Global/Generalized Sagnac Effect Formula

[sandokhan]

I am going to derive both the SAGNAC EFFECT and the CORIOLIS EFFECT formulas for the MGX interferometer, so that everyone will be able to see at a glance the difference.

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

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.
 

This is exactly what Professor Yeh's ingenious experiment entailed: the use of the phase conjugate mirror permitted, for the first time, to actually separate the clockwise/counterclockwise paths, while at the same time the open loops have different radii and thus different linear velocities.

 

Again, let us compare the derivations for both cases: SAGNAC and CORIOLIS.

 

CORIOLIS EFFECT derivation

dt=l₁/(c - v₁)+l₂/(c + v₂)-l₁/(c + v₁)-l₂/(c - v₂)
=l₁/(c - v₁)-l₁/(c + v₁)+l₂/(c + v₂)-l₂/(c - v₂)
=l₁(c + v₁-c + v₁)/(c² - v₁²)+l₂(c - v₂-c - v₂)/(c² - v₂²)
=2*l₁v₁/(c² - v₁²)-2*l₂v₂/(c² - v₂²) 

dt=2*l₁v₁/c²-2*l₂v₂/c²
=(2*l₁v₁-2*l₂v₂)/c²
=2*(l₁v₁-l₂v₂)/c²

We are comparing two OPEN SEGMENTS: defying the very definition of the Sagnac effect.

Path 1 - A>B, D>C.
Path 2 - C>D, B>A

 

By comparison, the 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)

 

2(v₁l₁ + v₂l₂)/c²

Since v1 = R1 x Ω, and v2 = R2 x Ω, the formula becomes:

2(R₁L₁ + R₂L₂)Ω/c² 

Since Δφ = 2πc/λ x Δt, we obtain: 4π(R₁L₁ + R₂L₂)Ω/λc which is of course Professor Yeh's formula.

 

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

 

A Sagnac light interferometer (MGX, RLGs) can detect BOTH EFFECTS: one is a physical effect proportional to the area - the CORIOLIS EFFECT; the other one is an electromagnetic effect proportional to the radius of rotation - the SAGNAC EFFECT.

[MaximT]

16 minutes ago, sandokhan said:

A Sagnac light interferometer (MGX, RLGs) can detect BOTH EFFECTS: one is a physical effect proportional to the area - the CORIOLIS EFFECT; the other one is an electromagnetic effect proportional to the radius of rotation - the SAGNAC EFFECT.

I must agree with you, but not the actual sciences, Sagnac effect results had been explained by relativity, you may look on Wikipedia, the paper from India is wrong, to me. But what is behind you tough, about Aether? Are you sustaining that ether is not fix about all the Universe? Because all that, can only be explained by a non uniform repartition of the Aether, if there is...

[sandokhan]

8 minutes ago, MaximT said:

Sagnac effect results had been explained by relativity

No.

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.

[MaximT]

21 hours ago, sandokhan said:

"The scalar portion of the original Maxwell equations expressed in quaternions was discarded (by Oliver Heaviside) to form "modern" EM theory; thus also the unified field interaction between electromagnetics and gravitation was discarded as well.

The quaternion scalar expression has, in fact, captured the local stress due to the forces acting one on the other. It is focused on the local stress, and the abstract vector space, adding a higher dimension to it.

One sees that, if we would capture gravitation in a vector mathematics theory of EM, we must again restore the scalar term and convert the vector to a quaternion, so that one captures the quaternionically infolded stresses. These infolded stresses actually represent curvature effects in the abstract vector space itself. Changing to quaternions changes the abstract vector space, adding higher dimensions to it.

Quaternions have a vector and a scalar part and have a higher topology than vector and tensor analysis."

I disagree, I revised Maxwell's work recently, and there is nothing like that. But Maxwell was searching for a reasoning to achieved a medium for propagation of light, but without confirming it. At the last chapter of his work, he made clear that he didn't know, with putting this in relation with the work of an Italian, Betti, a well known one. If you have some clues about quaternions, where are they? Give us more...

8 minutes ago, sandokhan said:

The Sagnac effect is a non-relativistic effect.

Personally, I agree, but I don't get what you are meaning. And, all the sciences, is against me.

