# Concepts of Mass in Contemporary Physics and Philosophy

# Concepts of Mass in Contemporary Physics and Philosophy

## Synopsis

## Excerpt

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 *m * 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 *m *, is well known to depend on the particle's motion in accordance with the equation where *m* 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, *m * also depends on *S* and is consequently a relativistic quantity and not an intrinsic property of the particle.

In an inertial reference frame *S* , in which the particle is at rest, *u* = 0 and *m * obviously reduces to *m* . For this reason *m* is usually called the *rest mass* (or *proper mass*) of the particle. From a logical point of view, *m* 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 *m* 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 . . .