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Adv. Studies Theor. Phys., 2013, Vol. 7, No. 17, p. 839–852.
Newton introduced the concept of mass in his Principia and gave an intuitive explanation for what it meant. Centuries have passed and physicists as well as philosophers still argue over its meaning. Three types of mass are generally identified: inertial mass, active gravitational mass and passive gravitational mass. In addition to the question of what role mass plays in dynamical equations and why, the origin of the particular amount of matter associated with an elementary particle as a consequence of fundamental fields has long been a topic of research and discussion. In this paper, various representations of inertial mass are discussed within the framework of fundamental (either Galilean or Poincar´e invariant) dynamical equations of waves and point particles. It is shown that the derived equations have mass-like and mass parameters for waves and point particles, respectively, and that the physical meaning of these parameters sheds a new light on the fundamental problem of the nature of inertial mass.
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Adv. Studies Theor. Phys., Vol. 7, 2013, no. 17, 839 - 852 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/astp.2013.3673
Inertial Mass and its Various Representations J. L. Fry and Z. E. Musielak Department of Physics The University of Texas at Arlington Arlington, TX 76019, USA c 2013 J. L. Fry and Z. E. Musielak. This is an open access article disCopyright tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract Newton introduced the concept of mass in his Principia and gave an intuitive explanation for what it meant. Centuries have passed and physicists as well as philosophers still argue over its meaning. Three types of mass are generally identified: inertial mass, active gravitational mass and passive gravitational mass. In addition to the question of what role mass plays in dynamical equations and why, the origin of the particular amount of matter associated with an elementary particle as a consequence of fundamental fields has long been a topic of research and discussion. In this paper, various representations of inertial mass are discussed within the framework of fundamental (either Galilean or Poincar´e invariant) dynamical equations of waves and point particles. It is shown that the derived equations have mass-like and mass parameters for waves and point particles, respectively, and that the physical meaning of these parameters sheds a new light on the fundamental problem of the nature of inertial mass.
Keywords: Galilean and Minkowski space-time, fundamental dynamical equations, inertial mass, and mass and mass-like parameters
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Introduction
The concept of mass was originally introduced by Newton [1] who wrote in his Principia: ’The quantity of matter is the measure of the same, arising from its density and bulk conjointly’. According to Jammer [2], a major step in interpretation of Newton’s concept of mass was made by Euler in his Mechanica
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J. L. Fry and Z. E. Musielak
[3], where he suggested that mass should be defined as the constant ratio between a constant force and the acceleration caused by this force. Euler’s definition of mass had been widely accepted in the nineteenth century, however, later in that century, Newton’s concept of force had become strongly criticized and as a result new definitions of mass independent of Newton’s second law were proposed. The first step was made by Saint-Venant [4] in 1845, when he used the principle of conservation of linear momentum to express the ratio of masses of two bodies in terms of their velocity increments after an impact. Then, Mach [5] in 1867 intro