Pub Date : 2024-03-07DOI: 10.1088/1361-6404/ad312e
Giorgio Margaritondo
The first historical steps of radioactivity research offer an excellent opportunity to teach a key concept of modern physics: non-deterministic phenomena. However, this opportunity is often wasted because of historical misconceptions and of the irrational fear of radioactive effects. We propose here a lecturing strategy - primarily for undergraduate students - based on interesting historical facts. In particular, on a key conceptual contribution by Marie Curie, an attractive figure for the young women and men of today. Paradoxically, this milestone is almost unknown, whereas it should contribute to her immortal fame -- perhaps as much as the discovery of radium.
{"title":"Teaching about non-deterministic physics: an almost forgotten fundamental contribution of Marie Curie","authors":"Giorgio Margaritondo","doi":"10.1088/1361-6404/ad312e","DOIUrl":"https://doi.org/10.1088/1361-6404/ad312e","url":null,"abstract":"\u0000 The first historical steps of radioactivity research offer an excellent opportunity to teach a key concept of modern physics: non-deterministic phenomena. However, this opportunity is often wasted because of historical misconceptions and of the irrational fear of radioactive effects. We propose here a lecturing strategy - primarily for undergraduate students - based on interesting historical facts. In particular, on a key conceptual contribution by Marie Curie, an attractive figure for the young women and men of today. Paradoxically, this milestone is almost unknown, whereas it should contribute to her immortal fame -- perhaps as much as the discovery of radium.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"19 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140261026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-04DOI: 10.1088/1361-6404/ad2fd8
I. Bonnet, Julien Gabelli
Grating and its well-known diffraction pattern are the basis of spectrometers to characterize light sources. Reciprocally, periodic peaks in the diffraction pattern of X-rays scattered by solids bring valuable information about the internal geometry of the crystal lattice, providing details about the arrangement of atoms in the solid. In both cases, periodic gratings are considered. What about non-periodic gratings? Is it possible to reconstruct any grating structure knowing its diffraction pattern? We answer this question by studying diffraction through the hologram hidden in a Canadian banknote. We measure the diffraction of near-infrared light to numerically reconstruct the grating structure using the Gerchberg-Saxton algorithm. We then compare this reconstructed grating structure with the picture of the grating structure observed with a phase-contrast microscope. Such an approach allows us to study diffraction from a perspective different from that usually taught at university.
光栅及其众所周知的衍射图样是光谱仪鉴定光源的基础。与此相对应，固体散射的 X 射线衍射图样中的周期性峰值也带来了有关晶格内部几何形状的宝贵信息，提供了有关固体中原子排列的详细信息。在这两种情况下，考虑的都是周期性光栅。那么非周期性光栅呢？是否可以通过衍射图样重建任何光栅结构？我们通过研究隐藏在加拿大钞票中的全息图的衍射来回答这个问题。我们测量近红外光的衍射，利用格希伯格-萨克斯顿算法对光栅结构进行数值重建。然后，我们将重建的光栅结构与相位对比显微镜观察到的光栅结构图进行比较。这种方法使我们能够从不同于大学通常教授的角度来研究衍射。
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Pub Date : 2024-02-15DOI: 10.1088/1361-6404/ad29d3
Manfred Euler
Although synchronization effects play an important role in many areas of basic and applied science, their treatment in undergraduate physics courses requires more attention. Based on acoustic experiments with a driven organ pipe, the article proposes analytical, numerical and qualitative approaches to this universal phenomenon, suitable for introductory teaching. The Adler equation is developed, a first-order nonlinear differential equation describing the phase dynamics of driven self-sustained oscillations in the weak coupling limit. Analytical solutions, intuitive mechanical analogues and properties of the resulting comb spectra are discussed. The underlying phase model is paradigmatic for synchronization-based self-organization phenomena in a wide range of fields, from physics and engineering to life and social sciences.
{"title":"Universal synchronization: Acoustic experiments, the phase oscillator model and mechanical analogues","authors":"Manfred Euler","doi":"10.1088/1361-6404/ad29d3","DOIUrl":"https://doi.org/10.1088/1361-6404/ad29d3","url":null,"abstract":"\u0000 Although synchronization effects play an important role in many areas of basic and applied science, their treatment in undergraduate physics courses requires more attention. Based on acoustic experiments with a driven organ pipe, the article proposes analytical, numerical and qualitative approaches to this universal phenomenon, suitable for introductory teaching. The Adler equation is developed, a first-order nonlinear differential equation describing the phase dynamics of driven self-sustained oscillations in the weak coupling limit. Analytical solutions, intuitive mechanical analogues and properties of the resulting comb spectra are discussed. The underlying phase model is paradigmatic for synchronization-based self-organization phenomena in a wide range of fields, from physics and engineering to life and social sciences.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"14 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139774497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-15DOI: 10.1088/1361-6404/ad29d3
Manfred Euler
Although synchronization effects play an important role in many areas of basic and applied science, their treatment in undergraduate physics courses requires more attention. Based on acoustic experiments with a driven organ pipe, the article proposes analytical, numerical and qualitative approaches to this universal phenomenon, suitable for introductory teaching. The Adler equation is developed, a first-order nonlinear differential equation describing the phase dynamics of driven self-sustained oscillations in the weak coupling limit. Analytical solutions, intuitive mechanical analogues and properties of the resulting comb spectra are discussed. The underlying phase model is paradigmatic for synchronization-based self-organization phenomena in a wide range of fields, from physics and engineering to life and social sciences.
