Modern Physics Education?

Being the physics department executive officer (on top of being a quantum physicist) makes me think a lot about our physics college program. It is exciting. We start with mechanics, and then go to electromagnetism (E&M) and relativity, then to quantum and statistical mechanics, and then to advanced mathematical methods, analytical mechanics and more E&M. The dessert is usually field theory, astrophysics and advanced lab. You can take some advanced courses, introducing condensed matter, quantum computation, particle theory, AMO, general relativity, nuclear physics, etc. By the time we are done with college, we definitely feel like we know a lot.

But in the end of all that, what do we know about modern physics? Certainly we all took a class called ‘modern physics’. Or should I say ‘”modern” physics’? Because, I’m guessing, the modern physics class heavily featured the Stern-Gerlach experiment (1922) and mentions of De-Broglie, Bohr, and Dirac quite often. Don’t get me wrong: great physics, and essential. But modern?

So what would be modern physics? What should we teach that does not predate 1960? By far the biggest development in my neck of the woods is easy access to computing power. Even I can run simulations for a Schroedinger equation (SE) with hundreds of sites and constantly driven. Even I can diagonalize a gigantic matrix that corresponds to a Mott-Hubbard model of 15 or maybe even 20 particles. What’s more, new approximate algorithms capture the many-body quantum dynamics, and ground states of chains with 100s of sites. These are the DMRG (density matrix renormalization group) and MPS (matrix product states) (see https://arxiv.org/abs/cond-mat/0409292 for a review of DMRG, and https://arxiv.org/pdf/1008.3477.pdf for a review of MPS, both by the inspiring Uli Schollwoeck).

Should we teach that? Isn’t it complicated? Yes and no. Respectively – not simultaneously. We should absolutely teach it. And no – it is really not complicated. That’s the point – it is simpler than Schroedinger’s equation! How do we teach it? I am not sure yet, but certainly there is a junior level time slot for computational quantum mechanics somewhere.

What else? Once we think about it, the flood gates open. Condensed matter just gave us a whole new paradigm for semi-conductors: topological insulators. Definitely need to teach that – and it is pure 21st century! Tough? Not at all, just solving SE on a lattice. Not tough? Well, maybe not trivial, but is it any tougher than finding the orbitals of Hydrogen? (at the risk of giving you nightmares, remember Laguerre polynomials? Oh – right – you won’t get any nightmares, because, most likely, you don’t remember!)

With that let me take a shot at the standard way that quantum mechanics is taught. Roughly a quantum class goes like this: wave-matter duality; SE; free particle; box; harmonic oscillator, spin, angular momentum, hydrogen atom. This is a good program for atomic physics, and possibly field theory. But by and large, this is the quantum mechanics of vacuum. What about quantum mechanics of matter? Is Feynman path integral really more important than electron waves in solids? All physics is beautiful. But can’t Feynman wait while we teach tight binding models?

And I’ll stop here, before I get started on hand-on labs, as well as the fragmented nature of our programs.

Question to you all out there: Suppose we go and modernize (no quotes) our physics program. What should we add? What should we take away? And we all agree – all physics is Beautiful! I’m sure I have my blind spots, so please comment!

28 thoughts on “Modern Physics Education?

  1. The physics curriculum spends way too much time on linear things and not enough time on nonlinear ones. There are a lot more of the latter. That is an aspirational comment, but some changes are also concrete: In classical mechanics, for example, one can modernize things by including more dynamical-systems approaches. (Goldstein is rather outdated.) At the ends of courses, one can give hints about active topics. The last bits of a statistical mechanics course can introduce people to subjects like complex systems (or active areas of condensed-matter physics, for that matter; pun intended). This would take only a small amount of course time but at least give more explicit hints about what else is out there and is of active interest.

    • A few years back I introduced Lax pairs, solitons, and inverse scattering methods to our advanced mathematical methods class when I taught it. Would that be a step in the right direction?

      • Those are really cool methods, though most systems aren’t integrable either (though it is true that one gives an example of nonlinearity that way). What I have in mind for classical systems is getting away from “closed-form” answers into qualitative approaches that are more generally applicable. I think a classical physics course is a good place to give an introduction to those methods, because many students may not take a full course in nonlinear systems (e.g., with some many other courses to take), and a reasonable set of core methodology in those methods should be required. In terms of classical mechanics, pendula and then forced, forced and damped, and coupled pendula are accessible examples. Then if people want more (and want examples outside of mechanics), I assume Mike Cross’s course is still occasionally taught.

  2. Quantum information. A qubit is simple. A quantum mechanics course needn’t be a veiled introduction to linear differential equations and greens functions. Even if your end goal is to understand quantum field theory, one could conceptually outline all the important ideas in quantum mechanics using a qubit with very simple linear algebra of 2×2 matrices.

