Mathematical derivations alone do not necessarily lead to physical understanding. Tools that can replace the mathematical treatment of a physical process and at the same time increase the physical understanding are computer-aided modeling programs, also called system dynamics software. Examples of such software are Stella, Berkeley Madonna, Wensim, Dynasys, Powersim or COACH 7. They solve differential equations and systems of differential equations with numerical methods. One works with a graphical user interface. We want to show how such a software can be used to get from a non relativistic model to a relativistic model with only minimal modifications. Equating mass and energy alone, ensures that the model provides essential statements of relativistic dynamics: the existence of a terminal velocity for all physical motions, the relativistic dependence of the velocity of a body on its momentum, the relativistic relation between momentum and energy of a body.

The teaching of relativity usually starts with kinematics: The invariance of the speed of light, clock synchronization, time dilatation and length contraction, the relativity of simultaneity, Lorentz transformation and the Minkowski diagram. The change of the reference frame is a central topic. Only afterwards problems of relativistic dynamics are discussed. Such an approach closely follows the historical development of the Special Theory of Relativity.

We believe that this access to relativity is unnecessarily complicated, and unsuitable for beginners. We present the basics of a teaching approach in which the initial postulate of relativity is the identity of energy and relativistic mass. Reference frame changes are largely avoided.

This chapter describes the main features of an introductory course about relativity at high-school level that focuses on relativistic dynamics. It is intended for readers who are interested in a novel approach to relativity that avoids the topic of changing reference frames, which students often find difficult. The chapter describes the basics of a course on special and general relativity. The laws of special theory of relativity, or special relativity for short, are derived from those of classical mechanics along with one extra postulate. In the Karlsruhe Physics Course , the extensive quantities, such as energy, momentum, electric charge, and entropy are introduced as basic quantities. The twin paradox plays a major role in the teaching of special relativity and is part of every textbook or course on special relativity. The development of a teaching concept for the school, in our case for the secondary school, is a balancing act.

Abstract: “What is heat?” was the title of a 1954 article by Freeman J. Dyson, published in Scientific American. Apparently, it was appropriate to ask this question at that time. The answer is given in the very first sentence of the article: heat is disordered energy. We will ask the same question again, but with a different expectation for its answer. Let us imagine that all the thermodynamic knowledge is already available: both the theory of phenomenological thermodynamics and that of statistical thermodynamics, including quantum statistics, but that the term “heat” has not yet been attributed to any of the variables of the theory. With the question “What is heat?” we now mean: which of the physical quantities deserves this name? There are several candidates: the quantities Q, H, E_therm and S. We can then formulate a desideratum, or a profile: What properties should such a measure of the quantity or amount of heat ideally have? Then, we evaluate all the candidates for their suitability. It turns out that the winner is the quantity S, which we know by the name of entropy. In the second part of the paper, we examine why entropy has not succeeded in establishing itself as a measure for the amount of heat, and we show that there is a real chance today to make up for what was missed.

At school and university, gravity is taught essentially in the Newtonian way. Newtonian mechanics originated at a time when there were no fields, when energy did not exist as a physical quantity, and when one still had to be satisfied with the concept of actions at a distance. A theory without such shortcomings, Maxwell’s electromagnetism, came into being about 150 years later. It could have served as a model for a modern theory of gravitation. In fact, such a theory of gravitation, gravitoelectromagnetism, was proposed by Heaviside. However, it did not establish itself, because, firstly, many effects it describes are very, very small, secondly, it makes certain statements that seemed unacceptable to some researchers, and thirdly, shortly thereafter, General Relativity was born, which removed the old deficiencies and seemed to make a classical field theory of gravity superfluous. We argue that the subject of gravitoelectromagnetism has its legitimacy in teaching at school and university even now.

