Global/Generalized Sagnac Effect Formula

[sandokhan]

7 minutes ago, swansont said:

Loops have an area

It is wonderful to have you comment here, again, in this thread swansontea.

No closed loop, no area.

L is the entire length of the fiber, Professor Yeh specifies that quite clearly.

(Open-ended (non-closed) loops: a single segment from end to end)

11 minutes ago, swansont said:

RL gives an area

L = 2*pi*R*n where n is the number of loops

RL = 2*Pi*R^2*n

pi*R^2 is the area of a circle.

There is no closed LOOP in the experiment, therefore no area of a circle.

17 minutes ago, swansont said:

Where does this equation show up in the paper? Page and equation number, please.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a206219.pdf

Phase-Conjugate Multimode Fiber Gyro

Published in the Journal of Optics Letters, vol. 12, page 1023, 1987

page 69 of the pdf document, page 1 of the article

 

second reference

https://apps.dtic.mil/dtic/tr/fulltext/u2/a170203.pdf

page 35 of the pdf document

page 3 of appendix 5.1

Self-Pumped Phase-Conjugate Fiber-Optic Gyro

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

The very same formula obtained for a Sagnac interferometer which features two different lengths and two different velocities.

27 minutes ago, swansont said:

What is the velocity referring to? Sagnac depends on rotation.

v₁ 

v₂

are the velocities of the rotation of the Earth at the corresponding latitudes (since there are two latitudes, one will have two velocities, one for each latitude)

Here are the variables used by Michelson:

26 minutes ago, studiot said:

The science of Physics has progressed further away from this than most other sciences, some of which have not moved very far at all.

The science of Physics will progress much further once it realizes that in a magnet there are TWO STREAMS OF PARTICLES, not only a South - North flux of lines, but also a North-South flux of lines. 

[Strange]

3 hours ago, sandokhan said:

Look seriously into this subject, and you will discover/see that my formula is perfectly derived and thus is correct.

So which peer reviewed journal is your perfect work published in?

[sandokhan]

See the previous message for the exact page numbers where the formula appears in the Journal of Optics Letters.

The derivation is not difficult at all, all we have to do is to respect the definition of the SAGNAC EFFECT, which involves TWO LOOPS.

The CORIOLIS EFFECT formula involves a comparison of TWO SIDES, no loops at all present there.

 

[Strange]

8 minutes ago, sandokhan said:

See the previous message for the exact page numbers where the formula appears in the Journal of Optics Letters.

That appears to be Yeh's publication, not yours. Where have you published? (And if not, why not?)

[sandokhan]

Sure it is Dr. Yeh's publication. 

The correct SAGNAC formula was derived for an interferometer which features two different velocities and two different lengths.

The interferometers in the Michelson-Gale experiment/ring laser gyroscope experiments also feature two different velocities and two different lengths.

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

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.

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.

A beautiful generalization of the SAGNAC effect formula for an interferometer whose center of rotation coincides with its geometrical center.

Edited April 12, 2019 by sandokhan

[Strange]

4 minutes ago, sandokhan said:

Sure it is Dr. Yeh's publication. 

So where is your work published?

[sandokhan]

Isn't it strange (no pun intended) to ask where is the work published, when you have the full derivation at your disposal and certainly by now you'd have been able to find any possible errors in it? I have not submitted the derivation to a journal, if that is what you are asking. However, the very same formula has been peer reviewed at the highest possible scientific level (Journal of Optics Letters) and is being used by the US Naval Research Office. Take a look at the final formula, it is a generalization of the Sagnac formula which features a single velocity.

Remember, the MGX and the RLGs feature TWO different velocities (one for each latitude) and two different lengths.

 

[Strange]

57 minutes ago, sandokhan said:

I have not submitted the derivation to a journal, if that is what you are asking.

Why not?

[studiot]

4 hours ago, sandokhan said:

The science of Physics will progress much further once it realizes that in a magnet there are TWO STREAMS OF PARTICLES, not only a South - North flux of lines, but also a North-South flux of lines. 

