User talk:Ems57fcva/sandbox/Sagnac Effect

Have removed the GPS stuff per your request. I agree that it is only tangentially related to Sagnac anyway. (Although one of your references does document a GPS Saganc experment.) Hopefully I have sectioned off the math well.

--EMS 16:59, 25 Mar 2005 (UTC)

The philosophy of choice of frame of reference

I have been making edits to the current Sagnac effect article, possibly some of those edit can be merged into your text.

In the current Sagnac effect article I make the following statements.

Attempts to think about the physics in terms of what is seen from the perspective of a rotating frame introduces complications, without adding any insight

The proper way to interpret the Sagnac effect is to look at it from the perspective of an inertial frame of reference. If a rotating frame of reference is adopted as point of view, no meaningful interpretation is possible.

These are bold statements, teetering on the brink of pushing point-of-view. (in wiki lingo: 'pushing POV') I believe these statements are defensible. If you want I will write that defence. --Cleon Teunissen | Talk 02:19, 26 Mar 2005 (UTC)

Light never moves faster-than-light

You wrote:

This describes a frame of reference in which the speed of light tangent to the ring is observed to be depending on whether the light is moving against or with the rotation of the ring. Note that only the case of ω = 0 is inertial. For this frame of reference is non-inertial, which is why the speed of light at positions distant from the observer (at r = 0) can vary from c.

It is this discrepany from the constancy of c in the frame of reference of the rotataing ring interferometer that describes why the Sagnac Effect must occur even in the frame of reference of the rotating ring itself.

It seems to me there is an inconsistency here. One of the axioms of relativistic physics is that the speed of light cannot exceed the speed of light. It would constitute a self-contradiction if it is stated that under particular circumstances the measured $c$ is larger.
For comparison: an observer in a spaceship accelerated by thrusters, pulling G's, will measure an apparent anisotropy in the speed of light. As his instrument readings are informing him that the space-ship he is in is pulling G's, he infers that the deviation from $c$ that he measures is only an apparent deviation. He will apply the appropriate transformation from his accelerating frame to an inertial frame, thus preserving consistency in the interpretation of measurements.

GPS and the Sagnac effect

I've had a change of mind about 'GPS and the Sagnac effect'. What I like about it is that is is not theory, it's technology. And it's cutting edge technology, any error will show up as a glaring inability to achieve the attainable accuracy.

Also it ties together aspects of physics that you wouldn't expect to be closely tied. Interferometry and disseminating time have important physics in common. Here is the GPS section of the current version of the article

GPS-technology takes several relativistic effects into account to achieve its level of accuracy. For the GPS-engineers, there is zero room for error, current GPS-accuracy is at the limit of what is attainable with the current atomic time-keeping technology. GPS-technology takes the Sagnac effect into account in the procedures of using radio signals to synchronize clocks.

Many aspects of motion can be "transformed away" by a suitable transformation. It can be shown that a calculation of the Sagnac effect in the context of a rotating reference frame shows the same Sagnac effect as is present from the point of view of an inertial reference frame. The Sagnac effect is not an artifact of choice of reference frame, it is independent of the choice of reference frame.

--Cleon Teunissen | Talk 08:13, 26 Mar 2005 (UTC)

Sagnac/Coriolis effect

You wrote:

The trajectory can be any trajectory that encloses an area containing the axis of rotation.

The Michelson-Gale experiment measured the rotation rate of Earth without circumnavigating Earth. The axis of rotation does not have to be inside the area enclosed by the trajectory. --Cleon Teunissen | Talk 08:26, 26 Mar 2005 (UTC)

The reason that I added a description of the Michelson-Gale experiment is that it's not only of historical interest, it displays some of the important unexpected properties of the sagnac effect. Sagnac probably calibrated his interferometer while it was non-rotating. But calibration of a Sagnac interferometer does not require comparison with an outside reference, the Michelson-Gale experiment shows that careful analysis of the geometry of the experimental setup is sufficient for calibration.

I have also seen descriptions of ring laser gyroscopes. In ring laser gyroscopes the laser cavity is torus-shaped. When the laser cavity rotates there is doppler shift. Effectively there are two doppler shifts then, depending on the direction of the back-and-forth traversing light. When the ring laser interferometer is rotating (effectively: when it is accelerating) the lasering produces two frequencies, very closely spaced. Interference of these two frequencies creates a beat frequency, which is measured. Thus, a constant angular velocity can be detected, and calibration does not require comparison with an outside reference. --Cleon Teunissen | Talk 09:08, 26 Mar 2005 (UTC)

Dependency on velocity in medium

You wrote:

The overall magnitude of the Sagnac Effect is δt = 4ωA / v2
v is the velocity of the particles being used in the experiment (c for light outside of a medium with a significant index of refraction)

There is a distinction that I hadn't appreciated until now.

Stedman calls setups like the original Sagnac experiment, and the Michelson-Gale experiment 'passive optics'. He writes that a frequency splitting will occur, but in the original setup this is an insignificant contribution and it is not measured. What is measured is a phase-shift interference pattern. The magnitude of this phase-shift is independent of the velocity.

On the other hand, there are also setups that employ laser-effect to get to a situation where all the light in the cavity is coherent. Then it is possible to measure something else than a phase-shift. Instead a beat frequency is measured. This particular Sagnac effect is dependent on the velocity of travel along the trajectories.

So there are fiber optic gyroscopes, that measure phase-shift, and there are ring laser gyroscopes, that rely on generating coherent light in the cavity. Both types of design are implemented in commercially available navigational equipment. --Cleon Teunissen | Talk 10:24, 26 Mar 2005 (UTC)

The geocentricity link

It is not clear to me why you added the link to the Geocentricity article. It's not even an article, it is rather a footnote. And it is wrong, the Geocentricity footnote makes the very mistake you want to refute: thinking that the sagnac effect falsifies relativistic physics. So why the link to wrong information? --Cleon Teunissen | Talk 07:50, 27 Mar 2005 (UTC)

Around the world experiment

You wrote:

In 1984, four GPS satellites and three ground stations where used to form an around-the-world ring interferometer. The expected restults were obtained to an accuracy of 2 %.

This was not an interferometric experiment, it was a dissemination-of-time-experiment. If you use radio signals to disseminate time in two opposite directions, going sequentially from station to station, then will everthing match in the end? The synchronisation will only be globally successfull if the Sagnac effect is taken into account. Dissemination of time is categorized as involving a Sagnac effect because geometrically it involves the same issues. --Cleon Teunissen | Talk 10:11, 27 Mar 2005 (UTC)

Ring laser gyroscope: principle of operation

I found a website that presents the principle.
Principle of Ring Laser
--Cleon Teunissen | Talk 12:10, 27 Mar 2005 (UTC)