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European Journal of Physics

All possible paths: bringing quantum electrodynamics to classrooms

R. K. Choudhary, D. G. Blair

Published Mar 16, 2021• 5 citations
Publisher

Abstract

Abstract Quantum electrodynamics was described by Feynman as the ‘jewel of physics’ [1985 QED: The Strange Theory of Light and Matter (Alix G. Mautner Memorial Lectures) (Princeton, NJ: Princeton University Press)] because of its ability to precisely describe the interaction of light and matter. It embodies the key concepts of quantum physics and yet also describes classical optics. It is normally considered to be too advanced for use in schools. Here we show that through the use of novel learning tools called phasor wheels , it is possible to make quantum electrodynamics accessible to students from middle school and higher. Our graphical approach is based on the summation of all possible paths (formally known as Feynman path integrals). It uses graphical vector addition, and gives students a deep understanding of vectors. It offers insights into the quantum world in which observations represent quantum probability density, while correctly describing the laws of classical optics. The phasor wheel is a tactile tool that allows students to compute the probability of photons arriving at a point in space and to explore phenomena such as matter–wave interference, diffraction, and reflection without any distinction between quantum or classical. To make it accessible, we combine the phasor tool with real-life analogies, and videos of single quanta interference. Needing only elementary mathematics, the approach is suitable for middle/upper secondary schools as well early undergraduate students.

DOI
10.1088/1361-6404/abef5b

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Abstract Quantum electrodynamics was described by Feynman as the ‘jewel of physics’ [1985 QED: The Strange Theory of Light and Matter (Alix G. Mautner Memorial Lectures) (Princeton, NJ: Princeton University Press)] because of its ability to precisely describe the interaction of light and matter. It embodies the key concepts of quantum physics and yet also describes classical optics. It is normally considered to be too advanced for use in schools. Here we show that through the use of novel learning tools called phasor wheels , it is possible to make quantum electrodynamics accessible to students from middle school and higher. Our graphical approach is based on the summation of all possible paths (formally known as Feynman path integrals). It uses graphical vector addition, and gives students a deep understanding of vectors. It offers insights into the quantum world in which observations represent quantum probability density, while correctly describing the laws of classical optics. The phasor wheel is a tactile tool that allows students to compute the probability of photons arriving at a point in space and to explore phenomena such as matter–wave interference, diffraction, and reflection without any distinction between quantum or classical. To make it accessible, we combine the phasor tool with real-life analogies, and videos of single quanta interference. Needing only elementary mathematics, the approach is suitable for middle/upper secondary schools as well early undergraduate students.
This chapter introduces the powerful Feynman path integral approach to quantum mechanics. It is intended for readers who are interested in a non-mathematical approach to quantum physics at the middle and high-school level. Einstein's discovery of light quanta played a major role in the birth of quantum mechanics. Einstein made the bold prediction that light comes as a stream of particles called “light quanta”. Photons, like bullets, carry momentum that applies forces to mechanical objects. The method of phasors that, the authors applied to radio waves works equally for visible photons and even for particles such as electrons and molecules. Feynman's method of all possible paths assumes a large number of possible paths. Single-photon counting experiments and laser technology allow the reader to see deeply into the quantum world. The videos of single-particle interference consolidate the idea of photons and their intrinsic randomness.
Quantum probability and quantum spin are foundational concepts in quantum physics, not normally taught in pre-university education. In line with recent efforts to modernize quantum science education in schools, this paper presents learning sequences designed to provide an introductory conceptual understanding of these core physical concepts. This is achieved by choosing physical models that provide tangible classical representations that can be contrasted with quantum observations relevant to modern science and technology. This approach allows activity-based learning without the use of algebra. The concept of quantum probability is taught through activities with phasor wheels in which quantum probability is obtained graphically and interpreted using single-photon interference data. Quantum spin and spin vectors are taught by contrasting quantum spin with classical spin, explored through activities with gyroscopes and spinning tops. Quantum concepts are evoked by emphasizing how spin is different and how it manifests in real-world technologies such as magnets and MRI imaging. We describe learning sequences developed following the Model of Educational Reconstruction in which historical discoveries are combined with activities based on classical models and relevant quantum applications. We summarize test results from programs conducted with students aged 11–15. Most students connect the models and activities to quantum concepts and retain knowledge of quantum spin six months after the program. The successful learning outcomes indicate that teachers can effectively introduce quantum probability and quantum spin concepts to middle school using learning sequences such as those presented here.
We analyse part of the implementation of a didactic sequence to teach different aspects of light in a unified non traditional framework. The goal was to propose the quantum theory of light as a universal framework to describe different phenomena observed. The laws of quantum mechanics for light using Feynman´s “Sum of all Paths” approach adapted to the mathematical level of the students was proposed as a model to explain the experiences. This particular denomination of Feynman´s approach is an intentional choice to avoid the language of "integral" because the students haven't had calculus. Graphic representations and basic operations with vectors capturing the essential aspects of the theory, were used. Simulations made with the software GeoGebra(R) and Modellus were created to help students visualize the formulation. The sequence was carried out in four courses (aged 15-16). For the data analysis, an answer categorization was formulated, considering among other aspects the quantum reformulation of experiment shown herein. This analysis seeks to understand the student´s conceptualization process about quantum interpretation. The results support the conclusion that the conceptualization is complex, and slow, due to both the concepts involved and the representation systems demanded by the situations.
The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.
This chapter introduces probabilistic methods in quantum mechanics, focusing on photon behavior, demonstrating their indivisibility through experiments with single-photon detectors and analyzing probabilistic reflection and transmission at an air-to-glass interface. It introduces phasors to represent quantum events, stating that event probabilities are the squares of phasor amplitudes, and applies this method to analyze partial reflection and transmission, while introducing Heisenberg's uncertainty principle through probabilistic quantum analysis. The chapter explores the quantum mechanical interpretation of photon reflection and transmission at optical interfaces, introducing probability phasors where event amplitudes relate to the square root of probabilities, and discusses partial reflection from optical windows, calculating probabilities of various paths and summing their phasors. It concludes with a quantum interpretation of the law of reflection, showing that classical reflection emerges from summing probability phasors for all possible paths. Additionally, the chapter examines quantum interpretations of classical optical phenomena, demonstrating that straight-line paths are most probable due to aligned probability phasors, and extends this analysis to refraction, slit experiments, and light focusing through lenses, all within a quantum framework accessible through algebra and trigonometry.
Abstract The Einstein-First project approaches the teaching of Einsteinian physics through the use of physical models and analogies. This paper presents an approach to the teaching of quantum physics which begins by emphasising the particle-nature of light through the use of toy projectiles to represent photons. This allows key concepts including the spacing between photons, and photon momentum to be introduced. This in-turn allows an intuitive understanding of the uncertainty principle. We present optical interference in the context of individual photons, using actual videos showing the development of images one at a time. This enables simple laser interference experiments to be interpreted through the statistical arrival of photons. The wave aspects of quantum phenomenon are interpreted in terms of the wavelike nature of the arrival probabilities.