The meanings of mass and E = mc2: an approach based on conceptual maps

Abstract

In this work, we discuss transformations in the meaning of the concept of mass, which are important to physics teaching, by means of three conceptual schemes, which emphasize visual patterns of knowledge organization. We begin by discussing how the meaning of a physical concept is constructed, through its relations with others. In physical theories, these connections usually involve mathematical operations. We focus on the concept of mass and its changes in three different contexts, namely classical mechanics, electromagnetism and relativity. Modifications are displayed as shifts in its relative position in conceptual schemes. These schemes enforce visual knowledge and may be used as didactical tools for teaching the subject, since they stress both the signification of mass in classical mechanics and its re-signification in relativity. This paves the way for a discussion of different approaches adopted for teaching the mass-energy relation in relativity, expressed by the famous formula E = mc 2 . As the terms rest mass, relativistic mass and invariant mass, which have different ontological and epistemological contents, are part of this discussion, we consider the main approaches to mass present in both relativity textbooks and discourses by some influential physicists.

Louis de Broglie's wave-particle duality: from textbooks’ blackboxes to a chain of reference presentation

“…Moreover, the conception of proper mass is no longer consensual in contemporary presentations of Special Theory of Relativity [78], [79] and de Broglie's relation be-tween momentum and wavelength was obtained in the context of the Principle of Uncertainty without having to perform any relativistic consideration [80] Not only the equations E = hν and p = h/λ received new demonstrations and meanings but also the duality conception itself assumed new interpretations and implication along the development of Quantum Physics. More specifically the Complementarity Principle of Copenhagen Interpretation assumed that every quantum system could behave as particle or as wave depending on the experimental set up.…”

“…We highlight that we are using the notation of rest mass and relativistic mass. Such notation is not original from Einstein's work and can imply conceptual problem[79],[84]. Nevertheless, we use it because de Broglie adopts such formulation.…”

Epistemological difficulties in implementing a teaching-learning sequence on the concept of mass

“…This kind of attitude suggests that epistemology is not needed for the understanding of physics. In our teaching sequence, the re-signification of mass was framed by epistemology and the change of its meaning was represented as a shift in its position in conceptual maps [24]. The course had the explicit didactic intention of promoting the understanding of why the meaning of mass has changed, how it has changed and the implications of that change.…”

“…Our DBR includes topic of modern physics, especially the notion of mass in relativity, which involves ontological controversies even among practicing physicists [24]. Therefore, we found it convenient to rely on ideas from the Didactic Transposition Theory, proposed by Chevallard [11], which discusses the transformation of scholarly knowledge into taught knowledge.…”

The Inertia of Mass and the Newtonian Force

“…The organization of concepts and laws constitutes a rigid structure and highly coherent [3]. In Physics, concepts acquire meaning through links with other concepts [4].…”