Modernizing classical physics: an oxymoron?

Open most textbooks titled “Modern Physics” and you will see chapters on all the usual suspects: special relativity, quantum mechanics, atomic physics, nuclear physics, solid state physics, particle physics and astrophysics. This is the established canon of modern physics. Notably missing from this list are modern topics in dynamics that most physics majors use in their careers: nonlinearity, chaos, network theory, econophysics, game theory, neural nets and curved geometry, among many others. These are among the topics at the forefront of physics that drive high-tech businesses and start-ups, which is where almost half of all physicists work. However, this modern reality of physics education has not (yet) filtered down to the undergraduate curriculum, but the community appears to be taking steps towards progress.

Our choice of topics that we teach our physics students has a very high inertia, and physics as a field has greater inertia than most. Most high school students today in their biology labs routinely do genetic engineering and make bacteria glow green, while the students in the physics labs down the hall are dropping lead weights and finding differences of squares almost the same way Galileo did it in 1610. It can be argued that college undergraduate physics majors get their bachelor’s degrees having learned topics that were last researched seriously about a hundred years ago. The time is overdue for the physics curriculum to catch up with the times.

There are two general reasons why the physics curriculum lags behind most other disciplines. The first has to do with the (false) expectation that physics majors will become academics. If we are going to teach students advanced physics in graduate school, then there is no better time to build a foundation for it than when they are undergraduates. We teach slowly and methodically, brick by brick, so the students have all the tools they need for graduate school in physics. The problem is that many undergraduate physics majors do not go on to physics graduate school, with 40% entering the workforce after their undergraduate degree. For those who do go to graduate school, a sizable fraction enter graduate programs other than in physics. For all of these students, the undergraduate curriculum has stranded them with hundred-year-old knowledge.

The second reason for the lag in upgrading the physics curriculum relates to the (false) expectation that advanced topics are too conceptually challenging for undergraduates and that advanced mathematical methods are needed that the undergraduates have not yet mastered. Yet students are hungry to learn the latest physics and willing to grapple with the concepts, going to Google or to Wikipedia in an instant to find out more. Fortunately, many of the advanced topics that spark their interest, like economic dynamics or game theory or network dynamics, have strong phenomenological aspects that can be understood intuitively through phase space portraits without the need for deep math. The students learn the concepts quickly, and can explore the systems with simple computer codes and interactive web sites, like Wolfram Alpha, that physics undergraduates are handling with ever increasing facility.

One example of a central concept that needs updating is the simple harmonic oscillator. It has been argued that most dynamics can be reduced to a simple harmonic oscillator (SHO) because the energy minimum of any potential can be approximated by a quadratic function. But the SHO is actually the most pathological of all oscillators: it has no dependence of frequency on amplitude. While this is a great asset for clocks, it is such a special case that it skews a student’s intuition about real-world oscillators for which anharmonic effects are the rule instead of the exception. Anharmonic oscillators break frequency degeneracy, opening the door to important topics like Hamiltonian chaos. Going further, autonomous oscillators, like the van der Pol oscillator, provide the paradigmatic foundation for a broad range of modern topics like synchronization, business cycles, neural pulses and social network dynamics.

Therefore, the time has come to bring the undergraduate physics curriculum into the 21st century. By relaxing our insistence that every student know how to calculate difficult Lagrangians or Poisson brackets (Lagrange and Poisson were at their peak about 200 years ago), there is plenty of room and time in the undergraduate curriculum to introduce them to truly modern dynamics. This task will be helped in part by burgeoning web resources and the increasing breadth of knowledge that students bring with them. It also will be helped by a new crop of textbooks that adopt a modern view of the purpose of physics in the modern world.