You could refer to his book: Maxwell book tome II

Edited April 13, 2019 by MaximT

[swansont]

3 hours ago, sandokhan said:

Did you even read the paper?

Yes. I quoted from it. Do you recall that?

3 hours ago, sandokhan said:

The description is very clear:

https://apps.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (page 34 of the pdf document)

where R1,2 and L1,2 are the radii and lengths of the fiber loops, and Ω is the rotation rate. You have two OPEN LOOPS of radii R1,2. The lengths of the paths of light are L1,2, and they are different for each open loop. Very simple.

How do you have radii, without having circles, which mean there is an enclosed area?

From the paper:

 

Light from a laser is split by beamsplitter BS into two fibers Fl and F2. Fibers F1 and F2 are coiled such that light travels clockwise in Fl and counterclockwise in F2.

...

R_1,2 and L_1,2 are the lengths and radii of the fiber loops

 

Coiled. Loops. Radii. Plus there's the drawing, showing the two coiled sections. 

 

 

53 minutes ago, sandokhan said:

I am going to derive both the SAGNAC EFFECT and the CORIOLIS EFFECT formulas for the MGX interferometer, so that everyone will be able to see at a glance the difference.

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.
 

Derive it for a setup that does not enclose an area.

[sandokhan]

1 hour ago, swansont said:

Derive it for a setup that does not enclose an area.

For the Coriolis effect derivation, one needs an area. This was proven in 1921 by Dr. Ludwik Silberstein:

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

For the Sagnac effect derivation, without an area, one needs to employ the use of a phase conjugate mirror.

The formulas have already been derived: you have already read Professor Yeh's papers, here is another paper written by Professor Ruyong Wang, in which the Sagnac effect is being derived without an area (what Dr. Wang calls "closed path"):

https://arxiv.org/ftp/physics/papers/0609/0609202.pdf

1 hour ago, swansont said:

How do you have radii, without having circles, which mean there is an enclosed area?

 

1 hour ago, swansont said:

Coiled. Loops. Radii. Plus there's the drawing, showing the two coiled sections. 

You do have an open loop and closed path.

Let me clarify matters even further by using Professor Yeh's first paper on the subject, where the Sagnac effect was recorded using only one arm (segment of light/open loop), as opposed to the second experiment, where two arms (open loops with different lengths/different radii) were employed.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (page 71 of the pdf document, appendix 5.4, Phase-Conjugate Fiber Optic Gyro)

To get from point A to point B and from point B to point A you need a continuous path and an open loop.

This is the first experiment carried out by Professor Yeh, using only one open loop/arm.

Then, we have the second experiment which uses TWO OPEN LOOPS, instead of just one.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf (page 31 of the pdf document), appendix 5.1)

Two continuous paths: BS to PCM, PCM to M using two OPEN LOOPS, just like in the first experiment.

No area involved at all.

One does not need to use an interferometer with an area, while utilizing the phase conjugate mirror.

 

Edited April 13, 2019 by sandokhan

[swansont]

4 hours ago, sandokhan said:

For the Coriolis effect derivation, one needs an area.

 

I didn't ask you about Coriolis (yet). I asked you to derive a Sagnac equation for a system that does not enclose an area, since it is your contention that this is not required.

From where does the phase difference arise?

 

4 hours ago, sandokhan said:

This was proven in 1921 by Dr. Ludwik Silberstein:

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

For the Sagnac effect derivation, without an area, one needs to employ the use of a phase conjugate mirror.

The formulas have already been derived: you have already read Professor Yeh's papers, here is another paper written by Professor Ruyong Wang, in which the Sagnac effect is being derived without an area (what Dr. Wang calls "closed path"):

 

Stop it with this nonsense. The schematic clearly shows a circle, which has an area. The description clearly models them as circles.

4 hours ago, sandokhan said:

https://arxiv.org/ftp/physics/papers/0609/0609202.pdf

 

You do have an open loop and closed path.

Let me clarify matters even further by using Professor Yeh's first paper on the subject, where the Sagnac effect was recorded using only one arm (segment of light/open loop), as opposed to the second experiment, where two arms (open loops with different lengths/different radii) were employed.

You don't need two loops to do a Sagnac measurement. This is irrelevant.

4 hours ago, sandokhan said:

 

 

To get from point A to point B and from point B to point A you need a continuous path and an open loop.