On the one hand, general relativity is impractical for many applications because the mathematical effort is high, and on the other hand, the theory of gravitoelectromagnetism by no means describes only tiny effects. Rather, it solves a problem that is deliberately ignored in the traditional teaching of Newtonian mechanics: To which system do we assign the so-called potential energy? Where is the “potential” energy located? We also encounter some peculiarities of gravitoelectromagnetism, the cause of which is the fact that compressive and tensile stresses within the gravitational field, are swapped against each other in comparison with the electromagnetic field.

We discuss a paradox from the field of relativistic thermodynamics: two heat reservoirs of the same proper temperature move against each other. One is at rest in the inertial reference frame SA, the other in SB. For an observer, no matter in which of the two reference frames he is at rest, the temperatures of the two reservoirs are different. One might, therefore, conclude that a thermal engine can be operated between the reservoirs. However, the observers in SA and SB do not agree upon the direction of the entropy flow: from SA to SB, or from SB to SA. The resolution of the paradox is obtained by taking into account that the 'drive' of an entropy current is not simply a temperature difference, but the difference of a quantity that depends on both temperature and velocity.

Aus dem Prolog: ,“Das Konzept der Entropie ist ohne Zweifel eines der okkultesten Konzepte der Physik" Heuser spricht mit diesem Satz, der in seinem Duktus jeden Widerspruch undenkbar erscheinen lässt, einer großen Menge von Physiklehrerinnen und Physiklehrern aus dem Herzen und treibt, einen amerikanischen Cartoonisten zitierend die Polemik auf die Spitze:“lf you can live with entropy, you can live with anything“. Dagegen steht H.L. Collendars (1863- 1930) Überzeugung, Entropie könne auf eine Weise verständlich gemacht werden, “which any schoolboy could understond“. …

 Es wird gezeigt, wie ein Physikunterricht, der in der Wärmelehre die Entropie neben der Temperatur als zentrale Begriffe vermittelt und, unterstützt durch ein Modellbildung wie POWERSIM™, physikalische Sachverhalte vermitteln kann, deren unterrichtliche Behandlung ohne ein computerunterstütztes Modellbildungssystem zu schwierig sind, obwohl sie der täglichen Erfahrung einer Schülerin /eines Schülers sehr nahe kommen. Die vorgestellte Aufsatz geht von den elementaren Modellen des Heizens und Abkühlens von Körpern aus, macht Fließgleichgewichte verständlich und zeigt schließlich ein einfaches Modell für eine globale Erwärmung der Erde. (Anmerkung: Die Modelle lassen sich einfach auch in andere Softwaremodelle (z.B. Coach 7 etc.) übertragen.)

Entropy is known to be one of the most difficult physical quantities. The difficulties arise from the way it is currently introduced, which is due to Clausius. Clausius showed that the ratio of the process quantity heat and the absolute temperature is the differential of a state variable, which he called entropy. About 50 years later, in 1911, H. L. Callendar, at that time the president of the Physical Society of London, showed that entropy is basically what had already been introduced by Carnot and had been called caloric, and that the properties of entropy coincide almost perfectly with the layman’s concept of heat. Taking profit of this idea could simplify the teaching of thermodynamics substantially. Entropy could be introduced in a way “which every schoolboy could understand”. However, in 1911 thermodynamics was already well-established and Callendar’s ideas remained almost unnoticed by the physics community. This fact should not be an excuse for ignoring Callendar’s idea. On the contrary, this idea should be established, especially since entropy plays an important part not only in Thermodynamics but in the whole of physics. A two-man play is included in the appendix to this paper, written to introduce this history to teachers to encourage them to consider this useful complementary model. 

Legt man sich nicht auf den traditionellen Weg fest, so kann man mit einfachen Mitteln schnell zu den wichtigen Ergebnissen der speziellen Relativitätstheorie gelangen. Man verwendet Kenntnisse, die man bereits auf anderen Gebieten der Physik gewonnen hat. Der Aufsatz zeigt diesen Weg auf und begründet ihn.