Abstract The Copenhagen interpretation allows probabilistic statements about individual quantum objects, whereas the ensemble interpretation, which is also used in school contexts, restricts probabilistic statements to ensembles and does not make such statements about individual quantum objects. This exploratory study investigated upper-secondary-school students’ responses to the Copenhagen and ensemble interpretations of a single-photon beam-splitter experiment. In particular, it examined students’ plausibility judgements, references to individual photons, and use of animistic language. Data were collected through guideline-based interviews with ten upper-secondary-school students who were introduced to either the Copenhagen or the ensemble interpretation. All five students introduced to the Copenhagen interpretation regarded it as plausible. Among the five students introduced to the ensemble interpretation, one regarded it as implausible and one reported difficulties understanding it. References to individual photons were observed in both groups, including four of the five students introduced to the ensemble interpretation. In contrast, animistic language was observed only among students introduced to the Copenhagen interpretation. The study suggests that the choice of interpretation influences students’ acceptance of explanations and their language use. In particular, the possibility of making probabilistic statements about individual quantum objects appears to be associated with students’ use of animistic language when explaining quantum-physical phenomena.
Abstract The Copenhagen interpretation allows probabilistic statements about individual quantum objects, whereas the ensemble interpretation, which is also used in school contexts, restricts probabilistic statements to ensembles and does not make such statements about individual quantum objects. This exploratory study investigated upper-secondary-school students’ responses to the Copenhagen and ensemble interpretations of a single-photon beam-splitter experiment. In particular, it examined students’ plausibility judgements, references to individual photons, and use of animistic language. Data were collected through guideline-based interviews with ten upper-secondary-school students who were introduced to either the Copenhagen or the ensemble interpretation. All five students introduced to the Copenhagen interpretation regarded it as plausible. Among the five students introduced to the ensemble interpretation, one regarded it as implausible and one reported difficulties understanding it. References to individual photons were observed in both groups, including four of the five students introduced to the ensemble interpretation. In contrast, animistic language was observed only among students introduced to the Copenhagen interpretation. The study suggests that the choice of interpretation influences students’ acceptance of explanations and their language use. In particular, the possibility of making probabilistic statements about individual quantum objects appears to be associated with students’ use of animistic language when explaining quantum-physical phenomena.
Despite formal instruction, secondary school students often struggle to move beyond classical interpretations when reasoning about quantum phenomena, especially concerning the statistical nature of quantum physics. This study explores how students conceptualize quantum randomness following instruction centered on two key experiments: the Michelson interferometer (MI) with single photons and the double-slit experiment. Qualitative content analysis of interviews with 25 students revealed three distinct reasoning types: (1) statistical ensemble interpretation, (2) ensemble reasoning involving hidden variables or spatial limitations, and (3) a focus on localization and spatial uncertainty. Notably, students referencing the MI context in their reasonings more often demonstrated advanced ensemble-based reasoning, distinguishing quantum probabilities from classical ones. In contrast, students who relied primarily on the DSE context were more capable of framing their reasoning in terms of spatial uncertainty. These findings highlight the pivotal role of experimental context in fostering students’ quantum thinking and point to promising directions for future research.
For around five decades, physicists have been experimenting with single quanta such as single photons. Insofar as the practised ensemble reasoning has become obsolete for the interpretation of these experiments, the non-classical intrinsic probabilistic nature of quantum theory has gained increased importance. One of the most important exclusive features of quantum physics is the undeniable existence of the superposition of states, even for single quantum objects. One known example of this effect is entanglement. In this paper, two classically contradictory phenomena are combined to one single experiment. This experiment incontestably shows that a single photon incident on an optical beam splitter can either be reflected or transmitted. The almost complete absence of coincident clicks of two photodetectors demonstrates that these two output states are incompatible. However, when combining these states using two mirrors, we can observe interference patterns in the counting rate of the single photon detector. The only explanation for this is that the two incompatible output states are prepared and kept simultaneously—a typical consequence of a quantum superposition of states. (Semi-)classical physical concepts fail here, and a full quantum concept is predestined to explain the complementary experimental outcomes for the quantum optical “non-waves” called single photons. In this paper, we intend to demonstrate that a true quantum physical key experiment (“true” in the sense that it cannot be explained by any classical physical concept), when combined with full quantum reasoning (probability, superposition and interference), influences students’ readiness to use quantum elements for interpretation.