This is the first experiment carried out by Professor Yeh, using only one open loop/arm.

Then, we have the second experiment which uses TWO OPEN LOOPS, instead of just one.

 

F1 and F2 are the loops to which he refers. They enclose an area.

 

 

 

4 hours ago, sandokhan said:

 One does not need to use an interferometer with an area,

Then it should be no problem to derive an expression for one.

4 hours ago, sandokhan said:

while utilizing the phase conjugate mirror.

These devices are not magic. Their use is to clean up polarization issues and increase sensitivity. See sec 2.3 (page 11) (emphasis added)

"Polarization scrambling is a well-known noise source in fiber-optic gyros. Birefringent polarization-holding fibers can be used to decouple the twostates of polarization and hence improve the sensitivity.8,9 In the phase- conjugate fiber-optic gyro, which we are studying, a polarization-preserving phase conjugator can be used to restore severely scrambled waves to their origi-nal state of polarization. This eliminates the noise due to polarization scrambling."

[sandokhan]

10 minutes ago, swansont said:

The schematic clearly shows a circle, which has an area. The description clearly models them as circles.

 

10 minutes ago, swansont said:

F1 and F2 are the loops to which he refers. They enclose an area.

Surely you can differentiate between an OPEN LOOP and a CLOSED LOOP.

The reason I brought up Professor Yeh's first paper is because in that article the OPEN LOOP is displayed right in front of reader.

In fact...

Starting point A

An OPEN LOOP

Then we arrive at point B

Very clearly and precisely defined.

You drew red circles over the two OPEN LOOPS. Now, if you want them to be closed at any cost, you can draw even more circles over them, but the facts won't change.

There is no area whatsoever in Professor Yeh's interferometer.

2(v₁l₁ + v₂l₂)/c²

Since v1 = R1 x Ω, and v2 = R2 x Ω, the formula becomes:

2(R₁L₁ + R₂L₂)Ω/c² 

Since Δφ = 2πc/λ x Δt, we obtain: 4π(R₁L₁ + R₂L₂)Ω/λc which is of course Professor Yeh's formula.

Edited April 13, 2019 by sandokhan

[Ghideon]

5 hours ago, sandokhan said:

TWO OPEN LOOPS

1: You keep on repeating this. As a comparison, can you please define what a closed loop is then? The reference https://apps.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf you provide does not mention what an open vs closed loop is. When looking for references for closed vs open loop devices and sagnac effects I find several references** to that seems more targeted towards open-loop / closed-loop control*. 

2: Why do you keep dodging my questions regarding subquarks?

 

 

*) https://en.wikipedia.org/wiki/Open-loop_controller

**)https://file.scirp.org/pdf/OPJ20120100010_57872338.pdf, https://books.google.se/books?open vs closed loop

[swansont]

15 minutes ago, sandokhan said:

 

Surely you can differentiate between an OPEN LOOP and a CLOSED LOOP.

I think that the problem is that you are not understanding what physicists mean by loop in this context. The loop is placing the fiber such that it crosses over itself and encloses an area.

Quote

The reason I brought up Professor Yeh's first paper is because in that article the OPEN LOOP is displayed right in front of reader.

In fact...

Starting point A

An OPEN LOOP

The fiber loop in this diagram also encloses an area. This is not carelessness on the part of the author. It's deliberate, because it's important.

Quote

Then we arrive at point B

Very clearly and precisely defined.

You drew red circles over the two OPEN LOOPS. Now, if you want them to be closed at any cost, you can draw even more circles over them, but the facts won't change.

Oh FFS. THEY ENCLOSE AN AREA. THAT"S ALL THAT MATTERS!

Quote

There is no area whatsoever in Professor Yeh's interferometer.

2(v₁l₁ + v₂l₂)/c²

Since v1 = R1 x Ω, and v2 = R2 x Ω, the formula becomes:

2(R₁L₁ + R₂L₂)Ω/c² 

Since Δφ = 2πc/λ x Δt, we obtain: 4π(R₁L₁ + R₂L₂)Ω/λc which is of course Professor Yeh's formula.

I will ask, for the last time, for you to derive the phase shift with a device that does not enclose an area — i.e. it does not make a shape that has an area inside of it. No circles, no rectangles, no trapezoids, etc.

