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The Meaning of Mass

Barry Holstein

Concepts of Mass in Contemporary Physics and Philosophy. Max Jammer. xi + 180 pp. Princeton University Press, 2000. $39.50.

Like Max Jammer's previous books, Concepts of Mass in Contemporary Physics and Philosophy provides an interesting and stimulating mix of solid physics and philosophical issues. I must confess that as a particle/nuclear phenomenologist, my initial reaction on hearing the title of this work was "Who needs it?" My attitude toward mass was not unlike that of Supreme Court Justice Potter Stewart toward pornography: "It's not easy to define, but I know it when I see it." Reading the book, however, made it clear that my thinking was rather naive. Jammer treats many facets of this subject and demonstrates that challenging and interesting issues remain to be addressed.

This slim volume is divided into chapters on inertial mass, relativistic mass, the mass-energy relation, gravitational mass and the nature of mass. Each is filled with interesting pieces of history and explores substantive issues. Except in the chapter on gravitational mass, where simple ideas from general relativity are introduced, the discussion is not particularly technical, and only simple physics—for example, Newton's second law, that force equals mass times acceleration—is employed.

At the most basic level, that of inertial mass, Jammer argues that the concept itself is slippery in that one usually defines mass by means of Newton's second law. That means that the fundamental quantities of length and time that are needed in order to define acceleration must be supplemented by an additional concept—for example, that of force. Once force is introduced, then one can define inertial mass as force divided by acceleration. Absent this, one must introduce mass itself as a fundamental concept, and any notion that it somehow can be inferred from other constructs must be circular. Jammer discusses various attempts to evade this problem and demonstrates that each is specious.

More interesting (and, I would argue, controversial) are the chapters on relativistic mass and on the mass-energy relation—E = mc2, which even otherwise scientifically illiterate people can quote from memory. Although again his discussion is thought-provoking and coherent, I must demur when he tries to support the concept of "relativistic mass" by means of the formula mrel = m0/√____1 – v2____/c2, in which m0 is the so-called rest mass (that is, the inertial mass as measured in the rest frame of the object), v is velocity and c is the speed of light. Jammer argues that this expression allows one to understand why it becomes increasingly difficult to accelerate an object as its velocity approaches the speed of light and why it is impossible for a massive object to exceed this limiting velocity. However, I would argue that the proper way to define mass relativistically is as a relativistic scalar m0, which means that it has the same value in every Lorentz frame. It is the energy, which is the time component of a Lorentz four-vector, that is given in terms of Jammer's relativistic mass times c2. This makes much more sense. This issue also comes up again when the author argues that with his definition mass is not created or destroyed. (I would call this energy conservation.) On the other hand, with the concept of mass as a relativistic scalar, one can easily picture how mass can be converted into energy using the equation Dm0c2 = DE. Jammer knows all of this, of course, but he argues that his picture is to be preferred. I remain unconvinced but found these chapters to be good reading.

At 52 pages, the chapter on gravitational mass is the longest and the most interesting in the book. In a few sections a bare-bones knowledge of general relativity can be helpful but is not really essential. In this chapter Jammer introduces not only the inertial mass mi (which is the mass in Newton's second law) but also two kinds of gravitational mass—ma, which produces gravitational field distortions, and mp, on which the field distortions act. One nearly always assumes all three masses to be the same (this assumption goes under the name of the weak equivalence principle), but Jammer examines the evidence that this is so. I found the historical discussion here particularly edifying and useful. The Hungarian nobleman Roland, Baron Eötvös of Vásárosnamóny, is generally credited with doing the first such experiments out on the Hungarian plains near the end of the 19th century by hanging different materials (including snakewood) from torsion pendula in order to compare the relation between their gravitational attraction to the earth and their inertial effects as manifested in the centrifugal force. Jammer informs us, however, that it was actually Newton who performed the first such measurements (by comparing the periods of pendula composed of different materials—silver, glass, sand, salt and wheat) and showed the equality of gravitational and inertial mass to one part in 103, a result that Baron Eötvös was able to improve by six orders of magnitude 200 years later. (Contemporary scientists have pushed this limit by two more orders during the past century.)

Another issue discussed here is whether gravity attracts gravitational self-energy (the so-called Nortvedt effect). The answer seems to be a resounding yes, as assessed by means of lunar ranging measurements, which are permitted by the corner reflectors placed on the moon's surface by the first astronauts in 1969. Also given their due are fascinating ideas such as antigravity and negative mass. Insightful analysis informs all of these discussions. (As a gauge of the level of scholarship involved in preparing this manuscript, I note that the author has even managed to dredge up a minor article that John Donoghue and I wrote 13 years ago on gravitational and inertial mass differences at nonzero temperature!)

The final chapter is a short one dealing with the meaning of mass. In it Jammer analyzes Mach's view that the issues of mass and acceleration are only well defined in the presence of the remaining components of the universe and the view of Dennis Sciama, who attempted to invent a theory in which this concept was manifest. The meaning of mass is perhaps the deepest issue discussed in the book and remains a challenging and unsolved problem.

Jammer has produced a fascinating look into the nature of a quantity that most of us take for granted. The historical references alone make this a book worth owning, but it's also a fun read.—Barry R. Holstein, Department of Physics, University of Massachusetts

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