Pub Date : 2024-01-16DOI: 10.1088/1361-6404/ad1531
Zeynep Tugce Ozkarsligil, Bayram Tekin
We give formulas for individual black hole masses in a merger, by using Newtonian physics, in terms of the three measured quantities in the detector: the initial wave frequency f1, the maximum detected frequency (chirp frequency) f2, and the time elapse τ between these two frequencies. Newtonian gravity provides an excellent pedagogical tool to understand the basic features of gravitational wave observations, but it must be augmented with the assumption of gravitational radiation from General Relativity for accelerating masses as there is no gravitational wave Newtonian gravity. The simplest approach would be to consider a binary system of two non-spinning masses (two black holes) circling their common center of mass. All the computations can be done within Newtonian physics, but the General Relativistic formula for the power carried by gravitational waves is required in this scheme. It turns out there is a subtle point: for the consistency of this simple, yet pedagogical computation, taking the lowest order power formula from General Relativity leads to complex individual masses. Here we remedy this problem and suggest a way to write down an average power formula coming from perturbative General Relativity.
{"title":"Mass formulas for individual black holes in merging binaries","authors":"Zeynep Tugce Ozkarsligil, Bayram Tekin","doi":"10.1088/1361-6404/ad1531","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1531","url":null,"abstract":"We give formulas for individual black hole masses in a merger, by using Newtonian physics, in terms of the three measured quantities in the detector: the initial wave frequency <italic toggle=\"yes\">f</italic>\u0000<sub>1</sub>, the maximum detected frequency (chirp frequency) <italic toggle=\"yes\">f</italic>\u0000<sub>2</sub>, and the time elapse <italic toggle=\"yes\">τ</italic> between these two frequencies. Newtonian gravity provides an excellent pedagogical tool to understand the basic features of gravitational wave observations, but it must be augmented with the assumption of gravitational radiation from General Relativity for accelerating masses as there is no gravitational wave Newtonian gravity. The simplest approach would be to consider a binary system of two non-spinning masses (two black holes) circling their common center of mass. All the computations can be done within Newtonian physics, but the General Relativistic formula for the power carried by gravitational waves is required in this scheme. It turns out there is a subtle point: for the consistency of this simple, yet pedagogical computation, taking the lowest order power formula from General Relativity leads to complex individual masses. Here we remedy this problem and suggest a way to write down an average power formula coming from perturbative General Relativity.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139509867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-15DOI: 10.1088/1361-6404/ad1ed6
J. Schilder, Ann-Marie Pendrill
Rotating swings are found in many different versions in parks around the world. They are beautiful examples of the equivalence between gravitational and inertial mass: Empty swings and swings with heavy adults hang at the same angle to the vertical. However, sometimes you may notice empty swings moving in a different pattern in an outdoor ride, where wind can induce additional motion, sideways or back to front, in addition to any oscillations caused by a tilted carousel head. This paper focuses on oscillations for the simpler case of a non-tilting roof. Even for this case, the oscillating motion is found to be complicated by the Coriolis effect, which leads to a gyroscopic coupling between sideways oscillations and back-to-front oscillations. This coupling is illustrated for a few special cases.
{"title":"The Coriolis effect and coupled oscillations in a rotating swings amusement ride","authors":"J. Schilder, Ann-Marie Pendrill","doi":"10.1088/1361-6404/ad1ed6","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1ed6","url":null,"abstract":"\u0000 Rotating swings are found in many different versions in parks around the world. They are beautiful examples of the equivalence between gravitational and inertial mass: Empty swings and swings with heavy adults hang at the same angle to the vertical. However, sometimes you may notice empty swings moving in a different pattern in an outdoor ride, where wind can induce additional motion, sideways or back to front, in addition to any oscillations caused by a tilted carousel head. This paper focuses on oscillations for the simpler case of a non-tilting roof. Even for this case, the oscillating motion is found to be complicated by the Coriolis effect, which leads to a gyroscopic coupling between sideways oscillations and back-to-front oscillations. This coupling is illustrated for a few special cases.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139623111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-29DOI: 10.1088/1361-6404/ad1398
Abdaljalel Alizzi, Zurab K Silagadze, Artem Uskov
We consider in detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties that require attention in order not to go astray.