If you can't do that, there is no point in continuing this discussion, and I will ask that it be closed. (And I will have zero trouble making my case)

[sandokhan]

3 minutes ago, Ghideon said:

Why do you keep dodging my questions regarding subquarks?

I won't accuse you of trolling this thread.

But I have made it clear that this subject (which was referenced while mentioning the potential) requires a different thread. 

4 minutes ago, Ghideon said:

As a comparison, can you please define what a closed loop is then?

 

These are open loops. Just like the interferometer created by Professor Yeh.

A closed loop? RLGs and the MGX.

The phase conjugate mirror has revolutionized the field of optics.

Please study this subject a little bit more, starting here:

Here is a paper written by Professor Ruyong Wang, in which the Sagnac effect is being derived without an area (what Dr. Wang calls "closed path"):

https://arxiv.org/ftp/physics/papers/0609/0609202.pdf

 

2 minutes ago, swansont said:

The loop is placing the fiber such that it crosses over itself and encloses an area.

But it does not cross itself.

3 minutes ago, swansont said:

The fiber loop in this diagram also encloses an area. This is not carelessness on the part of the author. It's deliberate, because it's important.

To get from point A to point B requires an OPEN LOOP.

4 minutes ago, swansont said:

Oh FFS. THEY ENCLOSE AN AREA. THAT"S ALL THAT MATTERS!

It does matter, if there is no area enclosed.

4 minutes ago, swansont said:

I will ask, for the last time, for you to derive the phase shift with a device that does not enclose an area — i.e. it does not make a shape that has an area inside of it. No circles, no rectangles, no trapezoids, etc.

If you can't do that, there is no point in continuing this discussion, and I will ask that it be closed. (And I will have zero trouble making my case)

It has already been done.

Here is the derivation for the SAGNAC without an area:

https://arxiv.org/ftp/physics/papers/0609/0609202.pdf

Here is the formula:

The Sagnac effect for a ROTATING LINEAR SEGMENT interferometer IS: 2vL/c^2, where v=RΩ.

No area involved at all.

Just like the interferometer featured in Professor Yeh's papers.

[Ghideon]

13 minutes ago, sandokhan said:

I have made it clear that this subject (which was referenced while mentioning the potential) requires a different thread. 

I think you have to do your homework regarding forum rules.

 

[swansont]

3 hours ago, sandokhan said:

I 

Please study this subject a little bit more, starting here:

Here is a paper written by Professor Ruyong Wang, in which the Sagnac effect is being derived without an area (what Dr. Wang calls "closed path"):

https://arxiv.org/ftp/physics/papers/0609/0609202.pdf

Owing to the rotation, the beam does not retrace its path, as shown in Fig 11. Thus, there is an area enclosed.

Quote

 

But it does not cross itself.

Are you kidding me? You have a coil! How do you make a coil without the fiber crossing over itself? It's in the f***ing diagram!

Quote

To get from point A to point B requires an OPEN LOOP.

It does matter, if there is no area enclosed.

It has already been done.

Here is the derivation for the SAGNAC without an area:

https://arxiv.org/ftp/physics/papers/0609/0609202.pdf

Here is the formula:

The Sagnac effect for a ROTATING LINEAR SEGMENT interferometer IS: 2vL/c^2, where v=RΩ.

No area involved at all.

Just like the interferometer featured in Professor Yeh's papers.

 

 

 

[sandokhan]

Try again.

Figure 11 refers to the section called Selecting proper PCMs.

Figures 5 and 6 refer to the phase conjugate single segment of light Sagnac experiment.

27 minutes ago, swansont said:

Are you kidding me? You have a coil! 

You have an OPEN LOOP.

You cannot get to point B from point A unless the beam of light travels in the OPEN LOOP.

Very simple.

There is no enclosed area.

The beam of light travels ONLY THROUGH THE SINGLE SEGMENT AB.

Please read.

This experiment shows us two important points. First, it confirms the phase reversal of a PCM and demonstrates the Sagnac effect in an arc segment AB, not a closed path. Second, it gives us important implications: The result, φ = 4πRΩL/cλ, can be re-written as φ = 4πvL/cλ where v is the speed of the moving arc segment AB (where R is the radius of the circular motion, Ω is the rotational rate).

