Translation:The Demonstration of the Luminiferous Aether

The luminiferous aether demonstrated by the effect of the wind relative to the aether in a uniformly rotating interferometer  (1913)
by Georges Sagnac, translated from French by Wikisource

The luminiferous aether demonstrated by the effect of the wind relative to the aether in a uniformly rotating interferometer

Note by G. Sagnac, presented by E. Bouty.

I. Principle of the method. - I set into uniform rotation around a vertical axis, at a speed of one or two turns a second, a horizontal plate (50cm in diameter) that bears, firmly anchored, the various parts of an interferometer similar to one which I employed in my former research and described in 1910 (Comptes rendus, t. 150, p. 1676). Both interfering rays, reflected by four mirrors located at the edge of the rotating table, are superimposed in opposite directions on the same horizontal circuit surrounding a certain area S. The rotating system also includes the light source, a small electric lamp, and the receiver, a fine-grained photographic plate that records the interference fringes located at the telescope focus.

On the d and s images, respectively obtained during a clockwise and a counter-clockwise rotation of the plate at the same rotation frequency, the center of the central fringe takes two different positions.[1] I measure this displacement of the interference center.

First method. - I mark on the d image, then on the s image, the position of the central fringe with respect to the image of the vertical graduations of a micrometer located in the focal plane of the light collimator.

Second method. - I measure directly the distance from the vertical central fringe of the d image to the central fringe of the s image, which is exactly adjacent to the first below a sharp, horizontal separation-line. I obtain these two adjacent images directly, without touching the photographic frame, by moving razor edges in the focal plane of the collimator into either of two adjacent positions corresponding to the illuminated slit, before each of the two exposures d and s.

II. Optical vortex effect. - Measured in distance between interference fringes, the displacement z of the center of interference, that I observed by the preceding method, is a particular case of the optical vortex effect which I defined before (Congrès de Bruxelles de septembre 1910, t. I, p. 217; Comptes rendus, t. 152, p. 310; Le Radium, t. VIII, 1911, p.1), and which, according to current understanding, must be regarded as a direct manifestation of the luminiferous aether:

In a system collectively moving with respect to the aether, the propagation time between two arbitrary points of the system must be altered in the same way as it would be in a stationary system subjected to the action of an aether wind, whose relative velocity at each point of the system would be equal and directly opposed to the velocity of that point, and which would carry the light waves in the same manner as atmospheric wind carrying sound waves. The observation of the optical effect of such a relative aether wind constitutes a proof of the aether, just as the observation of the influence of the relative wind of the atmosphere on the velocity of sound in a moving system would allow, in the absence of other significant effects, proof of the existence of a stationary atmosphere surrounding the moving system.

The need to bring together the vibrations from the same original luminous point to another point to make them interfere reduces to zero the first order interference effect of the collective translation of an optical system, unless the matter which constitutes the aether causes a circulation C of the aether in the optical circuit of area S, i.e. a vortex bS of the aether (Comptes rendus, t. 141, 1905, p. 1220; 1910 et 1911, loc. cit.). I showed interferometrically (1910 and 1911, loc. cit.), with an optical circuit enclosing 20m² of vertical projection, that the entrainment of aether in the vicinity of the ground does not produce a vortex density b in the aether of even ${\displaystyle {\tfrac {1}{1000}}}$ radian per second.

In a horizontal optical circuit, at latitude α, the diurnal rotation of the Earth must, if the aether is motionless, produce a relative aether vortex whose density is ${\displaystyle {\tfrac {4\pi \sin \alpha }{T}}}$ or ${\displaystyle {\tfrac {4\pi \sin \alpha }{86164}}}$ radian per second, where T is the duration of the sidereal day; notably lower than ${\displaystyle {\tfrac {1}{1000}}}$, the upper limit that I established for a vertical circuit. I hope to be able to determine whether a corresponding small optical vortex effect exists or not.

It was easier first for me to find a proof of the aether by setting into rotation a small optical circuit. A frequency N of two rotations per second provided to me a relative aether vortex density of 4πN, or 25 radians per second. A uniform clockwise rotation of the interferometer produces a counter-clockwise aether wind; it delays by x the phase of the beam (T), whose circulation around the area S is clockwise, and it advances the opposite beam R by an equal amount, thus causing a fringe displacement of 2x. The displacement z, that I observe comparing an s image with a d image, must be double that of the former.[2] On the basis of the value of x observed previously (loc. cit. 1910 and 1911), we have

${\displaystyle z=4x=4{\frac {b{\mathsf {S}}}{\lambda {\mathsf {v}}_{0}}}={\frac {16\pi {\mathsf {NS}}}{\lambda {\mathsf {v}}_{0}}};}$

where ${\displaystyle V_{0}}$ indicates the speed of light in vacuum, and λ is the wavelength used.

For a rotational frequency N of 2 turns per second, and an area S of the circuit of 860cm², the displacement attained by z has the value 0.07 when using indigo light, quite visible on the photographs which I have attached to this Note, and where the distance between interference fringes is 0.5mm to 1mm.

The interference displacement z, a constant fraction of the fringe spacing for a given rotation frequency N, becomes invisible on the photographs when the fringes are adjusted to be sufficiently narrow; this clearly shows that the observed effect is due to a phase difference related to the rotational motion of the system and that (thanks to the counter-screws which block movement of the optical parts) the displacement of the center of interference, observed by comparing an s image with a d image, does not result from accidental relative displacements or tensions of the optical parts during rotation.

A turbulent vortex of air, produced by a fan of vertical axis (above the interferometer) blowing in a downward direction, does not move the interference center, due to the carefully regulated superposition of the two opposite beams. Any similar and less intense flow of turbulent air produced by the interferometer during rotation should thus not have any sensible effect.

The interference effect observed is clearly an optical vortex effect due to the motion of the system with respect to the aether and directly demonstrates the existence of the aether, the necessary carrier of the light waves proposed by Huygens and Fresnel.

Translator's notes

1. Since Sagnac used a non-monochromatic light source, the interference pattern consisted of a central vertical fringe corresponding to equal optical path length, surrounded by colored fringes of diminishing intensity.
2. in other words, z = 2 times 2x.
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