## CUREs for Physics

The amount of course-based undergraduate research experiences (CUREs) happening in my own teaching and across physics and astronomy at Carleton ranges from rare to pervasive depending on how one defines the term, particularly when it comes to element 5 of a CURE’s defining features. Construed narrowly, one could imagine defining research as activities that lead to peer-reviewed publications in the faculty member’s area of study, or in other words, generating results similar to those produced by the faculty member’s normal scholarship. At least by conventional thinking, the road to the front lines of research in physics and astronomy seems sufficiently long that it’s often hard to engage students in genuine research while meeting a broad enough range of learning objectives for many undergraduate courses. If the definition of research is relaxed to include exploring things that are new (to the world?, to the faculty member?, to the student?), but not necessarily a publishable part of an active research area, the space of interesting possibilities for introducing CUREs seems to open considerably. In these contexts, students often practice the same habits of mind associated with publishable research, but the burden of finding a question that is simultaneously interesting to a wide audience as a ground-breaking result, accessible to the students, and aligned with the learning goals of the course is lifted.

## A narrow definition of “R”….

As I began engaging with the discussion of CUREs, it was my experience in the Advanced Mechanics (PHYS355) class in the fall of 2012 that I had in mind because it involved a class project that contributed to a publication [1], and that publication is related to my “normal” scholarly pursuits. An obvious question here is why I have not tried it again in the past dozen years – a question that will be easier to answer once I explain what we did and how it turned out.

## What we did

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.

## How it turned out

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.

## Why I haven’t done it again

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.

## A broader definition of “R”….

While more broadly defined notions of the “R” in CURE are something I would characterize as common in physics and astronomy at Carleton, I’ll describe my own main contact with this notion which comes in the context of Analytical and Computational Mechanics (PHYS231). There is a long and ongoing tradition of CURE-like projects in this class. Though the subject matter and details have varied based on who is teaching the class in a given year. When I taught the course, it was “The Trebuchet Project,” an experience that I inherited and adapted from my predecessor Bill Titus.

The trebuchet, a gravitationally powered cousin of the catapult and an iconic piece of medieval artillery, is a classical mechanics system having sufficient complexity that its motion can only be predicted approximately using computational methods. Trebuchets also have an alluring quality and lend themselves to class competitions, which engage our 200-level students’ interest. In the project, students work in teams of three to four to build a model trebuchet of their own design, ask questions about its motion, do a literature search related to their questions, address the questions computationally using the tools they learned in the course, write a journal-style paper on their results, and give a conference-style presentation to the rest of the class. Because the details of the system that every group builds are different, and because each student asks different questions, no one knows the answers ahead of time. I think of this as simulating the full research process in physics from beginning to end over the course of a few weeks.

As far as I can tell, this experience hits all of the elements of a CURE quite well but for the fact that there is little interest in the results that the students generate beyond the class. Perhaps this is something that could be cultivated in the future through publication of results on a web page, as there are plenty of hobbyists out there who are interested in Trebuchets. Perhaps I’ve previously thought too narrowly about strictly academic audiences for this work.

**References**

[1] T.H. Bertschinger, N.A. Flowers, S. Moseley, C.R. Pfeifer, J.D. Tasson and S. Yang, “Spacetime Symmetries and Classical Mechanics,” Symmetry 11 (2018) 1, 22.

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