October 2026
Volume 94, Issue No. 10
A floating body with no preferred orientation: An experimental realization
We present a simple experimental realization of a two-dimensional floating body that can remain in equilibrium in any orientation. This system is based on a class of shapes known as Zindler curves, which possess the remarkable geometric property that all chords dividing their area into equal parts have the same length. Using a multilayer fabrication approach, we construct a heart-shaped floating object with an effective density close to one-half of that of the surrounding liquid. We show experimentally that, under these conditions, the object exhibits neutral equilibrium with respect to rotation. When the density is slightly varied, preferred orientations emerge, consistent with a simple energy-based description. Our experiments highlight both the accessibility of this classical problem and the subtle role of physical effects such as density inhomogeneities and capillarity. They provide a simple platform to explore the interplay between geometry and buoyancy, and to test geometric results in a tangible setting.
EDITORIAL
In this issue: October 2026 by John Essick; Harvey Gould; Jennifer T. Heath; Jesse Kinder; Claire A. Marrache-Kikuchi; Beth Parks; Donald Salisbury; Daniel Schumayer; Todd Springer; Jan Tobochnik; Keith Zengel. DOI: 10.1119/5.0357587
PAPERS
Generative AI in physics education: Approaches for instructors to integrate new tools with proven practices by Melissa Eblen-Zayas. DOI: 10.1119/5.0326978
Editor's Note: This paper provides practical guidance for how instructors can integrate AI into their classrooms. It is based on A Guide to Effective Practices for Physics Programs (the EP3 guide) and shows how existing guidance can be combined with current research to aid instructors who want to find effective ways to teach physics in the age of AI.
Long-range systems, (non)extensivity, and the rescaling of energies by Michael Kastner. DOI: 10.1119/5.0296430
Editor's Note: If you thought that Hamiltonians were extensive, this paper will show you that, as mind-boggling as this may seem, this is not the case for systems with long-range interactions. It will also explain how to deal with those systems, how to recover an extensive energy through a rescaling of the Hamiltonian, and how strange things can occur for nonequilibrium systems. This paper certainly gives food for thought and is appropriate for advanced quantum mechanics classes.
A physical model of the sinc function: The center-of-mass spiral by Chenguang Zhang (张晨光). DOI: 10.1119/5.0288757
Editor's Note: It's sometimes hard for physics students to make sense of mathematical functions. Why are they introduced? Can they describe real-life physical situations? This paper introduces a physical interpretation of the sinc function. By analyzing the trajectory of the center of mass of a thin, uniform thread winding around a circular core, the author demonstrates that its horizontal position oscillates according to the sinc function. In addition, when visualized in two dimensions, the full trajectory forms a distinctive spiral, which also has fun properties. Appropriate for introductory mechanics or mathematical methods classes.
A floating body with no preferred orientation: An experimental realization by Lucie Pontiggia; Angélique Campaniello; Emmanuel Fort. DOI: 10.1119/5.0336528
Editor's Note: Few students will be surprised to hear that a buoyant sphere can float in any orientation. What might astonish them is the fact that there are other shapes that can float with no preferred orientation! Teachers covering buoyancy will appreciate this striking demonstration and simple tabletop experiment: a heart-shaped object that can settle at any angle.
The electromagnetic fields of a moving anapole by Jaad Jawdat; David C. Latimer. DOI: 10.1119/5.0335340
Editor's Note: The authors explore interesting features of the anapole, which is formed in the limit that a toroidal solenoid with surface current K shrinks to zero size while maintaining a constant integral of Kr2 (r is the distance from its center). Outside the anapole, the electric and magnetic fields are zero, whether the anapole is at rest or moving, but for the moving anapole, both the scalar and vector potentials are non-zero. Spin-1/2 fermions can have a non-zero anapole moment, and scattering of an anapole by a charged particle provides an example of the Aharonov–Bohm effect in which the interaction is via the potentials rather than the fields. The calculations of the potentials of a moving anapole could be incorporated into an undergraduate electrodynamics course, while the scattering problem could be part of an introductory course in quantum field theory.