Now I know this is a thread about Voodoo not Physics.

First you deny that photons are  particles suggest but they are actually scalar fields.

Then you suggest that magnetic fields are actually particulate, with not one but two types of particle.

Edited April 12, 2019 by studiot

[Ghideon]

7 hours ago, sandokhan said:

This is not the subject of this thread. What if I were to tell you that the concept of quarks was introduced in 1908, and also much more than that, including antimatter, bosons, Higgs field, neutrinos, and yes subquarks (subdivision of a quark, discovered at FermiLab). 

Then why did you introduce subquarks in the thread? How was it relevant? It does not improve the credibility of the speculations you provide regarding light.

 

[sandokhan]

46 minutes ago, studiot said:

First you deny that photons are  particles suggest but they are actually scalar fields.

I made no such suggestion. I did not even mention photons. I mentioned scalar waves, not scalar fields (aether).

Are you going to call the Aharonov-Bohm voodoo physics? It is being caused by the POTENTIAL, in the absence of vector fields.

Are you going to call Whittaker's proofs as voodoo physics? He proved, mathematically, the existence of scalar/longitudinal waves.

Are you going to call Maxwell's original set of equations, which are invariant under galilean transformations voodoo physics?

You better not.

Now, for those interested in the correct model of the atom, which does include the subquark, I can open a new thread, again with definite proofs. You will find out about Martin Ruderfer's celebrated experiment (1960), the first null result in the history of ether drift analysis, how the Riemann zeta function is related to the mass of a boson, and much more. But this would be the subject of a different thread.

Here we are concerned with the Sagnac effect formula for an interferometer which features different velocities for each arm, and different lengths for each arm.

44 minutes ago, Ghideon said:

It does not improve the credibility of the speculations you provide regarding light.

Go ahead and make my day: prove that my derivation is wrong. If you cannot, then you must replace the word speculations with proofs.

[Strange]

1 minute ago, sandokhan said:

Are you going to call the Aharonov-Bohm voodoo physics? It is being caused by the POTENTIAL, in the absence of vector fields.

Are you going to call Whittaker's proofs as voodoo physics? He proved, mathematically, the existence of scalar/longitudinal waves.

Are you going to call Maxwell's original set of equations, which are invariant under galilean transformations voodoo physics?

This is a bizarre variant of the straw man argument.

None of those things have to be voodoo for you to base voodoo on them.

3 minutes ago, sandokhan said:

You better not.

Oooooh. Scary.

 

 

[Ghideon]

12 minutes ago, sandokhan said:

Go ahead and make my day: prove that my derivation is wrong. If you cannot, then you must replace the word speculations with proofs.

Sorry, that is not how this forum works. 

8 hours ago, sandokhan said:

Now, it is incumbent upon you to do your homework

Indeed I do homework from time to time, in much less speculative and more productive areas of science. 

[sandokhan]

6 minutes ago, Strange said:

None of those things have to be voodoo for you to base voodoo on them.

Here is more "voodoo" for you: the Maxwell-Lodge effect.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.726.6101&rep=rep1&type=pdf

The Maxwell-Lodge effect: significance of electromagnetic potentials in the classical theory

G. Rousseaux, R. Kofman, and O. Minazzoli

The Aharonov-Bohm effect has been the starting point of the reconsideration of the reality of the vector potential within quantum physics. We argue that the Maxwell-Lodge effect is its classical equivalent: what is the origin of the electromotive force induced in a coil surrounding a (finite) solenoid fed by an alternative current? We demonstrate theoretically, experimentally and numerically that the effect can be understood using the vector potential while it cannot using only the fields.

http://www.ccsenet.org/journal/index.php/apr/article/view/26623/17220

The Physical Entity of Vector Potential in Electromagnetism

Vladimir A. Leus, Ray T. Smith and Simon Maher

 

 “...the vector potential appears to give the most direct description of the physics. This becomes more apparent the more deeply we go into quantum theory. In the general theory of quantum electrodynamics, one takes the vector and scalar potentials as the fundamental quantities in a set of equations that replace the Maxwell equations: E and B are slowly disappearing from the modern expression of physical laws; they are being replaced by A and φ” 

(Feynman et al, 1989, chapter 15, section 5, The Feynman Lecture on Physics (Vol. 2), 1989)

 

Did you know that there is also a Gravitational Aharonov-Bohm effect?

