The distortion of science

Those who have been on this forum for some while may have noted the much quoted Sagnac effect, and how a certain individual uses it in a large percentage of his voluminous copy/pate posts to prove his anti-facts. Since then there have been numerous experiments that have confirmed relativity, a fact ignored by those who love cherry picking.

What needs to be remembered is there is indeed a Sagnac effect named after rather conservative French physicist Georges Sagnac. You can look him up and find out what he did back in 1913. It is important to note that the experiment was carried out in an effort to disprove Einstein and his new and revolutionary ideas on relativity while attempting to confirming the presence of the aether. Sagnac was very much old school and apparently resented the new kid on the block, Einstein. This is why it is latched on to by FE believers. The question is what is it  they are latching on to?

Certain FE believers claim not only that the Sagnac effect disproves relativity but also suggests that we live on a flat and stationary world!  In the context of relativity, the Sagnac effect  can be  explained. If anything, the Sagnac effect is a demonstration of the validity of relativity. The problem is the mathematics makes it a bit impenetrable for most and this is where the problems start as it allows certain people to confuse the issue, misrepresent the results and blind people with anti-science. This is the deliberate distortion of science to prove a fixed and unmoving position. Some people will go to any lengths to support their beliefs.

What we need to remember is that FEers have a list of requirements that must be met regardless of what science actually tells us. They need to misrepresent experiments like this to meet these  requirements. In this case it’s the existance of the aether. Incidentally  I don’t think for one moment Sagnac thought the earth was either flat nor stationary. He believed that light, like sound required a propagating medium. To be fair  up until the 1900 it was a view held by most scientists. But as we all know things move on as new discoveries are made.

To get to the actual truth to be honest is not easy as most of the journals that have the best explanations of Sagnac are, like most academic journals, pay to read. It is true to say it’s interpretation has caused quite a stir in physics over the years some claiming it supports relativity and others disagreeing. What it doesn’t do is suggest the Earth is either stationary or flat and there lies the problem. Some FEers have hijacked this confusion then misrepresenting it.

The bottom line is if you are going to use science to back your case you have to be honest, not cherry pick and be open to all what science offers.

In the context of relativity, the Sagnac effect  can be  explained.

You simply haven't done your homework on the subject.

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.


The SAGNAC EFFECT has two different modes of operation: the center of rotation coincides with the geometric center of the interferometer, and the center of rotation is located away from the interferometer.

Michelson was awarded a Nobel prize for the WRONG formula.

But I was able to derive the CORRECT SAGNAC EFFECT FORMULA:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070907#msg2070907



From a topological point of view, the SAGNAC EFFECT represents a MULTIPLY-CONNECTED domain, it can only be described by the original set of Maxwell's equations:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2039636#msg2039636

Fields can be described by a U(1) group transformation: the modified Maxwell equations (actually, the Heaviside-Lorentz equations).

Potentials (ether theory) can ONLY be described by SU(2) group transformations (and higher).

The group algebra underlying the commonly used Maxwell equations is U(1): but this only relates to the ripples in the sea of ether.

The Sagnac effect, the Aharonov-Bohm effect, the Maxwell-Lodge effect can only be described by SU(2) group transformations (the quaternion formulation of the Maxwell equations).

You simply haven't done your homework on the subject.

You have repeatedly shown you either have no idea what you are talking about, or are lying about it.
That is why this thread is aimed at you. You are blatantly distorting science to try and prop up your lies.

STR has no possible function in explaining the Sagnac effect.

Except the general description of the propagation of light. It isn't a relativistic effect.

That doesn't mean it refutes relativity.

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

And it is completely wrong, as it treats a point on the ring as being in an inertial reference frame, even though it clearly isn't.

Do it yourself, or not at all.

Michelson was awarded a Nobel prize for the WRONG formula.

No, you not liking the formula doesn't magically mean it is wrong.
He derived the correct formula.
It is the same one I derived, which you were unable to show any problems with.
Meanwhile all your attempts to derive the formula have failed.

But I was able to derive the CORRECT SAGNAC EFFECT FORMULA:
https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070907#msg2070907

Yet you don't bother providing it here and instead just link to it.
But looking at the link it is quite clear your derivation is wrong. You even notice where it goes wrong, and just outright reject it and lie.

From a topological point of view, the SAGNAC EFFECT represents a MULTIPLY-CONNECTED domain, it can only be described by the original set of Maxwell's equations:

Yet you ignore one of the most important parts, how it connects.
You have a light beam travelling in the same direction along the loop, even though that is completely impossible.
For each segment you have a beam travelling with the rotation and a beam travelling against it.
The shift you calculate for each segment is the extra time taken for the beam travelling with the rotation.
But what you are completely ignoring is that the beam going with the rotation in one segment then goes against the rotation in the other segment.
So no, you need to subtract them, not add.

