Ricardo Coelho

Philosophers have disagreed on the composition of force for decades. The main divergence concerns the fundamental question: given a certain motion that is observable, which force or forces are present in it, component or resultant forces? The present paper focuses on the conditions for dealing with this problem. I will argue that we are not able to infer force from the observation of a motion, as required by the problem. I will further argue that the validity of the Newtonian algorithm is not a sufficient condition for that inference because the Gaussian algorithm, which is equally valid, differs from the former with regard to the forces present in motions. Under these circumstances, I will make recourse to an experiment available in physics in which the force present in a motion is measured. Thus, we obtain a numerical value for this force. This result, playing the role of a counterexample, clarifies the composition of force issue significantly.

Contemporary textbooks of general physics teach us that the second law of Newton is F = ma. However, historical research has shown that Newton never wrote the equation, that Euler announced that he had discovered F = ma as a new principle of mechanics, and that Newton's second law and F = ma are different. This paper looks at the question from a different angle, namely how the principles have been applied to problem solving. To do this, we examine the problem-solving strategies used in the eighteenth century, in the following two centuries, and in textbooks today. We find that eighteenth century authors, namely those who followed Newton, did not use F = ma. In the nineteenth century, the equation became important in the practice of mechanics, as well as for conceptual purposes, physicists were concerned with the concept of force. These physicists did not identify the equation with Newton's second law. By comparing the problem-solving strategies of the eighteenth century and today, we can clarify the concept of force and understand why solving the conceptual problem of force has been difficult.

This chapter introduces the problem with the concept of energy and gives an overview of how it will be dealt with. In presenting the problem, physicists appear first, who from the end of the nineteenth century to the present day tell us that we have no answer to the question of what energy is. This is followed by disagreements between physicists, as some define or characterize energy and others criticize these theses. Finally, the authors will be considered who use the substance metaphor. Some of these know that energy is not a substance but talk about it as if it were, because they cannot find anything better. To find a solution to the problem, it would be necessary to determine what it consists of. To do this, it is important to capture its origin and how it developed. The introduction gives an overview of the chapters where this is done, as well as of the final chapter, which answers the question of the book.

This chapter begins with the question that arises among experts in the theory of heat in the late 1840s: how to make this theory compatible with the new findings. Clausius resolved this issue. Thomson adhered then to the thesis that heat is motion and created the concept “mechanical energy”. This concept not only covers what was properly mechanical, but also the activity due to heat, which had become a kind of motion. This is how the term energy appeared in the heat theory. A year later, Thomson distinguishes between static and dynamic reserves of mechanical energy, which led to the distinction between potential and kinetic energy. It is, finally, shown how the different theses on energy that had appeared since the 1840s emerge as characteristics of energy in the 1870s. This accumulation of meanings of the term energy made it more difficult to understand the concept.

Chapter 4 is devoted to a new phase of the concept: energy becomes a substance. Based on Maxwell’s concept of the electromagnetic field, Poynting defends the thesis that energy moves in space. His argument is only theoretical. Nevertheless, Lodge finds here a reason to reinforce his idea of energy: it exists in bodies and in the aether and can be transferred between them. Understandably, energy was understood as a substance. There were, however, physicists who criticized the concept. Planck, Hertz and Poincaré will be considered. The third and final section of the chapter, “The Super Concept”, approaches a generalization of the concept of energy never seen in a scientific concept. This was Ostwald's work.

This chapter deals with concepts of energy and formulations of the conservation principle in bachelor-level physics textbooks. Each of the propositions under analysis, concepts and principles, is linked to a similar proposition from the nineteenth century. This connection makes it possible to understand that the present trends in textbooks stem from currents of thought from the past, about which contemporary physicists do not seem to be aware. Textbooks generally use Mayer's or Joule's calculations of the mechanical equivalent of heat and Joule's paddle wheel experiment to introduce the concept of energy. This experiment has been reassembled, with the calorimeter and paddle wheel replicated from the original. The results obtained with this apparatus and with those based on the Joule experiment schemes presented in the textbooks, make it possible to clarify some aspects of the Joule experiment and improve the textbook presentations.