 

3 minutes ago, Ghideon said:

Indeed I do homework from time to time

But you haven't done your homework here. You treated the entire subject matter superficially; hopefully, the attention you devote to your other areas of interest will be more focused.

[Ghideon]

7 minutes ago, sandokhan said:

But you haven't done your homework here. You treated the entire subject matter superficially; hopefully, the attention you devote to your other areas of interest will be more focused.

Then please answer my question, so I may have something worth analyzing: why did you introduce subquarks in the thread? How was it relevant?

 

[swansont]

5 hours ago, sandokhan said:

It is wonderful to have you comment here, again, in this thread swansontea.

No closed loop, no area.

In a word, no.

5 hours ago, sandokhan said:

L is the entire length of the fiber, Professor Yeh specifies that quite clearly.

“R1,2 and L1,2 are the lengths and radii of the fiber loops” (emphasis added)

Yes, they are specified quite clearly, which contradicts your assertion.

And they have to form a loop. 

5 hours ago, sandokhan said:

 

Exactly the formula obtained by Professor Yeh:


 2(V₁L₁ + V₂L₂)/c²

This is what I asked about. It is not where you said it was. 

 

6 hours ago, sandokhan said:

See the previous message for the exact page numbers where the formula appears in the Journal of Optics Letters.

The derivation is not difficult at all, all we have to do is to respect the definition of the SAGNAC EFFECT, which involves TWO LOOPS.

And the effect depends on the area of those loops. 

[Strange]

25 minutes ago, sandokhan said:

Here is more "voodoo" for you: the Maxwell-Lodge effect.

So you just repeat the same fallacy. Bizarre.

[sandokhan]

Don't you want to know what the potential consists of? What exactly causes the Aharonov-Bohm effect? How do subquarks relate to this very important branch of physics? Perhaps I will open a new thread, in the Speculations section of course, devoted to this subject.

For now, please study the topological implications of the Aharonov-Bohm effect:

http://redshift.vif.com/JournalFiles/Pre2001/V07NO1PDF/V07N1BAR.pdf (Dr. Terence W. Barrett, Stanford University)

 

3 minutes ago, swansont said:

Yes, they are specified quite clearly, which contradicts your assertion.

And they have to form a loop. 

None of my assertions have been contradicted.

Do you understand how a phase conjugate mirror functions? There is no area at all featured in Professor Yeh's interferometer, just two segments of light.

Please show to your readers where the area is in the following diagram:

5 minutes ago, swansont said:

This is what I asked about. It is not where you said it was. 

But it is.

Surely you know that v = R x Ω.

This is the formula published by Professor Yeh:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc

V1 = R1 x Ω

V2 = R2 x Ω

Do you understand this very easy substitution?

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

The very same formula obtained for a Sagnac interferometer which features two different lengths and two different velocities.

[swansont]

5 hours ago, sandokhan said:

1. Isn't it strange (no pun intended) to ask where is the work published, when you have the full derivation at your disposal and certainly by now you'd have been able to find any possible errors in it? I have not submitted the derivation to a journal, if that is what you are asking. However, the very same formula has been peer reviewed at the highest possible scientific level (Journal of Optics Letters) and is being used by the US Naval Research Office. Take a look at the final formula, it is a generalization of the Sagnac formula which features a single velocity.

It’s the Office of Naval Research (ONR), not US Naval Research Office, and the journal is called “Optics Letters”, not “Journal of Optics Letters”

Please at least get that detail right

[Ghideon]

9 minutes ago, sandokhan said:

Don't you want to know what the potential consists of? What exactly causes the Aharonov-Bohm effect? How do subquarks relate to this very important branch of physics? Perhaps I will open a new thread, in the Speculations section of course, devoted to this subject.