I understand your anger; however, it is not warranted at all.

EXPERIMENTAL PROOF

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)

Dr. P. Yeh
PhD, Caltech, Nonlinear Optics

Principal Scientist of the Optics Department at Rockwell International Science Center
Professor, UCSB

"Engineer of the Year," at Rockwell Science Center

Leonardo da Vinci Award in 1985

Fellow of the Optical Society of America, the Institute of Electrical and Electronics Engineers

The first phase-conjugate Sagnac experiment on a segment light path with an external pump configuration.



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.

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

To obtain the correct Sagnac effect for two separate segments (which feature different lengths and different speeds) of an interferometer which is located away from the center of rotation, one has to add (not substract) the two distinct components.


MATHEMATICAL/THEORETICAL PROOF



This is the global, generalized Sagnac effect formula.

Full derivation:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070591#msg2070591

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070907#msg2070907

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.

Michelson proceeded with his calculations AS IF he had placed a rectangular interferometer with the dimensions of 2010 ft (612.65 m) by 1113 ft (339.24 m) with its center of rotation coinciding with the center of rotation of the Earth (radius of 6,376.164 km).

Once the interferometer is moved away from the center of rotation, the Coriolis effect will be measured first: the formula involves the substraction of the separate phase differences.

By contrast, the much greater Sagnac effect formula will be derived by adding the separate phase differences.

I understand your anger; however, it is not warranted at all.

EXPERIMENTAL PROOF

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)

Dr. P. Yeh
PhD, Caltech, Nonlinear Optics

Principal Scientist of the Optics Department at Rockwell International Science Center
Professor, UCSB

"Engineer of the Year," at Rockwell Science Center

Leonardo da Vinci Award in 1985

Fellow of the Optical Society of America, the Institute of Electrical and Electronics Engineers

The first phase-conjugate Sagnac experiment on a segment light path with an external pump configuration.



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.

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

To obtain the correct Sagnac effect for two separate segments (which feature different lengths and different speeds) of an interferometer which is located away from the center of rotation, one has to add (not substract) the two distinct components.


MATHEMATICAL/THEORETICAL PROOF



This is the global, generalized Sagnac effect formula.

Full derivation:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070591#msg2070591

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070907#msg2070907

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.

Michelson proceeded with his calculations AS IF he had placed a rectangular interferometer with the dimensions of 2010 ft (612.65 m) by 1113 ft (339.24 m) with its center of rotation coinciding with the center of rotation of the Earth (radius of 6,376.164 km).

Once the interferometer is moved away from the center of rotation, the Coriolis effect will be measured first: the formula involves the substraction of the separate phase differences.

By contrast, the much greater Sagnac effect formula will be derived by adding the separate phase differences.

Aside from the constant tedious pleading to authority made by the previous poster, let’s come at this from a different direction. Though if you care to read my opening post you will see this poster behaved as predicted, copy and paste avalanche laced with cherries. There are just as many papers that would offer a very different interpretation of Sagnac. But the previous poster never refers to them as he and his beliefs require relativity to be wrong. That is not science, it’s a distortion of science as mentioned in the opening post.

Sagnac and the effect  has been used by some to try and refute Relativity. But what experimentation does relativity have in its favour?
Einstein predicted the following, to support or confirm relativity through experimentation:
Gravitational redshift of light
Perihelion precession of Mercury
Defection of light by the sun
All three experiments have been repeated over the years numerous times by various scientists and all the results appeared to prove Einstein and relativity to be correct. He also predicted gravity waves which were recently confirmed by the now famous LIGO experiment. Rather than copy and paste vast amounts of ‘stuff’ like you know who, you are at liberty to go and look all theses up’

There are also a plethora of more modern experiments that Einstein didn’t mention that others have gone on to carry out that confirm Relativity and prove Einstein  to be correct. The previous poster of course ignores all this inconvenient science as it proves his assertions to be wrong and other interpretations of the Sagnac effect to be correct.

Because relativity is so important and fundemental to science a great deal of experamental effort has been expended to determine if  is indeed true.
Here is a document that lists some of the successful experiments that confirm relativity. There are a great deal of others out there, all avoided by the previous poster. He will have his work cut out trying to debunk the thousands of experiments that have confirmed relativity.

https://arxiv.org/pdf/1705.04397.pdf

What we have on the one hand are a raft of radically different experiments carried out by thousands of different scientists since the 1920s that appear to show Einstein and relativity to be correct.

On the other hand we have one controversial experiment the results of which have created some consternation among the physics community  which the previous poster makes use of. He deliberately distorts the scientific facts in an effort to support the requirements of his world view which are:
The earth is flat
The aether exists
Relativity is wrong.

