as follows:

  • There is a conserved momentum, equal to the total mass times the velocity for an isolated body, and when it flows from one body to another, this is a force.

That's it. That's Newton's three laws. There is a further result

  • There is a conserved angular momentum, equal to the momentum cross the position for a point particle, and it is conserved under pairwise attraction repulsion events.

If you add the assumption that all matter is composed of points with pairwise forces which are attractions and repulsions, you get Newton's model of the world. The division of the laws into "1st law" "2nd law" "3rd law" is arbitrary and unnecessary, and only of historical interest. If you start with these two assumptions, you can state the three laws and show why and how they work, and the angular momentum law, and how and why it works, and then you can go to the special problems.

Newton's argument using infinitesimal triangles that the angular momentum is conserved during a radial attraction/repulsion event is essential, and it needs to be preserved unchanged. Newton's argument about the parabolic shape of spinning water needs to be preserved, although one should use the notion of potential energy in the argument. Newton's derivation of the speed of sound needs to be transmitted with both a derivation of the wave equation and an explanation of the adiabatic/isothermal distinction. Newton's analysis of the orbits of the planets is a little difficult to translate--- Feynman attempted to do this in "The Lost Lecture", but this is a place where improvements are possible, because one wants to use the modern insights about the central force, while keeping Newton's insights about the inverse-square special case. I don't know how to best present this.

All these things are usually skipped in elementary books, and instead you get an endless stream of unimaginative problems that are copied from one book to the next. These can be summarized in about a dozen or two orthogonal mechanical problems.

Regarding Laplace, the issue here is that the method of secular perturbations is greatly clarified by using action angle variables, and some special transcendental functions which flip from angle to time. The presentation in Laplace (which I haven't read) is not going to be optimal.

Translating Maxwell is going to be a pain, because you need to keep the modern insight that E and B (and A and $\phi$) are fundamental, not E and H. Maxwell is mislead by the fact that it wasn't appreciated that electric fields come from point sources, while B fields come from currents, so he wants the continuity conditions across material boundaries to be the same for the electric and magnetic field, and this picks out E and H as analogous and fundamental. This disease infects the literature right up to the 1950s, it is only fixed in the 1960s (and Feynman and Landau and Lifschitz help here).

The insights in Maxwell are so enormous that it is impossible to describe what is lost. These are the material dielectric and magnetic properties that are described phenomenologically. In my opinion, a good translation of Maxwell is essential to keep the 19th century E&M thinking alive.

For thermodynamics the problem is more severe, because the original authors did not understand that entropy was statistical, and energy was fundamental. They thought that the energy was the fundamental thermodynamic function, not the entropy. Here, one can start with stat mech, explain the thermodynamic potentials, and then go back and translate all the old papers into modern notation. These are all enormous projects, however. Thermodynamics has not been transmitted well--- most of the old thinking is lost. Statistical mechanics has been transmitted well, and includes the old thinking in principle, but the intuitions are different. If you don't believe me, look at any 19th century physics journals where they are busy measuring the heat capacities of materials at different temperatures, nd there are dozens of annoying thermodynamic identities you have to internalize. There is no way that studying this nonsense is productive, but it needs to be translated to modern language. The chemistry departments are responsible for this, and I don't think they are doing a great job of this.

Regarding 20th century physics, it is essential to modernize the treatment of Bohr, so that old-quantum theory is preserved. This is done in a wonderful way by Ter-Haar in the 1950s in a little book called "Old quantum theory". The Wikipedia pages on Adiabatic Invariant, Correspondence principle, and Old quantum theory try to present the results in a modern translation, without fussing over the ambiguities that are now known to be caused by working to leading order in h-bar.

