Bob Knodel and the laser ring gyroscope

Bob Knodel is a famous (?) Youtube flat earther who tried an experiment to prove the earth was fixed - non rotating. He obtained a UD$20,000 laser ring gyroscope, an extremely accurate device, to show that the earth was not spinning. The gyroscope registered a 15 degree per hour drift.

Does this prove a rotating earth? Or like Bob Knodel said, did it measure the "heavenly energies"?

If the gyroscope did measure a 15 degree per hour rotating earth, can this be possible still with a flat earth and local sun-moon circling system?




Edit: I see someone has already started a thread with the same information.

Really? Does no one see the glaring error? Not a lot of actual info, so maybe somebody did it correctly and glossed over the details, but otherwise this entire experiment is totally flawed.

An experiment is based on very precise formulas.

The formula used in laser optics is the CORIOLIS EFFECT equation; however, the counterpropagating beams of light in an interferometers is a SAGNAC EFFECT experiment.

The author of the video does not understand that such an experiment, where an arm of the interferometer was encased in lead, has already been done a long time ago:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2031383#msg2031383

A laser ring gyroscope is fully equipped to register/record TWO TYPES OF ROTATIONAL MOTIONS: either the ether drift rotation (CORIOLIS EFFECT) or the rotation of the Earth around its own axis (SAGNAC EFFECT). Each and every interferometer, since 1913, including the Michelson-Gale 1925 experiment, has registered ONLY the CORIOLIS EFFECT, nothing else.

Here we go again. Sandy and his hang up on the Sagnac effect while still ignoring the rest of the post.

I'm sure the manufactures of laser gyroscopes and their customers will be fascinated to learn that the instruments don't work as advertised.

Has anyone told them?

/sarc

I'm sure the manufactures of laser gyroscopes and their customers will be fascinated to learn that the instruments don't work as advertised.

Has anyone told them?

/sarc

I wonder how many unexplained plane crashes have caused by these gyroscopes believing Sandokhan.

Ring laser gyroscopes measure/detect rotation using a Sagnac interferometer.

Here is one of the best threads ever:

https://www.theflatearthsociety.org/forum/index.php?topic=50860.0

They are fully equipped to detect both the CORIOLIS EFFECT (a physical effect on the light beams proportional to the area of the interferometer) and the SAGNAC EFFECT (an electromagnetic effect proportional to the radius of the rotation).

However, it is either/or.

If the ring laser gyroscope measures/detects the CORIOLIS EFFECT, then the Earth is stationary (existence of the ether drift).

If the ring laser gyroscope measures/detects the SAGNAC EFFECT, then the Earth is rotating (no ether drift).

Since 1913, all interferometers, especially the ring laser gyroscopes have detected ONLY the CORIOLIS EFFECT, nothing else.

Now, let us compare the two formulas, Coriolis vs. Sagnac, using the latitude, for the Michelson-Gale experiment.

The turning of the MGX area at the hypothetical rotational speed of the Earth takes place a distance of some 4,250 km from the center of the Earth (latitude 41°46').

FULL CORIOLIS EFFECT FOR THE MGX:

4AΩsinΦ/c²

FULL SAGNAC EFFECT FOR THE MGX:

4Lv(cos²Φ₁ + cos²Φ₂)/c²


Sagnac effect/Coriolis effect ratio:

R((cos²Φ₁ + cos²Φ₂)/hsinΦ

R = 4,250 km

h = 0.33924 km

The rotational Sagnac effect is much greater than the Coriolis effect for the MGX.

Φ₁ = Φ = 41°46' = 41.76667°

Φ₂ = 41°45' = 41.75°

R((cos²Φ₁ + cos²Φ₂) = 4729.885

hsinΦ = 0.225967

4729.885/0.225967 = 20,931.72

THE ROTATIONAL SAGNAC EFFECT IS 21,000 TIMES GREATER THAN THE CORIOLIS EFFECT.

Michelson and Gale recorded ONLY the Coriolis effect, and not the rotational Sagnac effect.

The global/generalized Sagnac effect formula, the most important in all of physics:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2117351#msg2117351

The weird thing is you have these ring laser gyroscopes (RLG)/fiber optic gyroscopes (FOG) embedded in Inertial Navigation Systems (INS) in every commercial airliner on the planet. The system factors in earth rotation/coriolis into its calculations as part of many other earthly/atmospheric calculations for flight/navigation. Every one of those planes and flights are unabashedly dependent on the INS. Yet there is still some notion that it's all wrong. I don't see how, even Zetetically, the observation and experience of all of these successfully navigated flights based upon this technology and calculations is somehow...wrong. I't almost like the thousands of flights everyday reliant on this earth rotational assumption work out of sheer luck and happenstance.

And to Sandy's point, "If the ring laser gyroscope measures/detects the CORIOLIS EFFECT, then the Earth is stationary (existence of the ether drift).

Not true. Coriolis is a subset, a byproduct of one of two things:

- Earth rotation
- Aether rotation (Stationary earth)

The presence of Coriolis is not a default to a stationary earth, by any means.

The presence of Coriolis is not a default to a stationary earth, by any means.

You are not paying attention.

A ring laser gyroscope is equipped to detect BOTH the CORIOLIS EFFECT and the SAGNAC EFFECT.

If it detects ONLY the CORIOLIS EFFECT, and NOT the SAGNAC EFFECT, then the Earth is stationary (it has detected the ether drift, but not the rotation of the Earth).

If it detects the SAGNAC EFFECT, which is 21,000 times greater than the CORIOLIS EFFECT in the MGX, then and only then you can claim that the Earth would be rotating around its own axis.

Since 1913, each and every interferometer, including the ring laser gyroscopes, have detected ONLY the CORIOLIS EFFECT, nothing else.

The presence of Coriolis is not a default to a stationary earth, by any means.

You are not paying attention.

A ring laser gyroscope is equipped to detect BOTH the CORIOLIS EFFECT and the SAGNAC EFFECT.

If it detects ONLY the CORIOLIS EFFECT, and NOT the SAGNAC EFFECT, then the Earth is stationary (it has detected the ether drift, but not the rotation of the Earth).

If it detects the SAGNAC EFFECT, which is 21,000 times greater than the CORIOLIS EFFECT in the MGX, then and only then you can claim that the Earth would be rotating around its own axis.

Since 1913, each and every interferometer, including the ring laser gyroscopes, have detected ONLY the CORIOLIS EFFECT, nothing else.

Not true as you are not paying attention. It uses its detection of rotation of earth on its axis and as a byproduct can calculate the subset that is the coriolis effect.

It uses its detection of rotation of earth on its axis

You can only detect the rotation of the earth using the SAGNAC EFFECT.