As to the aether existing, now that we understand the propagational properties of light we know it is not a requirement. A quick call to the astronauts in the ISS would confirm that. That is the same ISS that can be seen whizzing by if you are in the correct predicted place at the predicted time and the weather is good. I think they would also tell you that the earth is not flat! All the previous poster has to do, when not working on his perpetual motion machine, is go out and look up! ( will he ever finish it?)

As for the one who constantly rebukes people for ‘not doing their homework’ He  needs, if using science to prove a point, to embrace all of science and it’s findings and not just the tiny bits he likes. He should also refrain from just making things up when it suits him or invoking conspiracy when all else fails.

There is also the constant  elephant in the room of space travel, which he refutes, not using science but looking at what his beliefs require.

All his posts are a selective abuse of science which he uses to produce his deluge of anti facts. Look up his so called advanced workings which are all make belive nonsense wrapped up in a veneer of cherry picked pseudo science to understand my point.

I think we may need a number of threads to slowly reveal the true nonsense of the poster sandokhan.

There are also a plethora of more modern experiments that Einstein didn’t mention that others have gone on to carry out that confirm Relativity and prove Einstein  to be correct.

Total demolition of TGR/TSR:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg769750#msg769750 (it includes how Einstein faked the gravitational redshift experiments of 1919/1922 and also how he fudged the Mercury perihelion equation)

Fake TSR experiments:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg865008#msg865008

Ether Shapiro delay, ether frame dragging, ether lensing, ether space probe B:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1911878#msg1911878

There are just as many papers that would offer a very different interpretation of Sagnac.

The physics of the Sagnac effect must be foreign to you, otherwise you wouldn't have made such a statement.

You can only do two things with the phase shifts of the Sagnac interferometer located away from the center of rotation (such as the Michelson-Gale experiment, or the ring laser experiments): either ADD them, or SUBSTRACT them.

Let us see what happens if you do substract them, just as A. Michelson did.

The original interferometer built by Michelson and Gale in Clearing, IL, measured 2010 ft x 1113 ft: the laser technology has permitted a great reduction in size of the interferometer to just a few meters.

This is the original paper published by Michelson and Gale in 1925:

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


http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1925ApJ....61..140M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

This is the formula for the MGX and the ring laser interferometers:



Here is the derivation:






However, this the CORIOLIS EFFECT formula for light beams.

Full derivation of the above formula using the CORIOLIS FORCE:

https://www.ias.ac.in/article/fulltext/pram/087/05/0071

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

Dr. Silberstein developed the formula published by A. Michelson using very precise details, not to be found anywhere else.

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.

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

Thus A. Michelson knew well in advance that he was going to actually measure the Coriolis effect and not the Sagnac effect.

But Michelson, a Nobel prize winner, claimed that the CORIOLIS EFFECT formula was the SAGNAC PHASE SHIFT formula, thus ensuring that for the next 90 years the RE would always win the debate on heliocentrism vs. geocentrism (not even the proponents of aether theory could not dismiss the MGX since they would have had to explain the fringe shifts measured by Michelson and by every ring laser interferometer since 1925).

Bilger et al (1995) and Anderson et al (1994) used the Sagnac phase shift formula derived by A. Michelson, which was actually the Coriolis effect equation.

H.R. Bilger, G.E. Stedman, Z. Li, U. Schreiber and M. Schneider, IEEE Trans. Instrum. Meas. 44(2), 468 (1995)
R. Anderson, H.R. Bilger and G.E. Stedman, Am. J. Phys. 62(11), 975 (1994)




However, the use the phase-conjugate mirror has allowed the greatest breakthroughs possible in ring laser interferometry.

Thus, the correct formula for the Sagnac phase shift for an interferometer located away from the center of rotation became possible:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070082#msg2070082

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070907#msg2070907

The rotational Sagnac effect formula is thousands of times greater than the Coriolis effect.

One is proportional to the velocity of the rotation (radius of Earth x angular velocity) and is an electromagnetic effect modifying the speed of the light beams; the other is proportional to the area of the interferometer and is a physical effect on the light beams.




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.


In order to obtain the GLOBAL SAGNAC EFFECT, you need to ADD the phase shifts.

EXPERIMENTAL PROOF

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)

Dr. P. Yeh
PhD, Caltech, Nonlinear Optics

Principal Scientist of the Optics Department at Rockwell International Science Center
Professor, UCSB

"Engineer of the Year," at Rockwell Science Center

Leonardo da Vinci Award in 1985

Fellow of the Optical Society of America, the Institute of Electrical and Electronics Engineers

The first phase-conjugate Sagnac experiment on a segment light path with an external pump configuration.



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.