    It introduces ideas from computer science which are becoming very useful in physics. It allows you to segway to the Bell inequality, arguably one of the most fundamental physics discoveries in the past few decades and then to entanglement. Similarly to what you said about computational quantum mechanics, it allows you to transition to other modern physics ideas based on your taste.

  3. How much of these suggestions are intended for an insanely packed undergraduate program, or do they mean a graduate program?

    • undergrad. Two comments though. First: recall that we can not pack the schedule more than 51 units per term at Caltech. I take responsibility for that 🙂 Second: the intention is to take out pieces of the curriculum and replace them with more modern things. So what should we take out?

    • good point! Not to say that physics is not an art, but I mean it this way (out of MWD):
      mod·ern
      ˈmädərn/
      adjective
      adjective: modern

      1.
      relating to the present or recent times as opposed to the remote past.
      “the pace of modern life”
      synonyms: present-day, contemporary, present, current, twenty-first-century, latter-day, modern-day, recent
      “modern times”

      noun
      noun: modern; plural noun: moderns

      1.
      a person who advocates or practices a departure from traditional styles or values.

  4. The open questions in Physics involve dark energy and dark matter. The Modern Physics course needs to prepare young Physicists to work in these disciplines.
    These are wide open areas of research. New approaches are needed to study the new unknowns.

    • Je suis bien heureux de constater que Mathieu a en tête de devenir enseignant au primaire. Nous avons besoin d’enseignanTs dans nos écoles. Cela permettra, entre autres, d’accorder plus d’importance à l&p8t17;ap#ren2issage au masculin. Tous les élèves s’y retrouveront gagnants.

  5. Any professor/specialist can list here at least dozen ‘most important topics of modern physics’ (e.g. plasma physics, numerical modelling of complex systems, dark matter and dark energy, (I have excluded quantum physics as thoroughly discussed before), etc.). As long, as we cannot build the time machine (and superhuman students) we cannot put all contemporary knowledge in the undergraduate course (in fact even postgraduate will be too small). It is also unnecessary – the absolute basics of “modern physics” (this up to 1930s) would be enough and should be intro to ‘selected (one!) problem of contemporary physics’.

      • Perhaps it’s possible to build a course that provides a basic – but not comprehensive – introduction into some “contemporary” physics concepts. My experience is that students find such courses an engaging and rewarding part of the larger physics programme.

    • With pleasure! Our heroic lab lecturer, Frank Rice, with help from Eric Black, put together an entangled photon experiment. Then they took it apart, and are now letting a group of 4 daring techers put together an apparatus of their own. As we gain support, we will make more apparatuses available, and bring experiments like that in additional tracks on line.

  6. The Hilbert Book Model is a purely mathematical model of the foundations and the lower layers of the structure of physical reality. This is a region that conventional physics ignores. The reason is that the results of this investigation cannot be verified by experiments. It is a false reason because the foundations of physical reality are relatively simple and therefore easily comprehensible. The Wikiversity Hilbert Book Model project teaches the Hilbert Book Model and reveals the origin of many physics subjects and introduces some new mathematics.
    See and join https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project.

  7. renormalization group of wilson and kadanoff and others. Being able to understand the possible behaviors and dominant degrees of freedom of a complicated system is of great importance. Otherwise, being able to diagonalize 20×20 matrices is mere gymnastics.

    • Agreed! RG is one of the most modern pieces of our curriculum, and is taught as a second quarter of stat mech to a mix of undergrads and grads. For the techers out there: ph127b. Heartily recommend. Here is one reincarnation of it:
      http://www.cmp.caltech.edu/refael/ph127b/

      Now, that said, I think it is equally important for students to know how to make a simple tight binding model for, hmmm, everything 🙂

  8. I’ve always felt that the standard “modern physics” course is a kludge: you have to teach special relativity, there’s not a full course worth of material there, so you need to squeeze something else in and the current candidate for that “something else” is pre-modern quantum mechanics: Compton scattering, deBroglie wavelengths, bremsstrahlung, etc. I think this sort of half-hearted heuristic intro to quantum mechanics is a waste of curricular space. I think it’d be better to pair special relativity with an intro to parts of modern classical dynamics that don’t otherwise get taught (except maybe at Caltech?!): chaos, fractals, cellular automata, turbulence, etc. Then quantum mechanics can be taught as its own thing.

  9. The undergraduate curriculum splits between analytics (the majority) and experiment, while research now has split into three categories of different thought, analytics, experiment, AND numerics. Honestly, I did get a solid grounding in computation in my time as a UG at Caltech, though it certainly quite expanded during my first few months as a graduate student. I think I lot of the principles for good computational research could be worked through the curriculum regardless of the subject matter they’re taught through, like premature optimization, code cleanliness, documentation, orthogonality and scalability, testing and debugging, etc.

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