Notes on the Concept of Mass in Classical Dynamics

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概要

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• Investigations are made for the inertial mass concept relating to the inertial reference system. With the postulate that there exist some conserving physical quantities, and that the conservation law is invariant under the transformation between inertial reference systems, the functional form representing the conserving quantities are studied. These quantities are restricted for scalar and vector ones, and it is assumed that they are some analytical functions of velocity of the free moving particle. From above mentioned postulates, the procedure leads us to the analysis of these universal functions of velocity u, which appear to be scalar constants in both of the case of Galillean and Lorentzian transformations. These scalar constants which should concern to the quantities characterizing the material property of the subject bodies in motion, are interpreted as inertial masses of the bodies. It must be insisted here, that these constants are not equal for scalar and vector quantities properly, because they are defined mutualy independently relating to the conserving quantities of scalar and vector. However, though this is the case for the constants in Galillean transformations, it appears that there exist relations between these constants in the case of Lorentzian transformations. Therefore, it is able to reduce these (three) constants only to one with the aid of the condition concerning to transformation property, in the Lorentzian case. Thus, the concept of mass is well established, if it is considered in the framework of Lorentzian transformations strictly. However, with the concept of correspondence principle, which means that the limiting value of corresponding quantities should be in agreement with ones of Galillean case in the limit of c→∞, where c is the velocity of light, it is possible to obtain the mass concepts in Galillean case also. This result, giving rightly the velocity dependence formulae of mass in special relativity, indicates that the concept of inertial mass could be well defined and confirmed only in the framework of special relativity.

• 横浜国立大学の論文

著者

• Fujimura Jun

  Department Of Physics Faculty Of Education Yokohama National University

• Fujimura Jun

  Department Of Physics Yokohama National University

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