For more details about the files, please open "readme.docx". Abstract This article reports an empirical study involving N = 82 secondary school students, exploring their conceptions of quantum entanglement. The study utilizes a teaching-learning sequence based on photon polarization, covering both single-photon and photon-pair entanglement. Adopting a mixed-methods approach, we analyzed student responses to a questionnaire using quantitative methods and qualitative content analysis. The findings reveal a fragmented knowledge structure among learners. Students demonstrated functional reasoning and competency with mathematical formalism, often anchoring their explanations in specific experimental contexts. However, they frequently reverted to classical, causal, or hidden-variable narratives when interpreting the nature of correlations. While students aligned with quantum perspectives regarding holism and non-separability, they exhibited persistent classical thinking regarding causal influence and interaction. We also observed that students often engaged in overgeneralization of cases of perfect correlation. We conclude that competence in formalism does not necessarily imply a coherent, quantum-consistent understanding. Consequently, we propose specific refinements to the educational material through a design-based methodology — such as the inclusion of partially entangled states and explicit contrasts between classical causation and quantum correlations — to better address deeply rooted classical intuitions and foster a coherent understanding of entanglement.
Clear and rigorous quantum reasoning is needed to explain quantum physical phenomena. As pillars of true quantum physical explanations, we suggest specific quantum reasoning derived from quantum physical key ideas. An experiment is suggested to support such a quantum reasoning, in which a quantized radiation field interacts with an optical beam splitter, leading to experimental results conflicting with classical physical predictions. The results, however, can be explained consistently with a quantum reasoning based on the key ideas of probability, superposition, and interference (PSI). In this quantum optical key experiment the optical beam splitter prepares a superposition of single photon states and a Michelson interferometer is used to detect the superposition via controlled propagation phases. Although different single photon experimental setups (aimed at helping students to gain access to foundational issues in quantum physics) have been discussed in the past, the wave-particle dualism bound to classical physics maintains its predominance as an explanation pattern for the interpretation of these experiments. The study presented here investigates the effect of the quantum optical key experiment on the ability of students to use quantum reasoning based on the key ideas of PSI to overcome the naive wave-particle dualism. The current state of relevant studies that test student access to quantum physics can roughly be divided into two distinct areas: one tests how mathematical abilities help them to understand quantum physics and one tests how nonmathematical representations of a set of specific quantum theoretical traits (“Wesenszüge”) lead to a deeper understanding of quantum physics. There is a lack of questionnaires that focus on the idea of developing quantum reasoning based on superposition, probability, and interference of quantum states combined with a real experiment using true quantum light. In the first part of the article, we describe the physical modeling and present the development of the questionnaire. The set of items has been constructed from newly developed items and combined with well-tested ones. The validation of the set addresses qualitative and quantitative methods. In the second part, we give a pre- and poststudy examination of the impact of the quantum optical key experiment on students’ quantum reasoning. A significant increase in the number of students using quantum arguments is based on PSI reasoning for the explanation of an interference, such as the behavior of single photon states. Though the increase is significant, we found only minor changes in a particular issue to the students’ reasoning when approaching quantum physics as illustrated by a sample of answers given in the second part of the article. The concept of quantum states and the principle of superposition still appear particularly difficult. Published by the American Physical Society 2024
Quantum mechanics is included in many curricula across countries because of its cultural value and technological application. In the last decades, two-state approaches to quantum mechanics became popular because of the age of quantum computers. This article presents an experiment with 24 Hungarian high school students on teaching/learning quantum mechanics according to Dirac’s approach to concepts and basic formalism developed in the context of light polarization. Tutorials, pre/post-tests, and oral interviews are the main monitoring tools used to collect data on the students’ learning path. From the qualitative and quantitative data analysis, learning progressions emerged in the phenomenology exploration and on the probabilistic nature of single quantum measurement. The students’ conceptions of quantum state are enriched, confirming the importance to focus educational approaches on fundamental topics. For one section of students, the complex relationship between quantum state and property remained problematic, but the students’ interpretations of a quantum state can be categorized. Two lines of reasoning emerged regarding the impossibility to attribute a trajectory to a quantum system, one more orthodox and one that seeks to avoid the probabilistic nature of the quantum world.
Abstract Physics education research has revealed that students have multiple ways of understanding the concept of the photon and that students’ use of it is often incoherent and incomplete. In this study, we explore what kinds of statements pre-service physics teachers and university physics students choose on a multiple-choice questionnaire, designed to reveal students’ stances on three conceptual views of the photon (quantum state, quantum realistic, and naïve dualistic) in the context of quantum optical experiments. The questionnaire was conducted in a pre-post manner. The test group (pre-service physics teachers N = 13) attended an introductory quantum physics course which emphasised coherent use of natural language, and the control group (university physics students pre N = 33, post N = 25) attended a standard introductory course in quantum physics. Pre-test results show that both groups expressed incoherent use of the concept of the photon. The post-test results reveal that after teaching intervention, the test group showed significant improvement in the coherent use of the concept of the photon as a quantum state. The post-test results of the control group remained incoherent. The results show that paying attention to the coherent use of natural language in teaching quantum physics helps pre-service physics teachers to recognise and choose coherent expressions about the photon.