OD′ = OC √(1-(v²/c²)), therefore (PP/QQ) = (1/√(1-(v²/c²))

This is the sense of Lorentz’s hypothesis about the contraction of electrons in case of motion. On the other hand, if we conceive the second electron to be at rest, and therefore adopt the system (x′, t′,) then the cross-section P′P′ of the strip of the electron parallel to OC′ is to be regarded as its length and we shall find the first electron shortened with reference to the second in the same proportion, for it is,

P′P′/Q′Q′ = OD/OC′ = OD′/OC = QQ/PP

Lorentz called the combination t′ of (t and x) as the local time (Ortszeit) of the uniformly moving electron, and used a physical construction of this idea for a better comprehension of the contraction-hypothesis. But to perceive clearly that the time of an electron is as good as the time of any other electron, i.e. t, t′ are to be regarded as equivalent, has been the service of A. Einstein [Ann. d. Phys. 891, p. 1905, Jahrb. d. Radis. ... 4-4-11-1907.] There the concept of time was shown to be completely and unambiguously established by natural phenomena. But the concept of space was not arrived at, either by Einstein or Lorentz, probably because in the case of the above-mentioned spatial transformations, where the (x′, t′) plane coincides with the x-t plane, the significance is possible that the x-axis of space some-how remains conserved in its position.

We can approach the idea of space in a corresponding manner, though some may regard the attempt as rather fantastical.

According to these ideas, the word “Relativity-Postulate” which has been coined for the demands of invariance in the group G, seems to be rather inexpressive for a true understanding of the group Gc, and for further progress. Because the sense of the postulate is that the four-dimensional world is given in space and time by phenomena only, but the projection in time and space can be handled with a certain freedom, and therefore I would rather like to give to this assertion the name “The Postulate of the Absolute world” [World-Postulate].

III

By the world-postulate a similar treatment of the four determining quantities x, y, z, t, of a world-point is possible. Thereby the forms under which the physical laws come forth, gain in intelligibility, as I shall presently show. Above all, the idea of acceleration becomes much more striking and clear.

I shall again use the geometrical method of expression. Let us call any world-point O as a “Space-time-null-point.” The cone

c²t² - x² - y² - z² = O