This chapter analyzes the texts of the authors considered to be the discoverers of energy: Robert Mayer, James Joule, Ludvig Colding and Hermann von Helmholtz. Although they have in common that they defend a thesis on heat that was contrary to the science of the time, they differ in their interpretation of the experiments, namely on the nature of heat, and in the theories they developed. This diversity was mitigated when they began to appear as having discovered the same thing. The present analysis aims to provide a sharper idea of the authors by focusing on the texts of each of them and making a systematic distinction between experiments and interpretations. After that, some of their theses will be compared with each other and with the current principle of conservation of energy.

The final chapter brings together the results of this study and provides the answer to the book's question, what is energy? The chapter begins with an overview of the evolution of the concept. The way in which the concept has changed over time and the diversity in contemporary times lead us to ask the question of whether there is something that is necessarily part of the concept. Two necessary conditions are then determined. Therefore, a concept that does not satisfy one of them cannot be an energy concept. Based on this, we arrive at an understanding of the concept of energy. The reasons for the problems with the concept are then explained. These problems that have arisen since the 19th century are thus overcome.

This book provides a solution to the problem with the energy concept. This problem manifests itself in the fact that physicists clearly diverge regarding the question of what energy is. Some define it but others state that we do not know what it is. Although this is a problem for physicists who need to explain the concept, it is not a problem for physics that can be solved by laboratory means. Penetrating into the origin of the notion of energy, this book offers a clear idea of what was discovered and what was invented to interpret the findings. Following the development of the concept, it provides an explanation of the trends in contemporary textbooks. The author's repetition, in his "History and Philosophy of Physics Laboratory", of Joule’s famous experiment – the paddle wheel experiment – with a calorimeter as originally used by Joule and with a calorimeter as proposed in textbooks, is presented, yielding new insight into the phenomenon. Thus, science teachers and students will benefit from reading the book as well as historians, philosophers, students of the history and philosophy of science, and all who are interested in knowing about what it is that we call energy.

Mechanics was the foundation of physics in the 19th century. Its own foundation was, however, problematic. Mach proposed a new foundation of mechanics. As we shall see, the cause of acceleration is no longer the force, which was the great problem at that time, but rather the mass. The definition of force, which is a reading of the equation of force, did not solve, however, the conceptual problem. If we want to know what force is and we require that force is F in the equation F=ma, then we have to analyze F and not define it through the other side of the equation, as it has been done. This analysis enables us to conclude that force stems from a mathematical manipulation; it is not something that we can find in nature. This conclusion, in turn, enables us to understand those authors who looked for force in nature and did not find it, as well as those who said that force is a mathematical fiction, a mere human concept, etc.

O presente artigo compõe-se de três partes: filosofia, imagem e literatura. Na primeira, o autor esclarece o conceito de imagem nos Princípios de Mecânica de Heinrich Hertz (1857-1894) através das suas conexões com os conceitos de sistema e de modelo. Aqui se mostra de que modo uma teoria física deve ser entendida como uma imagem construída por nós. Na segunda parte do artigo, aborda-se a teoria física de Hertz em função do conceito de imagem: primeiramente, os fundamentos, incluindo a sua relação à experiência; segundo, a dedução, que é um trabalho de imaginação; finalmente, como se testam os resultados da dedução. O artigo demonstra de que modo o estudo conjugado da filosofia e da física de Hertz permite ultrapassar dificuldades e mal-entendidos na literatura acerca da sua obra, facto de que se dá conta sobretudo na terceira parte do artigo. Em questão estão sobretudo os conceitos de imagem (Bild), exposição da imagem (Darstellung), espaço, partícula de massa, força e aplicação da teoria mecânica. De relevar ainda é o facto de estes assuntos serem também de grande interesse para um aprofundamento do nosso conhecimento da obra de Ludwig Wittgenstein, sobretudo na sua primeira fase. /// The present article consists of three parts: philosophy, image and literature. In the first one the pivotal concept of image in Heinrich Hertz's Principles of Mechanics 15 investigated through its connections with the concepts of system and model. It is shown that a physical theory is an image formed by us. In the second part of the article, Hertz's mechanics is presented as an image: firstly, the fundaments, where their relationship to experiments is dealt with; secondly, the deduction, which is work of imagination; finally, how to test the results of the deduction. The study of the philosophical and physical part of Hertz's Principles together illuminates typical misunderstandings and problems of interpretation of the Principles, as will be seen in the third part of the article. This concerns the concepts of image (Bildj, presentation of the image (Darstellung), space, mass-particle, force and the application of the theory. The subjects clarified in this article are also of interest for a deepening of our understanding of Wittgensteins early work.