{"title":"Berry phase of spin-one system in a rotating electric field","authors":"Abdaljalel Alizzi, Zurab K Silagadze, Artem Uskov","doi":"10.1088/1361-6404/ad1398","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1398","url":null,"abstract":"We consider in detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties that require attention in order not to go astray.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-29DOI: 10.1088/1361-6404/ad139a
Jonas Bley, Vieri Mattei, Simon Goorney, Jacob Sherson, Stefan Heusler
The Bloch sphere representation is a geometric model for all possible quantum states of a two-level system that can be used to describe the time dynamics of a qubit. As explicit application, we consider the time dynamics of a particle in a double-well potential. In particular, we adopt a recent method for off-resonant excitations, the so-called SUPER principle (Swing Up of the quantum emitter population) driven by periodic electromagnetic fields, to the context of quantum tunnelling. We show that the tunnelling probability can be enhanced significantly when an appropriate oscillation of the potential height is introduced. Driven by a collaborative approach we call educator-developer dialogue, an updated version of the software Quantum Composer is presented. For educational purposes, we map the two lowest energy states of the 1D-Schrödinger equation to the Bloch sphere representation, leading to a rather clear and intuitive physical picture for the pertinent time dynamics.
布洛赫球表示法是两级系统所有可能量子态的几何模型，可用来描述量子比特的时间动力学。作为明确的应用，我们考虑了双阱势中粒子的时间动力学。特别是，我们采用了一种最新的非共振激发方法，即在周期性电磁场驱动下的所谓 SUPER 原理（量子发射器群的摆动上升），将其应用于量子隧穿。我们的研究表明，当引入适当的势高振荡时，隧穿概率会显著提高。在我们称之为 "教育者-开发者对话 "的合作方法的推动下，我们推出了软件 Quantum Composer 的更新版本。出于教育目的，我们将一维薛定谔方程的两个最低能量状态映射到布洛赫球表示法中，从而为相关的时间动力学提供了一幅相当清晰直观的物理图景。
{"title":"Modelling assisted tunneling on the Bloch sphere using the Quantum Composer","authors":"Jonas Bley, Vieri Mattei, Simon Goorney, Jacob Sherson, Stefan Heusler","doi":"10.1088/1361-6404/ad139a","DOIUrl":"https://doi.org/10.1088/1361-6404/ad139a","url":null,"abstract":"The Bloch sphere representation is a geometric model for all possible quantum states of a two-level system that can be used to describe the time dynamics of a qubit. As explicit application, we consider the time dynamics of a particle in a double-well potential. In particular, we adopt a recent method for off-resonant excitations, the so-called SUPER principle (Swing Up of the quantum emitter population) driven by periodic electromagnetic fields, to the context of quantum tunnelling. We show that the tunnelling probability can be enhanced significantly when an appropriate oscillation of the potential height is introduced. Driven by a collaborative approach we call <italic toggle=\"yes\">educator-developer dialogue</italic>, an updated version of the software Quantum Composer is presented. For educational purposes, we map the two lowest energy states of the 1D-Schrödinger equation to the Bloch sphere representation, leading to a rather clear and intuitive physical picture for the pertinent time dynamics.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139096195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reply to Comment on ‘Covariant formulation of electrodynamics in isotropic media’","authors":"Palash B Pal","doi":"10.1088/1361-6404/ad0dea","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0dea","url":null,"abstract":"This note contains my response to the comment written by J Franklin on my paper ‘Covariant formulation of electrodynamics in isotropic media’.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139054611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-15DOI: 10.1088/1361-6404/ad0f9b
P-M Binder
The predominantly Greek and Latin etymological roots that form the core introductory physics vocabulary are identified. They number slightly over 260. Words with other origins and common suffixes are also listed. Definitions are also given for a group of words that have caused difficulties for students in physics classes, contrasting meanings that are, and are not related to physics. A reverse dictionary of roots, showing the individual origin of about 400 words in all areas of introductory physics is presented in an appendix. The information presented here can inform and assist in developing a physics lexicon in minority and indigenous languages and to create classroom moments that connect the origin of words with everyday life.