{"title":"Universal synchronization: Acoustic experiments, the phase oscillator model and mechanical analogues","authors":"Manfred Euler","doi":"10.1088/1361-6404/ad29d3","DOIUrl":"https://doi.org/10.1088/1361-6404/ad29d3","url":null,"abstract":"\u0000 Although synchronization effects play an important role in many areas of basic and applied science, their treatment in undergraduate physics courses requires more attention. Based on acoustic experiments with a driven organ pipe, the article proposes analytical, numerical and qualitative approaches to this universal phenomenon, suitable for introductory teaching. The Adler equation is developed, a first-order nonlinear differential equation describing the phase dynamics of driven self-sustained oscillations in the weak coupling limit. Analytical solutions, intuitive mechanical analogues and properties of the resulting comb spectra are discussed. The underlying phase model is paradigmatic for synchronization-based self-organization phenomena in a wide range of fields, from physics and engineering to life and social sciences.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"431 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139833979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-06DOI: 10.1088/1361-6404/ad26b4
Michael V Berry
Waves in the plane, punctured by excision of a small disk with radius much smaller than the wavelength, can be modified by being forced to vanish on the boundary of the disk. Such waves exhibit a logarithmically thin ‘pinprick’, and logarithmically weak oscillations persisting far away. As the radius vanishes, these modifications become asymptotically invisible. Examples are punctured plane waves, and a punctured unit disk; in the latter case, the pinprick causes a logarithmic shift in the eigenvalues. It is conjectured that the plane can be densely covered with asymptotically invisible pinpricks, and that there are analogous phenomena in higher dimensions. The curious phenomenon of pinpricks is not hard to understand, and would be worth presenting in graduate courses on waves.
{"title":"Logarithmic pinpricks in wavefunctions","authors":"Michael V Berry","doi":"10.1088/1361-6404/ad26b4","DOIUrl":"https://doi.org/10.1088/1361-6404/ad26b4","url":null,"abstract":"\u0000 Waves in the plane, punctured by excision of a small disk with radius much smaller than the wavelength, can be modified by being forced to vanish on the boundary of the disk. Such waves exhibit a logarithmically thin ‘pinprick’, and logarithmically weak oscillations persisting far away. As the radius vanishes, these modifications become asymptotically invisible. Examples are punctured plane waves, and a punctured unit disk; in the latter case, the pinprick causes a logarithmic shift in the eigenvalues. It is conjectured that the plane can be densely covered with asymptotically invisible pinpricks, and that there are analogous phenomena in higher dimensions. The curious phenomenon of pinpricks is not hard to understand, and would be worth presenting in graduate courses on waves.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"18 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139861971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-06DOI: 10.1088/1361-6404/ad26b4
Michael V Berry
Waves in the plane, punctured by excision of a small disk with radius much smaller than the wavelength, can be modified by being forced to vanish on the boundary of the disk. Such waves exhibit a logarithmically thin ‘pinprick’, and logarithmically weak oscillations persisting far away. As the radius vanishes, these modifications become asymptotically invisible. Examples are punctured plane waves, and a punctured unit disk; in the latter case, the pinprick causes a logarithmic shift in the eigenvalues. It is conjectured that the plane can be densely covered with asymptotically invisible pinpricks, and that there are analogous phenomena in higher dimensions. The curious phenomenon of pinpricks is not hard to understand, and would be worth presenting in graduate courses on waves.