Michelson and Gale, each manufacturer of the ring laser gyroscopes, claim they are using the SAGNAC EFFECT, and they are not.

The formula put forward/published is the CORIOLIS EFFECT equation.

Can you understand this much?

Two very different formulas.


If the ring laser gyroscope measures/detects the CORIOLIS EFFECT, then the Earth is stationary (existence of the ether drift).

If the ring laser gyroscope measures/detects the SAGNAC EFFECT, then the Earth is rotating (no ether drift).

Since 1913, all interferometers, especially the ring laser gyroscopes have detected ONLY the CORIOLIS EFFECT, nothing else.

Now, let us compare the two formulas, Coriolis vs. Sagnac, using the latitude, for the Michelson-Gale experiment.

The turning of the MGX area at the hypothetical rotational speed of the Earth takes place a distance of some 4,250 km from the center of the Earth (latitude 41°46').

FULL CORIOLIS EFFECT FOR THE MGX:

4AΩsinΦ/c²

FULL SAGNAC EFFECT FOR THE MGX:

4Lv(cos²Φ₁ + cos²Φ₂)/c²


Sagnac effect/Coriolis effect ratio:

R((cos²Φ₁ + cos²Φ₂)/hsinΦ

R = 4,250 km

h = 0.33924 km

The rotational Sagnac effect is much greater than the Coriolis effect for the MGX.

Φ₁ = Φ = 41°46' = 41.76667°

Φ₂ = 41°45' = 41.75°

R((cos²Φ₁ + cos²Φ₂) = 4729.885

hsinΦ = 0.225967

4729.885/0.225967 = 20,931.72

THE ROTATIONAL SAGNAC EFFECT IS 21,000 TIMES GREATER THAN THE CORIOLIS EFFECT.

Michelson and Gale recorded ONLY the Coriolis effect, and not the rotational Sagnac effect.

The global/generalized Sagnac effect formula, the most important in all of physics:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2117351#msg2117351

It uses its detection of rotation of earth on its axis

You can only detect the rotation of the earth using the SAGNAC EFFECT.

Michelson and Gale, each manufacturer of the ring laser gyroscopes, claim they are using the SAGNAC EFFECT, and they are not.

The formula put forward/published is the CORIOLIS EFFECT equation.

Can you understand this much?

Incorrect. Much of this you are not understanding. Ring laser gyroscopes (RLG)/fiber optic gyroscopes (FOG) embedded in Inertial Navigation Systems (INS) in every commercial airliner on the planet uses its detection of rotation of earth on its axis and as a byproduct can calculate the subset that is the Coriolis effect.

Much of this you are not understanding. Ring laser gyroscopes (RLG)/fiber optic gyroscopes (FOG) embedded in Inertial Navigation Systems (INS) in every commercial airliner on the planet uses its detection of rotation of earth on its axis and as a byproduct can calculate the subset that is the Coriolis effect.

Do you understand basic physics? You cannot detect the rotation of the Earth, UNLESS you are measuring the SAGNAC EFFECT.

Then, let's put your word to the test.

Here is the formula published by the manufacturers of the ring laser gyroscopes:



The same formula was put forward in 1925 by Michelson and Gale.

However, this is the CORIOLIS EFFECT formula.

You cannot detect the rotation of the Earth with this formula at all.

What you need is the SAGNAC EFFECT formula:



Two very different formulas.

For the MGX, the SAGNAC EFFECT is 21,000 times greater than the CORIOLIS EFFECT for the same interferometer.

Much of this you are not understanding. Ring laser gyroscopes (RLG)/fiber optic gyroscopes (FOG) embedded in Inertial Navigation Systems (INS) in every commercial airliner on the planet uses its detection of rotation of earth on its axis and as a byproduct can calculate the subset that is the Coriolis effect.

Do you understand basic physics?

Yes.

Ring laser gyroscopes (RLG)/fiber optic gyroscopes (FOG) embedded in Inertial Navigation Systems (INS) in every commercial airliner on the planet uses its detection of rotation of earth on its axis and as a byproduct can calculate the subset that is the Coriolis effect.[/i]

If you have an issue with this, perhaps take it up with the airline industry and the folks who devise, engineer and build the Inertial Navigation Systems that are employed on every single commercial plane you fly on.

They say that ring laser gyroscopes are used to detect the rotation of the Earth, but they are using the CORIOLIS EFFECT formula. In order to detect the rotation of the Earth you need the SAGNAC EFFECT formula.

If you have an issue with this, perhaps take it up with the airline industry and the folks who devise, engineer and build the Inertial Navigation Systems that are employed on every single commercial plane you fly on.

The claims they make are based on Michelson's flawed 1925 experiment. He was the first physicist to state that he measured the supposed rotation of the Earth. However, Michelson published the CORIOLIS EFFECT formula, not the SAGNAC EFFECT formula.

Since then, each and every physicist/engineer has used the same formula, without giving the entire matter a second thought.

That is, until now.

Here is the GLOBAL/GENERALIZED SAGNAC EFFECT FORMULA, the most important formula in physics, since it reveals everything we want to know about the universe:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2117351#msg2117351

Well, this thread went about as expected.

Fellow cannot get his head out of that cloud he has stuck it in.

No matter what Sandy wants to insinuate with his long diet of copypasta, ring laser gyroscopes still work in all inertia guidance systems they are used in. They still show the orientarion of the air craft with respect to the earth.

So either Sandy is spouting a heap great big  bowl of bovine excrement, or RLGs have been lied to by thu conspiraceh into believeing they can measure orientation with regards to the earth.

Personally, I go with the first one.

The one that detects the earth spinning at 15 degrees an hour.

ring laser gyroscopes still work in all inertia guidance systems they are used in.

Sure they work.

Here is the formula published by the manufacturers of RLGs (same formula used for the MGX experiment):



However, this is the CORIOLIS EFFECT formula.

You cannot detect the rotation of the Earth with this formula at all.

What you need is the SAGNAC EFFECT formula:



Two very different formulas.

For the MGX, the SAGNAC EFFECT is 21,000 times greater than the CORIOLIS EFFECT for the same interferometer.

The one that detects the earth spinning at 15 degrees an hour.

Again, you need to understand basic physics.

You cannot detect the rotation of the Earth UNLESS you are using the SAGNAC EFFECT FORMULA.

If the RLG detects ONLY the CORIOLIS EFFECT, then the Earth is stationary.

So, what the RLG is actually detecting is the ROTATION OF THE ETHER DRIFT: a CORIOLIS EFFECT.

If you want to prove the rotation of the Earth, you need the SAGNAC EFFECT formula.

ring laser gyroscopes still work in all inertia guidance systems they are used in.

