February 2025
Volume 93, Issue No. 2
The spinorial ball: A macroscopic object of spin-1/2
In quantum physics lectures, half-integer spins are generally introduced as “objects that do not come back to their original state after one full turn but that do after two.” As a consequence, students often consider this behavior to be purely quantum mechanical. However, spin-1/2 is above all a geometrical property of the rotations group and can, therefore, also have practical consequences at the macroscopic scale. To illustrate this, we introduce and describe in this work a new pedagogical tool named the spinorial ball. It allows students to concretely manipulate a macroscopic 1/2-spin, which helps them to build intuition as to how the latter behaves under rotations. This object can also be used to introduce several general concepts from the theory of Lie groups, such as group homomorphism and homotopy classes of loops through the example of the groups SU(2) and SO(3). The spinorial ball provides a macroscopic visualization of all these concepts, which are ubiquitous in quantum physics.
EDITORIAL
In this issue: February 2025 by Joanna Behrman; John Essick; Harvey Gould; Claire A. Marrache-Kikuchi; Beth Parks; B. Cameron Reed; Jan Tobochnik; Keith Zengel. DOI: 10.1119/5.0254806
PAPERS
Ergodic Lagrangian dynamics in a superhero universe by I. L. Tregillis; George R. R. Martin. DOI: 10.1119/5.0228859
Editor's Note: Looking for a new way to engage your students' imagination, encourage their exploration and curiosity around open-ended physics research questions, and help them find new ways to understand their life, their studies, and their careers through the power of science fiction? If so, these authors (of both this article and some of the Wild Cards science fiction series) have an idea that might interest you: a mathematical study of a fictional super hero universe where an extraterrestrial pathogen—the “wild card” virus—causes death most of the time, physical mutation some of the time, and superhuman abilities in rare cases. This long-term project might serve as a recurring theme over a semester in a related course, as an honors seminar, or as a fun elective during a brief term.
A story with twists and turns: How to control the rotation of the notched stick Scilight by Martin Luttmann; Michel Luttmann. DOI: 10.1119/5.0225847
Editor's Note: Many readers have asked the question: why does the Gee-Haw-Whammy-Diddle spin the way it does? They would ask this question if they had seen someone rub a wooden dowel against a notched stick with a propeller attached at its end and claim to cause the propeller to rotate one way by exclaiming “gee!” and the other way by exclaiming “haw!” Well, these authors have a new and more complete explanation for how the trick works: it is all about how you hold the notched stick. In addition to a persuasive model and video demonstration, they present an elegant experimental test of the model that might make a nice project or demo in your classical mechanics courses.
The most efficient thermodynamic cycle under general engine constraints by Christopher Ong; Shaun Quek. DOI: 10.1119/5.0199979
Editor's Note: Thermodynamics courses normally consider heat engines that exchange energy with thermal reservoirs at fixed temperatures, showing that the Carnot cycle is the most efficient engine cycle under these constraints. However, most real heat engines have different constraints, such as limitations on volume ratios or pressure extremes. This very readable paper shows how to find the most efficient cycle based on the type of constraint and applies this methodology to show that the Brayton and Otto cycles are the most efficient if the engine is constrained to a rectangular region of P–V space.
Introducing key theoretical and data analysis tools in computational physics via Earth's temperature and climate by David Syphers. DOI: 10.1119/5.0224293
Editor's Note: This paper provides two introductory computing activities on topics that students will find both compelling and understandable. The author has identified common pitfalls in computing and carefully designed exercises that will help students avoid them. The activities can be used together or separately. They are appropriate not only for courses that focus on computing but also for those that focus on climate, if the instructor wishes to introduce computational exercises.
Beneath and beyond frustrated total reflection: A practical demonstration by Carolina Filgueira-Rama; Alejandro Doval; Yago Arosa; Raúl de la Fuente. DOI: 10.1119/5.0207113
Editor's Note: Total internal reflection occurs when light passes from one medium into another of lower refractive index at an angle greater than the so-called critical angle. However, the term is misleading; the field of the incident wave actually penetrates evanescently into the second medium to a depth of the order of a wavelength. This effect can be “frustrated” by introducing a third medium of refractive index greater than the lower-index medium close to the interface so that the low-index medium becomes an intermediate thin layer; in this case, the evanescent wave couples to the new medium and continues to propagate. In the experiment described in this paper, this effect is investigated by trapping a thin layer of air or water between two prisms and using a laser as the light source. In most such experiments, the width of the trapped layer is varied while the angle of incidence is kept fixed and transmitted/reflected intensities are measured. Adjusting the width is difficult, and the novel aspect here is that the thickness of the layer is fixed while the angle of incidence is varied. This allows the authors to investigate intensities at angles both above and below the critical angle. Results are in respectable accord with theory; the authors also discuss an analogy with quantum tunneling. Appropriate for upper-level optics/electromagnetic theory students.
