350 H. A. LORENTZ As to the second-order effect, the situation was much more difficult. The experimental results could be accounted for by transforming the co-ordinates in a certain manner from one system of coordinates to another. A transformation of the time was also necessary. So I introduced the conception of a local time which is different for different systems of reference which are in motion relative to each other. But I never thought that this had anything to do with the real time. This real time for me was still represented by the old classical notion of an absolute time, which is independent of any reference to special frames of co-ordinates. There existed for me only this one true time. I considered my time transformation only as a heuristic working hypothesis. So the theory of relativity is really solely Einstein’s work. And there can be no doubt that he would have conceived it even if the work of all his predecessors in the theory of this field had not been done at all. His work is in this respect independent of the previous theories. I shall have little to say about the theory of the Michelson-Morley experiment, which was the first ever made of those in which we are concerned with effects of the second order. That here again the result must be negative is immediately clear if we follow the theory of relativity. If, instead of that, we apply to the experiment our old stationary ether, we must carefully consider the paths of the interfering rays of light and the time in which the light is propagated along each of them from the source of the point where the interference takes place. For this purpose we can again use the fundamental equation (i). Confining ourselves to the propagation in ether, we may put u = c, k = i so that the equation becomes Taking into account terms of the second order w C T T ( W W - = - i i— cos$H—- (cos | CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 351 Now let there be two paths, 1 and 2, along which light can go from the point P to the point P fë-ljds — — and we shall be able to calculate the two times, if we know the lines along which the integrals are to be taken. Let the lines h and l As has been shown, these lines are not altered by the motion so long as we confine ourselves to terms of the order w/c. They may, however, be somewhat changed when, as is now proposed, quantities of the second order are taken into account. We shall then have, for instance, the dotted p lines l[ and l and Z these lines, are of the second order. We must now calculate the times of propagation for the paths l[ and l We are thus led to the ordinary theory of the experiment, which would make us expect a displacement of the fringes, the absence of which is accounted for by the well-known contraction hypothesis (Lorentz contraction). Asked if I consider this contraction as a real one, I should answer “yes.” It is as real as anything that we can observe. |