Sure they work.
Here is the formula published by the manufacturers of RLGs (same formula used for the MGX experiment):


However, this is the CORIOLIS EFFECT formula.

You cannot detect the rotation of the Earth with this formula at all.

What you need is the SAGNAC EFFECT formula:

Two very different formulas.

Yes, but I have seen how you derived that and I do not accept it.
If yours is the correct expression for the Sagnac delay how is ot that none of the references support that result?

I would far prefer the analysis by, say, Ludwik Silberstein in his July 1921 paper that starts as:


This paper was written at a time when Einstein's GR was not widely accepted and there was still the question of where a fully or partially dragged aether might explain the Sagnac effect.
Note Silberstein's opening words:
"The purpose of the present paper is to investigate some ques­tions concerning light propagation in a uniformly rotating rigid system, such as the Earth, on both the aether theory and the relativity theory."

1) Analysis assuming aether
So he first presents an analysis for a system without GR and including "the rotatory dragging coefficient, κ - 1, at and near the surface of the Earth".
In his analysis, he includes the Coriolis deflection on the light paths between the mirrors, though that turns out to be completely negligible for a Sagnac loop on the earth's surface.

The result he ends up with is: ε = 4κ ῶ_n σ/(c λ) where: ε is the number of fringes shifter,  κ - 1 is the aether rotatory dragging coefficient, ῶ_n is the angular velocity normal to the area of the loop and σ is the area of the loop.
And this boils down to exactly the first result that you presented, vis: if κ = 0 and A ω sin φ is recognised as the same as ῶ_n σ

2) General Relativistic Analysis on page: 302.
This starts with:

    2. Let us now try to find out what aspect the same problem assumes from the standpoint of the theory of relativity, the special
and the generalized one.
 It goes without saying that with neither of these theories can there be any question of an aether and its being dragged by the Earth in its daily rotation around its
axis, or in its annual motion around the sun.

And ends up the same result, without any aether dragging coefficient: ε = 4ῶ_n σ/(c λ) where the symbols have the same significance as before.

---

The first-order analysis always gives a result where the Sagnac delay in quite independent of the centre of rotation and many reference in effect say as does E. J. POST the Sagnac delay,
          "does not depend on the shape of the surface A;]"
          "does not depend on the location of the centre of rotation;"
As in:

2.7  The Sagnac Effect

where A = πR² is the area enclosed by the loop. The corresponding phase difference for light of frequency n radians/second (in the rest frame of the center of rotation) is simply Df = nDt, and since n = 2πc/l, the phase difference can be written as (8πAcw/l)/(c² – v²).

Just note, "where A = πR² is the area enclosed by the loop".

And again in Sagnac Effect, E. J. POST, Rev. Mod. Phys. 39, 475 (1967) – Published 1 April 1967 we have "in which A is the area enclosed by the loop" and
further on in Section III. General Aspects of the Theory, near end p. 478

Summarizing, the experiments of Sagnac, Pogany and Michelson-Gale and the results of Harress, as re-interpreted by Harzer, demonstrate beyond doubt the following features  of the Sagnac effect. The observed fringe shift
a) obeys formula (1);
b) does not depend on the shape of the surface A;
c) does not depend on the location of the centre of rotation;
d) does not depend on the presence of a comoving refracting medium in the path of the beam.

---

Now Ludwik Silberstein only does a first-order analysis, ignoring second order effects and it is possible that these are significant if the centre of rotation is far outside the loop.

But this paper gives a the simple analysis and then a General Relativistic analysis for a loop with the centre of rotation far outside: General relativistic Sagnac formula revised by Paolo Maraner · Jean-Pierre Zendri
He first presents the usual result, without relativistic correction at the start:
                             

And then, you will be glad to know that they did a general analysis including relativistic effects for a Sagnac Loop rotating about a point a distance R outside the loop.
Here is their result:
                             
had they not used the relativistic correction the loop delay would have been independent of the centre of rotation.

You do not have the necessary mathematical understanding to quote from Zendri's paper.

Do you understand the significance of a power series expansion?

The main term is the Coriolis effect formula.

The next term is O(wr/c)².

Do you understand the meaning of the symbol O()?

The relativistic correction is MUCH SMALLER IN MAGNITUDE THAN THE MAIN TERM.


What you have just done, here in front of all of the readers, is to prove that your messages belong to the complete nonsense section.

You do not even understand the meaning of the symbol O().


There is no such thing as general relativity:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg769750#msg769750 (total demolition of STR/GTR)

The most extraordinary proofs on HOW EINSTEIN FAKED HIS 1919/1922 DATA FOR THE SO CALLED EINSTEIN SHIFT:

http://einstein52.tripod.com/alberteinsteinprophetorplagiarist/id9.html


http://www.ekkehard-friebe.de/dishones.htm (scroll down to the section: With regard to the politics that led to Einstein's fame Dr. S. Chandrasekhar's article [46] states...)


http://web.archive.org/web/20070202201854/http://www.nexusmagazine.com/articles/einstein.html

Dr. F. Schmeidler of the Munich University Observatory has published a paper  titled "The Einstein Shift An Unsettled Problem," and a plot of shifts for 92 stars for the 1922 eclipse shows shifts going in all directions, many of them going the wrong way by as large a deflection as those shifted in the predicted direction! Further examination of the 1919 and 1922 data originally interpreted as confirming relativity, tended to favor a larger shift, the results depended very strongly on the manner for reducing the measurements and the effect of omitting individual stars.

Moreover, Einstein made a terrible blunder.

Einstein, 1905:

"The principle of the constancy of the velocity of light is of course contained in Maxwell's equations”

Here are the censored Heaviside-Lorentz equations, USED BY EINSTEIN to justify his erronous claim regarding the speed of light:



However, the original set of dynamical Maxwell equations are invariant under Galilean transformations, a variable speed of light:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2058884#msg2058884



Silberstein's paper first quoted by me, here on this forum, is very clear.

The derivation of the Coriolis effect for light beams is undergraduate level.

Very easy to do.

Two papers which prove that the formula derived by Michelson is the Coriolis effect equation:

Full derivation of the above formula using the CORIOLIS FORCE:

https://www.researchgate.net/publication/308921264_Spinning_Earth_and_its_Coriolis_effect_on_the_circuital_light_beams_Verification_of_the_special_relativity_theory

Dr. Ludwik Silberstein derived the same formula in 1921:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2068289#msg2068289

In 1921, Dr. Silberstein proposed that the Sagnac effect, as it relates to the rotation of the Earth or to the effect of the ether drift, must be explained in terms of the Coriolis effect: the direct action of Coriolis forces on counterpropagating waves.

http://www.conspiracyoflight.com/Michelson-Gale/Silberstein.pdf

The propagation of light in rotating systems, Journal of the Optical Society of America, vol. V, number 4, 1921


The quote you provided, pg 298 of the paper, has nothing to do with the Sagnac or the Coriolis effect.

