Michelson-Morley Experiment.—In 1881 Michelson (22, 120, 1881) conceived an ingenious and bold method of measuring the orbital motion of the earth through the luminiferous ether. As the experiment was one involving considerable expense, Bell, the inventor of the telephone receiver, was appealed to successfully for the funds necessary to carry it through. Michelson’s experimental plan was as follows: A beam of light traveling in the direction of the earth’s motion strikes an unsilvered mirror m at an angle of 45°. Part of the light passes through, the rest being reflected at right angles to its original direction. Each ray is returned by a mirror at a distance l from m. On meeting again, the ray whose path has been at right angles to the direction of the earth’s motion passes on through the mirror, while the other ray is reflected so as to bring the two in line and form interference fringes. Now consider the effect of the earth’s motion on the paths of the two rays. In fig. 4 the earth is supposed to be moving to the right. The unsilvered mirror m bifurcates a beam of light coming from a source a. By the time the ray reflected from m has traveled to the mirror b and back, m will have moved forward to m’; a distance 2βl, where the small quantity β is the ratio of the earth’s velocity to the velocity of light. Hence the length of the path traversed by this ray is approximately
2l(1 + ½β2).
The other ray will reach the mirror c after the latter has moved forward a distance
βl/(1 − β2)
and on returning find m at m’. Hence its path has a length of roughly 2l(1 + β2). The difference in path of the two rays is β2l and consequently they should be a little out of phase on meeting at d. By rotating the apparatus clockwise through 90° the directions of the two rays relative to the earth’s motion are interchanged, and the interference fringes would be expected to shift an amount corresponding to a difference in path of 2β2l. This quantity is of course small,—β2 is about one one hundred millionth,—but so sensitive are the methods of interferometry that Michelson felt confident that he would be able to detect the earth’s motion through the ether. The apparatus consisted of a table which could be rotated about a vertical axis in much the same way as a spectrometer table, and provided with arms a meter long to carry the mirrors b and c. With this length of arm the interference fringes from sodium light should shift by an amount corresponding to four hundredths of a wave length when the table is rotated through a right angle. When the experiment was first performed the apparatus was placed on a stone pier in the Physical Institute at Berlin. So sensitive was the instrument to outside vibrations that even after midnight it was found impossible to get consistent readings. Finally a satisfactory foundation was constructed in the cellar of the Astrophysical observatory at Potsdam. But what was the astonishment of the experimenters to find that the expected shift of the interference fringes did not exist!
Fig. 4.
The extreme delicacy of the experiment made it desirable to confirm the result by repeating it. This was done by Michelson and Morley (34, 333, 1887) in 1887. In place of a revolving table a massive slab of stone floating on mercury was used to carry the apparatus. This slab was kept in constant rotation, the observer following it around. Moreover, the precision of the experiment was greatly increased by reflecting each ray back and forth across the slab a number of times between leaving and returning to the mirror m. The accuracy attained was such as to justify Michelson in declaring that if the effect sought actually existed it could not be so great as one-twentieth of its calculated value. In 1905 Morley and Miller[[166]] repeated the experiment for the second time and succeeded in increasing the sensitiveness of the apparatus to a point such that a motion through the ether of one-tenth of the earth’s orbital velocity could have been detected.
The displacement looked for in the Michelson-Morley experiment is known as a second-order effect in that it depends upon the square of the ratio of the velocity of the earth to that of light. Michelson at first considered that the negative result obtained confirmed a theory proposed by Stokes in which it was assumed that the ether inside and near its surface partakes of the motion of the earth, while that at a distance is practically quiescent. But there are many objections to Stokes’ theory, one of which was brought out by an experiment of Michelson’s (3, 475, 1897) in which he attempted by an interference method to detect a difference in the velocity of light at different levels above the earth’s surface. The negative result obtained led him to conclude that if Stokes’ theory were true the earth’s influence on the ether would have to extend to a distance above its surface comparable with its diameter. Meanwhile a more satisfactory explanation was forthcoming. It has been pointed out that a uniformly convected electric field is derivable from an electrostatic field by contracting dimensions in the direction of motion in the ratio
√(1 − β2) : 1.