Some things missing from all modern books:

  • The Lee model: This was historically essential for understanding renormalization, and this needs a modern translation. It doesn't appear in any modern field theory book.
  • The Bethe-Salpeter equation: This is important for bound states, although a full bound-state formalism is lacking today.
  • The pion-nucleon models: these don't work, but they are an important source of intuition. The magical pion decay rate calculations, the false theorem on identity of the pseudovector vs. vector coupling, etc, these are all forgotten.
  • Regge theory: This is unforgivable. There is a short intro in Landau and Lifschitz quantum mechanics, but the only good source is Gribov's book "The theory of Complex Angular Momentum". You need to know which hadrons are on which trajectory, and you won't find this presented in modern language or notation.
  • S-matrix theory: This is also unforgivable. I don't know the best book here, there are a few. This is coming back in style, so it might get fixed soon. This includes what Chew was doing with pions and nucleons, that I still can't figure out. But Weinberg eventually concludes it's all equivalent to effective field theory (it should be, but then you need to show the equivalence in some way).

There are a bunch of other things that can be dispensed of quickly today, I can't think of them at this moment.

So the main reason is that the historical documents need to be modernized to be pedagogical, and nobody does this. The only person who (secretly) did this is Feynman! He would rework the results with incredible fidelity to the historical literature, but without saying he is doing history. Almost all his elementary textbook arguments are reworked forgotten results from the old literature, done in his own way. This is why they are such classics, in my opinion, they are extremely historically faithful.

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  • $\begingroup$ I think even Maxwell isn't worth reading today because he predates special relativity. Far better to read the works of talented teachers who teach as a profession and get feedback such as Griffiths with his Classical Electrodynamics book. Prof Lewin is another fantastic teacher who hasn't written a book, but has lectured on the web and maybe this is his medium. Maybe you're starting to fall asleep in the past and not keeping upto date with modern books. $\endgroup$ – Physiks lover Jun 22 '12 at 22:14
  • $\begingroup$ @Physikslover: I think the modern books on everything elementary are a total scandal, with the exception of Feynman's lectures and Landau and Lifschitz. The issue is that you just haven't read Maxwell. Maxwell's concerns do not involve special relativity, but analyzing systems of materials in interaction with electricity, magnetism and light. The reason it is annoying to read is the lack of vector notation and the annoying multiplicity of fields (E,H,B,D), plus the lack of computation. But it would be worthwhile to read a condensed modern version which updates the thing, but keeps the results. $\endgroup$ – Ron Maimon Jun 23 '12 at 2:13
  • $\begingroup$ Interesting, as always. "The only person who (secretly) did this is Feynman! He would rework the results with incredible fidelity to the historical literature, but without saying he is doing history." So by "(secretly)" are you saying Feynman is misleading us into thinking that he's being original? $\endgroup$ – MMa Jul 1 '17 at 8:34

Much of Physics is now far better understood than when it was first formulated. For example, if you wanted to learn Maxwell's equations you are far better off using a modern textbook than going back to Maxwell's original work. Likewise Einstein's General Relativity. You mention Newton, but he used a notation that would flummox most modern students.

There are exceptions, for example Dirac's book on quantum mechanics is widely regarded as a classic and valuable even for modern students. However, apart from these exceptions the original documents are of most interest to historians of science.

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Because it's in Latin.

That is not the only reason though, just read for yourself a relative modern translation:

SCHOLIUM. If the ellipsis, by having its centre removed to an infinite distance, de generates into a parabola, the body will move in this parabola; and the force, now tending to a centre infinitely remote, will become equable. Which is Galileo's theorem. And if the parabolic section of the cone (by changing the inclination of the cutting plane to the cone) degenerates into an hyperbola, the body will move in the perimeter of this hyperbola, having its centripetal force changed into a centrifugal force. And in like manner as in the circle, or in the ellipsis, if the forces are directed to the centre of the figure placed in the abscissa, those forces by increasing or diminishing the ordinates in any given ratio; or even by changing the angle of the inclination of the ordinates to the abscissa, are always augmented or diminished in the ratio of the distances from the centre; provided the periodic times remain equal; so also in all figures whatsoever, if the ordinates are augmented or diminished in any given ratio, or their inclination is any way changed, the periodic time remaining the same, the forces directed to any centre placed in the abscissa are in the several ordinates augmented or diminished in the ratio of the distances from the centre.