Dr. Silberstein is deriving the equation of the light path in relation to Fermat's principle.

Did you even read the paper?

How then could make such a catastrophic blunder?

He starts the derivation of the Coriolis effect on page 298 at the bottom.

The fact that you CONFUSED and MIXED UP two different situations tells volumes about your miserable training as physicist.


Remember, the CORIOLIS EFFECT is a physical effect.

It relates directly to the area of the interferometer.

In 1922, Dr. Silberstein published a second paper on the subject, where he generalizes the nature of the rays arriving from the collimator:

http://gsjournal.net/Science-Journals/Historical%20Papers-Mechanics%20/%20Electrodynamics/Download/2645

In 1924, one year before the Michelson-Gale experiment, Dr. Silberstein published a third paper, where he again explicitly links the Coriolis effect to the counterpropagating light beams in the interferometer:

https://www.tandfonline.com/doi/abs/10.1080/14786442408634503




Dr. Silberstein reveals the error committed by M. von Laue in the paper published in 1911:

"Laue seems, by the way, to be under the misapprehension that the light rays relative to the rotating table are straight lines, which they are not."

Dr. Silberstein proved that the effect measured by Sagnac is A PHYSICAL EFFECT, a deflection/inflection of the light beams due to the CORIOLIS FORCE.


Dr. Silberstein is describing the Coriolis effect, whether the lines are straight or not, NOT the electromagnetic effect (the Sagnac effect).

HERE IS THE PROOF THAT DR. SILBERSTEIN DERIVED THE CORIOLIS EFFECT:

One of the most in-depth treaties on the ring laser interferometers.

https://books.google.ro/books?id=8c_mBQAAQBAJ&pg=PA15&lpg=PA15&dq=malykin+silberstein+coriolis&source=bl&ots=JrMqF2vmto&sig=xCnMB4hL_J_ESg9Xdfhye1ahVjA&hl=en&sa=X&ved=2ahUKEwiE0ZDWxeXeAhXwkYsKHYxwBMYQ6AEwCXoECAUQAQ#v=onepage&q=malykin%20silberstein%20coriolis&f=false

CAN YOU READ ENGLISH RABINOZ?

Silberstein (798, 799) suggested an explanation for the Sagnac effect based on the direct consideration of the effect of the Coriolis force on the counterpropagating waves.

Those two references, 798 and 799 are EXACTLY the ones I provided in my messages.


Make no mistake about it: Dr. Silberstein derives the Coriolis effect, which is directly related to the area of the interferometer.

Dr. Silberstein:

He uses the expression kω for the angular velocity, where k is the aether drag factor.

He proves that the formula for the Coriolis effect on the light beams is:

dt = 2ωσ/c^2

Then, Dr. Silberstein analyzes the area σ and proves that it is actually a SUM of two other areas (page 300 of the paper, page 10 of the pdf document).

The effect of the Coriolis force upon the interferometer will be to create a convex and a concave shape of the areas: σ1 and σ2.

The sum of these two areas is replaced by 2A and this is how the final formula achieves its final form:

dt = 4ωA/c^2

A = σ1 + σ2

That is, the CORIOLIS EFFECT upon the light beams is totally related to the closed contour area.


If yours is the correct expression for the Sagnac delay how is ot that none of the references support that result?

What ?!



The most ingenious experiment performed by Professor Yeh: light from a laser is split into two separate fibers, F1 and F2 which are coiled such that light travels clockwise in F1 and counterclockwise in F2.

https://www.researchgate.net/publication/26797550_Self-pumped_phase-conjugate_fiber-optic_gyro

Self-pumped phase-conjugate fiber-optic gyro, I. McMichael, P. Yeh, Optics Letters 11(10):686-8 · November 1986 

http://www.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (appendix 5.1)

The first phase-conjugate Sagnac experiment on a segment light path with a self-pumped configuration.

The Sagnac phase shift for the first fiber F1:

+2πR₁L₁Ω/λc

The Sagnac phase shift for the second fiber F2:

-2πR₂L₂Ω/λc

These are two separate Sagnac effects, each valid for the two fibers, F1 and F2.

The use of the phase conjugate mirror permits the revealing of the final formula, the total phase difference:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc

2(v₁l₁ + v₂l₂)/c²

Exactly the formula obtained by Professor Yeh:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc = 4π(V₁L₁ + V₂L₂)/λc

Since Δφ = 2πc/λ x Δt, Δt = 2(R₁L₁ + R₂L₂)Ω/c² = 2(V₁L₁ + V₂L₂)/c²

CORRECT SAGNAC FORMULA:

2(V₁L₁ + V₂L₂)/c²


http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1925ApJ....61..137M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf



The promise made by A. Michelson, "the difference in time required for the two pencils to return to the starting point will be...", never materialized mathematically.

Instead of applying the correct definition of the Sagnac effect, Michelson compared TWO OPEN SEGMENTS/ARMS of the interferometer, and not the TWO LOOPS, as required by the exact meaning of the Sagnac experiment.

As such, his formula captured the Coriolis effect upon the light beams.

Not even the formal derivation of the Sagnac effect formula is not entirely correct.





This is the correct way to derive the Sagnac formula:

Sagnac phase component for the clockwise path:

2πR(1/(c - v))

Sagnac phase component for the counterclockwise path:

-2πR(1/(c + v))

The continuous clockwise loop has a positive sign +

The continuous counterclockwise loop has a negative sign -

The net phase difference will be (let us remember that the counterclockwise phase difference has a negative sign attached to it):

2πR(1/(c - v)) - (-){-2πR(1/(c + v))} = 2πR(1/(c - v)) - (+)2πR(1/(c + v)) = 2πR(1/(c - v)) - 2πR(1/(c + v)) = 2vL/c²


The definition of the Sagnac effect is applied to a closed loop (either circular or a uniform path).

Loop = a structure, series, or process, the end of which is connected to the beginning.

Thus, from a mathematical point of view, Michelson did not derive the Sagnac effect formula at all, since he compared two open segments, and not two loops.

Using the correct definition, we recover not only the error-free formula, but also the precise velocity addition terms.



Practically, A. Michelson received the Nobel prize (1907) for the wrong formula (published in 1904 and 1887; E.J. Post proved in 1999 that the Michelson-Morley interferometer is actually a Sagnac interferometer).

No other physicist has been able to derive the correct Sagnac formula: for the past 100 years they have been using the wrong formula (the Coriolis effect equation) to describe a very different physical situation.

Here, for the first time, the correct Sagnac formula for an interferometer located away from the center of rotation has been derived in a precise manner.




