Concepts of Mass in Contemporary Physics and Philosophy

By Max Jammer | Go to book overview

CHAPTER THREE
The Mass-Energy Relation

IT IS CERTAINLY NO exaggeration to say that the mass-energy relation, usually symbolized by E = mc2, is one of the most important and empirically best confirmed statements in physics. Although initially conceived as a purely theoretical theorem without any practical applications, E = mc2 eventually became the symbol that marks the beginning of a new era in the history of civilization—the age of nuclear energy with its promises and dangers for the human race. As we are interested in this relation only within the context of our study of the notion of mass, we ignore all these far-reaching implications and focus our attention on the conceptual issues involved. We have to admit, however, that because of its epoch-making consequences the discovery of the massenergy relation is itself an important event in the history of physics. It is therefore interesting to note that the very first proof of this relation— Einstein's 1905 derivation—has been criticized as being a logical fallacy involving a vicious circle.

The first to claim that “the reasoning in Einstein's 1905 derivation of the mass-energy relation is defective” was Herbert E. Ives.1 Ives's claim described in chapter 13 of Concepts of Mass was recently rejected as unjustified, but had enjoyed rather widespread endorsement.2 The alleged circularity in Einstein's reasoning was even interpreted as indicative of his genius when it was said: “Ives has shown (beyond any doubt) that this [Einstein's] derivation is circular. That is, Einstein implicitly postulates the energy-mass relation in his proof. This may be in a way a tribute to Einstein's genius, for he seems to intuitively know answers before he derives them.”3

____________________
1
H. E. Ives, “Derivation of the Mass-Energy Relation,” Journal of the Optical Society of America42, 540–543 (1952).
2
See, e.g., H. Arzeliès, Études Relativistes: Rayonnement et Dynamique du corpuscule chargé fortement accéléré (Paris: Gauthier-Villars, 1966), pp. 74–79; A. Miller, Albert Einstein's Special Theory of Relativity (Reading, Mass.: Addison-Wesley, 1981), p. 377; U. E. Schröder, Spezielle Relativitätsthoerie (Thun: H. Deutsch, 1981), p. 118; K. J. Köhler, “Die Aequivalenz von Materie und Energie,” Philosophia Naturalis19, 315–341 (1982); C. A. Zapffe, A Reminder onE = mc2 (Baltimore: CAZLab, n.d.), p. 46.
3
A. F. Antippa, “Variations on a Photon-in-a-Box by Einstein,” UQTR-TH-8 (Quebec: UniversitéduQuébec à Trois-Rivières, May 1975), pp. 1–52.

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Concepts of Mass in Contemporary Physics and Philosophy
Table of contents

Table of contents

  • Title Page *
  • Contents v
  • Preface vii
  • Acknowledgments xi
  • Concepts of Mass in Contemporary Physics and Philosophy *
  • Introduction 3
  • Chapter One - Inertial Mass 5
  • Chapter Two - Relativistic Mass 41
  • Chapter Three - The Mass-Energy Relation 62
  • Chapter Four - Gravitational Mass and the Principle of Equivalence 90
  • Chapter Five - The Nature of Mass 143
  • Index 169
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