For now, please study the topological implications of the Aharonov-Bohm effect:

Why did you introduce subquarks in the thread? How is it relevant and connected to your speculation in this thread?

[sandokhan]

1 minute ago, Ghideon said:

speculation

No speculation at all.

Just a straightforward and direct derivation, using the correct definition of the Sagnac effect.

Remember this: the CORIOLIS EFFECT is a physical effect upon the light beams. It is directly proportional to the area of the interferometer. The SAGNAC EFFECT is an electromagnetic effect upon the velocities of the light beams, as such it must be directly proportional to the RADIUS of rotation. A huge difference.

As for the subquarks, I should open a new thread, where we will investigate the nature of the potential, which, as R. Feynman stated, is much more important than the vector field.

[swansont]

52 minutes ago, sandokhan said:

  

None of my assertions have been contradicted.

Yoiu said L was the length of the entire fiber. I showed a direct quote that says it's the length of the fiber in the loop

Quote

Do you understand how a phase conjugate mirror functions? There is no area at all featured in Professor Yeh's interferometer, just two segments of light.

Please show to your readers where the area is in the following diagram:

So is it your contention that L1 and L2 are not circular, and there is no area enclosed by them?

I mean, it seems obvious that they are. I don't know how to convince you otherwise. The author refers to them as "loops". Do you understand what a "loop" is?

 

Quote

But it is.

Surely you know that v = R x Ω.

This is the formula published by Professor Yeh:

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc

Yes. It is. But you said the other equation is what he published ("Exactly the formula obtained by Professor Yeh"), and it's not.

That was my objection.

Quote

V1 = R1 x Ω

V2 = R2 x Ω

That assumes the rotation is around the center of the loop. Otherwise it makes no sense. Certainly not in the context of your earlier response, which was not referencing the same geometry of interferometer as Dr Yeh's

Quote

Do you understand this very easy substitution?

4π(V₁L₁ + V₂L₂)/λc

But you didn't say the formula was easily derived, you said it was "Exactly the formula obtained by Professor Yeh" and I had difficulty finding it, because, well, it's not the exact formula. It's derived, and would only work under a specific case that both loops were rotating at the same speed around a common center. Otherwise the V's are meaningless. 

 

36 minutes ago, sandokhan said:

No speculation at all.

Just a straightforward and direct derivation, using the correct definition of the Sagnac effect.

Remember this: the CORIOLIS EFFECT is a physical effect upon the light beams. It is directly proportional to the area of the interferometer. The SAGNAC EFFECT is an electromagnetic effect upon the velocities of the light beams, as such it must be directly proportional to the RADIUS of rotation. A huge difference.

You can get Sagnac in free space, and get it with neutrons, so how is it an electromagnetic interaction?

[Ghideon]

18 minutes ago, sandokhan said:

No speculation at all.

Just a straightforward and direct derivation, using the correct definition of the Sagnac effect.

Remember this: the CORIOLIS EFFECT is a physical effect upon the light beams. It is directly proportional to the area of the interferometer. The SAGNAC EFFECT is an electromagnetic effect upon the velocities of the light beams, as such it must be directly proportional to the RADIUS of rotation. A huge difference.

As for the subquarks, I should open a new thread, where we will investigate the nature of the potential, which, as R. Feynman stated, is much more important than the vector field.

Why did you introduce subquarks in this thread? Can we safely assume that subquarks are an irrelevant addition you made?

[studiot]

As regards loops I am completely with swansont about this.

You said

On ‎4‎/‎2‎/‎2019 at 6:43 AM, sandokhan said:

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.

So yes, you did mention closed loops, which undoubtedly possess the property of enclosing an area.

 

1 hour ago, sandokhan said:

I made no such suggestion. I did not even mention photons. I mentioned scalar waves, not scalar fields (aether).

Actually you didn't. you mentioned EM fields and waves (AKA photons)

11 hours ago, sandokhan said:

Ether = longitudinal waves (telluric currents) of subquarks = potential/scalar Whittaker waves

Aether = medium through which these waves propagate/travel

E.T. Whittaker, in 1904, showed that all EM fields and waves can be decomposed into differential functions of two scalar potentials.