The spinorial ball: A macroscopic object of spin-1/2 by Samuel Bernard-Bernardet; Emily Dumas; Benjamin Apffel. DOI: 10.1119/5.0160770
Editor's Note: If you ever wanted to hold a spin-1/2 particle in your hands, this paper is for you. If you follow the authors' instructions, you will end up with a polyhedron with faces that light up according to rules defined in the SU(2) group, and which you will be able to rotate at will (and thus explore the SO(3) rotation group). The so-called spinorial ball then behaves as a spin-1/2 object in that it has to experience a rotation about a given axis to come back to its initial state. As you will be able to show by playing with the ball, this important property of spins-1/2 is actually a consequence of the interplay between two rotation groups. This paper, which will help you build a demonstration experiment for introductory quantum mechanics classes, could also be the basis of an exercise in undergraduate group theory classes or electronics labs.
Teaching quantum mechanics within a nature-of-science framework
In Special Collection: Celebrating the International Year of Quantum Science and Technology by Marco Giliberti; Luisa Lovisetti. DOI: 10.1119/5.0210636
Editor's Note: In order for the general public to understand the process by which science progresses, secondary school teachers need to develop an understanding of the nature of science. This paper shares an approach for teaching quantum mechanics to pre-service and in-service secondary teachers that develops their understanding of the nature of science by carefully considering experimental evidence, then developing a set of physical principles, extracting axioms, and developing mathematical representations. Instructors who want to ground their teaching of quantum mechanics in a careful consideration of how the theory developed will appreciate the many teaching resources shared in this paper and its online supplementary material.
INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS
A versatile Hong–Ou–Mandel interference experiment in optical fiber for the undergraduate laboratory by Cyrus Bjurlin; Theresa Chmiel. DOI: 10.1119/5.0210869
Editor's Note: The Hong–Ou–Mandel (HOM) experiment provides an intuitive demonstration of quantum interference and particle indistinguishability. However, the original free-space version of this experiment is notoriously difficult to align, requiring excellent spatial and temporal overlap of two identical photons. This paper presents a simplified version of the HOM experiment that is suitable for the undergraduate instructional laboratory, enabling students to gather data on the signature “HOM dip.” The use of a commercial photon-pair source and fused-fiber coupler greatly reduces the required optical alignments, while students gain hands-on experience by constructing a free-space propagation section. This versatile system allows students to explore the consequences of degrading the indistinguishability of the two interfering photons through manipulating their path length differences, by introducing slightly nondegenerate frequencies, and varying polarizations. Typical experimental results are presented, along with the theory needed to analyze those data.
Advanced undergraduate lab on quantum beats by M. J. Wright; R. Beban; O. Chierchio; L. McCluney; T. Peña; J. P. St. John. DOI: 10.1119/5.0223788
Editor's Note: This paper presents a modern take on the quantum beat experiment. The authors use a commercially available distributed feedback laser, along with electro-optical and acousto-optical modulators, to generate short laser pulses. These laser pulses are used to excite rubidium atoms into a superposition of multiple atomic states, and the resulting polarized fluorescence decay data are collected. The necessary quantum theory for analyzing these data is presented and then used to determine the lifetime of the Rb excited state. In addition, the oscillatory behavior present in the decay data is analyzed via a Fourier transform, yielding values for the frequency differences of the excited Rb hyperfine levels. This project offers a clear demonstration of important quantum concepts and is suitable as an instructional laboratory for advanced undergraduates.
COMPUTATIONAL PHYSICS
Monte Carlo, blocking, and inference: How to measure the renormalization group flow by Luca Di Carlo. DOI: 10.1119/5.0223788
Editor's Note: Working in the context of the Ising model, this computational physics paper introduces numerical methods used to measure renormalization group flow. Recent developments in inverse Ising model techniques and increases in computational power now allow students to verify this aspect of renormalization group theory.
Additional Resources
 |