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

To obtain the correct Sagnac effect for two separate segments (which feature different lengths and different speeds) of an interferometer which is located away from the center of rotation, one has to add (not substract) the two distinct components.


MATHEMATICAL/THEORETICAL PROOF



This is the global, generalized Sagnac effect formula.

Full derivation:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070591#msg2070591

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070907#msg2070907

Michelson proceeded with his calculations AS IF he had placed a rectangular interferometer with the dimensions of 2010 ft (612.65 m) by 1113 ft (339.24 m) with its center of rotation coinciding with the center of rotation of the Earth (radius of 6,376.164 km).

Once the interferometer is moved away from the center of rotation, the Coriolis effect will be measured first: the formula involves the substraction of the separate phase differences.

By contrast, the much greater Sagnac effect formula will be derived by adding the separate phase differences.

I understand your anger; however, it is not warranted at all.

You clearly don't as it isn't anger at all.

EXPERIMENTAL PROOF

How about before trying to derail the thread with more nonsense, you deal with what you already have.

Why do you choose to add the shifts, rather than subtract them?
This requires the one beam of light to be moving with the direction of rotation on both segments of the loop. That is physically impossible.
If it is going with the rotation for one section of the loop it needs to be going against the direction for the other segment to complete the loop.


What you are calling the coriolis effect, is the Sagnac effect.
They are the same effect, produce the same result and have the same formula.

There are also a plethora of more modern experiments that Einstein didn’t mention that others have gone on to carry out that confirm Relativity and prove Einstein  to be correct.

Total demolition of TGR/TSR:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg769750#msg769750 (it includes how Einstein faked the gravitational redshift experiments of 1919/1922 and also how he fudged the Mercury perihelion equation)

Fake TSR experiments:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg865008#msg865008

Ether Shapiro delay, ether frame dragging, ether lensing, ether space probe B:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1911878#msg1911878

As soon as you resort to the word fake, it’s a cleat admission of defeat.
Providing lists to your own posts? What does that prove, absolutely nothing.
While I reference real proven scientific experiments, you reference yourself.
When you are unable to refute something scientifically you cry fake. That’s not science.
Nowhere have taken on board that list of scientific experiments that prove relativity,
Unable to put together a coherent argument and out of fear you resort instead to a tirade of cut and paste. Why do you bother?

I think Sandokan’s last post is a clear example of how NOT to make a point. Like most of his other posts it’s a stream of incoherent cut and paste that proves absolutely nothing. Exactly what point is he trying to make? You tell me.

EXPERIMENTAL PROOF

Have YOU done any experiments?  The equipment is well within the reach of the home hobbyist, as demonstrated by this guy

The use of science in a debate can be dangerous ground. If you decide to go down that route then you should be open to arguments that are also based on science that may not agree with your own. Cherry picking scientists and their work and using only a small part of what they have said and using it out of context also puts you on shakey ground.

Much of this and other discussions revolve around Sagnac and his much quoted experiment.  Sagnac was a true man of science who worked in many areas connected with the the electromagnetic  spectrum, with optics being his main speciality. The background to his now much vaunted experiment was to prove the existance of the aether. He was an opponent to the then new ideas of Relativity, It had nothing at all to do with the earth being flat. Sagnac let’s make it clear did not believe in a flat earth he was conducting an experiment to prove his case in regards to how light traveled in space, and being as he thought, a wave, it required a medium.

The experiment was first performed by Georges Sagnac in 1913. At the time it was a challenging experiment, with lasers and modern equipment it’s pretty easily done. The basic idea is to take a beam of light and split it so that half the light goes around a path clockwise, and the other half counterclockwise. The two light beams are then combined so that they create an interference pattern. Any shift in the speed of light will then cause a shift in the interference pattern. This is similar to the method Michelson and Morley used. The big difference is that you take the entire apparatus and spin it. ( I’ll deal with the M and M in another thread)

If there really is an aether, then the device must be rotating through it, so there should be an observed shift in the interference pattern. Sure enough, when Sagnac performed this experiment he observed a shift. This experiment has been done countless times in a variety of ways, and the shift is consistently observed. The Sagnac effect is very real. Let’s be clear about that!

Sagnac thought this experiment confirmed the existence of the aether, and he’s partly right ish! A shift in the interference pattern is exactly what the aether model predicts. Sagnac also thought the experiment disproved relativity, and that’s where he’s wrong. A shift in the pattern is also predicted by special relativity, as Max von Laue predicted two years before Sagnac performed his experiment. It funny how FE types always skip over or ignore that fact.

