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A New Repetition of the Michelson Experiment1
The occasion for Kennedy’s experiment, reviewed in the present note, was the puzzling positive results of Miller’s experiments, obtained recently on Mount Wilson. Miller’s experiments have been described in detail in other issues of our journal,2 to which we refer the reader. The new repetition of the Michelson experiment was carried out in Pasadena in the Millikan laboratory. In Kennedy’s apparatus several very important changes were introduced in comparison with the Michelson–Morley and Miller interferometer. Miller used a large interferometer with a light path of about 65 m in air. Under these conditions a negligible nonuniform change in the temperature of the air, by thousandths of a degree, may be accompanied by such a change in the refractive index as is capable of producing a displacement of the interference fringes of the same magnitude as was observed by Miller. Kennedy’s interferometer is placed on a square marble slab with sides of 122 cm and a thickness of 10.5 cm. The total length of the light path is reduced to 4 m. The interferometer floats in mercury. The entire optical system is covered with an airtight metallic casing and the space is filled with helium at atmospheric pressure. Helium is chosen because for it \(\mu - 1\) (\(\mu\) is the refractive index) is about ten times smaller than for air at the same pressure and, consequently, variations of refraction will have a considerably smaller effect than in air. Under these conditions, as soon as the temperature had become established, all tremors and displacements of the fringes ceased. The source of light was a small mercury lamp (the green line 5461 Å). The light used was polarized. By this, first, noninterfering rays, polarized in two mutually perpendicular planes, which diminish the sharpness of the interference pattern, were eliminated. Secondly, with polarized light one can achieve complete equality of the intensities of the interfering beams by correspondingly changing the reflecting power of the mirrors. Thanks to this, the greatest sharpness of the fringes is attained.
The length of the optical path in Kennedy’s apparatus, as indicated, is 16 times less than in Miller’s. To obtain the same sensitivity as Miller’s, Kennedy applies a new device. Half of the surface of one of the mirrors (Fig. 1) is—
accounts for a small fraction of a wavelength over the other half, which is achieved by the corresponding deposition of platinum (cathode sputtering). Let the distance from mirror \(M_1\) to the mean line of mirror \(M_2\) be \(x\), and let the two halves of \(M_2\) be removed from the mean line by distances \(\pm\alpha\). A plane wave falls on the mirror from left to right:
\[ \xi=A\cos\frac{2\pi c}{\lambda}\left(t+\varepsilon-\frac{x}{c}\right). \]
The wave reflected from \(M_1\) will be:
\[ \xi_1=A\cos\frac{2\pi c}{\lambda}\left(t+\varepsilon\right). \]
The wave reflected from the upper step of mirror \(M_2\):
\[ \xi_2=A\cos\frac{2\pi c}{\lambda}\left[t+\varepsilon-\frac{2(x-\alpha)}{c}\right]. \]
For the intensity of the interference pattern for the upper half of the field, by the usual method we obtain:
\[ I_1=KA^2\left[1+\cos\frac{4\pi}{\lambda}(x-\alpha)\right] \]
and for the lower half:
\[ I_2=KA^2\left[1+\cos\frac{4\pi}{\lambda}(x+\alpha)\right]. \]
It is easy to see that for \(x=\dfrac{n\lambda}{4}\), \(I_1=I_2\), and to the observer both halves of the interference field will be equally illuminated. If \(x\) differs from \(\dfrac{n\lambda}{4}\), then the intensity of the two halves of the field will be different. The difference in intensities \(\Delta I\) will be noticeable to the eye, according to Kennedy’s estimate, if \(\dfrac{\Delta I}{I}>8\cdot 10^{-3}\). The magnitude \(\alpha\) was equal to \(0.025\lambda\). Under these conditions the smallest change \(\Delta x\) that one may hope to notice is equal to \(5\cdot 10^{-5}\lambda\). Owing to imperfections of the mirrors and other causes, this limiting sensitivity is not attained in practice. Kennedy determines the real sensitivity of the installation as \(10^{-3}\lambda\). “Such changes, according to him, are detected quite definitely.” The “Miller effect,” i.e. a velocity \(v\) relative to the ether of 10 km/sec, should correspond to \(4\cdot 10^{-3}\lambda\), i.e. at least four times greater than those intensity changes that are quite noticeable in Kennedy’s apparatus.
The experiments were carried out in a room with constant temperature in September 1926, at various times of day, but most often at those hours when, according to Miller, the greatest effect is observed. “The result was entirely definite,” writes Kennedy. “There was no trace whatever of displacements depending on the orientation of the instrument.”
The experiments were also repeated at the Mount Wilson Observatory (at an altitude of 1850 m), in the building of the 100-inch telescope, and likewise without any effect. It is proposed to continue the experiments with certain changes in order to increase the sensitivity. It should be noted that Kennedy’s interference photometric method opens new paths in various problems of optics.
S. Vavilov.