Appendix C - More about E=mc²

Summary

In chapter 11, I noted that the equation E=mc² has given rise to a host of misconceptions. There are other issues associated with the equation, too, among them an issue of definition, and this appendix addresses some of those issues. It is written primarily for an instructor, but a student who has read appendix B will be able to understand most of it and will gain a greater perspective.

Mass in history

The word “mass” has a long history and a correspondingly long string of meanings and nuances. Max Jammer provides a fine discourse on the topic in his Concepts of Mass in'Classical and Modern Physics, cited in the “Additional resources” for chapter 11; I rely on Professor Jammer for the early history. In Roman times, the Latin word “massa” denoted a lump of dough. This sense of “lump of stuff” is what we have in mind when we “hang a mass from a spring.” By Newton's time, the word “massa” (still in Latin, of course) had come to denote “quantity of matter,” a valuable concept but one that defied attempts to make it both operationally precise and independent of any prior notion of density.

Newton recognized clearly the physical notion of inertia and hence what we would today call “inertial mass.” It was Leonhard Euler, however, who first defined inertial mass operationally as the ratio of force to acceleration (more precisely, as the ratio of their magnitudes).