What Sagnac failed to understand is that special relativity applies to frames of reference that are not rotating,.........ok.......so it doesn’t predict that light’s trip around the loop is the same in both directions when the device is rotating. If you were to look at the rotating device from above, you’d see that light that travels in the direction of the rotation actually travels a longer distance because the device is rotating away from it a bit. The light going in the opposite direction makes a shorter trip, since the device rotates into it. So relativity also predicts a shift in the interference pattern. This appears to be the bit that constantly stumps certain people.

As a result, the Sagnac experiment is inconclusive, since it agrees with both the aether and relativity models. This happens sometimes, and when it does you need a tie-breaker to distinguish one model from another. In this case there are several such experiments, but one very clear one comes from Einstein’s most famous prediction, E = mc2. If relativity is right, then mass and energy must be connected. If Einstein equation fails, then relativity is decidedly wrong. Of course if that were the case, things like nuclear power wouldn’t work, but since lots of people rely upon nuclear power every day, we can declare relativity the winner. There are of course a whole host of other experiments but let that one be the clincher.

Point to note that was a post on the Sagnac thingy that used no equations to baffle and confuse, but rather plain English.  I rest my case.

In fact what do people find better? Posts in plain English, or posts that include hard to comprehend equations? Just wondering if people had a preference.

Einstein’s most famous prediction, E = mc2

Einstein's report card:



6 is rock bottom

1 is top grade

German-5, French-3, Italian-5, History-6, Geography-4, Algebra-6, Geometry-6, Physics-6, Chemistry-5, Biology-5, Technical drawing and Art-4

In 1895, Einstein failed a simple entrance exam to an engineering school in Zurich.. This exam consisted mainly of elementary and basic mathematical problems, and Einstein showed himself to be mathematically inept in this exam.

While at the university, Paul Biefeld did Einstein's homework.

By the way, it was J.C. Maxwell who coined up the relation E=mc2:

http://gsjournal.net/Science-Journals/Research%20Papers-Mathematical%20Physics/Download/6371

Einstein's report card:

Has nothing to do with this topic and thus is just pathetic spam to try and avoid another defeat.
Grow up, stay on topic.

Now I will ask again:
WHY DID YOU ADD THE 2 SHIFTS? That means that the one beam of light needs to travel along the 2 segments in the direction of rotation, while the other travels against the direction of rotation. That is impossible.

Perhaps a better question:
Can you draw a diagram showing the path of the light and the time required to travel each segment?

Has nothing to do with this topic

But it does, in a most direct way.

The fact that Einstein failed math and physics in high school and could not pass a simple engineering exam speaks volumes of the fact that someone else wrote his papers on relativity for him.

WHY DID YOU ADD THE 2 SHIFTS?

If you substract the shifts, you get the Coriolis effect formula.

What we want is the SAGNAC EFFECT FORMULA.

I have already explained in great detail the experimental proof provided here earlier, which you seem not to remember.

In order to obtain the GLOBAL SAGNAC EFFECT, you need to ADD the phase shifts.

EXPERIMENTAL PROOF

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)

Dr. P. Yeh
PhD, Caltech, Nonlinear Optics

Principal Scientist of the Optics Department at Rockwell International Science Center
Professor, UCSB

"Engineer of the Year," at Rockwell Science Center

Leonardo da Vinci Award in 1985

Fellow of the Optical Society of America, the Institute of Electrical and Electronics Engineers

The first phase-conjugate Sagnac experiment on a segment light path with an external pump configuration.



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.

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

To obtain the correct Sagnac effect for two separate segments (which feature different lengths and different speeds) of an interferometer which is located away from the center of rotation, one has to add (not substract) the two distinct components.


MATHEMATICAL/THEORETICAL PROOF



This is the global, generalized Sagnac effect formula.

Full derivation:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070591#msg2070591

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070907#msg2070907

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.

Michelson proceeded with his calculations AS IF he had placed a rectangular interferometer with the dimensions of 2010 ft (612.65 m) by 1113 ft (339.24 m) with its center of rotation coinciding with the center of rotation of the Earth (radius of 6,376.164 km).

Once the interferometer is moved away from the center of rotation, the Coriolis effect will be measured first: the formula involves the substraction of the separate phase differences.

By contrast, the much greater Sagnac effect formula will be derived by adding the separate phase differences.

That means that the one beam of light needs to travel along the 2 segments in the direction of rotation, while the other travels against the direction of rotation. That is impossible.

You need to update your level of understanding of physics, which is quite poor given the caliber of your statement.



FOR A SAGNAC INTERFEROMETER WHICH FEATURES TWO DIFFERENT LENGTHS AND TWO DIFFERENT VELOCITIES YOU NEED TO ADD THE PHASE SHIFTS.

Experimentally proven by Dr. Yeh.

Published in the Journal of Optics Letters.

Confirmed by the US Naval Research Lab.

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.

