Introducing the basic concepts of general relativity in high schools

INTRODUCTION Unlike the case of quantum mechanics, the teaching at the high school level of general relativity (GR) has been the target of relatively minor efforts by researchers in physics education (Kersting, Henriksen, Boe & Angell 2018), despite both subjects being included in the curricula in many countries. Although its foundations are not as controversial as those of quantum mechanics, GR also rests on some subtle conceptual steps, and, moreover, it cannot be probed using real experiments. Hence, teaching it at the high school level presents important challenges. However, the conceptual steps needed for GR are firmly founded in classical mechanics, electromagnetism, and special relativity (Sciama 1969), and when suitably presented and supported by adequate material, they can be within grasp of final year pupils. In this presentation, we outline and discuss a proposal in which these basic concepts are gradually introduced as natural extensions of those that physics pupils know, in a simple yet nontrivial way, which goes beyond the current textbook approaches. The latter, indeed, usually present little more than a popular level account. Typically, they rely on the famous elastic sheet analogy, which in turn is based on the iconic fact that GR geometrizes the gravitational field. However, such a statement takes quite a long route to be established, hence without adequate motivation, usually results in students getting the impression that the theory comes out of the blue. Also, the analogy is not very accurate, failing to highlight the role of time in the theory. FROM CLASSICAL MECHANICS TO GR: A PROPOSAL Our proposal starts from a critical rethinking of the principles of Newtonian mechanics, focusing on the role of inertia and of inertial forces, and on the principle of equivalence of gravitational and inertial mass. This part can be supplemented by real experiments and simulations. The next step involves special relativity, discussing the apparently unrelated problems of extending the relativity principle to non-inertial frames, and of reconciling gravity with the universal speed limit. Then, the way in which the equivalence principle allows to extend the special relativity principle is discussed with the help of Einstein’s elevator thought experiment. Crucial here is the discussion of how the equivalence principle is elevated from mechanics to all physical phenomena and how it is reconciled with the fact that special relativity teaches us that inertial mass is a form of energy. By means of some thought experiments, in fact, it is possible to quantitatively show that the same is true for the gravitational mass (Einstein, 1911). Then, by further thought experiments and simple calculations, some consequences of this principle can be explored: the gravitational redshift and time-dilation, the application to the Global Positioning System, and the gravitational bending of light. At this point, students should be invited to reflect on the special features that a theory based on special relativity and on Einstein’s equivalence principle should have, in comparison with electromagnetism, and the consequences should be explored. Finally, the thought experiment of the rotating disc (Janssen, 2014) can provide a way of motivating the well-known geometric picture. REFERENCES Einstein A. (1911). Einfluss der Schwerkraft auf die Ausbreitung des Lichtes. Ann. Phys. (Ser.4), 35, 898. Janssen M. (2014). “No success like failure…”. Einstein’s quest for general relativity, 1907-1920. In M.Janssen & C. Lehner (Eds.), The Cambridge companion to Einstein (pp. 167-227). Cambridge: Cambridge University Press. Kersting, M., Henriksen, E. K., Boe, M.V., & Angell. C. (2018). General relativity in upper secondary school: Design and evaluation of an online environment using the model of educational reconstruction. Phys. Rev. Phys. Educ. Res. 14, 010130. Sciama, D. (1969). The physical foundations of general relativity, New. York: Doubleday

Trait-oriented Programming in Java 8

International audienceJava 8 was released recently. Along with lambda expressions, a new language construct is introduced: default methods in interfaces. The intent of this feature is to allow interfaces to be extended over time preserving backward compatibility. In this paper, we show a possible, different use of interfaces with default methods: we introduce a trait-oriented programming style based on an interface-as- trait idea, with the aim of improving code modularity. Starting from the most common operators on traits, we introduce some programming patterns mimicking such operators and discuss this approach

When physics meets biology: a less known Feynman

We discuss a less known aspect of Feynman's multifaceted scientific work, centered about his interest in molecular biology, which came out around 1959 and lasted for several years. After a quick historical reconstruction about the birth of molecular biology, we focus on Feynman's work on genetics with Robert S. Edgar in the laboratory of Max Delbruck, which was later quoted by Francis Crick and others in relevant papers, as well as in Feynman's lectures given at the Hughes Aircraft Company on biology, organic chemistry and microbiology, whose notes taken by the attendee John Neer are available. An intriguing perspective comes out about one of the most interesting scientists of the XX century.Comment: On the centenary of the birth of Richard P. Feynman (May 11, 1918 - February 15, 1988

Deriving electromagnetism from special relativity: A novel teaching-learning module