If we increase the radius of the circular motion as shown in Fig. 6, the arc segment AB will approach a linear segment AB, the circular motion will approach the linear motion, the phase-conjugate Sagnac experiment will approach the phase-conjugate first-order experiment as shown in Fig. 4, and the phase shift is always φ = 4πvL/cλ. 

NOT A CLOSED PATH! NO AREA.

Yet, you drew, again, an area where none exists, the figure referenced is figure 6, not figure 11: the beam of light travels ONLY within segment AB.

 

Another reference: SAGNAC effect without an area.

https://arxiv.org/pdf/gr-qc/0401005.pdf

Edited April 13, 2019 by sandokhan

[swansont]

10 minutes ago, sandokhan said:

Try again.

Figure 11 refers to the section called Test of the one way speed of light.

Figures 5 and 6 refer to the phase conjugate single segment of light Sagnac experiment.

You have an OPEN LOOP.

You cannot get to point B from point A unless the beam of light travels in the OPEN LOOP.

Very simple.

There is no enclosed area.

The beam of light travels ONLY THROUGH THE SINGLE SEGMENT AB.

Please read.

This experiment shows us two important points. First, it confirms the phase reversal of a PCM and demonstrates the Sagnac effect in an arc segment AB, not a closed path. Second, it gives us important implications: The result, φ = 4πRΩL/cλ, can be re-written as φ = 4πvL/cλ where v is the speed of the moving arc segment AB (where R is the radius of the circular motion, Ω is the rotational rate).

If we increase the radius of the circular motion as shown in Fig. 6, the arc segment AB will approach a linear segment AB, the circular motion will approach the linear motion, the phase-conjugate Sagnac experiment will approach the phase-conjugate first-order experiment as shown in Fig. 4, and the phase shift is always φ = 4πvL/cλ. 

NOT A CLOSED PATH! NO AREA.

Yet, you drew, again, an area where none exists: the beam of light travels ONLY within segment AB.

Fig 11 shows the beam path. 

10 minutes ago, sandokhan said:

 

Another reference: SAGNAC effect without an area.

https://arxiv.org/pdf/gr-qc/0401005.pdf

It's quite obvious that the path encloses an area.

 

How could I draw in those blue lines if an area was not enclosed? Zero area would not give me that option.

[sandokhan]

13 minutes ago, swansont said:

Fig 11 shows the beam path. 

Fig 11 refers to the Selecting Proper PCMs, NOT to Section 3, entitled Phase Conjugate Sagnac Experiment.

In section 3, we have this caption:

This experiment shows us two important points. First, it confirms the phase reversal of a PCM and demonstrates the Sagnac effect in an arc segment AB, not a closed path. Second, it gives us important implications: The result, φ = 4πRΩL/cλ, can be re-written as φ = 4πvL/cλ where v is the speed of the moving arc segment AB (where R is the radius of the circular motion, Ω is the rotational rate).

If we increase the radius of the circular motion as shown in Fig. 6, the arc segment AB will approach a linear segment AB, the circular motion will approach the linear motion, the phase-conjugate Sagnac experiment will approach the phase-conjugate first-order experiment as shown in Fig. 4, and the phase shift is always φ = 4πvL/cλ. 

13 minutes ago, swansont said:

How could I draw in those blue lines if an area was not enclosed? Zero area would not give me that option.

Take a look at the derivation, ONLY A CONTINUOUS PATH OF LIGHT.

No area is present in the final formula.

You have a single line/segment.

The words used by the authors: "No enclosed area appears in this expression."

The Sagnac effect is distributed along a line, not an enclosed area.

Edited April 13, 2019 by sandokhan

[swansont]

1 hour ago, sandokhan said:

 

No area is present in the final formula.

Don’t be obtuse. You can make substitutions to make different variables appear. You did it yourself earlier in the thread. 

[DanMP]

On 3/24/2019 at 4:48 PM, sandokhan said:

In this thread the new, global/generalized Sagnac effect formula will be derived.

If it really is "global/generalized", you must also take into consideration (and deal with) the cases where n, the refractive index, is greater than 1 (e.g. when light is traveling through optical fibers, with the speed c/n). Did you?

 

On 4/13/2019 at 11:59 AM, sandokhan said:

No.