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

To obtain the correct Sagnac effect for two separate segments (which feature different lengths and different speeds) of an interferometer which is located away from the center of rotation, one has to add (not substract) the two distinct components.

But it does, in a most direct way.

Not the topic you started to focus on.
You were focusing on the Sagnac effect, so deal with that before moving on.

WHY DID YOU ADD THE 2 SHIFTS?
If you substract the shifts, you get the Coriolis effect formula.

Which is more commonly known as the Sagnac effect formula. It is the formula you want.

What we want is the SAGNAC EFFECT FORMULA.

Which means you subtract, not add.
So again, why did you add?

I have already explained in great detail the experimental proof provided here earlier, which you seem not to remember.

No you just sprouted a bunch of garbage.

In order to obtain the GLOBAL SAGNAC EFFECT, you need to ADD the phase shifts.

Repeating your same baseless assertion doesn't magically make it true.

EXPERIMENTAL PROOF
Self-pumped phase-conjugate fiber-optic gyro

Is a completely different setup to the one you showed, and it uses angular velocity, not linear velocity.

To obtain the correct Sagnac effect for two separate segments (which feature different lengths and different speeds) of an interferometer which is located away from the center of rotation, one has to add (not substract) the two distinct components.

Not for the one you provided. You provided a simple loop, without any phase conjugate mirror.

Don't bother linking to more crap elsewhere, do it here.
Provide an image of the interferometer (a simple loop) clearly showing the path of each light and indicate how long it takes for the light to travel each segment.

Again, adding them equates to one beam of light going forward in both arms, and one going backwards in both arm.
Meanwhile in reality you have one beam go forward in one arm and backwards in the other, with the other beam going the other way. That requires subtracting the shifts from each arm.

Using your lack of reasoning you would end up with a sagnac shift for a circular loop rotating about the centre of 0.

Stop spamming a bunch of crap. Show the light path and the time for each to show why you need to add. Until you do that, you are just spouting garbage.

Has nothing to do with this topic

But it does, in a most direct way.

The fact that Einstein failed math and physics in high school and could not pass a simple engineering exam speaks volumes of the fact that someone else wrote his papers on relativity for him.

Rubbish!  For someone who "failed math and physics in high school and could not pass a simple engineering exam" even Einstein's Special Relativity has had a great impact on modern science and there is tremendous amount of supporting evidence, see:
            What is the experimental basis of Special Relativity?
Sandokhan, would you please list the impact your "Advanced Flat Earth Theory" has had on the world at large?

Then, more importantly, is the effect that General Relativity developed by this person who "failed math and physics in high school and could not pass a simple engineering exam" has had on modern science.
And there is considerable experimental evidence for Einstein's General Relativity too:
            Experimental Tests of General Relativity, Slava G. Turyshev
So remind us again the impact your "Advanced Flat Earth Theory" has had on the world at large?

By the way your might compare your Sagnac calculations with these General relativistic Sagnac formula revised, Paolo Maraner · Jean-Pierre Zendri.

And please show us experimental verification of your claimed sun height of 12 to 20 km above the earth.

PS Have there been any recent reports of aircraft colliding with the sun?

Einstein’s most famous prediction, E = mc2

Einstein's report card:



6 is rock bottom

1 is top grade

German-5, French-3, Italian-5, History-6, Geography-4, Algebra-6, Geometry-6, Physics-6, Chemistry-5, Biology-5, Technical drawing and Art-4

In 1895, Einstein failed a simple entrance exam to an engineering school in Zurich.. This exam consisted mainly of elementary and basic mathematical problems, and Einstein showed himself to be mathematically inept in this exam.

While at the university, Paul Biefeld did Einstein's homework.

By the way, it was J.C. Maxwell who coined up the relation E=mc2:

http://gsjournal.net/Science-Journals/Research%20Papers-Mathematical%20Physics/Download/6371

Irrelevent. How about we see yours!

Which is more commonly known as the Sagnac effect formula. It is the formula you want.

Your lack of knowledge on the subject is astounding.

This is the CORIOLIS EFFECT formula:



However, this the CORIOLIS EFFECT formula for light beams.

Full derivation of the above formula using the CORIOLIS FORCE:

https://www.ias.ac.in/article/fulltext/pram/087/05/0071

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

Dr. Silberstein developed the formula published by A. Michelson using very precise details, not to be found anywhere else.

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.

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

Thus A. Michelson knew well in advance that he was going to actually measure the Coriolis effect and not the Sagnac effect.

But Michelson, a Nobel prize winner, claimed that the CORIOLIS EFFECT formula was the SAGNAC PHASE SHIFT formula, thus ensuring that for the next 90 years the RE would always win the debate on heliocentrism vs. geocentrism (not even the proponents of aether theory could not dismiss the MGX since they would have had to explain the fringe shifts measured by Michelson and by every ring laser interferometer since 1925).


