Page:The principle of relativity (1920).djvu/127

 APPENDIX

It would be very unsatisfactory, if the new way of looking at the time-concept, which permits a Lorentz transformation, were to be confined to a single part of Physics.

Now many authors say that classical mechanics stand in opposition to the relativity postulate, which is taken to be the basis of the new Electro-dynamics.

In order to decide this let us fix our attention upon a special Lorentztransformation represented by (10), (11), (12), with a vector v in any direction and of any magnitude q < 1 but different from zero. For a moment we shall not suppose any special relation to hold between the unit of length and the unit of time, so that instead of t, t´, q, we shall write ct, ct´, and q/c, where c represents a certain positive constant, and q is < c. The above mentioned equations are transformed into

r´_{v̄} = r_{v̄}, r´_{v} = c(r_{v} - qt)/[sqrt](c^2 - q^2), t´ = (qr_{v} + c^2t)/c[sqrt](c^2 - q^2)

They denote, as we remember, that r is the space-vector (x, y, z), r´ is the space-vector (x´ y´ z´)

If in these equations, keeping v constant we approach the limit c = [infinity], then we obtain from these

r´_{v̄} = r_{[=v]}, r´_{v} = r_{v} - qt t´ = t.

The new equations would now denote the transformation of a spatial co-ordinate system (x, y, z) to another spatial co-ordinate system (x´ y´ z´) with parallel axes, the