Thermodynamic temperature without a heat engine by Wayne M. Saslow. DOI: 10.1119/5.0315487
Editor's Note: How does a thermometer work? The most precise methods of thermometry rely on statistical mechanics to measure temperature. In contrast, thermodynamic methods like Kelvin's use of the Carnot cycle yield temperature by measuring the flow of heat. Practical thermometers such as a platinum-resistance thermometer rely on a calibrated temperature-dependent property, but the state of a thermodynamic system never depends on temperature alone. All of this can make the seemingly simple idea of measuring temperature abstract and unintuitive. In this article, the author uses Maxwell relations for the Gibbs and Helmholtz free energies to establish a new thermodynamic method for measuring absolute temperature—one that does not require a closed thermodynamic cycle. The approach fits naturally into a course on thermodynamics and illustrates how fundamental principles can be used to map out the equation of state T(P,V) without reference to a particular system or process.
When is quantum mechanics required to describe the thermodynamics of the ideal gas? by Yohannes Shiferaw. DOI: 10.1119/5.0319007
Editor's Note: The manuscript discusses a longstanding conceptual puzzle in statistical mechanics by carefully distinguishing entropy differences within a single phase from those across phase transitions. Combining Jaynes's interpretation of the Gibbs paradox with the historical Sackur–Tetrode analysis, the author offers a compelling explanation of when quantum mechanics is (or is not) required in the thermodynamics of the ideal gas. Readers will appreciate the pedagogical clarity and valuable guidance for teaching the concept of entropy, making it a worthwhile contribution for instructors of thermodynamics and statistical physics.
Rabi profile framework: A simple analytical and graphical toolkit for quantum control by Duje Bonacci. DOI: 10.1119/5.0280145
Editor's Note: This paper extends the rotating wave approximation for Rabi oscillations, creating a framework for assessing coherent state control in systems with arbitrarily many levels. It can be taught in an advanced quantum mechanics or quantum optics classroom or used as a research diagnostic
The spinorial ball (II): A manipulable qubit at human scale by Samuel Bernard-Bernardet; Benjamin Apffel. DOI: 10.1119/5.0268275
Editor's Note: This paper builds on a previously published article by the same authors showing how to build a polyhedron with faces that light up according to rules defined in the SU(2) group. It can be rotated at will in space to explore the SO(3) rotation group. The current paper shows how this so-called spinorial ball can mimic the behavior of a spin-1/2 particle and its evolution under a given Hamiltonian. In particular, it shows how the ball can be manipulated to explain basic concepts of quantum information, such as the Berry phase and the Hopf fibration. This paper is appropriate for advanced quantum mechanics classes but could also serve in group theory courses.
A digital version of Rossi's coincidence circuit by Marcello Carlà; Giacomo Poggi; Tommaso Righi; Samuele Straulino. DOI: 10.1119/5.0325826
Editor's Note: In particle detection, signal coincidence is an important tool for distinguishing true from random events. This work revisits a timing circuit and associated experiments from early cosmic-ray experiments by Rossi. Here, the direct analysis of digital timing data allows coincidences to be more closely studied. This provides a useful, detailed introduction to such timing analysis while replicating Rossi's results and providing insight into these important historical experiments.
NOTES AND DISCUSSIONS
ChatGPT as a tutor?—between supporting students and giving away all the answers by Eva Glomski; Cem Yilmaz; Holger Dau; Marcus Kubsch. DOI: 10.1119/5.0311016
Editor's Note: The authors share their experience in creating a customized LLM-based chatbot that provided a sufficient level of assistance that students were willing to use it when solving homework problems. They found that students wanted more direct assistance than they received from the initial Socratic-style chatbot and would instead choose to get the full answer directly from an LLM. However, when they adjusted the prompt so that the LLM told the students how to get started without fully solving the problem, they found higher levels of student buy-in.
INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS
A portable wave–particle duality experiment by Renaud Mathevet; Benoit Chalopin. DOI: 10.1119/5.0333246
Editor's Note: This paper presents a compact, robust apparatus designed to introduce the concept of wave–particle duality. The combination of single-photon detection and time-to-digital conversion is used to observe how interferences in a Michelson interferometer transition from the quantum to the classical limit, with fringes being progressively built up. The setup is design to demonstrate wave–particle duality to a range of audiences, from classroom physics students to the general public at outreach events.
