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

<div><p>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 = m c 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.</p>