{"title":"The origins of physics words","authors":"P-M Binder","doi":"10.1088/1361-6404/ad0f9b","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0f9b","url":null,"abstract":"The predominantly Greek and Latin etymological roots that form the core introductory physics vocabulary are identified. They number slightly over 260. Words with other origins and common suffixes are also listed. Definitions are also given for a group of words that have caused difficulties for students in physics classes, contrasting meanings that are, and are not related to physics. A reverse dictionary of roots, showing the individual origin of about 400 words in all areas of introductory physics is presented in an appendix. The information presented here can inform and assist in developing a physics lexicon in minority and indigenous languages and to create classroom moments that connect the origin of words with everyday life.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138685252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-13DOI: 10.1088/1361-6404/ad0de9
Jerrold Franklin
A recent paper Pal (2022 Eur. J. Phys.43 015204) puts into covariant form an extension of relativistic classical electromagnetism from free space to a linearly polarizable medium. The paper is based on the assumption that the relativistic tensor, Fμν, which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives Fμν for a medium moving with constant velocity, v, in terms of Fμν for the medium at rest. However, although Fμν has been proven to be a relativistic tensor in free space, we show that it is not a tensor in a linear medium. This means that the covariant extension proposed by Pal fails.
最近的一篇论文 Pal (2022 Eur. J. Phys.43 015204) 以共变形式将相对论经典电磁学从自由空间扩展到线性可极化介质。论文基于这样一个假设：相对论张量 Fμν 在自由空间中是一个张量，在线性介质中也是一个张量。Pal 提出了一种协变公式，用静止介质的 Fμν 来表示以恒定速度 v 运动的介质的 Fμν。然而，尽管 Fμν 已被证明是自由空间中的相对论张量，但我们证明它在线性介质中并不是张量。这意味着帕尔提出的协变扩展失败了。
{"title":"Comment on ‘Covariant formulation of electrodynamics in isotropic media’","authors":"Jerrold Franklin","doi":"10.1088/1361-6404/ad0de9","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0de9","url":null,"abstract":"A recent paper Pal (2022 <italic toggle=\"yes\">Eur. J. Phys.</italic>\u0000<bold>43</bold> 015204) puts into covariant form an extension of relativistic classical electromagnetism from free space to a linearly polarizable medium. The paper is based on the assumption that the relativistic tensor, <italic toggle=\"yes\">F</italic>\u0000<sup>\u0000<italic toggle=\"yes\">μ</italic>\u0000<italic toggle=\"yes\">ν</italic>\u0000</sup>, which is a tensor in free space, will also be a tensor in a linear medium. Pal constructs a proposed covariant formulation that gives <inline-formula>\u0000<tex-math>\u0000<?CDATA ${F}^{mu nu }$?>\u0000</tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi><mml:mi>ν</mml:mi></mml:mrow></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ejpad0de9ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> for a medium moving with constant velocity, <bold>v</bold>, in terms of <italic toggle=\"yes\">F</italic>\u0000<sup>\u0000<italic toggle=\"yes\">μ</italic>\u0000<italic toggle=\"yes\">ν</italic>\u0000</sup> for the medium at rest. However, although <italic toggle=\"yes\">F</italic>\u0000<sup>\u0000<italic toggle=\"yes\">μ</italic>\u0000<italic toggle=\"yes\">ν</italic>\u0000</sup> has been proven to be a relativistic tensor in free space, we show that it is not a tensor in a linear medium. This means that the covariant extension proposed by Pal fails.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138685133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-13DOI: 10.1088/1361-6404/ad1530
K. Dupraz, Guillaume Dupuis, A. Martens, J. Rax, F. Zomer
A method to derive the Fraunhofer diffraction integral by making use of the theory of distributions is presented. With respect to standard textbooks, the pedagogical benefit of this method is that it uniquely uses the far field approximation of the Fresnel diffraction integral. An operator representation of Fresnel diffraction is also derived.
