Page:CarmichealMass.djvu/2

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furnishes a possible means for the experimental proof or disproof of the theory of relativity. The researches of Bucherer have been thought to afford the requisite experimental confirmation in the first case; this matter is treated in § 5. In § 6 suggestions are given for a new crucial experiment for testing the theory of relativity, this being associated with the second essential equivalent of R in § 4. The writer desires to call especial attention to this proposed experiment.

In § 7 the intimate relation of the mass and the total energy of a body is pointed out and two theoretical means are suggested for determining the velocity of light indirectly, that is, without direct measurement of this velocity. These experiments, if they could be performed with sufficient accuracy, would afford an interesting and striking confirmation of the theory of relativity, provided of course that they turn out according to the predictions of this theory.

A few remarks on the principle of least action are found in § 8, and § 9 is given to some speculative considerations which are intended as brief suggestions of means by which one may represent to himself the conclusions of relativity as natural parts of a consistent view of physical phenomena.

§ 1. Fundamental Definitions and Postulates.

If m, M and v are respectively the mass, momentum and velocity of a body we shall assume (as in the classical mechanics) that they are connected by a relation of the form

M=mv;

and hence any one of these quantities is determined in terms of the other two (except that mass is not thus determined when velocity and momentum are zero). We shall take mass and velocity to be the two fundamental quantities, so that momentum is defined in terms of them.

Likewise we shall define the kinetic energy E of a moving body by means of the usual relation

E=\int_{0}^{v}Mdv=\int_{0}^{v}mvdv

Later we shall see that "mass" is variable and is not in general independent of the direction in which it is measured; consequently, we must take for m in the above formulae the mass of the body in the direction of its motion.

We shall take for granted the following laws of conservation of momentum and energy and electricity: