REPETITIONS OF THE MICHELSON EXPERIMENT *

(In Memory of A. A. Michelson, 1852–1931)

Georg Joos (Jena)

When a theory requires that some single quantity have an entirely definite numerical value, for example zero, the experimental confirmation of such a theory is associated with a certain difficulty. To determine any quantity with perfect exactness by experiment is, of course, impossible, and in connection with this doubts arise in the interpretation of the observed deviations, especially if the theory is being disputed on one ground or another. It is precisely in such a difficult position that the investigator finds himself in the question of the influence of the translational motion of the earth on optical laboratory experiments.

The only experiment of this kind in which, on the basis of the idea of a stationary world ether, one may expect a measurable effect is the Michelson experiment. The negative result of this experiment serves as the starting point of the theory of relativity, which cannot admit even the slightest measurable influence of the motion of the earth. When the experiment was first carried out, in 1881, the accuracy of the measurements achieved only slightly exceeded the magnitude of the expected effect; therefore, subsequently a number of repetitions of the Michelson experiment were performed. The principal reason for this was the desire to increase—

* Naturwissenschaften 19, 784, 191.

of accuracy, if possible, lower the upper limit of the possible effect, or else to investigate whether a change in the conditions of the experiment will not cause the appearance of a measurable positive effect.

To obtain a measure of the required sensitivity of the apparatus, one should estimate, on the basis of the conception of the ether, the limits of the possible effect. The number \(\Delta z\) of fringes by which the interference pattern is displaced when the apparatus is rotated through \(90^\circ\) from the position in which one of the arms is directed along the motion of the Earth is given by the well-known equation:

\[ \Delta z=\frac{2l}{\lambda}\left(\frac{v}{c}\right)^2, \]

where \(l\) is the length of the interferometer arms, \(\lambda\) is the wavelength of light (equal to \(5\cdot10^{-5}\) cm), and \(v\) is the component of the Earth’s velocity in the plane of the apparatus.

Since the time of the first experiment, it has become customary to take as the expected effect, for \(v\), the value \(30\) km/sec, which corresponds to the Earth’s orbital velocity, and consequently for \(\left(\frac{v}{c}\right)^2\) the number \(10^{-8}\) is taken. This value is, of course, chosen arbitrarily, since in addition to the velocity of the Earth’s motion around the Sun there is also the general velocity of motion of the entire solar system relative to the fixed stars, equal to \(19\) km/sec and therefore of the same order of magnitude. The apex of this motion has the following celestial coordinates: declination \(32^\circ\) and right ascension \(270^\circ\). Such a motion would cause a strong dependence of the effect on the time of year. The greatest total effect would be \(45\) km/sec for the beginning of April. This influence of the time of year will, however, be intensified as a result of the motion of the entire Milky Way system relative to the extragalactic world, which is at present firmly established. The speed of the latter is estimated at no less than \(300\) km/sec, while the speed of the solar system is comparatively very small, so that the effect, being referred to sidereal time, should remain constant throughout the year. The positive effect that should be expected under all

circumstances, should consist in some more or less plausible diurnal course of the position of the interference pattern.

Fig. 1. Path of the rays in Michelson’s interferometer, 1887.

The point of the sky toward which the vector of the resultant velocity is directed, and from which, so to speak, the ether wind blows, should describe on the sky, like a star, a circle of parallel. If only this circle does not merge into the polar point (which would correspond to the disappearance of the diurnal motion), then the observed azimuth of the ether wind should undergo simple oscillations, attaining equal maximum values to the east and to the west during the course of the day.

The first repetition was undertaken by Michelson himself jointly with Morley* in 1887 in Cleveland. The principle they used—increasing the optical path by means of multiple reflection (mirrors) without increasing the basic dimensions of the apparatus—was preserved in all subsequent experiments. The path of the rays is shown in Fig. 1. All the optics, including the light source (an Argand burner), was assembled on a square stone slab.

Fig. 2. Mounting of the mirrors in the 1887 experiment.

* A. A. Michelson and E. W. Morley, Philosophic. Mag. (V), 24, 449 (1887).

with a side of 1.5 m. With the threefold reflection used, the path of the light reached 11 m. Thus, taking \(v\) to be \(30\ \text{km/sec}\), one could expect an effect of 0.4 of a fringe. The apparatus employed, in which smooth rotation of the instrument was achieved, also served as a model for almost all subsequent experimenters. The stone slab \(a\) (Fig. 3) was fastened to a wooden ring \(b\), floating in an annular vessel with mercury \(c\). The floating system was set into rotation by means of the central axle \(d\). The visual reading was taken every \(1/16\) of a revolution. The results of a series of experiments are given in Fig. 4;

Fig. 3. Apparatus by means of which the rotation of the 1887 interferometer was carried out.

Fig. 4. Total shift observed in the experiments of 1887. (Abscissae—orientation of the apparatus.)

the dotted curve indicates the expected fringe shift upon rotation of the apparatus, its ordinates being reduced by a factor of 4. As the highest possible limit of the effect, Michelson gives 0.01 of a fringe width.

At the initiative of Kelvin, who called the result of the Michelson–Morley experiment the only cloud in the clear sky of ether theory, Morley and Miller* constructed an even more sensitive instrument of a somewhat modified design. The actual lengths of the arms were increased to 4 m, which, with the fourfold reflection used, gives a total optical path of 32 m. Thus, for \(v = 30\ \text{km/sec}\), an effect of \(1/3\) of a fringe width was expected. The mirrors were at first mounted on a wooden crosspiece, which, however, did not prove to be a sufficiently rigid system. As a result, the wooden crosspiece was replaced by the corresponding—

* E. W. Morley and D. C. Miller, Phil. Mag. (VI), 9, 680 (1905).

...of the existing construction made of steel pipes. The use of iron for making the sensitive parts of the apparatus, by means of which the distance between the mirrors is established, is highly risky. The Earth’s field, when such an interferometer is rotated, produces magnetostriction, which should be accompanied by exactly the same effect as the ether wind; for two positions of the instrument differing by \(180^\circ\), if iron is used in the construction, with a 32-meter length of the light path, the fringe displacement caused by the indicated phenomenon should reach several tenths of a fringe. Taking this circumstance into account, Miller later replaced the iron with a nonmagnetic material, strangely enough without obtaining even the slightest change in comparison with the previous, not entirely negative result. The optical parts were placed on a structure made of sheet steel, which in turn floated with its middle part in mercury.

The results of the experiments performed with the described apparatus in 1904 were acknowledged by Morley and Miller in their report at the time to be negative. Later, however, for example in 1928,* at the conference on Mount Wilson, Miller, contrary to Morley’s opinion, declared the former conclusion about a negative result to be incorrect and based on an impermissible averaging of readings obtained at different times of the day.

The experiments were carried out by Morley and Miller, and from 1906 by Miller alone, near Cleveland in a special light building. By conducting experiments in a space enclosed only by thin walls, Miller caused no small number of difficulties for his opponents. Because of its high sensitivity, the interferometer used required constancy of temperature to within \(1/100\) of a degree. Naturally, such constancy cannot be achieved in a light hut, especially one with windows. Taking into account the fundamental premise of the ether hypothesis—its ability to penetrate any bodies—it would have been possible to surround the interferometer with a stone wall, all the more since, according to Miller himself, an atmosphere with a height of

* Astrophys. J., 68, 341—402 (1928).

REPETITIONS OF THE MICHELSON EXPERIMENT

1800 m has no effect on the entrainment of the ether. Miller’s remark verges on mysticism: that the structure at the place from which, apparently, the ether wind was supposed to blow had a large glass window. Unfortunately, it is not indicated whether there was a window in the opposite wall to achieve a good through draft!

With the same apparatus, after it had received certain mechanical improvements, a series of experiments was carried out in 1921–1926, partly on Mount Wilson and partly in Cleveland. The results of these experiments, which caused an enormous sensation throughout the world, were interpreted as a positive effect of \(10 \text{ km/sec}\). Contrary to his initial statements, in his concluding communication Miller emphasized the fact that the effect in Cleveland was just as large as at an altitude of 1800 m on Mount Wilson. However, the results obtained by no means corresponded to the requirement considered above of a definite plausible course during the day; the azimuth of the ether wind does not take, over the course of 24 hours, equal extreme positions—eastern and western. Furthermore, for example, from the curve given by Weber* according to Miller’s data, it is evident that the deviations from the theoretical course are just as large as the effect obtained itself.

Despite the presence of so many doubtful points, the results of Miller’s experiments aroused extraordinary enthusiasm among opponents of the theory of relativity; and only after a calm discussion were demands for repetition heard from all sides. Indeed, it was impossible to form a final judgment about the results of experiments decisive for the fundamental principles of physics on the basis of the confidence of a single investigator.

Among the numerous repetitions of the experiment that then followed, one should first of all mention the work of Michelson himself, carried out by him jointly with F. G. Pease and F. Pearson*** on Mount Wilson. The interferometer

* Astrophys. J., 68, 341—402 (1928).

** J. Weber, Physik. Z., 27, 5, (1926).

*** A. A. Michelson, F. G. Pease a. F. Parson, Nature, 123, 88 (1929); J. opt. Am. Soc., 18, 181 (1929).

corresponded in its general features to the Morley and Miller apparatus. The optical path of the light was 25 m. The light source was mounted on the axis of the instrument and rotated together with the instrument. After the two interfering beams were recombined, the light was likewise directed upward along the axis, where the observer, rotating with the entire system, was located. In this experiment the reading was made subjectively. In the published report, what is indicated as the main reason for undertaking the experiments is not Miller’s experimental results, but rather the very small effect derived by Strömberg from taking into account the high velocity of motion of the entire Milky Way system. The effect expected by him should have corresponded to a displacement of \(17/1000\) of a fringe width for an optical path of 16 m. However, the grounds for this calculation are not given in the article. In any case, the result of the experiment proved to be less than \(1/15\) of the value calculated by Strömberg, or, in round numbers, less than \(1/1000\) of a fringe width.

Fig. 5. Arrangement of the optics in the Zeiss interferometer.

An apparatus of similar dimensions was built by the Zeiss firm, with the participation of the author of this article, for a further test—

REPLICATIONS OF THE MICHELSON EXPERIMENT

verification of Miller’s results.* The aim was an apparatus of high sensitivity, i.e., with a large optical path, permitting the registration of interference fringes so that anyone who wished could check the objective records obtained in this way. With arm lengths of 3.5 m and triple reflection, the optical path was brought up to 21 m. The mirrors were mounted on a crosspiece of fused quartz, clearly visible

Fig. 6. Mechanical mounting of Joos’s interferometer.

in Fig. 5. The mechanical construction of the apparatus differs considerably from all previous models. The part carrying the optics does not float in mercury, but is suspended by means of hundreds of springs from a special rotating frame. The frame, by means of a motor equipped with a regulator, rotates while very accurately preserving the direction of the axis thanks to a special ball bearing and four brackets sliding along the axis and serving for its precise adjustment. All this is enclosed in a casing made of silumin casting, intended—

* A detailed account in Ann. d. Physik (5), 7, 385 (1930).

... designed to reduce temperature disturbances and allowing some defocusing of the apparatus, which, however, proved unnecessary in the experiment. The light source is a small point-like mercury lamp, placed on the axis of the apparatus and moving together with it (see Fig. 6). The light, recombined after passing along both paths, is deflected downward along the axis by means of a concave mirror, which gives an image of the fringes, and by another plane mirror. A movable photographic camera is placed below. From the interference pattern, by means of a slit \(0.2\) mm wide, perpendicular to the fringes, a small section is cut out, past which the photographic plate passes as the apparatus rotates. If there is a positive effect, the system of fringes should execute two complete sinusoidal oscillations with an amplitude of \(3/4\) of a fringe at each revolution.

Fig. 7. Record of interference fringes for two revolutions of the apparatus.

Figure 7 presents the results obtained during two revolutions of the interferometer; the marks designated in the photograph by the letter \(M\) were obtained with the aid of a wire stretched in place of the fringes, hence in front of one of the mirrors returning the light. It is completely impossible to notice with the naked eye the oscillations of the curves recorded in this way. In order to obtain a numerical value for the extreme deviations, the photographs were photometered across the fringes at eight points for each revolution, and on the recording plate the distances between the extreme blackenings were measured with the aid of the marks applied. In this way oscillations of a few thousandths of the fringe width were detected, which are already caused by the presence of grains in the emulsion. It is enough to examine the results of a series of experiments carried out over 24 hours, pre-

set forth in Fig. 8, in order to make sure that there can be no question of any systematic trend.

Thus, with sufficient confidence one may indicate, as an upper limit of the still possible effect, \(1/1000\) of the width of a fringe. It should be noted, moreover, that such a conclusion can already be drawn from the results of a single day. The value obtained, when converted to the velocity of the ether wind, gives somewhat more than \(1.5\ \text{km/sec}\).