Which means you subtract, not add.

This is Michelson's derivation where he listened to your advice and SUBSTRACTED the phase shifts:

Let us see what happens if you do substract them, just as A. Michelson did.

The original interferometer built by Michelson and Gale in Clearing, IL, measured 2010 ft x 1113 ft: the laser technology has permitted a great reduction in size of the interferometer to just a few meters.

This is the original paper published by Michelson and Gale in 1925:

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

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1925ApJ....61..140M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

Here is the derivation:






If you substract the phase shifts, you get the CORIOLIS EFFECT formula.

Is a completely different setup to the one you showed, and it uses angular velocity, not linear velocity.

Your readers are simply laughing at you.

Can you read basic English?

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 = 4π(V1L1 + V2L2)/λc


You provided a simple loop, without any phase conjugate mirror.

The phase conjugate mirror is an integral part of today's nonlinear optics, a subject matter which seems to be foreign to you.

Again, adding them equates to one beam of light going forward in both arms, and one going backwards in both arm.
Meanwhile in reality you have one beam go forward in one arm and backwards in the other, with the other beam going the other way. That requires subtracting the shifts from each arm.

Read Michelson's derivation again.

Can you read the formula provided by Michelson?

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.

The Coriolis effect means that the phase shift will be caused by the physical modification of the light paths (inflection and deflection due to the Coriolis force effect on the light beams).


l₁/(c - v₁) - l₂/(c - v₂) (we combine the terms which feature c - v_1,2)

(l₁c - l₁v₂ - l₂c + l₂v₁)/(c² - cv₂ - cv₁ +v₁v₂)

Factoring out c and observing that the terms l₁v₂/c, l₂v₁/c and v₁v₂/c can be neglected, we obtain:

(l₁ - l₂)/(c - v₂ - v₁)

Since l₁ ~= l₂, we can see that the velocity addition equations for the true Sagnac effect, c + v and c - v (in this case c + v₁ + v₂ and c - v₁ - v₂) are not applicable to the Coriolis effect situation.

The Coriolis effect is caused by the physical deflection/inflection of the light beams, not by the modification of the velocities.


Let us proceed now exactly as Professor Yeh did in the phase conjugate mirror experiment described above:

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

2[(l₁v₁ + l₂v₂)]/c²

Now, we have the correct, true Sagnac effect formula valid for an interferometer which is located away from the center of rotation.

Averaging (v₁ + v ₂)/2 = v, and (l₁ + l₂)/2 = l, v₁ ~= v₂ = v, l₁ ~= l₂ = l, we obtain:

4lv/c²

Moreover, we can see that now the velocity addition equations are valid:

(l₁ + l₂)/(c - v₂ - v₁)

To obtain the Coriolis effect phase shift, we substract the phase differences for each separate segment.

This formula is proportional to the area and the angular velocity.

To get the Sagnac effect phase shift, we have to add the phase differences for each separate segment

This formula is proportional to the linear velocity (and the radius of rotation), and will feature the addition of the two separate speeds and segment lengths. We can average the lengths and the velocities, to get a final formula which features one length and one velocity.

This is the great omission in the calculation done by A. Michelson.

Again, adding them equates to one beam of light going forward in both arms, and one going backwards in both arm.
Meanwhile in reality you have one beam go forward in one arm and backwards in the other, with the other beam going the other way. That requires subtracting the shifts from each arm.

Completely wrong.

Here are the initial phase shifts:

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

For each separate segment/arm of the interferometer, each with a slightly different length and a slightly distinct velocity, the calculations proceed as follows:

l₁/(c - v₁) - l₁/(c + v₁) = 2l₁v₁/c²

l₂/(c - v₂) - l₂/(c + v₂) = 2l₂v₂/c²

The phase differences have already been obtained.

By substracting these phase differences, one is actually going to derive the Coriolis effect formula:

https://www.ias.ac.in/article/fulltext/pram/087/05/0071

Spinning Earth and its Coriolis effect on the circuital light beams

Since the phase differences have already been calculated, one has to ADD them in order to get the final, total Sagnac effect:

2[(l₁v₁ + l₂v₂)]/c²

This fact has never been observed to the present day.

For a Sagnac interferometer, located away from the center of rotation, one has to ADD the separate phase differences in order to obtain the full Sagnac effect:

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


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.

Using your lack of reasoning you would end up with a sagnac shift for a circular loop rotating about the centre of 0.

Are you back to your old drinking habits?

Sagnac formula for an interferometer whose center of rotation coincides with its geometrical center:

Δt = l/(c - v) - l/(c + v)

Sagnac formula for an interferometer located away from the center of rotation (different radii, different velocities):

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

A beautiful generalization of the Sagnac formula for interferometers which are located away from the center of rotation.

