Translation:Sagnac Effect and Emission Theory

by Hans Witte

Sagnac Effect and Emission Theory;

by Hans Witte.

(Received July 24, 1914.)

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In my article^[1] previously mentioned, I also referred to the emission theory and have spoken out the view: the Sagnac effect can be interpreted as an experimentum crucis against the emission theory.

Meanwhile, the question was presented to me: It is about a rotational process; the pure emission theory stand upon the foundation of mechanics; in mechanics, rotating systems throughout cause deviations relative to inertial systems, thus shouldn't the Sagnac effect also be demanded in the case of emission theory?

The question can be most easily answered for the ideal limiting case, that both halves of the light ray are tangentially starting from $O$, thus the circulation polygons become identical to the circle (Fig. 1). Thus the matter is as follows: Starting at $O$, two material points are inevitably moving at the border of the ring with equal initial velocity relative to $O$. Since the inevitable trajectory is perpendicular to the apparent forces, it is given without further ado, that the time of orbit and the meeting place ($O$) remain the same, independent on whether the system is at rest or in rotation. One can also say: If one considers the rotating system from the view of the rest-system, then the light ray which is following the same direction of the rotation, experiences a path-elongation corresponding to the factor $\left(1+{\tfrac {v}{c}}\right)$, yet also a velocity increase corresponding to the same factor $\left(1+{\tfrac {v}{c}}\right)$, which is canceling each other; the same arises at the oppositely moving ray $\left(1-{\tfrac {v}{c}}\right)$; there, $v$ is the orbit velocity of ($O$), $c$ is the speed of light.

Fig.1.

Fig.2.

With finite number of edges (Fig. 2), a path elongation and velocity change is given according to the factor $\left(1+{\tfrac {v}{c}}\cdot \cos {\tfrac {\vartheta }{2}}\right)$ at first approximation. Conservation of velocity is assumed in a known way at the reflecting points, because the mirrors are moving in their plane. However, there it is presupposed, that the process of reflection as such, exerts no disturbing influence of observable order of magnitude.

Braunschweig, Technische Hochschule.

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1. H. Witte, Verh. d. D. Phys. Ges. 16, 142, 1914.