Point A is located at the detector
Point B is in the bottom right corner
Point C is in the upper right corner
Point D is in the upper left corner

l₁ is the upper arm.
l₂ is the lower arm.

Here is the most important part of the derivation of the full/global Sagnac effect for an interferometer located away from the center of rotation.

A > B > C > D > A is a continuous counterclockwise path, a negative sign -

A > D > C > B > A is a continuous clockwise path, a positive sign +

The Sagnac phase difference for the clockwise path has a positive sign.

The Sagnac phase difference for the counterclockwise has a negative sign.


Sagnac phase components for the A > D > C > B > A path (clockwise path):

l₁/(c - v₁)

-l₂/(c + v₂)

Sagnac phase components for the A > B > C > D > A path (counterclockwise path):

l₂/(c - v₂)

-l₁/(c + v₁)


For the single continuous clockwise path we add the components:

l₁/(c - v₁) - l₂/(c + v₂)

For the single continuous counterclockwise path we add the components:

l₂/(c - v₂) - l₁/(c + v₁)


The net phase difference will be (let us remember that the counterclockwise phase difference has a negative sign attached to it, that is why the substraction of the phase differences becomes an addition):

{l₁/(c - v₁) - l₂/(c + v₂)} - (-){l₂/(c - v₂) - l₁/(c + v₁)} = {l₁/(c - v₁) - l₂/(c + v₂)} + {l₂/(c - v₂) - l₁/(c + v₁)}

Rearranging terms:

l₁/(c - v₁) - l₁/(c + v₁) + {l₂/(c - v₂) - l₂/(c + v₂)} =

2(v₁l₁ + v₂l₂)/c²

Exactly the formula obtained by Professor Yeh:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc = 4π(V₁L₁ + V₂L₂)/λc

Since Δφ = 2πc/λ x Δt, Δt = 2(R₁L₁ + R₂L₂)Ω/c² = 2(V₁L₁ + V₂L₂)/c²

CORRECT SAGNAC FORMULA:

2(V₁L₁ + V₂L₂)/c²

Self-pumped phase-conjugate fiber-optic gyro, I. McMichael, P. Yeh, Optics Letters 11(10):686-8 · November 1986 

http://www.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (appendix 5.1)


This is how the correct Sagnac formula is derived: we have single continuous clockwise path, and a single continuous counterclockwise path.

If we desire the Coriolis effect, we simply substract as follows:

dt = l₁/(c - v₁) - l₁/(c + v₁) - (l₂/(c - v₂) - l₂/(c + v₂))

Of course, by proceeding as in the usual manner for a Sagnac phase shift formula for an interferometer whose center of rotation coincides with its geometrical center, we obtain:

2v₁l₁/(c² - v²₁) - 2v₂l₂/(c² - v²₂)

l = l₁ = l₂

2l[(v₁ - v₂)]/c²

2lΩ[(R₁ - R₂)]/c²

R₁ - R₂ = h

2lhΩ/c²

By having substracted two different Sagnac phase shifts, valid for the two different segments, we obtain the CORIOLIS EFFECT formula.


However, for the SAGNAC EFFECT, we have a single CONTINUOUS CLOCKWISE PATH, and a single CONTINUOUS COUNTERCLOCKWISE PATH, as the definition of the Sagnac effect entails.

HERE IS THE DEFINITION OF THE SAGNAC EFFECT:

Two pulses of light sent in opposite direction around a closed loop (either circular or a single uniform path), while the interferometer is being rotated.

Loop = a structure, series, or process, the end of which is connected to the beginning.

A single continuous pulse A > B > C > D > A, while the other one, A > D > C > B > A is in the opposite direction, and has the negative sign.


We can see at a glance each and every important detail.


For the Coriolis effect, one has a formula which is proportional to the area; only the phase differences of EACH SIDE are being compared, and not the continuous paths.

For the Sagnac effect, one has a formula which is proportional to the velocity of the light beam; the entire continuous clockwise path is being compared to the other continuous counterclockwise path exactly as required by the definition of the Sagnac effect.

Experimentally, the Michelson-Gale test was a closed loop, but not mathematically. Michelson treated mathematically each of the longer sides/arms of the interferometer as a separate entity: no closed loop was formed at all. Therefore the mathematical description put forth by Michelson has nothing to do with the correct definition of the Sagnac effect (two pulses of light are sent in opposite direction around a closed loop) (either circular or a single uniform path). By treating each side/arm separately, Michelson was describing and analyzing the Coriolis effect, not the Sagnac effect.

Loop = a structure, series, or process, the end of which is connected to the beginning.

Connecting the two sides through a single mathematical description closes the loop; treating each side separately does not. The Sagnac effect requires, by definition, a structure, the end of which is connected to the beginning.

"It is also shown that all the nonrelativistic interpretations of the Sagnac effect, which are unfortunately sometimes found in scientific papers, monographs and textbooks, are wrong in principle, even though the results they yield are accurate up to relativistic corrections in some special cases."

https://www.researchgate.net/publication/231153281_The_Sagnac_effect_Correct_and_incorrect_explanations

"It is also shown that all the nonrelativistic interpretations of the Sagnac effect, which are unfortunately sometimes found in scientific papers, monographs and textbooks, are wrong in principle, even though the results they yield are accurate up to relativistic corrections in some special cases."

Right.

The Sagnac effect is far larger than the effect forecast by relativity theory.

STR has no possible function in explaining the Sagnac effect.

The Sagnac effect is a non-relativistic effect.

COMPARISON OF THE SAGNAC EFFECT WITH SPECIAL RELATIVITY, starts on page 7, calculations/formulas on page 8

http://www.naturalphilosophy.org/pdf/ebooks/Kelly-TimeandtheSpeedofLight.pdf

page 8

Because many investigators claim that the
Sagnac effect is made explicable by using the
Theory of Special Relativity, a comparison of
that theory with the actual test results is given
below. It will be shown that the effects
calculated under these two theories are of very
different orders of magnitude, and that
therefore the Special Theory is of no value in
trying to explain the effect.

COMPARISON OF THE SAGNAC EFFECT WITH STR

STR stipulates that the time t' recorded by an observer moving at velocity v is slower than the time t_o recorded by a stationary observer, according to:

t_o = t'γ

where γ = (1 - v²/c²)^-1/2 = 1 + v²/2c² + O(v/c)⁴...

t_o = t'(1 + v²/2c²)


dt_R = (t_o - t')/t_o = v²/(v² + 2c²)

dt_R = relativity time ratio



Now, t_o - t' = 2πr/c - 2πr/(c + v) = 2πrv/(c + v)c

dt' = t_o - t' = t_ov/(c + v)


dt_S = (t_o - t')/t_o = v/(v + c)


dt_S = Sagnac ratio


dt_S/dt_R = (2c² + v²)/v(v + c)

When v is small as compared to c, as is the case in all practical experiments, this ratio
reduces to 2c/v.


