Sagnac effect

The relative phases of the two exiting beams, and thus the position of the interference fringes, are shifted according to the angular velocity of the apparatus.

In other words, when the interferometer is at rest with respect to a nonrotating frame, the light takes the same amount of time to traverse the ring in either direction.

Georges Sagnac set up this experiment in 1913 in an attempt to prove the existence of the aether that Einstein's theory of special relativity makes superfluous.

[1][2] A gimbal mounted mechanical gyroscope remains pointing in the same direction after spinning up, and thus can be used as a rotational reference for an inertial navigation system.

A conventional gyroscope relies on the principle of conservation of angular momentum whereas the sensitivity of the ring interferometer to rotation arises from the invariance of the speed of light for all inertial frames of reference.

The effect is a consequence of the different times it takes right and left moving light beams to complete a full round trip in the interferometer ring.

To test this hypothesis, Oliver Lodge in 1897 proposed that a giant ring interferometer be constructed to measure the rotation of the Earth; a similar suggestion was made by Albert Abraham Michelson in 1904.

) the same positive result for both special relativity and the stationary aether (the latter he called "absolute theory" in reference to the 1895-theory of Lorentz).

[6] The first interferometry experiment aimed at observing the correlation of angular velocity and phase-shift was performed by the French scientist Georges Sagnac in 1913.

Not aware of the Sagnac effect, Harress had realized the presence of an "unexpected bias" in his measurements, but was unable to explain its cause.

[16][17] Harress' results were published together with an analysis by von Laue, who showed the role of the Sagnac effect in the experiment.

[18][19][20] From these coordinates, one can derive the different arrival times of counter-propagating rays, an effect which was shown by Paul Langevin (1921).

[23] Einstein specifically stated that light speed is only constant in the vacuum of empty space, using equations that only held in linear and parallel inertial frames.

"[25] Also, Irwin Shapiro in 1964 explained General Relativity saying, "the speed of a light wave depends on the strength of the gravitational potential along its path".

[26] However, since the gravitational field would have to be significant, Laue (1920) concluded it is more likely that the effect is a result of changing the distance of the path by its movement through space.

Although this simple derivation is for a circular ring with an index of refraction of one, the result holds true for any shape of rotating loop with area A.(Fig.

4) For more complicated shapes, or other refractive index values, the same result can be derived by calculating the optical phase shift in each direction using Fermat's principle and taking into account the different phase velocities for the different propagation directions in an inertial laboratory frame, which can be calculated using relativistic addition of velocities.

In this case the phase difference formula necessarily involves the area enclosed by the light path due to Stokes' theorem.

(The case of a circular ring interferometer rotating about its center in free space is recovered by taking the index of refraction of the fiber to be 1.)

[37] A relay of pulses that circumnavigates the Earth, verifying precise synchronization, is also recognized as a case requiring correction for the Sagnac effect.

In 1984 a verification was set up that involved three ground stations and several GPS satellites, with relays of signals both going eastward and westward around the world.

[38] In the actual Hafele–Keating experiment[39] the mode of transport (long-distance flights) gave rise to time dilation effects of its own, and calculations were needed to separate the various contributions.

Ring laser gyroscopes are extremely sensitive to rotations, which need to be accounted for if an inertial guidance system is to return accurate results.

Global navigation satellite systems (GNSSs), such as GPS, GLONASS, COMPASS or Galileo, need to take the rotation of the Earth into account in the procedures of using radio signals to synchronize clocks.

The period of this beat frequency is linearly proportional to the angular velocity of the ring laser with respect to inertial space.

By rotationally dithering the laser cavity back and forth through a small angle at a rapid rate (hundreds of hertz), lock-in will only occur during the brief instances where the rotational velocity is close to zero; the errors thereby induced approximately cancel each other between alternating dead periods.

They differ considerably in various cost, reliability, size, weight, power, and other performance characteristics that need to be considered when evaluating these distinct technologies for a particular application.

[citation needed] RLGs are capable of logging in excess of 100,000 hours of operation in near-room temperature conditions.

In addition, the major optical components of FOGs have proven performance in the telecom industry, with lifespans measured in decades.

The Sagnac topology was actually first described by Michelson in 1886,[43] who employed an even-reflection variant of this interferometer in a repetition of the Fizeau experiment.