# Concepts of Mass in Contemporary Physics and Philosophy

By Max Jammer | Go to book overview

CHAPTER ONE
Inertial Mass

MECHANICS, AS UNDERSTOOD in post-Aristotelian physics,1 is generally regarded as consisting of kinematics and dynamics. Kinematics, a term coined by André-Marie Ampère,2 is the science that deals with the motions of bodies or particles without any regard to the causes of these motions. Studying the positions of bodies as a function of time, kinematics can be conceived as a space-time geometry of motions, the fundamental notions of which are the concepts of length and time. By contrast, dynamics, a term probably used for the first time by Gottfried Wilhelm Leibniz,3 is the science that studies the motions of bodies as the result of causative interactions. As it is the task of dynamics to explain the motions described by kinematics, dynamics requires concepts additional to those used in kinematics, for “to explain” goes beyond “to describe.”4

The history of mechanics has shown that the transition from kinematics to dynamics requires only one additional concept—either the concept of mass or the concept of force. Following Isaac Newton, who began his Principia with a definition of mass, and whose second law of motion, in Euler's formulation F = ma, defines the force F as the product of the mass m and the acceleration a (acceleration being, of course, a kinematical concept), the concept of mass, or more exactly the concept of inertial mass, is usually chosen. The three fundamental notions of mechanics are therefore length, time, and mass, corresponding to the three physical

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1
In Aristotelian physics the term “mechanics” or μηχανικ́η (τέχνη), derived from μ́ηχος (contrivance), meant the application of an artificial device “to cheat nature,” and was therefore not a branch of “physics,” the science of nature. “When we have to produce an effect contrary to nature … we call it mechanical.” Cf. the pseudo-Aristotelian treatise Mechanical Problems (847 a 10).
2
“C'est à cette science où les mouvements sont considérés en eux-mêmes … j'ai donné le nom de cinématique, de κίνημα, mouvement.” A.-A. Ampère, Essai sur la philosophie des sciences (Paris: Bachelier, 1834), p. 52.
3
G. W. Leibniz, “Essai de Dynamique sur les loix du mouvement,” in C. I. Gerhardt, ed. Mathematische Schriften (Hildesheim: Georg Olms, 1962), vol. 6, pp. 215–231; “Specimen Dynamicum,” ibid., pp. 234–254.
4
M. Jammer, “Cinematica e dinamica,” in Saggi su Galileo Galilei (Florence: G. Barbèra Editore, 1967), pp. 1–12.

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Concepts of Mass in Contemporary Physics and Philosophy

• 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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