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 Pr (Fig. 5). For each of them the time required for propagation will be represented by expressions of the form
fë-ljds — —2^w cos & w2 (cos2 sin2 ê) ds , (3)
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 l2 (Fig. 5) represent the paths of the two rays as they would be if the ether did not move through the diagram.
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 l2 whose distances from h Fig
and Z2, reckoned along the normals to
these lines, are of the second order. We must now calculate the times of propagation for the paths l[ and lf2, say Tl[ and Tl2. Since, however, T is a minimum for lx, as compared with neighboring lines, and since the displacements from lx to l'x are of the second order, the difference between Th and Tl[ will be of the fourth order. This may be neglected when we confine ourselves to quantities of the second order. Similarly, we may replace Tl'2 by Tl2. This means that, in the determination of the phase differences, we may use the values of (3) for the rays, such as they would be according to the ordinary laws of optics in the absence of the earth’s motion.
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.
352
DAYTON C. MILLER
ni. PROFESSOR DAYTON C. MILLER (CASE SCHOOL OF APPLIED SCIENCE)
The experiments on which I shall report today seem to lead to conclusions which are in contradiction to the common interpretation of the Michelson-Morley experiment. To make the story complete, I shall start with the conclusion of the experiments performed by Michelson and Morley in 1887, in Cleveland, which were interpreted as giving no indication of an ether drift. Dr. Lorentz, in 1895, proposed the first explanation for this unexpected result by assuming that the motion of translation of a solid through the ether might produce a contraction in the direction of the motion, with extension transversely, the amount of which is proportional to the square of the ratio of the velocities of translation and of light, and which might have a magnitude such as to annul the effect of the ether drift in the Michelson-Morley interferometer. The optical dimensions of this instrument were determined by the base of sandstone on which the mirrors were supported. If the contraction depends upon the physical properties of the solid, it was suggested that pine timber would suffer greater compression than sandstone, while steel might be compressed in a lesser degree. If the compression annuls the expected effect in one apparatus, it might in another apparatus give place to an effect other than zero, perhaps with the contrary sign.
At the International Congress of Physics, held in Paris in 1900, Lord Kelvin gave an address in which he considered theories of the ether. He remarked that “the only cloud in the clear sky of the theory was the null result of the Michelson-Morley experiment.” Professor Morley and the writer were present, and in conversation Lord Kelvin expressed the conviction that the experiment should be repeated with a more sensitive apparatus. The writer, in collaboration with Professor Morley, constructed an interferometer about four times as sensitive as the one used in the first experiment, having a light-path of 214 feet, equal to about 130,000,000 wavelengths. In this instrument a relative velocity of the earth and ether equal to the earth’s orbital velocity would be indicated by a displacement of the interference fringes equal to 1.1 fringes. This is the size of the instrument which has been used ever since. The optical