{"title":"Logarithmic pinpricks in wavefunctions","authors":"Michael V Berry","doi":"10.1088/1361-6404/ad26b4","DOIUrl":"https://doi.org/10.1088/1361-6404/ad26b4","url":null,"abstract":"\u0000 Waves in the plane, punctured by excision of a small disk with radius much smaller than the wavelength, can be modified by being forced to vanish on the boundary of the disk. Such waves exhibit a logarithmically thin ‘pinprick’, and logarithmically weak oscillations persisting far away. As the radius vanishes, these modifications become asymptotically invisible. Examples are punctured plane waves, and a punctured unit disk; in the latter case, the pinprick causes a logarithmic shift in the eigenvalues. It is conjectured that the plane can be densely covered with asymptotically invisible pinpricks, and that there are analogous phenomena in higher dimensions. The curious phenomenon of pinpricks is not hard to understand, and would be worth presenting in graduate courses on waves.","PeriodicalId":505733,"journal":{"name":"European Journal of Physics","volume":"112 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139802163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-05DOI: 10.1088/1361-6404/ad261c
Anastasios Kapodistrias, J. Airey
Researchers generally agree that physics experts use mathematics in a way that blends mathematical knowledge with physics intuition. However, the use of mathematics in physics education has traditionally tended to focus more on the computational aspect (manipulating mathematical operations to get numerical solutions) to the detriment of building conceptual understanding and physics intuition. Several solutions to this problem have been suggested; some authors have suggested building conceptual understanding before mathematics is introduced, while others have argued for the inseparability of the two, claiming instead that mathematics and conceptual physics need to be taught simultaneously. Although there is a body of work looking into how students employ mathematical reasoning when working with equations, the specifics of how physics experts use mathematics blended with physics intuition remain relatively underexplored. In this paper, we describe some components of this blending, by analyzing how physicists perform the rearrangement of a specific equation in cosmology. Our data consist of five consecutive forms of rearrangement of the equation, as observed in three separate higher education cosmology courses. This rearrangement was analyzed from a conceptual reasoning perspective using Sherin’s framework of symbolic forms. Our analysis clearly demonstrates how the number of potential symbolic forms associated with each subsequent rearrangement of the equation decreases as we move from line to line. Drawing on this result, we suggest an underlying mechanism for how physicists reason with equations. This mechanism seems to consist of three components: narrowing down meaning potential, moving aspects between the background and the foreground and purposefully transforming the equation according to the discipline’s questions of interest. In the discussion section we highlight the potential that our work has for generalizability and how being aware of the components of this underlying mechanism can potentially affect physics teachers’ practice when using mathematics in the physics classroom.
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Pub Date : 2024-02-05DOI: 10.1088/1361-6404/ad261e
J. Stergar, S. Čopar
A good experimental task for a high school physics competition requires an interesting and relatable topic, careful testing, and meeting constraints of time, budget and curriculum. This article presents the experimental task from the European Physics Olympiad in the year 2022. The students explored the properties of light sources, such as their colour temperature, angular light distribution, efficacy and heating. The task was stated without explicit instructions, inviting the students to devise their own approach to measurement and data processing. The original task was designed for the level slightly above the European high-school curriculum, so parts of it can be directly used as a lab exercise at a university level, or simplified and given more specific instructions for inclusion in high school level education.
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Pub Date : 2024-02-05DOI: 10.1088/1361-6404/ad261e
J. Stergar, S. Čopar
A good experimental task for a high school physics competition requires an interesting and relatable topic, careful testing, and meeting constraints of time, budget and curriculum. This article presents the experimental task from the European Physics Olympiad in the year 2022. The students explored the properties of light sources, such as their colour temperature, angular light distribution, efficacy and heating. The task was stated without explicit instructions, inviting the students to devise their own approach to measurement and data processing. The original task was designed for the level slightly above the European high-school curriculum, so parts of it can be directly used as a lab exercise at a university level, or simplified and given more specific instructions for inclusion in high school level education.
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Pub Date : 2024-02-05DOI: 10.1088/1361-6404/ad261c
Anastasios Kapodistrias, J. Airey
Researchers generally agree that physics experts use mathematics in a way that blends mathematical knowledge with physics intuition. However, the use of mathematics in physics education has traditionally tended to focus more on the computational aspect (manipulating mathematical operations to get numerical solutions) to the detriment of building conceptual understanding and physics intuition. Several solutions to this problem have been suggested; some authors have suggested building conceptual understanding before mathematics is introduced, while others have argued for the inseparability of the two, claiming instead that mathematics and conceptual physics need to be taught simultaneously. Although there is a body of work looking into how students employ mathematical reasoning when working with equations, the specifics of how physics experts use mathematics blended with physics intuition remain relatively underexplored. In this paper, we describe some components of this blending, by analyzing how physicists perform the rearrangement of a specific equation in cosmology. Our data consist of five consecutive forms of rearrangement of the equation, as observed in three separate higher education cosmology courses. This rearrangement was analyzed from a conceptual reasoning perspective using Sherin’s framework of symbolic forms. Our analysis clearly demonstrates how the number of potential symbolic forms associated with each subsequent rearrangement of the equation decreases as we move from line to line. Drawing on this result, we suggest an underlying mechanism for how physicists reason with equations. This mechanism seems to consist of three components: narrowing down meaning potential, moving aspects between the background and the foreground and purposefully transforming the equation according to the discipline’s questions of interest. In the discussion section we highlight the potential that our work has for generalizability and how being aware of the components of this underlying mechanism can potentially affect physics teachers’ practice when using mathematics in the physics classroom.
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