What Do CUREs Look Like in Physics?

As a bit of context, one arm of my research focuses on tests of special and general relativity performed by searching for violations of fundamental symmetries.  Perhaps the easiest example of such a symmetry is rotation invariance, which basically says that the outcome of an experiment does not depend on its orientation in space.  Or, roughly speaking, there are no preferred directions in empty space.  These effects are normally introduced at the level of relativistic quantum field theory and are sought in comparatively complex systems such as atomic clocks.  As a bi-product of my graduate research, I ended up writing down the Newtonian limit of one of these symmetry-violating theories such that I achieved a modified version of Newton’s Second Law.  Hence students were able to explore the implications of a modification to known physics stemming from an active area of research at a level that was accessible to them.  Grappling with how to think about symmetry violation is notoriously hard for experts in the field, and the sorts of simple examples that could be produced at the Newtonian level are very helpful to those in the field, which was the publishability hook. 

Solving problems in this symmetry-violating world is tricky, even in the Newtonian limit.  It requires questioning assumptions, intuition, and mathematical steps often taken for granted.  This is what gives these projects the character of “real” theoretical physics research, and what made the project fit well as a capstone experience for my Advanced Mechanics class.  

Over the course of a few weeks, students each considered a classical mechanics system that was familiar to them from the  three terms of classical mechanics they had studied.  They each set off to “re-solve” this system in the presence of symmetry violation.  The spinning ice skater presented in section 5 of Ref. [1] was one such student project.

As I recall (it’s been a decade after all), about three quarters of the students generated results that were both new and interesting to me.  There were a few cases in which the student didn’t engage strongly with the project, as well as a case or two where the project got stuck.  Having a project ‘get stuck’ may be somewhat idiosyncratic to theoretical physics.  I suppose it’s just what it sounds like, progress toward answering the original question has stopped.  This is sometimes due to the inability to solve equations without taking time out to learn new mathematical techniques, a discovery that the original question doesn’t quite make sense and new questions must be formulated, a realization that answers to the questions are beyond reach within the scope of the project, etc.  In any case, it’s common enough in doing this sort of work that having a few students encounter it is an authentic part of the experience.  

Although this endeavor seemed like the best example of a CURE from my own experience because it fits element 5 the best, it perhaps fell short in other areas relative to some of the projects I’ll describe in the next section.  In particular, students worked individually, so there was less required collaboration, though they were all poking at the same ideas, so in many cases there were collaborative discussions.  There was also no explicit requirement of iteration, though many of them did iterate quite a bit as they revisited calculations following the discovery of errors.  

In addition to the work produced by students in this class, a number of relatively junior students in my research group also pursued related questions both before and after the fall of 2012.  With a relatively large body of complete and partial results, I set out to write a paper in 2018.  I quickly found that I had many complementary examples in varied states of completeness, some of which made the key points I aimed to emphasize in the paper better than others.  Hence it would not be practical to include every student’s work in the paper.  This feature, along with the varied outcomes of students’ work made authorship a complicated question as well.  Ultimately, just one student from the fall 2012 PHYS355 class is an author on the paper, while the rest of the class, which engaged broadly with the ideas but not the results that I wrote up, are acknowledged.  

I have not tried something similar since 2012 mostly because I have not found myself in the situation of having a research project come in such close proximity to the focus of a course, and I suppose I have not worked hard to bend either my research or the focus of my courses to make them meet up.  It would seem that a CURE lends itself most naturally to a course that is narrow and deep.  I typically feel constrained to some level of breadth in the courses I teach either because (a) they need to hit certain notes in order to prepare students for what they’ll encounter in subsequent classes or (b) they introduce a subject (for example, my General Relativity course) and I prioritize giving a more holistic sense of the subject over going deep in one area.  When it comes to projects in 300-level classes, we’ve also prioritized experiences that provide preparation for our comps process, which is a review of a broader topic, rather than original research.