Similar records were obtained by Piccard and Stahel.* Their apparatus was small in size, since it was intended chiefly for work in a balloon. The actual optical path was only \(1.4\ \text{m}\), and the inaccuracy of an individual result was compensated by a large number of measurements. During the balloon exposures the whole balloon rotated by means of small propellers driven by electric motors. The number of revolutions was considerable (up to two per minute). The results of the experiments with the balloon, in which, to be sure, fluctuations of temperature caused considerable interference, did not reveal at an altitude of \(2500\ \text{m}\) any Miller effect of \(10\ \text{km/sec}\); however, the limits of error were also not far from this value. Considerably greater accuracy is afforded by the terrestrial experiments carried out with the same apparatus at Rigi, and consequently at the altitude of Mount Wilson, and in Brussels. On the basis of a large number of experiments, as the upper limit of the possible effect there was likewise obtained the value—

Fig. 8. Series of observations obtained over 24 hours in the Jena experiment.

* A. Piccard et E. Stahel, J. Physique et Radium (6), 8, 56 (1927).

value of 1.5 km/sec; but the accuracy of these measurements should be considered somewhat overestimated, since the photographs were not photometered, and only the distance from the marks was measured visually with the aid of a comparator.

A new idea was introduced into his design by Mac-Kennedy.* He successfully attempted to increase the sensitivity of his apparatus by applying the method of half-shadow reading. By this means he was able to reduce considerably the total length of the arms, which substantially diminished temperature disturbances. The whole instrument was mounted on a square plate with a side of 122 cm, with an optical path of 4 m. To further weaken temperature disturbances, the apparatus was filled with helium, which, owing to the small refractive index of this gas, is equivalent to evacuation down to \(1/10\) atmosphere. The method of half-shadow observation consisted in the following: one of the mirrors, on whose surface the interference fringes are projected, is divided, perpendicular to the fringes, by a sharp line into two halves, so that the surface of one of them protrudes forward by a fraction of a wavelength (approximately by \(1/10\,\lambda\)) (Fig. 9). Such a difference in thickness was achieved by cathodic sputtering of metal.

Fig. 9. Mac-Kennedy half-shadow interference principle.

When set to the interference fringes, two systems of fringes are visible, slightly shifted relative to one another. Places of equal brightness lie where the interfering beams have a path difference of \(\frac{n\lambda}{4}\), reckoned for the stepped mirror \((s_2)\) from the middle line \((\Sigma)\). The slightest change in the path difference immediately makes one half appear brighter than the other. The sensitivity of this method was estimated by Kennedy at \(2\cdot 10^{-3}\) of the fringe width. The “Miller” ether wind should have amounted, for this instrument, to \(8\cdot 10^{-3}\) of a fringe width. However, neither on Mount Wilson nor on the plain was even the slightest trace of its presence detected. Illin—

* R. J. McKennedy, Proc. Nat. Acad. Wash., 12, 621 (1926).

Illingworth, who continued to work with Kennedy’s apparatus, believes* that, taking into account the totality of a large number of observations, one may take \(1\ \mathrm{km/sec}\) as the upper limit of the effect.

Thus the general picture of all the experiments carried out after Miller makes it possible to assert that the ether wind, if such exists, cannot be more than \(1\ \mathrm{km/sec}\). This result, expressed in fringe width, gives a value one hundred times smaller than that observed by Miller. Finally, this means that the effect must be at least 900 times smaller than the expected one, if the latter is taken to be \(30\ \mathrm{km/sec}\). With the accuracy attained, one may be quite satisfied and regard this chapter of physics as completed.

However, proceeding from the conception of the ether, one may suppose the existence of different properties for light sent by extraterrestrial sources, especially by the fixed stars. This question was resolved by Tomaschek in a very elegant manner. Since here the issue is only the difference in displacement relative to terrestrial light sources, it is evidently possible to work with a stationary interferometer, the rotation of the apparatus being effected by the rotation of the Earth. In other experiments it had not seemed possible to use such a method, since it is very difficult to keep the interference fringes at rest for hours. In the present case, however, in relative measurements the simultaneous motion of both fringe systems does not hinder the measurements. Tomaschek’s apparatus had an arm length of \(8.6\ \mathrm{m}\). A sodium flame served as the comparison light source; the light of the Sun, the Moon, Sirius, and Arcturus was investigated. The observed deviations did not exceed \(1/100\) of a fringe width, which lies within the limits of possible errors. Thus this last possibility, too, should be considered experimentally excluded.

* K. K. Illingworth, Physic. Rev., 30, 692 (1927).