Thus the Sagnac effect is far larger than any
purely Relativistic effect. For example,
considering the data in the Pogany test (8 ),
where the rim of the disc was moving with a
velocity of 25 m/s, the ratio dtS/dtR is about
1.5 x 10^7. Any attempt to explain the Sagnac
as a Relativistic effect is thus useless, as it is
smaller by a factor of 10^7.


Referring back to equation (I), consider a disc
of radius one kilometre. In this case a fringe
shift of one fringe is achieved with a velocity
at the perimeter of the disc of 0.013m/s. This
is an extremely low velocity, being less than
lm per minute. In this case the Sagnac effect
would be 50 billion times larger than the
calculated effect under the Relativity Theory.


Post (1967) shows that the two (Sagnac and STR) are of very different orders of magnitude. He says that the dilation factor to be applied under SR is “indistinguishable with presently available equipment” and “is still one order smaller than the Doppler correction, which occurs when observing fringe shifts” in the Sagnac tests. He also points out that the Doppler effect “is v/c times smaller than the effect one wants to observe." Here Post states that the effect forecast by SR, for the time dilation aboard a moving object, is far smaller than the effect to be observed in a Sagnac test.

You do not have the necessary mathematical understanding to quote from Zendri's paper.

 It really is not about mathematical understanding. Your walls of text are meaningless and your supposed understanding of mathematics also because when you believe flat earth then you by definition do not understand or just willfully ignore simple and basic trigonometry.

"It is also shown that all the nonrelativistic interpretations of the Sagnac effect, which are unfortunately sometimes found in scientific papers, monographs and textbooks, are wrong in principle, even though the results they yield are accurate up to relativistic corrections in some special cases."

Right.

The Sagnac effect is far larger than the effect forecast by relativity theory.

You are incorrect and missing the entire point and are like a runaway train of copy and paste walls of data that spiral out into oblivion and ultimately mean nothing to anyone.

The operative words are: relativistic corrections

Look it up.

You do not have the necessary mathematical understanding to quote from Zendri's paper.

Do you understand the significance of a power series expansion?

Yes!

The main term is the Coriolis effect formula.

So you say.
But Maraner and Zendri never mention "the Coriolis effect" other than briefly when comparing the Sagnac effect with the  Aharanov-Bohm effect.

The next term is O(wr/c)².
Do you understand the meaning of the symbol O()?

Yes!

The relativistic correction is MUCH SMALLER IN MAGNITUDE THAN THE MAIN TERM.

Yes, and so the effect of the off-centre rotation is "MUCH SMALLER IN MAGNITUDE THAN THE MAIN TERM" for the example chosen.

Please read this again!
                             
had they not used the relativistic correction the loop delay would have been independent of the centre of rotation.

The "large ring laser G in Wettzell" mentioned is referred to below.

But I'd believe Maraner and Zendri rather than you any day,  thank you!

What you have just done, here in front of all of the readers, is to prove that your messages belong to the complete nonsense section.
You do not even understand the meaning of the symbol O().

Quote from: sandokhan

I understand that perfectly well, thank you.

There is no such thing as general relativity:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I'll let you believe all that if it makes you happy.
If, however, you claim that there is "There is no such thing as general relativity" please explain all the times that GR has been verified.
Just one example: Einstein gets it right again—weak and strong gravity objects fall the same way, July 4, 2018, Green Bank Observatory

And if you have all this wonderful information why don't you publish in the open literature and collect your Nobel Prize for disproving GR?

Many physicists and astrophysicists try to prove  GR wrong or incomplete - it's what scientists do!
Here's one case: Was Einstein WRONG? Scientists probe supermassive BLACK HOLE to disprove theory of gravity.

---

In the meantime, I'd rather believe that devices like the "GINGERino, a deep underground ring-laser" installed in Italy are able to measure the rate of the earth's rotation very accurately.
See First Results of GINGERino, a deep underground ring-laser

And note that it starts with:

1. Introduction
Ring laser gyroscopes (RLG) are, at present, the most precise sensors of absolute angular velocity for an Earth based apparatus. They are based on the Sagnac effect arising from a rigidly rotating ring laser cavity.

The resolution is quite impressive.

The Gross Ring ”G” at the Wettzell Geodetic Observatory has obtained a resolution on the Earth rotation rate of 3 × 10⁻⁹ (about 15 × 10⁻¹⁴ rad/s with 4 hours integration time).

That paper did not give the rotation rate, just the stability etc.
But this paper does: Ring-Lasers seismic rotational sensing, Angela Di Virgilio-INFN-Pisa

And the result is:

Earth Rot. Rate (7.2921150±0.0000001)×10⁻⁵ radians/sec

which is  guess what  a period of 23.93447 hours and the currently quoted sidereal day is 23.9345 hours - the GINGER result is more precise than that.

The GINGERino deep underground ring-laser proves that the earth rotates on its axis at (7.2921150±0.0000001)×10⁻⁵ radians/sec.

Look, I've seen the end result of your logic and it convinces me not to put any weight on what your interpretations.

This is the paper you put forth in front of the readers:

https://arxiv.org/pdf/1110.1643.pdf

General relativistic Sagnac formula revised
Paolo Maraner · Jean-Pierre Zendri

From the abstract:

We derive the necessary modification and demonstrate it through a detailed analysis of the square Sagnac interferometer rotating about its symmetry axis in Minkowski space-time.


There is no such thing as Minkowski space-time continuum.

As such, the computation of the correction terms (the time shift) is wrong.

No Minkowski space-time, no valid computations.

Moreover, the leading term is proportional to the area, the CORIOLIS EFFECT formula.


And, again, the authors make the same ERROR as did Michelson, to compare the two sides and not the two loops as required by the definition of the Sagnac effect.

They are analyzing the CORIOLIS EFFECT with relativistic corrections, NOT the SAGNAC EFFECT which requires two loops.

Convince yourself that there is no such thing as general relativity or a Minkowski space-time continuum:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg769750#msg769750


Let us now use the theory of general relativity to prove that the CORIOLIS EFFECT will be derived first, IF the two arms of the interferometer are located away from the center of rotation:


https://link.springer.com/article/10.1023/A:1023972214666

https://arxiv.org/pdf/gr-qc/0103091.pdf

Coriolis Force and Sagnac Effect

Because of acting of gravity-like Coriolis force the trajectories of co- and anti-rotating photons have different radii in the rotating reference frame, while in the case of the equal radius the effective gravitational potentials for the photons have to be different.