A Mecânica clássica parte da lei de inércia e usa um conceito de força que é consequência lógica da lei (§ 2-3). Acontece porém que nem a lei de inércia tem fundamento experimental (§ 1) nem o conceito de força tem referente nos fenómenos (§ 4). O estudo da função da lei e da força nas teorias mecânicas veio mostrar que a lei de inércia expressa apenas um movimento unidade e a força desvios à unidade (§ 5). Segue-se que a ciência praticava uma metodologia, mas expressava-se como possuindo um conhecimento dos meandros da natureza. Isto coloca pelo menos uma questão à filosofia, porquanto a caracterização da ciência pela epistemologia usual se mostra inadequada para a mecânica. /// The classical mechanics assumes the law of inertia and uses a concept of force that is a logical consequence of the law (§ 2-3). As a matter of fact the law of inertia has no experimental basis (§ 1) and beyond that the concept of force does not correspond to anything in the mechanical phenomena (§ 4). The study of the structure of the mechanical theories has shown that the law of inertia expresses only a reference motion and the force represents deflections from that motion (§ 5). Therefore it can be concluded that even though science seems to have a far reaching knowledge of nature, it has indeed only practiced a methodology. This poses a problem for the philosophy insofar as it makes the usual epistemological framework inadequate to characterize mechanics.

The principle of conservation of energy tells us that ‘energy can neither be created nor destroyed but only transformed’. The validity of the principle is without question. The problem is the concept. Contemporary physicists have asserted that we do not know what energy is. We find, however, 19th century physicists, contemporary physicists and historians of science who converge on the point: Mayer and Joule discovered energy. Therefore, we do not know what energy is, but we know these authors discovered it. What did they then discover? What can we learn from this with regard to the energy concept problem? To deal with this issue, I will distinguish between what the authors did experimentally and what they said about the phenomena. This method of analysis makes the difference in relation to historical works on the subject. In a second step, I will consider the introduction of the energy concept, which is from 1850s, and the reification of the energy in 1880s. Finally, I will address the energy conservation principle and the concept of energy conveyed by this principle in contemporary textbooks. As we shall see, the conservation of a magnitude that we call energy nowadays was discovered by Mayer and Joule; an indestructible and transformable entity was not. Adopting the original conservation principle would be enough to avoid the energy concept problem.

Philosophers have disagreed on the composition of force for decades. The main divergence concerns the fundamental question: given a certain motion that is observable, which force or forces are present in it, component or resultant forces? The present paper focuses on the conditions for dealing with this problem. I will argue that we are not able to infer force from the observation of a motion, as required by the problem. I will further argue that the validity of the Newtonian algorithm is not a sufficient condition for that inference because the Gaussian algorithm, which is equally valid, differs from the former with regard to the forces present in motions. Under these circumstances, I will make recourse to an experiment available in physics in which the force present in a motion is measured. Thus, we obtain a numerical value for this force. This result, playing the role of a counterexample, clarifies the composition of force issue significantly.