{"title":"Fraunhofer approximation of Fresnel integrals","authors":"K. Dupraz, Guillaume Dupuis, A. Martens, J. Rax, F. Zomer","doi":"10.1088/1361-6404/ad1530","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1530","url":null,"abstract":"\u0000 A method to derive the Fraunhofer diffraction integral by making use of the theory of distributions is presented. With respect to standard textbooks, the pedagogical benefit of this method is that it uniquely uses the far field approximation of the Fresnel diffraction integral. An operator representation of Fresnel diffraction is also derived.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139004554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-08DOI: 10.1088/1361-6404/ad1397
Yi-Fen Zhao, Fei-Jie Huang
A pedagogical approach to introducing the honeycomb lattice gauge theory is presented. Lattice gauge theory, which is an important theory for understanding strongly correlated systems, is a significant topic covered in the quantum field theory course for graduate students. Typically, quantum field theory textbooks introduce lattice gauge theory using the square lattice. However, beginners often find it challenging to grasp such an abstract theory only through the example of the square lattice. In this paper, we introduce lattice gauge theory using an alternative lattice - the honeycomb lattice. By comparing the differences between honeycomb and square lattice gauge theories, we highlight the fundamental principles of lattice gauge theory. This pedagogical approach will assist students in gaining a fresh perspective on grasping lattice gauge theory.
{"title":"A pedagogical approach to introducing the honeycomb lattice gauge theory","authors":"Yi-Fen Zhao, Fei-Jie Huang","doi":"10.1088/1361-6404/ad1397","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1397","url":null,"abstract":"\u0000 A pedagogical approach to introducing the honeycomb lattice gauge theory is presented. Lattice gauge theory, which is an important theory for understanding strongly correlated systems, is a significant topic covered in the quantum field theory course for graduate students. Typically, quantum field theory textbooks introduce lattice gauge theory using the square lattice. However, beginners often find it challenging to grasp such an abstract theory only through the example of the square lattice. In this paper, we introduce lattice gauge theory using an alternative lattice - the honeycomb lattice. By comparing the differences between honeycomb and square lattice gauge theories, we highlight the fundamental principles of lattice gauge theory. This pedagogical approach will assist students in gaining a fresh perspective on grasping lattice gauge theory.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-08DOI: 10.1088/1361-6404/ad1399
C. Sutrini, G. Zuccarini, M. Malgieri, Maria Bondani, Chiara Macchiavello
In this paper we present the outline of an educational path to introduce a crucial historical turnpoint of quantum information research – namely the Deutsch algorithm – to secondary school students. We discuss a basic elementarization strategy allowing students to single out and focus on the individual features of quantum mechanics involved in the different steps of the algorithm information processing phase, which can potentially be useful for the educational reconstruction of other algorithms and protocols. The sequence includes the experimental realization on the optical bench of an analogue of the Deutsch algorithm, working with classical coherent light. The educational path was tested both in curricular and out-of-school settings, and preliminary results will be discussed.
{"title":"An educational model of the Deutsch algorithm for secondary school","authors":"C. Sutrini, G. Zuccarini, M. Malgieri, Maria Bondani, Chiara Macchiavello","doi":"10.1088/1361-6404/ad1399","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1399","url":null,"abstract":"\u0000 In this paper we present the outline of an educational path to introduce a crucial historical turnpoint of quantum information research – namely the Deutsch algorithm – to secondary school students. We discuss a basic elementarization strategy allowing students to single out and focus on the individual features of quantum mechanics involved in the different steps of the algorithm information processing phase, which can potentially be useful for the educational reconstruction of other algorithms and protocols. The sequence includes the experimental realization on the optical bench of an analogue of the Deutsch algorithm, working with classical coherent light. The educational path was tested both in curricular and out-of-school settings, and preliminary results will be discussed.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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