Just pick up Dirac's book "The Principles of Quantum Mechanics" and read it in conjunction with "The Feynman Lectures on Physics Vol III". Don't waste time with linear algebra, the entire content of the undergraduate courses can be learned in half a day. Don't worry about the infinite dimensional nature of the thing, just reduce all the spaces to finite dimensions.

Also, be aware that "gifted" is a political label that has nothing to do with you, it's just a way for schools to segregate students by their future social class. It's not the analog of special needs, because the students in gifted classes are no different from the students in usual classes, except that they are given a slightly better education. Don't be fooled by a label into thinking you are somehow special, everyone is ordinary, including Einstein and Dirac. One has to do good work despite this, and those folks show it is possible by assiduous effort.

Most of the "intermediate scale" problems were "solved" long ago, and are now mostly the domain of engineering: application of physics to real world problems. I put "solved" in quotes: "real world" solutions require that you don't make all the simplifying assumptions that make many problems "solvable" - this is no such thing as a spherical cow. Nonlinearity, instability, turbulence, chaos... all these things conspire to make a full analysis of real world problems really, really hard: while there are physical principles that apply, you need to open a bigger tool box to really get a handle. The result, as David Hammen pointed out, is the emergence of many subspecialties: not the stuff of undergraduate physics courses, but very much the path to many professional careers.

That leaves the more interesting, "esoteric" stuff as the material at the frontier; this is where research is happening, and that becomes the material that the lecturers (most of whom are researchers) find most interesting.

In the end, the macroscopic phenomena are mostly a manifestation of the microscopic mechanisms underlying them. So to understand heat capacity, conductivity, or almost any macroscopic phenomenon, you are quickly looking for explanations on the microscopic level. It all comes from a desire to figure out "how it works", rather than "how to make it work". The former is physics, the latter engineering.

If it is "completely neglected", you are either expected to come in with a very full bag of tricks - or you are indeed being somewhat short-changed. I know I learnt a lot of "classical" physics as an undergraduate - plenty of stuff that had not been covered in high school. As an example, Landau and Lifshitz volume 1 - "Mechanics" - certainly goes far beyond the high school level. It was one of the texts we studied in university, and it was challenging!

## Best Answer

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

keepthe statement of the three laws of motion (the least important part of the Principia) andthrow awayall 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:That's it. That's Newton's three laws. There is a further result

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:

anymodern field theory book.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.