June 2026
Volume 94, Issue No. 6
Viking navigation: From speculative history to laboratory exercise on polarization
Although the actual techniques used by Viking navigators remain uncertain, some historical and optical hypotheses suggest they may have relied on the polarization of skylight to estimate the Sun's position under cloudy conditions. While this idea is speculative, it offers a compelling context for a physics laboratory exercise. In this article, we present a hands-on activity designed for undergraduate students in introductory astronomy or optics courses. The activity explores solar geometry using a simplified sun compass and introduces basic polarimetric sky measurements. The activity combines physical modelling with historical curiosity, aiming to stimulate student engagement and critical thinking. Student results indicate that navigation based on polarimetry would be most beneficial under partly cloudy conditions, while polarization of skylight becomes difficult or impossible to observe when the sky is fully obscured.
EDITORIAL
In this issue: June 2026 by John Essick; Jennifer T. Heath; Claire A. Marrache-Kikuchi; Beth Parks; Donald Salisbury; Todd Springer; Keith Zengel. DOI: 10.1119/5.0341348
AWARDS
2026 Richtmyer Lecture Award: Physics beyond the textbook by Rhett Allain. DOI: 10.1119/5.0328129
Editor's Note: This paper is based on the Richtmyer Lecture Award given by the author at the AAPT Winter 2026 meeting.
PAPERS
Viking navigation: From speculative history to laboratory exercise on polarization by Kateřina Karlíková; Jonáš Kubeček; Leontýna Šlégrová; Jan Šlégr. DOI: 10.1119/5.0295411
Editor's Note: How did early Norse sailors successfully navigate vast expanses of ocean, often in terrible weather? Based on Viking sagas and artifacts, it's been hypothesized that polarized skylight was the key, perhaps analyzed by a birefringent calcite crystal “sunstone.” The authors explore these ideas and describe a laboratory exercise in which students can determine their feasibility, while also learning about sun position and sky polarization.
General features of brachistochrones by David Agmon; Ady Mann. DOI: 10.1119/5.0303237
Editor's Note: In the classic brachistochrone problem, a particle subject to a conservative force is guided by a wire along the shortest-time-path between two points. Here, the authors reveal interesting relationships between the conservative force, the wire force, and the net force. These clever derivations will appeal to teachers of classical mechanics seeking new insights into the old problem. Teachers of introductory mechanics may find the simple geometric arguments valuable for conceptual discussions of the problem.
On the general problem of tautochrones by Stefano Siboni. DOI: 10.1119/5.0304879
Editor's Note: The tautochrone is the famous same-time curve. A mass released from rest and constrained to follow a tautochrone curve under the influence of gravity will arrive at the lower endpoint of the tautochrone curve in a fixed amount of time—regardless of where it starts on the curve. Readers interested in a general treatment of the problem, including different forces and friction effects, will enjoy this paper.
Roller coaster dynamics—From point particles to a continuum model using Lagrange density by Michael Kaschke; Holger Cartarius. DOI: 10.1119/5.0237959
Editor's Note: The amusement park is a wonderful place for students to explore classical mechanics concepts. Rides with complicated motion lead to a more exciting experience for passengers, but such rides necessarily require more advanced physics to accurately describe their motion. The authors of this article use Lagrangian mechanics, computational tools, and a series of increasingly sophisticated models of a roller coaster to study both the car's motion and passenger experience. Even risk-averse physicists will find this article to be a thrilling read!
Magnetic impulse damping of conducting pendulums by Peter F. Hinrichsen. DOI: 10.1119/5.0311567
Editor's Note: Damped oscillators are famous undergraduate physics experiments. Most often, textbooks and teachers discuss the exponential amplitude decay associated with damping forces that are proportional to the velocity of the object. Here, the author presents a magnetically damped pendulum system that exhibits a linear amplitude decay. This simple setup will interest teachers of classical mechanics, electromagnetism, and lab courses.
A simple quantum dot: Numerical and variational solutions by Connor M. Walsh; Ian MacPherson; Davidson Noby Joseph; Suyash Kabra; Ripanjeet Singh Toor; Mason Protter; Frank Marsiglio. DOI: 10.1119/5.0275290
Editor's Note: The one-dimensional potential well is a standard exercise in quantum mechanics, familiar to every student as an introduction to bound states and quantization. This paper extends that paradigm to a 2D situation in which two perpendicular troughs cross, forming a simple quantum dot defined purely by geometry rather than by a conventional closed well. Classically, no bound state is expected; nevertheless, quantum mechanically, the intersection region localizes a quantum particle and supports a true bound state. This problem is also used to illustrate and put into practice several standard methods such as matrix mechanics, finite differences, and mode matching. Appropriate for advanced quantum mechanics classes as well as for courses dealing with numerical methods in this field.
Modified Fronsdal coordinates for maximally extended Schwarzschild spacetime by Andrei Galiautdinov. DOI: 10.1119/5.0282904
Editor's Note: For the first time, the components of the metric of the extended Schwarzschild spacetime are expressed explicitly as functions of spacetime coordinates. This will assist students enormously in understanding the behavior of timelike and null trajectories in the region connecting two universes.
NOTES AND DISCUSSIONS
A driven disk with chaotic motion by Kirk T. McDonald. DOI: 10.1119/5.0317722
Editor's Note: The driven disk is a simple and familiar chaotic system. Wedged between two motorized rollers and confined to the vertical plane, the disk is driven upward. The result is a chaotic mix of spinning and pendulum motion that will surprise and delight experimenters. The new model presented here is accessible to undergraduate physics students in courses on classical mechanics and chaotic systems.
INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS
A portable LED-based diamond magnetometer for outreach and teaching labs by Hollis Williams; Alex Newman; Stuart Graham; Colin Stephen; Gavin Morley. DOI: 10.1119/5.0295777
Editor's Note: This Note presents a low-cost, transportable setup to probe the nitrogen-vacancy center in diamond via optically detected magnetic resonance (ODMR). By replacing the green excitation laser typically used in such experiments with a high-power green light-emitting diode, the authors have developed a system that is substantially safer to use in the instructional laboratory or as a classroom demonstration due to the reduced risk of eye damage. ODMR spectra acquired using the setup as well as its use as a magnetometer are presented, while the supplementary material provides construction details and suggestions for student investigations.
Low-cost cross-correlation noise setup for measuring the Boltzmann constant and the elementary charge by Zitong Peng; Jie Zheng; Xiaokai Yue. DOI: 10.1119/5.0309456
Editor's Note: This paper presents two electronic circuits designed to obtain high-precision values of the Boltzmann constant and elementary charge from measurements of thermal and shot noise, respectively. The use of cross-correlation signal processing allows the low-level thermal and shot noise to be accurately acquired using a low-cost amplifier chip and an analog-to-digital module. The background theory, circuit design, and experimental procedure for this project are well described, making it well-suited for adoption in instructional laboratory courses.
Additional Resources
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