This paper shares a hands-on activity that introduces Feynman diagrams and the accompanying idea of using pictorial representations to describe the behavior of subatomic particles—specifically, for electrons and photons—in place of mathematical expressions. Built collaboratively by scientists and artists, it exemplifies a triumph of lateral thinking by highlighting the vital role Feynman diagrams have played in modern physics. While the student may initially treat this activity as a glimpse into the quantum realm, the teacher should recognize this as a demonstration of lateral thinking as an insight tool.
This paper shares a hands-on activity that introduces Feynman diagrams and the accompanying idea of using pictorial representations to describe the behavior of subatomic particles—specifically, for electrons and photons—in place of mathematical expressions. Built collaboratively by scientists and artists, it exemplifies a triumph of lateral thinking by highlighting the vital role Feynman diagrams have played in modern physics. While the student may initially treat this activity as a glimpse into the quantum realm, the teacher should recognize this as a demonstration of lateral thinking as an insight tool.
Lateral thinking1 should be one of many tools in a thinker’s toolbox. It involves thinking about a problem with effortful creativity and a tangential approach. Solutions found through lateral thinking are rarely immediately apparent and are sometimes not even obvious with the benefit of hindsight. Lateral thinking, which focuses on the “movement value” of statements and ideas, can be distinguished from critical thinking, which focuses on judging the true value of statements and seeking errors. De Bono et al.1 provide the insightful analogy of critical thinking as digging the same hole deeper, while lateral thinking digs a hole in a different place: one cannot dig a hole in a different place by digging the same hole deeper. One is not a substitute for the other; instead, they are complementary approaches. Lateral thinking cuts across the distinctions of subject and is generally applicable to any field. It is not some new magical system, as Feynman diagrams nicely demonstrate.
In the mid-1940s, physicists faced the problem of describing quantum interactions in a way that was consistent with Einstein’s theory of special relativity. The interactions of sub-atomic particles, such as particles with opposite charges attracting each other, can be complicated and difficult to understand intuitively. A theory describing these interactions called quantum electrodynamics (QED) requires calculating the probabilities of all possible outcomes of particle interactions. However, it faces some seemingly insurmountable problems. Primary among them, writing down the equations meant keeping track of all possible particle interactions. In 1948, Feynman2 presented a simple diagrammatic scheme to account for all of these interactions. The representation of complex math with doodles is a striking example of lateral thinking.
A Feynman diagram is a story of a particle interaction in space and time. In these diagrams, the straight lines are particles of matter, like electrons, and the wavy lines are particles that convey forces, like photons. The diagrams have found great use in describing a variety of particle interactions,3 ranging from the Higgs boson4 to superconductivity.5
The Feynman diagram activity
Called the Feynman Diagram Collage, this activity was one of two that were created for the outreach event Night Shift: Quantum Futures.6,7 Participants of the outreach event could be roughly characterized as science enthusiasts, with broad ranges in age and educational backgrounds. The creation of this activity was a collaborative effort between physicists from the University of British Columbia and artists from the Curiosity Collider in Vancouver. The concept of alternative representations was at the core of the activity, and it was constructed with attention to the artistic component of creative scientific thinking (i.e., somewhat domain-specific lateral thinking).
The notion of alternative representations resonates with artists and scientists alike. Defined as the use of "signs" to substitute for something else, representations8 can be arranged to form semantic constructions and express relations. People organize and come to understand their reality, in part, through the act of naming its elements (i.e., via representations). In the domain of QED, where the physics is fundamentally counterintuitive, Feynman diagrams expressed the concepts more tangibly. With respect to an outreach event, for which the attendees tend to have limited relevant background exposure, it was a compelling challenge to identify quantum concepts that were both appropriate and interesting.
The collaborative process began with having the physicists brainstorm the alternate representations they use to understand and explain their work in quantum materials. Through iterative conversations with the artists, this list was reduced to one that also worked with non-experts. This back-and-forth culminated in a commitment to a few ideas for activities that could work (one of which is presented here). Specific learning goals guided our process. We intended that participants of the Feynman Diagram Collage activity would subsequently be able to: (1) discuss the influence of art/culture/language on our understanding of science; (2) appreciate the role of pictorial representations used by physicists; (3) explain what a Feynman diagram is; and (4) describe a given (simple) QED interaction.
The participants play the role of quantum interaction architects by imagining possible interactions between electrons and photons. The instructions invite participants to “learn the symbolic language physicists use to describe how particles behave and contribute to the creation of a collage of Feynman diagrams with us.” The materials required for this activity are nothing more than neutral-colored card stock (8.5 in x 11 in, halved) and colored markers.