An interferometer with DIFFERENT RADII (located away from the center of rotation) will manifest the Coriolis force in the form of a phase shift 4AΩ/c2.


What Maraner and Zendri did is to derive the CORIOLIS EFFECT formula with relativistic corrections which are dependent on the center of rotation, and NOT the SAGNAC EFFECT.

They used the SAME derivation as did Michelson based on a comparison of two sides, AND NOT THE TWO LOOPS as required by the definition of the Sagnac error, a huge error on their part.


The papers you provided in favor of TGR are using A CONSTANT SPEED OF LIGHT context, and the HEAVISIDE-LORENTZ EQUATIONS.

Einstein, 1905:

"The principle of the constancy of the velocity of light is of course contained in Maxwell's equations”

Here are the censored Heaviside-Lorentz equations, USED BY EINSTEIN to justify his erronous claim regarding the speed of light:



However, the original set of dynamical Maxwell equations are invariant under Galilean transformations, a variable speed of light:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2058884#msg2058884

Einstein made a terrible blunder in having assumed that the speed of light is constant.

If we remove this error, the experiments used as a proof of TGR are much better explained in terms of a VARIABLE SPEED OF LIGHT.


In the meantime, I'd rather believe that devices like the "GINGERino, a deep underground ring-laser" installed in Italy are able to measure the rate of the earth's rotation very accurately.


They are NOT measuring the rotation of the Earth at all, they simply recorded the CORIOLIS EFFECT using Michelson's formula published in 1925.



And they are using the same relativistic correction terms, as did Maraner and Zendri, obtained in terms of the CORIOLIS EFFECT formula.


Dr. Silberstein is describing the Coriolis effect, whether the lines are straight or not, NOT the electromagnetic effect (the Sagnac effect).

HERE IS THE PROOF THAT DR. SILBERSTEIN DERIVED THE CORIOLIS EFFECT:

One of the most in-depth treaties on the ring laser interferometers.

https://books.google.ro/books?id=8c_mBQAAQBAJ&pg=PA15&lpg=PA15&dq=malykin+silberstein+coriolis&source=bl&ots=JrMqF2vmto&sig=xCnMB4hL_J_ESg9Xdfhye1ahVjA&hl=en&sa=X&ved=2ahUKEwiE0ZDWxeXeAhXwkYsKHYxwBMYQ6AEwCXoECAUQAQ#v=onepage&q=malykin%20silberstein%20coriolis&f=false

CAN YOU READ ENGLISH RABINOZ?

Silberstein (798, 799) suggested an explanation for the Sagnac effect based on the direct consideration of the effect of the Coriolis force on the counterpropagating waves.

Those two references, 798 and 799 are EXACTLY the ones I provided in my messages.


Make no mistake about it: Dr. Silberstein derives the Coriolis effect, which is directly related to the area of the interferometer.




The most ingenious experiment performed by Professor Yeh: light from a laser is split into two separate fibers, F1 and F2 which are coiled such that light travels clockwise in F1 and counterclockwise in F2.

https://www.researchgate.net/publication/26797550_Self-pumped_phase-conjugate_fiber-optic_gyro

Self-pumped phase-conjugate fiber-optic gyro, I. McMichael, P. Yeh, Optics Letters 11(10):686-8 · November 1986 

http://www.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (appendix 5.1)

The first phase-conjugate Sagnac experiment on a segment light path with a self-pumped configuration.

The Sagnac phase shift for the first fiber F1:

+2πR₁L₁Ω/λc

The Sagnac phase shift for the second fiber F2:

-2πR₂L₂Ω/λc

These are two separate Sagnac effects, each valid for the two fibers, F1 and F2.

The use of the phase conjugate mirror permits the revealing of the final formula, the total phase difference:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc

2(v₁l₁ + v₂l₂)/c²

Exactly the formula obtained by Professor Yeh:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc = 4π(V₁L₁ + V₂L₂)/λc

Since Δφ = 2πc/λ x Δt, Δt = 2(R₁L₁ + R₂L₂)Ω/c² = 2(V₁L₁ + V₂L₂)/c²

CORRECT SAGNAC FORMULA:

2(V₁L₁ + V₂L₂)/c²

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1925ApJ....61..137M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf



The promise made by A. Michelson, "the difference in time required for the two pencils to return to the starting point will be...", never materialized mathematically.

Instead of applying the correct definition of the Sagnac effect, Michelson compared TWO OPEN SEGMENTS/ARMS of the interferometer, and not the TWO LOOPS, as required by the exact meaning of the Sagnac experiment.

As such, his formula captured the Coriolis effect upon the light beams.

HERE IS THE DEFINITION OF THE SAGNAC EFFECT:

Two pulses of light sent in opposite direction around a closed loop (either circular or a single uniform path), while the interferometer is being rotated.

Loop = a structure, series, or process, the end of which is connected to the beginning.

A single continuous pulse A > B > C > D > A, while the other one, A > D > C > B > A is in the opposite direction, and has the negative sign.


We can see at a glance each and every important detail.


For the Coriolis effect, one has a formula which is proportional to the area; only the phase differences of EACH SIDE are being compared, and not the continuous paths.

For the Sagnac effect, one has a formula which is proportional to the velocity of the light beam; the entire continuous clockwise path is being compared to the other continuous counterclockwise path exactly as required by the definition of the Sagnac effect.

Experimentally, the Michelson-Gale test was a closed loop, but not mathematically. Michelson treated mathematically each of the longer sides/arms of the interferometer as a separate entity: no closed loop was formed at all. Therefore the mathematical description put forth by Michelson has nothing to do with the correct definition of the Sagnac effect (two pulses of light are sent in opposite direction around a closed loop) (either circular or a single uniform path). By treating each side/arm separately, Michelson was describing and analyzing the Coriolis effect, not the Sagnac effect.

Loop = a structure, series, or process, the end of which is connected to the beginning.

Connecting the two sides through a single mathematical description closes the loop; treating each side separately does not. The Sagnac effect requires, by definition, a structure, the end of which is connected to the beginning.


Let us now compare the MGX with the correct SAGNAC FORMULA, the same analysis would apply for the Gingerino RLG.

Now, let us compare the two formulas, Coriolis vs. Sagnac, using the latitude, for the Michelson-Gale experiment.

The turning of the MGX area at the hypothetical rotational speed of the Earth takes place a distance of some 4,250 km from the center of the Earth (latitude 41°46').

FULL CORIOLIS EFFECT FOR THE MGX:

4AΩsinΦ/c²

FULL SAGNAC EFFECT FOR THE MGX:

4Lv(cos²Φ₁ + cos²Φ₂)/c²


Sagnac effect/Coriolis effect ratio:

R((cos²Φ₁ + cos²Φ₂)/hsinΦ

R = 4,250 km

h = 0.33924 km

The rotational Sagnac effect is much greater than the Coriolis effect for the MGX.

