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arXiv:2005.07560 · American Journal of Physics

Can students apply the concept of “which-path” information learned in the context of Mach–Zehnder interferometer to the double-slit experiment?

Alexandru Maries, Ryan Sayer, Chandralekha Singh

Published Jun 18, 2020• 25 citations
arXivHTMLPDF

Abstract

The ability to use concepts learned in one context to solve problems in a different context (i.e., transfer of learning) is often one of the major goals of physics instruction. After all, the ability to transfer learning from one context to another is a prerequisite to recognizing the applicability of compact physical laws to a multitude of contexts and is a hallmark of expertise in physics. The majority of the studies on transfer of learning in physics have focused on introductory students and it has often been found that introductory students have difficulty in effectively transferring their learning and applying what they learned in one situation to another situation. However, compared to advanced students, introductory students have significantly less prior relevant knowledge and skills, which may be crucial for promoting effective transfer. Here, we examine upper-level undergraduate and graduate students' ability to transfer their learning about the concept of “which-path” information and its relation to whether or not interference is observed from the context of the Mach Zehnder interferometer (MZI) to a new context of the double-slit experiment (DSE). Students worked through a tutorial on the MZI in which they learned to use the concept of which-path information to reason about interference of single photons when polarizers with various orientations are placed in one or both paths of the MZI. After working on the MZI tutorial, students were asked similar questions in the isomorphic context of the DSE before any instruction about the DSE and we examined the extent to which transfer of learning about which-path information occurred from the MZI to the DSE context. We find evidence suggesting that positive transfer of learning from the MZI to the DSE occurred despite the lack of an instructional intervention designed to help students recognize the similarity between the two contexts. The effectiveness of the MZI tutorial in promoting positive transfer of learning from one context to another in quantum mechanics sheds light on the expertise of the advanced physics students. Instructors of advanced physics courses can take advantage of the findings presented here, which show the difference between introductory and advanced physics students' expertise and ability to transfer from one context to another.

DOI
10.1119/10.0001357

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The ability to use concepts learned in one context to solve problems in a different context (i.e., transfer of learning) is often one of the major goals of physics instruction. After all, the ability to transfer learning from one context to another is a prerequisite to recognizing the applicability of compact physical laws to a multitude of contexts and is a hallmark of expertise in physics. The majority of the studies on transfer of learning in physics have focused on introductory students and it has often been found that introductory students have difficulty in effectively transferring their learning and applying what they learned in one situation to another situation. However, compared to advanced students, introductory students have significantly less prior relevant knowledge and skills, which may be crucial for promoting effective transfer. Here, we examine upper-level undergraduate and graduate students' ability to transfer their learning about the concept of “which-path” information and its relation to whether or not interference is observed from the context of the Mach Zehnder interferometer (MZI) to a new context of the double-slit experiment (DSE). Students worked through a tutorial on the MZI in which they learned to use the concept of which-path information to reason about interference of single photons when polarizers with various orientations are placed in one or both paths of the MZI. After working on the MZI tutorial, students were asked similar questions in the isomorphic context of the DSE before any instruction about the DSE and we examined the extent to which transfer of learning about which-path information occurred from the MZI to the DSE context. We find evidence suggesting that positive transfer of learning from the MZI to the DSE occurred despite the lack of an instructional intervention designed to help students recognize the similarity between the two contexts. The effectiveness of the MZI tutorial in promoting positive transfer of learning from one context to another in quantum mechanics sheds light on the expertise of the advanced physics students. Instructors of advanced physics courses can take advantage of the findings presented here, which show the difference between introductory and advanced physics students' expertise and ability to transfer from one context to another.
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We describe an investigation focusing on advanced students' and faculty members' reasoning about two questions related to the double-slit experiment with single particles.One question posed was a standard double slit question while the other question was more speculative.First, students in advanced quantum mechanics courses were asked the questions in written form and individual interviews were conducted with six students in which they were asked follow up questions to make their thought processes explicit.We also interviewed five faculty members who had taught modern physics, quantum mechanics and/or solid state physics to understand their reasoning and thought processes.The faculty members' responses shed light on what it means to think like a physicist.Student responses varied greatly in their correctness and sophistication of reasoning, suggesting that even advanced students need scaffolding support in order to learn to think like a physicist.
Abstract The Mach–Zehnder interferometer has played an important role both in quantum and classical physics research over the years. In physics education, it has been used as a didactic tool for quantum physics teaching, allowing fundamental concepts, such as particle–wave duality, to be addressed from the very beginning. For a student to understand the novelties of the quantum scenario, it is first worth introducing the classical picture. In this paper, we introduce a new version of the software developed by our research group to deepen the discussion on the classical picture of the Mach–Zehnder interferometer. We present its equivalence with the double slit experiment and we derive the mathematical expressions relating to the interference pattern. We also explore the concept of visibility (which is very important for understanding wave–particle complementarity in quantum physics) to help students become familiar with this experiment and to enhance their knowledge of its counterintuitive aspects. We use the software articulated by the mathematical formalism and phenomenological features. We also present excerpts of the discursive interactions of students using the software in didactic situations.
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In optical experiments involving a single photon that takes alternative paths through an optical system and ultimately interferes with itself (e.g., Young's double-slit experiment, Mach-Zehnder interferometer, Sagnac interferometer), there exist fundamental connections between the linear and angular momenta of the photon on the one hand, and the ability of an observer to determine the photon's path through the system on the other hand. This paper examines the arguments that relate the photon momenta (through the Heisenberg uncertainty principle) to the "which path" (German: welcher Weg) question at the heart of quantum mechanics. We show that the linear momenta imparted to apertures or mirrors, or the angular momenta picked up by strategically placed wave-plates in a system, could lead to an identification of the photon's path only at the expense of destroying the corresponding interference effects. We also describe a thought experiment involving the scattering of a circularly-polarized photon from a pair of small particles kept at a fixed distance from one another. The exchange of angular momentum between the photon and the scattering particle in this instance appears to provide the "which path" information that must, of necessity, wipe out the corresponding interference fringes, although the fringe-wipe-out mechanism does not seem to involve the uncertainty principle in any obvious way.