# Concepts of Mass in Contemporary Physics and Philosophy

By Max Jammer | Go to book overview

CHAPTER TWO
Relativistic Mass

HAVING CONFINED our attention thus far to the concept of the inertial mass of classical physics we turn now to its relativistic analogue, the concept of mass in the special theory of relativity. If we ignore for the time being Mach's principle, which will be discussed in a different context, we can say that in classical physics inertial mass mi is an inherent characteristic property of a particle and, in particular, is independent of the particle's motion. In contrast, the relativistic mass, which we denote by mr, is well known to depend on the particle's motion in accordance with the equation

where m0 is a constant with the dimensionality of mass, u is the velocity of the particle as measured in a given reference frame S, and c is the velocity of light. Since u depends on the choice of S relative to which it is being measured, mr also depends on S and is consequently a relativistic quantity and not an intrinsic property of the particle.

In an inertial reference frame S0, in which the particle is at rest, u = 0 and mr obviously reduces to m0. For this reason m0 is usually called the rest mass (or proper mass) of the particle. From a logical point of view, m0 is just a particular case of the relativistic mass and there is not yet any cogent reason to identify it with the Newtonian mass of classical physics. However, as in the so-called nonrelativistic limit, i.e., for velocities that are small compared with the velocity of light (u << c), the mathematical equations of special relativity reduce to the corresponding equations of classical physics, many theoreticians regard this correspondence as a warrant to identify m0 with the Newtonian mass of classical physics. However, as we shall see later on, this inference can be challenged—at least on philosophical grounds.

In order to comprehend fully the importance of modern debates on the status of the concept of relativistic mass and its role in physics it seems worthwhile to retrace the historical origins of this concept. Its history is as old as the theory of relativity itself. In his very first paper on relativity, the famous 1905 essay, “On the Electrodynamics of Moving

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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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