 

This quote also shows why Ghideon is correct to chase you over the introductions of quarks.

 

A word of observation.

You tend to respond with reams of quotes from august people, rather than with your thoughts.

All this constant 'appeal tov authority' 'does is obscure the matter in hand.

You would be better employed taking swansont's advice and making sure your own statements are consistent.

1 hour ago, swansont said:

Please at least get that detail right

 

 

[sandokhan]

7 hours ago, studiot said:

So yes, you did mention closed loops, which undoubtedly possess the property of enclosing an area.

 

8 hours ago, swansont said:

So is it your contention that L1 and L2 are not circular, and there is no area enclosed by them?

I mean, it seems obvious that they are. I don't know how to convince you otherwise. The author refers to them as "loops". Do you understand what a "loop" is?

Those are open loops, and you know this fact very well. Not closed loops. No area. No enclosure whatsoever.

(Open-ended (non-closed) loops: a single segment from end to end)

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

The use of the phase conjugate mirror means that you have an interferometer where there is no need to actually have an enclosed area. 

The paths of light in the figure are the two segments of light which connect BS and M with PCM, back and forth. The path of the light is described as follows:

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.

Both of you already know these very simple facts.

You have TWO CLOSED PATHS and TWO OPEN LOOPS.

8 hours ago, swansont said:

Yoiu said L was the length of the entire fiber. I showed a direct quote that says it's the length of the fiber in the loop

Did you even read the paper?

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.

8 hours ago, swansont said:

Yes. It is. But you said the other equation is what he published ("Exactly the formula obtained by Professor Yeh"), and it's not.

But it is.

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc

V1 = R1 x Ω

V2 = R2 x Ω

Do you understand this very easy substitution?

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

8 hours ago, swansont said:

That assumes the rotation is around the center of the loop. Otherwise it makes no sense. Certainly not in the context of your earlier response, which was not referencing the same geometry of interferometer as Dr Yeh's

But it is the same.

You have two different radii, thus two different linear velocities. Exactly the same case as in the Michelson-Gale experiment, or the ring laser gyroscopes interferometers.

This is why the experiment carried out by Dr. Yeh is so ingenious.

8 hours ago, swansont said:

and I had difficulty finding it, because, well, it's not the exact formula.

It is the same.

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc

V1 = R1 x Ω

V2 = R2 x Ω

4π(V₁L₁ + V₂L₂)/λc

8 hours ago, swansont said:

It's derived, and would only work under a specific case that both loops were rotating at the same speed around a common center. Otherwise the V's are meaningless. 

You have two different velocities, for each latitude, in the Michelson-Gale experiment. Each open loop has a different linear velocity, since both open loops have different radii, in the figure shown by Professor Yeh. 

Remember, we are dealing with a Sagnac interferometer which is located away from the center of rotation (as in the case of all ring laser gyroscopes or the MGX). Then, you will automatically have two different linear velocities, for each arm, and two different lengths of the arms. 

8 hours ago, swansont said:

You can get Sagnac in free space, and get it with neutrons, so how is it an electromagnetic interaction?

The Sagnac effect is an electromagnetic effect.

https://www.researchgate.net/publication/253792325_Sagnac_Effect

What S.A. Werner measured in 1979 is the CORIOLIS EFFECT upon the neutron phase:

https://arxiv.org/pdf/1701.00259.pdf

Once the area of the interferometer is mentioned you get the CORIOLIS EFFECT.

If you want the SAGNAC EFFECT, you must derive a formula which is proportional to the RADIUS OF ROTATION, just like I did, just like Professor Yeh did.

 

The derivation I provided obeys the RULES of the Sagnac effect, while Michelson's derivation did not. He compared two open arms of the interferometer, thus obtaining the Coriolis effect formula. I compared two loops, one counterclockwise, one clockwise, thus I obtained the correct Sagnac effect formula.

Edited April 13, 2019 by sandokhan