CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 349
potential requires the equality of the derivatives dwx/dy and dwv/dx, the observed aberration can exist only when, in addition to the supposed motion in a horizontal direction, there is a vertical velocity of the ether of sufficient magnitude, varying from one point of the surface to the other.
So far there was question of first-order effects only, i.e., of effects that would be proportional to the first power of the ratio between the velocity of the earth and the speed of light. In almost all cases in which astronomers and physicists have tried to detect an influence of the earth’s motion on optical and electromagnetic phenomena, only effects of this order of magnitude could have been observed. The fact that all these attempts have been fruitless, and that this could be accounted for by theoretical considerations of the kind just preceding, led by and by to the conviction that the motion of the earth can never produce a first-order effect. This conviction was greatly strengthened when Einstein developed his theory of relativity and simply postulated that the result of all experiments which we perform in our laboratories must be independent of the motion of the earth, whatever may be the refinement of our measurements and the order of the effects which we can reach by them. To the experimental evidence which we already had, the charm of a beautiful and self-consistent theory was then added.
. Historically, I might add that before the relativity theory was developed the situation was somewhat similar to that which now characterizes the quantum problem. There were, of course, not so many people working in the field as there are now. Nevertheless, we had often very lively discussions about the subject. I remember especially the assembly of the German Society of Natural Sciences in Düsseldorf in 1898, at which numerous German physicists were present, Planck, W. Wien, Drude, and many others. We discussed especially the question of the first-order effects. Some devices with which such an effect might be observed were proposed, but none of these attempts was ever made, so far as I know. The conviction that first-order effects do not exist became by and by too strong. We even got, finally, into the habit of looking only at the summary of experimental papers which dealt with such effects. In case the result was properly negative we felt perfectly satisfied.
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 w2/c2, we deduce from it
C2=V2 + W2 — 2VW COS &
T T ( W W2
- = - i i— cos$H—- (cos2 #+|sin2#) V C ( c c