Φ₁ = Φ = 41°46' = 41.76667°

Φ₂ = 41°45' = 41.75°

R((cos²Φ₁ + cos²Φ₂) = 4729.885

hsinΦ = 0.225967

4729.885/0.225967 = 20,931.72

THE ROTATIONAL SAGNAC EFFECT IS 21,000 TIMES GREATER THAN THE CORIOLIS EFFECT.

Michelson and Gale recorded ONLY the Coriolis effect, and not the rotational Sagnac effect.

The global/generalized Sagnac effect formula, the most important in all of physics:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2117351#msg2117351




If the ring laser gyroscope measures/detects the CORIOLIS EFFECT, then the Earth is stationary (existence of the ether drift).

If the ring laser gyroscope measures/detects the SAGNAC EFFECT, then the Earth is rotating (no ether drift).

Since 1913, all interferometers, especially the ring laser gyroscopes have detected ONLY the CORIOLIS EFFECT, nothing else.

This is the paper you put forth in front of the readers:

https://arxiv.org/pdf/1110.1643.pdf General relativistic Sagnac formula revised Paolo Maraner · Jean-Pierre Zendri
From the abstract:
We derive the necessary modification and demonstrate it through a detailed analysis of the square Sagnac interferometer rotating about its symmetry axis in Minkowski space-time.

Sure and what's wrong with that, especially as his end result agrees with E. J. Post, MathPages, Ludwik Silberstein and most others I've seen.

There is no such thing as Minkowski space-time continuum. As such, the computation of the correction terms (the time shift) is wrong.

According to you!
But as I said before, I'll believe Paolo Maraner and Jean-Pierre Zendri (and "Old Uncle Tom Cobley and all" if it comes to that) before you any day so repeatedly posting the same material is a total waste of space!

Michelson was awarded the Nobel prize (1907) for the wrong formula (published in 1904 and 1887; E.J. Post proved in 1999 that the Michelson-Morley interferometer is actually a Sagnac interferometer).

No one else, no other physicist was able, or has been able, to derive the correct SAGNAC EFFECT formula; all of them have been content to copy Michelson's glaring error, including Post.

The definition of the Sagnac effect is applied to a closed loop (either circular or a uniform path).

Loop = a structure, series, or process, the end of which is connected to the beginning.

Thus, from a mathematical point of view, Michelson did not derive the Sagnac effect formula at all, since he compared two open segments, and not two loops.

The promise made by A. Michelson, "the difference in time required for the two pencils to return to the starting point will be...", never materialized mathematically.

Instead of applying the correct definition of the Sagnac effect, Michelson compared TWO OPEN SEGMENTS/ARMS of the interferometer, and not the TWO LOOPS, as required by the exact meaning of the Sagnac experiment.

For the Coriolis effect, one has a formula which is proportional to the area; only the phase differences of EACH SIDE are being compared, and not the continuous paths.

For the Sagnac effect, one has a formula which is proportional to the velocity of the light beam; the entire continuous clockwise path is being compared to the other continuous counterclockwise path exactly as required by the definition of the Sagnac effect.

Experimentally, the Michelson-Gale test was a closed loop, but not mathematically. Michelson treated mathematically each of the longer sides/arms of the interferometer as a separate entity: no closed loop was formed at all. Therefore the mathematical description put forth by Michelson has nothing to do with the correct definition of the Sagnac effect (two pulses of light are sent in opposite direction around a closed loop) (either circular or a single uniform path). By treating each side/arm separately, Michelson was describing and analyzing the Coriolis effect, not the Sagnac effect.

Loop = a structure, series, or process, the end of which is connected to the beginning.

Connecting the two sides through a single mathematical description closes the loop; treating each side separately does not. The Sagnac effect requires, by definition, a structure, the end of which is connected to the beginning.

I think they ecpected an inconclusive result. One they could twist into a flat earth win.

Just like Antonio Subirats. He proposed an experiment using a tube to look at the horizon from one end. He said if looking through the other end one sees the horizon again, then the earth would be flat. If one sees the sky above the horizon, the earth must be a globe. Low and behold, Critical Think does said experiment and it conforms to a globe. Antonio subirats has shifted the goal posts so much in trying to explain away the results that he is no longer in the same ball park as when he started.

Flat earthers look only for things that will confirm their bias and seem to think if they say it enough, everyone else would believe like they do and then maybe the earth would somehow conform to their wishes. Like Sandy up there. Truth isn't the aim. Confirmation of their belief is.

In 2007, R. Sungenis and R. Bennett published a 1147 page treatise, Galileo Was Wrong. They included copious amounts of information which was very well presented, having outdone any previous work on the subject.

Yet, on page 745 they state:

The Sagnac time difference is (for the Michelson-Gale experiment):

Δt = 4Aω (sinφ)/c²

As such, they practically stated to their readers that Galileo was right.

For the MGX, the figures for the area of the path, latitude (41deg. 46'), wavelength of the light, speed of light, and the expected fringe shifts are well known.

Expected fringe shift: 0.2364

Measured fringe shift: 0.230 +/- 0.005

Then, the angular velocity of the Earth can be easily computed.

By having made the outrageous claim that the above formula is the SAGNAC EFFECT formula, Albert Michelson put an end to any debate on geocentrism vs. heliocentrism.

Modern day ring laser interferometers also feature the same formula, while the physicists running the experiment are claiming that it is the Sagnac formula.

That is why the author of the video finds himself facing the same conundrum.

Sungenis and Bennett, each geocentrist, the author of the video, CANNOT claim that it is the ether which is rotating above the surface of the Earth, since THEY ACCEPT that the formula published by Michelson is the SAGNAC EFFECT formula (exactly as Sungenis and Bennett did on page 745 of their treatise).

Encasing one arm of the interferometer in lead will result in Hammar's experiment, which then will have the heliocentrists claim that there is no ether entrapment.

Few scientists, especially including all of the geocentrists, understand that the MGX put an end in 1925 to any debate on heliocentrism vs. geocentrism.

If the heliocentrists are told that the formula published by Michelson is wrong, as a last attempt to provide any kind of an explanation for the MGX, all they have to do is respond: "show us the correct formula then", "go ahead and derive the right formula". They do this because they know that if Einstein, Lorentz, Michelson, Pauli, Langevin, Post were not able to derive the SAGNAC EFFECT formula, no one else will.

Unless the geocentrists come up with the SAGNAC EFFECT formula, there isn't any debate at all: the heliocentrists win hands down, since they claim that the formula published by Michelson is the SAGNAC EFFECT formula which measures rotation.