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Non-Newtonian Mechanics.– Some Transformation Equations.

By Richard C. Tolman, Ph.D., Assistant Professor of Chemistry at the University of California.^[1]

There have previously been presented some of the consequences^[2] of a system of mechanics which is based on the conservation laws of mass, energy, and momentum and the Einstein transformation equations for coordinate systems in relative motion. It will be shown in the present article, that the principles of this system of mechanics lead directly to a number of further transformation equations, and in particular to the same transformation equations for force as chosen by Planck^[3] to agree with electromagnetic considerations. An application of the equations to electromagnetic and gravitational problems will also be presented.

If we consider two systems of "space time" coordinates in relative motion in the X direction with the velocity $v$, the Einstein theory of relativity has led to the following equations for transforming the description of any kinematic phenomenon from the variables of system S to those of system S'.

$x'=\kappa (x-vt),$

(1)

$y'=y,$

(2)

$z'=z,$

(3)

$t'=\kappa \left(t-{\frac {v}{c^{2}}}x\right);$

(4)

1. Communicated by the Author.
2. Lewis and Tolman, Phil. Mag. xviii. p. 510 (1909), Online; Tolman, Phil. Mag. xxi. p. 296 (1911), xii. p. 458 (1911), xxiii. p. 375 (1912).
3. Planck, Ann. d. Physik, xxvi. p. 1 (1908).