INTRODUCTION In this presentation, a novel teaching-learning module on electromagnetism is proposed, which finds its inspiring source in two sets of unpublished notes by R. P. Feynman (Feynman 1963, 1967-68). It relies on an ab initio derivation of Lorentz's force and Maxwell's equations from special relativity (De Luca et al., 2019), which is the opposite of the usual standard historical route. This approach works with the potentials rather than the fields from the very beginning, which implies simpler mathematics. From a methodological point of view, in order to derive electromagnetism from special relativity in a consistent way, one has to develop the latter independently from electromagnetic quantities (e.g., the speed of light), which is indeed possible as shown by some authors (see, for instance, Ugarov 1979). The key observation is that the invariance of the speed of light is not postulated from the beginning, so that the theory builds upon the idea that any interaction should have a limiting speed, which is required to be an invariant according to the principle of relativity. Then, Lorentz transformations can be derived in the usual way and depend on a parameter, the invariant speed, whose value can be fixed by experiments and identified with the speed of light only at the end. These guidelines are the basis for the development of our proposal, which is aimed at introducing electromagnetism at the advanced undergraduate level. Finally, the advantages of this approach with respect to more traditional ones are briefly discussed. A BRIEF OUTLINE OF THE MODULE The module is designed for an advanced undergraduate level, so that a basic knowledge of variational principles is required. The starting point is an alternative introduction to special relativity according to the above guidelines. For instance, it is possible to derive Lorentz transformations relying only on the requirements of relativity of inertial reference frames, homogeneity of space and time, isotropy of space and group structure. The next step consists in deriving the form of the Lorentz force from first principles, i.e., building only on the Lorentz invariance of the electric charge and on relativity. That allows one to obtain, as a further bonus, the correct transformation laws for the electric and magnetic fields under Lorentz boosts. A further key point is the introduction of the 4-potential, which allows one to generalize the least action principle of classical mechanics to the relativistic case. Upon varying the action, it is possible to get the homogeneous Maxwell equations. The derivation of non-homogeneous Maxwell equations then follows from the previous results together with one more assumption, i.e., the validity of Coulomb's law. Finally, qualitative properties and shapes of fields in various situations, as well as a bunch of more applicative topics are introduced in the usual way. REFERENCES De Luca, R., Di Mauro, M., Esposito, S. & Naddeo, A. (2019). Feynman's different approach to electromagnetism. European Journal of Physics, 40, 065205. Feynman, R. P. (1963, December 13). Alternate way to handle electrodynamics. Retrieved January 20, 2019, from      http://feynmanlectures.caltech.edu/info/other/Alternate_Way_to_Handle_Electrodynamics.html Feynman, R. P. (1967-68). Feynman Hughes Lectures. Volume 2: Relativity, Electrostatics, Electrodynamics, Matter-Wave Interactions. Notes taken and transcribed by John T. Neer. Retrieved February 8, 2019, from http://www.thehugheslectures.info/wp-content/uploads/lectures/FeynmanHughesLectures_Vol2.pdf Ugarov, V. A. (1979). Special Theory of Relativity. Paris: MIR

A roadmap for Feynman's adventures in the land of gravitation

Feynman's multifaceted contributions to gravitation, as can be inferred from several published and unpublished sources, are here reviewed. Feynman thought about this subject at least from late 1954 to the late '60s, giving several contributions to it. Even if he only published three papers on gravity, much more material is available, especially the records of his many interventions at the Chapel Hill conference in 1957, which are here analyzed in detail. There, Feynman showed that he had already developed much of his picture of gravity, and he expressed deep thoughts about fundamental issues in quantum mechanics, such as superpositions of the wave functions of macroscopic objects and the role of the observer, which were suggested by the problem of quantum gravity. Moreover, Feynman lectured on gravity several times. Besides the famous lectures given at Caltech in 1962-63, he extensively discussed this subject in a series of lectures given at the Hughes Aircraft Company in 1966-67, whose focus was astronomy and astrophysics. Here Feynman gave a somewhat simplified exposition with respect to the Caltech lectures, but with many original points. All this material allows to reconstruct a detailed picture of Feynman's ideas on gravity and of its evolution until the late sixties. The main points are that gravity, like electromagnetism, has a quantum foundation, so that classical general relativity has to be regarded as emerging from an underlying quantum theory, and that this quantum theory has to be investigated by computing physical processes, as if they were measurable. The same attitude is shown with respect to gravitational waves, as evident both from the Chapel Hill records and a letter written to V. Weisskopf. As a bonus, an original approach to gravity, which closely mimics the derivation of the Maxwell equations he gave in that period, is hinted at in the unpublished lectures.Comment: 35 pages, no figures, submittet for publicatio

A Prototype Mild-solar-Hybridization Kit: Design and Challenges

Abstract This paper deals with the development of an automotive hybridization kit (equipment, along with associated techniques and methodologies), aimed at converting conventional cars into hybrid solar vehicles (Mild-Solar-Hybrid). The main aspect of the projects consists into the integration of state-of-the-art components (in-wheel motors, photovoltaic panels, batteries), and into the development of an optimal controller for the power management. A prototype of the hybridizing equipment – patented by the University of Salerno (Italy)- is installed on a FIAT Grande Punto. A mild parallel hybrid structure is obtained by substituting/integrating the rear wheels with 7 kW in-wheel motors and adding a lithium battery to manage on-board energy. Thus, the vehicle can operate in electric mode (when ICE is switched off or disconnected by the front wheels) or in hybrid mode (when the ICE drives the front wheels and the rear in-wheel motors operate in traction mode or in generation mode, corresponding to a positive or negative torque). The battery can be recharged both by rear wheels, when operating in generation mode, and by photovoltaic panels. The vehicle is also equipped with an EOBD gate (On Board Diagnostics protocol), which allows accessing data such as pedal position, vehicle speed, engine speed, manifold pressure and other variables. The Vehicle Management Unit (VMU), which is part of the invention and implements control logics compatible with typical drive styles of conventional-car users, receives the data from OBD gate, from battery (SOC estimation) and drives in-wheel motors by properly acting on the electric node. The paper, focused on the main aspects of prototype design and realization, also provides insights on control issues related to the integration of the above-mentioned components, drivability and safety

Mechanical refraction in action

Abstract We study the analog of Snell's law for particles moving across the interface of two regions with two different potential energies, from two different points of view. First, a simple demonstration involving marbles and a potential step is shown. Then, from a theoretical point of view, this law describing mechanical refraction is derived from the Maupertuis and Jacobi variational principles, in close analogy with the well known derivation of Snell's law for refraction from Fermat's least time principle. Finally, the relativistic version of mechanical refraction is obtained by the Maupertuis principle, by trading the Newtonian dispersion relation with the relativistic one. The pedagogical significance of this treatment is discussed