Participants were asked to follow a small and simple set of rules to create their own Feynman diagrams. A lay explanation of how these rules come about can be found in Ref. 10. In principle, the rules below should include numbers associated with relevant parameters (e.g., coupling strengths and particle masses). In practice, however, the essence of the theory can be realized intuitively by ignoring the math and simply looking at the diagrams directly. The activity provides the following six instructions:
Use the following three components, shown below in Fig. 1, to make up your diagram. The direction of arrows on the electron lines must be conserved at a vertex; for every arrow going in, you must have an arrow coming out.
Lines may be drawn as straight or curved; it is only how they connect that matters.
Draw your diagram from left-to-right or top-to-bottom. Think of the left (or top) of your diagram as the start of your interaction, and the right (or bottom) as the end of your interaction.
Feel free to make multiple diagrams. For practice, consider limiting your first diagram to fewer than 10 lines. If you want to, use color.
Call an expert over to get feedback on your diagram. An expert can help you to check if you have followed the rules and can let you know what sort of particle interaction you have dreamed up.
Make a good copy of your diagram and add it to the wall.
We also show several examples of Feynman diagrams, as shown in Figs. 2 and 3, to help get participants started. Figure 4 shows some of what the participants created.
Given the outreach nature of the event, we did not perform any assessment of those involved in the implementation or whether there were positive learning outcomes. Anecdotally, the activity was popular and enjoyed by all who stopped by to participate. Most folks spent between five and 10 minutes working on multiple Feynman diagram creations. The most common difficulty faced by the participants was conserving the number of lines at a vertex, although this rule was sometimes intentionally ignored in the name of artistic freedom.
Conclusion
Although some exist—e.g., Kontokostas et al.9—this activity was created to fill a scarcity of imaginative and thought-provoking, hands-on activities about quantum physics for the public. Its creation was in collaboration with artists intent on pursuing interactive engagement with the public in discussions about quantum physics. It provides novices access to abstract quantum physics concepts, in terms understood with simple line drawings. What began as a seed conversation between scientists and the public about quantum phenomena at an outreach event has since become a valuable tool at a local physics summer camp program, educating students on basic concepts of quantum physics. We see even further potential.
As outlined, this activity likely requires the support of a practicing physicist. However, it can be adapted to work for a variety of classroom abilities, and sufficient teacher background knowledge can be acquired with online reading. (There are some exceptional online resources.10) With that, it is highly accessible to teachers and involves only a few materials that are available in any standard classroom.
Extensions and offshoots of the activity described above are plentiful. Students could focus on a different fundamental principle—quantum mechanical in nature or not—and, through lateral thinking, develop an analogy for teaching their chosen principle. Discussion on the strengths and weaknesses of their analogy, as solutions are compared and contrasted against one another, could follow. Alternatively, students could compile a list of real-world, lateral thinking solutions (examples can be found with an Internet search). From this list, they could try to develop strategies for creating lateral thinking solutions (e.g., think of the obviously wrong answer first and work back from there; try subtracting from, rather than adding to, the currently accepted solution; begin by asking a silly question like “How would Chuck Norris solve this?”). They could then identify fields for which advancement has slowed and practice their lateral thinking to generate solutions. This can provide the teaching opportunity to share that those who generate the best ideas are often simply the ones who generate the most ideas. Finally, an appealing sense-making exercise would be to present the solutions (i.e., samples of the diagrams we intend for them to create) and have the students derive the original rules. Any adaptation that permits artistic expression and promotes analogical reasoning and modeling will benefit students.
The public awareness of and interest in quantum physics has never been higher—see Quantum Canada,11 for example. Upper secondary schools have begun to incorporate quantum physics into their curricula, and the demand is now for resources to engage students through exploratory learning. The incorporation of arts in the training of scientists (i.e., STEM becomes STEAM)12 provides a fruitful complement to conventional pedagogy and training approaches in the sciences. Allowing learners to exercise their creativity and innovative thinking is essential to confront the technological and societal issues we face. Such STEAM initiatives have wide-spanning benefits: broader access and inclusion in STEM, enhanced learning of scientific concepts, building technical skills that are underserved in the curriculum, and enhancing students’ mastery of design and cross-disciplinary collaboration.13 Historically, lateral thinking is lacking in the physics toolbox, but such STEAM initiatives can foster the growth and development of our learning traditions.