Visualizing Mathieu-type dynamics in a tabletop magnetic trap: A coil-driven parametric oscillator by William Ho; Anna Klales; Daniel Davis; Jieping Fang; Robert Hart; Ali Kurmus; Louis Deslauriers. DOI: 10.1119/5.0321142
Editor's Note: The authors present a setup in which a permanent magnet is confined within anti-Helmholtz coils by a time-averaged harmonic (ponderomotive) restoring force, an effect crucial in ion trapping. The paper provides a clear exposition of the underlying mathematics of the problem, along with a detailed description of experimental procedures in which most of the features of interest are directly visible to the eye. Quantitative studies are possible by employing video tracking of the trapped magnet's motion. This project can be used as a classroom demonstration or adopted for an advanced undergraduate laboratory, and will be of special interest to institutions with an experimental group working with ion traps.
Simulated gravitational lensing in the undergraduate laboratory by Daniel FitzGreen. DOI: 10.1119/5.0292430
Editor's Note: Gravitational lensing is an extraordinary prediction of general relativity, and the visual effects it produces are striking: distortions, multiple images, Einstein rings. Many of these optical effects can be demonstrated with custom-made lenses, or even the base of a wine glass. This article takes the optical analogy further and presents a quantitative study of CNC-machined acrylic lenses, suitable for undergraduate laboratories. The author demonstrates experiments with strong lensing (Einstein rings), weak lensing (gravitational shear), and microlensing (apparent brightening of a source). Image analysis techniques from modern astronomy applied to data collected in the lab yield the effective mass of the object used in the design of the lens. The experiments described here could be incorporated across the physics curriculum—from standard three-hour labs in introductory physics, optics, astronomy, or astrophysics courses, to longer experiments in an advanced lab course, to student projects. The author has provided a comprehensive supplement for anyone who wishes to introduce and explore gravitational lensing in their own lab: instructional videos, notes, CAD files for lenses, ImageJ macros for image analysis, and Python code for designing lenses, collecting data, and analyzing data.
COMPUTATIONAL PHYSICS
Introduction to the neural network-based variational Monte Carlo method by William Freitas. DOI: 10.1119/5.0348107
Editor's Note: The author explains how neural networks can act as a trial wave function to produce essentially exact results for the ground state and wave function and perform better than traditional variational methods. Examples are given for the Yukawa potential and the hydrogen molecule. The paper also provides some guidance into how to construct neural networks for machine learning in physics problems.
ADVANCED TOPICS
Boomeranging through the Earth: When free fall doesn't maximize proper time by Henrique Gomes. DOI: 10.1119/5.0332126
Editor's Note: This analysis offers insights that will likely surprise students who have only just recently commenced a study of general relativity. Contrary to the special theory of relativity, there do exist geodesics along which the elapse of proper time is less than along non-geodesics paths. It is a simple theoretical situation in which an evacuated cylinder provides a geodesic passage through the center of the earth, reaches the opposite side, and then returns. This could indeed lead instructors to attract more students to general relativity studies. Many additional features of this straightforward discussion will provide incentive to delve more deeply into the theory.
NOTES AND DISCUSSIONS
The leaning tower of Lire with variable block mass by Chenguang Zhang (张晨光). DOI: 10.1119/5.0309013
Editor's Note: A classic block-stacking puzzle becomes more interesting when the blocks have different masses. Readers discover how changing thickness or density can make the total overhang shrink, grow slowly, or even increase linearly. The “Lire Tower Transform,” a neat way to turn a mass sequence into an overhang pattern, is also introduced, which may be interesting for teaching sequences. By blending physical intuition, analytical results, and simple numerical tools, one may explore different stacking behaviors with ease.
Entropy as the geometric mean of partitioning: A pedagogical derivation from effective state counting by Kyongwan Kim; Gyeong-Pil Kwon; Jinho Lee. DOI: 10.1119/5.0330859
Editor's Note: Demonstrating the equivalence of the Boltzmann formulation of the entropy, , and the Gibbs–Shannon formulation of entropy, , normally requires significant mathematical manipulations. For instructors of statistical mechanics who would like to provide a more intuitive justification, this manuscript provides a teaching strategy involving counting the effective number of states available to the system.
Comment on “The ‘Littlewood's’ hopping hoop dynamics” [Am. J. Phys. 94, 359–362 (2026)] by Rod Cross. DOI: 10.1119/5.0340419
Editor's Note: Readers of our recent article on Littlewood's hopping hoop will be interested in this expanded discussion, which includes friction effects, different initial conditions, and new experimental data.
Additional Resources
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