Page:SahaSpaceTime.djvu/14

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APPENDIX
83

"Thermodynamics and Radiation,"[1] for "Electromagnetic phenomena",[2] and finally for "Mechanics with the maintenance of the idea of mass."

For this last mentioned province of physics, the question may be asked: if there is a force with the components X, Y, Z (in the direction of the space-axes) at a world-point (x, y, z, t), where the velocity-vector is , then how are we to regard this force when the system of reference is changed in any possible manner? Now it is known that there are certain well-tested theorems about the ponderomotive force in electromagnetic fields, where the group Gc is undoubtedly permissible. These theorems lead us to the following simple rule; if the system of reference be changed in any way, then the supposed force is to be put as a force in the new space-coordinates in such a manner, that the corresponding vector with the components

where

(the rate of which work is done at the world-point), remains unaltered. This vector is always normal to the velocity-vector at P. Such a force-vector, representing a force at P, may be called a moving force-vector at P.

Now the world-line passing through P will be described by a substantial point with the constant mechanical mass m. Let us call m-times the velocity-vector at P as the

  1. Planck, Zur Dynamik bewegter systeme, Ann. d. physik, Bd. 26, 1908, p. 1.
  2. H. Minkowski; the passage refers to paper (2) of the present edition.