The Sagnac effect is a non-relativistic effect.

Maybe it is (as I wrote in this here  forum), but it is very well explained using special relativity, as you can see here.

Edited April 17, 2019 by DanMP

[sandokhan]

1 hour ago, DanMP said:

but it is very well explained using special relativity

You haven't done your homework on this one.

Sagnac Effect, E.J. Post, Reviews of Modern Physics, April 1967

"The search for a physically meaningfull transformation is not aided in any way whatever by the principle of general space-time covariance, nor is it true that the space-time theory of gravitation plays any direct role in establishing physically correct transformations."

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.

By the way, Post proved in 1999 the equivalence between the Michelson-Morley experiment and the Sagnac experiment.

E. J. Post, A joint description of the Michelson Morley and Sagnac experiments.
Proceedings of the International Conference Galileo Back in Italy II, Bologna 1999,
Andromeda, Bologna 2000, p. 62

E. J. Post is the only person to notice the substantial identity  between the 1925 experiment and that of 1887: "To avoid possible confusion, it may be  remarked that the beam path in the more well-known Michelson-Morley interferometer, which was mounted on a turntable, does not enclose a finite surface area; therefore no fringe shift can be expected as a result of a uniform rotation of the latter".

E. J. Post, Reviews of Modern Physics. Vol. 39, n. 2, April 1967

A. Michelson and E. Morley simply measured the Coriolis effect. The Coriolis effect can be registered/recorded either due to the rotation of the Earth or due to the rotation of the ether drift (Whittaker's potential scalar waves). The deciding factor is of course the Sagnac effect, which is much greater than the Coriolis effect, and was never registered.

Since MM did not use a phase-conjugate mirror or a fiber optic equipment, the Coriolis force effects upon the light offset each other. 

The positive (slight deviations) from the null result are due to a residual surface enclosed by the multiple path beam (the Coriolis effect registered by a Sagnac interferometer). Dayton Miller also measured the Coriolis effect of the ether drift in his experiment (Mount Wilson, 1921-1924 and 1925-1926, and Cleveland, 1922-1924).

Dr. Patrick Cornille (Essays on the Formal Aspects of Electromagnetic Theory, pg. 141):

1 hour ago, DanMP said:

If it really is "global/generalized", you must also take into consideration (and deal with) the cases where n, the refractive index, is greater than 1 (e.g. when light is traveling through optical fibers, with the speed c/n). Did you?

https://www.osapublishing.org/ol/abstract.cfm?uri=ol-6-8-401

Sagnac effect in fiber gyroscopes

H.J. Arditty and H.C. Lefevre

Optics Letters, vol. 6, 1981

We review the kinematic explanation of the Sagnac effect in fiber gyroscopes and recall that the index of the dielectric medium does not have any influence. 

Your explanation/"theory" is based on the conventional approach to optics (the Heaviside-Lorentz equations). You need to upgrade your understanding, and use the original Maxwell equations, written in quaternion form, and which are invariant under galilean transformations.

As for the Fizeau experiment (and the Fresnel drag factor) you need to study Ockert's analysis (1968 and 1969).

Edited April 17, 2019 by sandokhan

[DanMP]

1 hour ago, sandokhan said:

Sagnac effect in fiber gyroscopes

H.J. Arditty and H.C. Lefevre

So I need to buy the above article in order to see how you(?) explain the Sagnac effect through optical fibers, where the speed of light is c/n?

 

[sandokhan]

That article is available elsewhere for full reading.

It is also discussed in several other works on the subject.

It is fundamental in understanding the subject of the first part of your message.

Here is Carl Ockert's analysis of the Fizeau experiment:

http://adsabs.harvard.edu/abs/1968AmJPh..36..158O

http://adsabs.harvard.edu/abs/1969AmJPh..37..335O

 

Edited April 17, 2019 by sandokhan

[Ghideon]

2 hours ago, sandokhan said:

That article is available elsewhere for full reading.

Where?

[swansont]

AG Kelly’s credibility is poor (though he does note that Sagnac depends on area, which is contrary to your position)

Here he makes a fundamental error in thinking that if it’s relativistic, then it must be due to time dilation, which is not the case.

