Sagnac effect

A Sagnac interferometer is an interferometer, which makes it possible to measure rotation absolute. That is, an observer is able to determine from this arrangement, whether it is in rotation or not.

This is in no way contrary to the principle of relativity. This indicates only the possibility of defining the uniform translatory self-motion of the observer, provided that the experimental arrangement used to as a whole in the same inertial frame rests as the observer. The most well-known confirmation of this view is the Michelson - Morley experiment, with the uniform translatory self-motion of the earth should be "absolute" measure, which, however, yielded a negative result. Uniform translational motion is therefore relative. With rotary motion, but this is different. Rotations compared to an inertial system can be measured absolutely with a closed experimental arrangement, since it is not possible to define an inertial frame in which the entire experimental arrangement is located in peace.

The oldest method for measuring absolute rotation is the Foucault pendulum, which was the first time to measure the rotation of the earth without sky observations and thus to confirm the heliocentric worldview of Nicolaus Copernicus. Also gyros and laser gyro function according to this principle. What is the Foucault pendulum for the mechanics, the Sagnac effect for the appearance. Here can be observed that between two beams of coherent light which are directed clockwise and anticlockwise through the same route in the mirror circuit, a phase shift occurs, as long as it rotates the entire apparatus, i.e., during the rotation is used for to a beam of light, the distance longer, for others shorter.

This confirms all the theories in which the speed of light is independent of the speed of the rotating body - including the special theory of relativity and the theory of stationary aether (the correspondence is given between the two theories only at low speeds). However, since the classical ether theory was refuted by numerous other experiments (especially the Michelson - Morley experiment ), the Special Theory of Relativity and the experimentally equivalent to her, but conceptual overtook Lorentz ether theory are the only theories that can explain all the experiments.

History

First hypotheses for the existence of such an effect were by Oliver Joseph Lodge (1897 ) and Albert Abraham Michelson (1904 ) argued. Two light beams, which describe a circular path in the opposite direction would require due to the Earth's rotation different maturities, which would have to be demonstrated as a shift of the interference fringes. This should be determined whether the earth the ether, a hypothetical substance which should fill the space after the former ideas,

• Carries, which should yield a negative result,
• Or whether the ether at rest, which should give a positive result.

In 1911, Max von Laue, this theoretical investigation continues, said he already took into account the special theory of relativity. The result of his calculations was that both according to the special theory of relativity as well as according to the theory of the stationary luminiferous ether is to be expected in a first approximation, in approximately the same time difference, due to the independence of the speed of light by the movement of the experimental arrangement in the two theories. Only when fully Äthermitführung (this theory was, however, already been refuted at this time because of the Fizeau experiment ) would result in a negative result. While Laue herleitete the effect of view of any inertial frame, which is quite sufficient for a consistent explanation of the effect in the context of the SRT, the effect was by other authors such as Paul Langevin (1921 /35) also from the perspective of a co-rotating reference frame, according to both the special and the general theory of relativity, depicted.

1913 such an experiment has now been actually performed by Georges Sagnac, with the point of view of the theory of relativity (and the stationary ether ) already expected shift of the interference fringes. Sagnac saw the effect as a refutation of the source function of the speed of light, that is, as a refutation of the emission theory of light, and as direct evidence of a luminiferous ether to - the theory of relativity, he did not mention, however. However, this omission was meaningless, since, as mentioned, Laue had two years earlier predicted such an effect as a consequence of special relativity.

As it became known only later, a similar experiment was carried out by Franz Harress 1909-1911, which can be regarded as a synthesis of the Fizeau and Sagnac experiments. He tries to measure the osmotic drag coefficient in glass, but he used a rotating experimental arrangement, which is later used by Sagnac very similar. The shifts found by him was not interpreted correctly by Harress, but Laue showed in 1920 that the result found by Harress corresponded to the Sagnac effect.

The structure

A coherent light beam from a light source, Sagnac used a mercury vapor lamp is split by a semitransparent mirror into two beams. This will be done with the help of mirrors in the opposite direction in a circle and meet each other again at the beam splitter. The interference pattern is observed on a detector screen. The assembly is at rest, the paths of the two beams are of equal length and in the middle of the screen you can see destructive interference, because of the reflection each a phase shift of 90 °, which is in the running in the image counterclockwise beam a phase shift arises from 180 ° results compared to the current clockwise beam. But in case the whole construction rotated around an axis perpendicular to the beam plane, the optical path for both of the beams is not the same length, as in the time it takes for the light to a current, the beam splitter has been further rotated a little. Thus one sees a shift in the interference fringes.

The remarkable thing about this experiment is mainly that all parts of the system - light source, intermediate apparatus and meter (Observer ) - to be moved, they nevertheless observed an influence of the rotation.

Theory

In each inertial light propagates at a constant speed c. Next, the inertial system is the reference system, and the interferometer is rotated with the angular velocity. Light runs around on an arbitrarily shaped closed path length. It is deflected by mirrors accordingly. The time required for the light to travel the distance is,

During this time, the apparatus rotates by the angle. The light must therefore assuming in a tangential direction to

Longer or shorter stretch cover. (R is the distance between the rotational axis and the distance piece, but the distance between the axis of rotation and adjacent to the tangent. is therefore pointing in the tangential component of the rotational speed. ) for the complete revolution is therefore clear

Where A is the area enclosed by the beam area ( easy to understand in the case of a circle: ). The difference in the distances that have to cover the two rotating light waves is, as a back increased by more way, the other less. The fringe shift ( path difference as a phase difference ) is therefore

At an area A = 1 m ( in the drawing designated with S ), and a wavelength λ = 633 nm is required to an angular velocity of 1360 ° / s (227 rpm), to change from the maximum signal-to- extinction ().

Michelson - Gale experiment

1925 succeeded Albert Abraham Michelson and Henry G. Gale with an interferometer of 613 m length and 339 m width according to this principle to measure the rotation of the Earth with a relative accuracy of 2%. The relative fringe shift was 0.23. In order to obtain sharp interference fringes, the entire light path was evacuated to 17 mbar. For sufficiently light was provided by a carbon arc. The special feature of the Michelson - Gale experiment is that - unlike the rotating Sagnac interferometer - is no relative motion to the reference system of the earth.

Michelson and Gale already recognized itself correctly, that their experiment does not make any statement about the existence of the ether. It can be explained both with the theory of relativity as well as with a stationary ether. The Michelson - Gale experiment, however, is of great importance in this respect than it is to explain all the experiments, the negative result of the Michelson -Morley experiment by an entrainment of the ether, the soil extracts. It would indeed appear paradoxical that in translation ( Michelson -Morley experiment) full entrainment of the ether takes place through the earth in rotation ( Michelson - Gale experiment), however, the ether at rest relative to the fixed stars.