I personally think this is not a straightforward way to express a physical law. As an undergraduate I would have really disliked to read such a text, even if it is written by Newton himself. As our knowledge advances we can connect different areas of physics, these connections might have not been obvious at all at the time of their discovery. Compare this with the lecture from Feynman (can be found online) about the same law.

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  • $\begingroup$ Yes, but this passage has some ideas that can be rephrased in modern language in two or three sentences: the first part says that if the gravitating mass is infinitely far, the gravitational field becomes constant, and the motion parabolic a-la Galileo. The second part is simply deriving the scaling law for the force by dimensional analysis from the speed with which you traverse the orbit. Both need to be expressed in any modern textbook, and neither are, because the textbooks don't read the Principia and translate as I did in the comment. $\endgroup$ – Ron Maimon Jun 22 '12 at 19:47
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    $\begingroup$ @RonMaimon: I agree that it can be rephrased in a few sentences. But isn't this exactly the reason that we don't read the original because it is in a language that is hard to understand? Your idea to create a better translation is tempting and I don't know any publisher that started a project in that direction. $\endgroup$ – Alexander Jun 22 '12 at 19:53
  • $\begingroup$ This is something I try to do online when I can. Chandrashekhar did something like this. The issue for me is that nobody translates the ideas, so that all of them are present. They always pick the least interesting points and transmit these. So you end up having to go back to the original to get all the ideas. $\endgroup$ – Ron Maimon Jun 22 '12 at 19:54

It's because knowledge is being continually updated and errors corrected. Newton's Principia Mathematica doesn't even contain his second law where force is proportional to the rate of change of momentum. Lagranges's Analytical Mechanics is very difficult to follow where he used concepts such as "the living force" to represent $mv^2$ and levers and pulleys to justify his use of the principle of virtual work. Both these books can be summarised in a few pages without losing the basic principles of what they were doing.

Productive young people at the cutting edge of research are lead by their peers and modern textbooks. Please, please don't look at the old text books until you understand the modern ones, otherwise you'll end up on a merry go around in the past, convinced you've discovered something new.

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  • $\begingroup$ -1: sorry, this answer is both factually incorrect and ridiculous. Newton's Principia contains the second law, and the concept of "vis-viva" is not "living force", but Leibnitz's term for what we now call energy. The levers and pullies justification for virtual work is essential, and must be presented to students in order to explain the concept of work. Feynman does this in vol 1, and this is one of the highlights of his presentation. There is not a single physicist who does original research who doesn't know the history, and the modern textbook treatments are woefully inadequate in every way. $\endgroup$ – Ron Maimon Jun 23 '12 at 11:21
  • $\begingroup$ yeah, his second law as in "A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed" which isn't expressed as proportional to the rate of change of momentum. And Lagranges Analytical Mechanics is very long winded when it comes to explaining virtual work, whereas Feynman does it in a paragraph - why? because we've moved on from 250 years ago as teachers and researchers refine and improve the interpretation and techniques. Please remove the -1 $\endgroup$ – Physiks lover Jun 25 '12 at 17:05
  • $\begingroup$ Newton defines "quantity of motion" two paragraphs previously as mass times velocity! So that "a change in motion" is a change in momentum, except he doesn't use the word "momentum", and calls it "motion". Please read the book, I would -1 the comment too if I could. Newton doesn't mean "proportional", by the way, but "proportional with a universal coefficient", i.e. what we would today call "equal" (up to units). One reason you know the coefficient of proportionality between F and $\dot{p}$ is universal is the third law, but Newton assumes you have some other F notion to fix units. $\endgroup$ – Ron Maimon Jun 25 '12 at 18:37
  • $\begingroup$ @RonMaimon goddamnit you're right on Newton. $\endgroup$ – Physiks lover Jun 25 '12 at 22:24
  • $\begingroup$ @Physicslover: I read the book. As far as "moving on", if you don't read the book, it is hard to determine if we've moved on or not. We have, but at the cost of leaving behind some stuff which is not obsolete. $\endgroup$ – Ron Maimon Jun 26 '12 at 3:20

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