[sandokhan]

8 hours ago, swansont said:

AG Kelly’s credibility is poor (though he does note that Sagnac depends on area, which is contrary to your position)

It cannot be any poorer than Michelson's, who derived the WRONG equation (Coriolis effect) while claiming all the while it was the Sagnac effect formula.

It cannot be any poorer than Einstein's, who made this statement in 1905:

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

However, those are the HEAVISIDE-LORENTZ equations, NOT the original J.C. MAXWELL equations which are invariant under galilean transformations.

Dr. A.G. Kelly discovered the humongous fudging of the data in the Hafele-Keating experiment:

http://www.cartesio-episteme.net/h%26kpaper.htm

His credibility is as good as any of the top researchers in the field.

Certainly he will include the CORIOLIS EFFECT formula as a substitution for the SAGNAC EFFECT formula, since this subject was not thoroughly investigated/researched at all in the 20th century.

However, now there is no reason to do so anymore: we have a generalized/global SAGNAC EFFECT formula which essentially and beautifully captures the entire phenomenon.

8 hours ago, swansont said:

Here he makes a fundamental error in thinking that if it’s relativistic, then it must be due to time dilation, which is not the case.

E.J. Post made the same comments as did Dr. Kelly.

Sagnac Effect, E.J. Post, Reviews of Modern Physics, April 1967

"The search for a physically meaningful transformation is not aided in any way whatever by the principle of general space-time covariance, nor is it true that the space-time theory of gravitation plays any direct role in establishing physically correct transformations."

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.

 

It is essential to understand that the SAGNAC EFFECT requires the use of the original MAXWELL equations to be properly described since the SAGNAC interferometer represents A TOPOLOGICAL OBSTRUCTION, hence requiring a higher topology.

https://books.google.ro/books?id=qsOBhKVM1qYC&pg=PA85&dq=Lakhtakia+Barrett,+T.W.+electromagnetism&hl=ro&sa=X&ved=0ahUKEwiV3IXAmbnZAhXKJVAKHeebCnUQ6AEIJjAA#v=onepage&q=Lakhtakia%20Barrett%2C%20T.W.%20electromagnetism&f=false

Dr. T.W. Barrett, "Electromagnetic Phenomena Not Explained by Maxwell's Equations" pg 6 - 85 

https://www.researchgate.net/publication/288491190_SAGNAC_EFFECT_A_consequence_of_conservation_of_action_due_to_gauge_field_global_conformal_invariance_in_a_multiply-joined_topology_of_coherent_fields

Dr. Terence W. Barrett (Stanford Univ., Princeton Univ., U.S. Naval Research Laboratory, Univ. of Edinburgh, author of over 200 papers on advanced electromagnetism):

Topology has been used to provide answers to questions concerning what is most fundamental in physical explanation. That question itself implies the question concerning what mathematical structures one uses with confidence to adequately “paint” or describe physical models built from empirical facts. For example, differential equations of motion cannot be fundamental, because they are dependent on boundary conditions which must be justified—usually by group theoretical considerations. Perhaps, then, group theory is fundamental.

Group theory certainly offers an austere shorthand for fundamental transformation rules. But it appears to the present writer that the final judge of whether a mathematical group structure can, or cannot, be applied to a physical situation is the topology of that physical situation. Topology dictates and justifies the group transformations. So for the present writer, the answer to the question of what is the most fundamental physical description is that it is a description of the topology of the situation. With the topology known, the group theory description is justified and equations of motion can then be justified and defined in specific differential equation form. If there is a requirement for an understanding more basic than the topology of the situation, then all that is left is verbal description of visual images. So we commence an examination of electromagnetism under the assumption that topology defines group transformations and the group transformation rules justify the algebra underlying the differential equations of motion.

Those situations in which the A_μ potentials are measurable possess a topology, the transformation rules of which are describable by the SU(2) group; and those situations in which the A_μ potentials are not measurable possess a topology, the transformation rules of which are describable by the U(1) group.

https://pdfs.semanticscholar.org/a9bc/aee223173c4fef38a36623c550a05c584801.pdf

Topology and the Physical Properties of Electromagnetic Fields
 

Edited April 18, 2019 by sandokhan

[hypervalent_iodine]

!

Moderator Note

Since the OP appears impervious to reason and genuine scientific rebuttal, this thread is closed.