I Is the Sagnac Effect a Relativistic Phenomenon?

[Hepper]

TL;DR Summary

Different explanations for the Sagnac effect have been proposed: the aether, coriolis effect... which is it?

Wikipedia explains the Sagnac effect as a result of the rotating disk, which moves the target so that one of the light beams has farther to travel and consequently, will arrive later than the other light beam which goes around the disc in the same angular direction as the rotating disc. However, the source and the target of the light beam are always the same distance apart, since both of them are rotating with the disc. So this explanation doesn't make much sense to me. Maybe I just misunderstood the experimental setup which is used to demonstrate the Sagnac effect.

In the first half of the 20th century, the Sagnac effect was interpreted by some physicists as evidence for the aether theory, but this was discarded by Einstein's STR.

In a https://www.researchgate.net/publication/308921264_Spinning_Earth_and_its_Coriolis_effect_on_the_circuital_light_beams_Verification_of_the_special_relativity_theory written by Sankar Hajra, it was postulated that the Coriolis force acts on the propagation of light. Hajra concluded: "Coriolis effect (not the Sagnac effect) is responsible for the non-null result of the Michelson–Gale experiment assisted by Pearson[...]." All of this is just very confusing to me. The Wikipedia explanation seems to be the simplest out of them... aether theory is generally not accepted in the scientific community and I just fail to comprehend Hajra's explanation. Is there anyone who can explain the Sagnac effect in Einstein's relativistic framework? Is Hajra's model possible or is it hogwash?

 

[Drakkith]

However, the source and the target of the light beam are always the same distance apart, since both of them are rotating with the disc.

True, but that's not important. Because the interferometer is rotating, the light beams themselves travel different distances on each 'leg', or through the fiber optic cable if one is being used.

In a https://www.researchgate.net/publication/308921264_Spinning_Earth_and_its_Coriolis_effect_on_the_circuital_light_beams_Verification_of_the_special_relativity_theory written by Sankar Hajra, it was postulated that the Coriolis force acts on the propagation of light. Hajra concluded: "Coriolis effect (not the Sagnac effect) is responsible for the non-null result of the Michelson–Gale experiment assisted by Pearson[...]." All of this is just very confusing to me.

The question isn't whether the coriolis effect causes the sagnac effect in general (it doesn't), but rather if the coriolis effect can give similar results as the sagnac effect in specific situations (maybe). The Earth is rotating, and objects at different latitudes experience different velocities with the those at the equator moving faster than those closer to the poles. The paper you linked claims:

Earth, just like all other physical objects, carries
electromagnetic fields along with it at the vicinity of its
surface. Therefore, Coriolis force due to the spinning
of Earth must act on the propagation of light on the
surface of Earth.

Unfortunately I'm not experienced enough with electrodynamics and relativity to verify this claim.

Note that the paper specifically talks about the Michelson-Gale experiment. It does not claim that the sagnac effect is always caused by the coriolis effect. This is trivial to demonstrate as false since merely rotating an interferometer in your hand will give the sagnac effect, and the magnitude of the change in the interference pattern changes directly with the angular velocity of the interferometer.

 

[Dale]

Summary: Different explanations for the Sagnac effect have been proposed: the aether, coriolis effect... which is it?

Is Hajra's model possible or is it hogwash?

His analysis is fairly flawed. There is no “either or” here. The Sagnac effect is the name of the phenomenon measured in the Michelson Gale experiment, so his claims of “Coriolis effect (not Sagnac effect)” are obviously silly.

The Sagnac effect is an observed effect where a laser ring interferometer detects a fringe shift proportional to the angular velocity. There are two possible ways to analyze the experiment, one is with respect to an inertial frame and the other is with respect to a rotating frame.

In the rotating frame the apparatus is stationary but centrifugal and Coriolis effects do impact Maxwells equations and hence the propagation of light.

In the inertial frame Maxwells equations and the propagation of light take their standard form but the apparatus moves during the experiment.

Both derive the same equations and are simply different ways of looking at the same scenario. The explanations are completely equivalent.

 

[Dale]

one of the light beams has farther to travel and consequently, will arrive later than the other light beam which goes around the disc in the same angular direction as the rotating disc. However, the source and the target of the light beam are always the same distance apart, since both of them are rotating with the disc. So this explanation doesn't make much sense to me.

The distance that the light travels is different from the distance between the source and target when they are moving.

Here is an example that may help you understand the point. Suppose I board a plane in New York entering in the back door and during the flight I slowly walk to the front and deplane in Chicago. Although the back and front of the plane are at all times a couple of hundred feet apart, I traveled more than a thousand miles, not a couple of hundred feet.

 

[Drakkith]

Here is an example that may help you understand the point. Suppose I board a plane in New York entering in the back door and during the flight I slowly walk to the front and deplane in Chicago. Although the back and front of the plane are at all times a couple of hundred feet apart, I traveled more than a thousand miles, not a couple of hundred feet.

And if I start in the front and end up in the back then I've traveled a few hundred feet less than you have, relative to the Earth's surface.

 

[Sagittarius A-Star]

Is there anyone who can explain the Sagnac effect in Einstein's relativistic framework?

A good relativistic explanation can be found here:
http://www.physicsinsights.org/sagnac_1.html

An interesting aspect of the Sagnac effect is often over-looked: In the SR calculation, the signal velocity in the rotating frame cancels-out. So the ∆t of the Sagnac effect does not depend on the signal velocity in the rotating frame. It is purely a difference in the clock synchonization around the rim of the disk, which comes from the "relativity of simultaneity" term in the Lorentz transformation: v x/c². Therefore, the Sagnac effect is a relativistic effect.

The clock synchronization issue in the rotating frame is shown in the following animation:
https://commons.wikimedia.org/w/index.php?title=File:Simultaneity.webm