Proven by Dr. Yeh's experiment.

Proof:

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

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)

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc

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


l₁/(c - v₁) + l₂/(c - v₂) = (l₁c - l₁v₂ + l₂c - l₂v₁)/(c² - cv₁ - cv₂ + v₁v₂)

l₁/(c + v₁) + l₂/(c + v₂) = (l₁c + l₁v₂ + l₂c + l₂v₁)/(c² + cv₁ + cv₂ + v₁v₂)

Since we have already added the correct Sagnac differences, corresponding to the (l₁ + l₂)/(c - v₁ - v₂) and (l₁ + l₂)/(c + v₁ + v₂) terms, now the final phase difference can be correctly derived:

(l₁c - l₁v₂ + l₂c - l₂v₁)/(c² - cv₁ - cv₂ + v₁v₂) - (l₁c + l₁v₂ + l₂c + l₂v₁)/(c² + cv₁ + cv₂ + v₁v₂) = 2[(l₁v₁ + l₂v₂)]/c²

The Coriolis effect formula by contrast is just the physical effect of the Coriolis force upon the light beams, a modification of the paths of the light beams leading to a final formula where the effect is directly proportional to the area and to the angular velocity.

The Sagnac effect is an electromagnetic effect, the modification of the velocities of the light beams, c + v₁ + v₂ and c - v₁ - v₂, leading to the final formula where the Sagnac effect is directly proportional to the linear velocity (radius of rotation x angular velocity) and the length of the segments of the interferometer.

In fact what do people find better? Posts in plain English, or posts that include hard to comprehend equations? Just wondering if people had a preference.

Conversation length posts are best.

A general rule of thumb is if someone needs to spin their scroll wheel more than 27 times to get past your post you are singing in the shower, going through the 10 items or less lane with two over stuffed shopping carts and paying with an out of state check and trying to impress yourself with your ability to assemble various Google searches into a single incoherent blog.

Anyone who actually knows what they are talking about can get it done in two paragraphs.

Has nothing to do with this topic

But it does, in a most direct way.

The fact that Einstein failed math and physics in high school and could not pass a simple engineering exam speaks volumes of the fact that someone else wrote his papers on relativity for him.

WHY DID YOU ADD THE 2 SHIFTS?

If you substract the shifts, you get the Coriolis effect formula.

What we want is the SAGNAC EFFECT FORMULA.

I have already explained in great detail the experimental proof provided here earlier, which you seem not to remember.

In order to obtain the GLOBAL SAGNAC EFFECT, you need to ADD the phase shifts.

EXPERIMENTAL PROOF

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)

Dr. P. Yeh
PhD, Caltech, Nonlinear Optics

Principal Scientist of the Optics Department at Rockwell International Science Center
Professor, UCSB

"Engineer of the Year," at Rockwell Science Center

Leonardo da Vinci Award in 1985

Fellow of the Optical Society of America, the Institute of Electrical and Electronics Engineers

The first phase-conjugate Sagnac experiment on a segment light path with an external pump configuration.



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.

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

To obtain the correct Sagnac effect for two separate segments (which feature different lengths and different speeds) of an interferometer which is located away from the center of rotation, one has to add (not substract) the two distinct components.


MATHEMATICAL/THEORETICAL PROOF



This is the global, generalized Sagnac effect formula.

Full derivation:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070591#msg2070591

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2070907#msg2070907

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.

Michelson proceeded with his calculations AS IF he had placed a rectangular interferometer with the dimensions of 2010 ft (612.65 m) by 1113 ft (339.24 m) with its center of rotation coinciding with the center of rotation of the Earth (radius of 6,376.164 km).

Once the interferometer is moved away from the center of rotation, the Coriolis effect will be measured first: the formula involves the substraction of the separate phase differences.

By contrast, the much greater Sagnac effect formula will be derived by adding the separate phase differences.

That means that the one beam of light needs to travel along the 2 segments in the direction of rotation, while the other travels against the direction of rotation. That is impossible.

You need to update your level of understanding of physics, which is quite poor given the caliber of your statement.



FOR A SAGNAC INTERFEROMETER WHICH FEATURES TWO DIFFERENT LENGTHS AND TWO DIFFERENT VELOCITIES YOU NEED TO ADD THE PHASE SHIFTS.

Experimentally proven by Dr. Yeh.

Published in the Journal of Optics Letters.

Confirmed by the US Naval Research Lab.

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.

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

To obtain the correct Sagnac effect for two separate segments (which feature different lengths and different speeds) of an interferometer which is located away from the center of rotation, one has to add (not substract) the two distinct components.

Another poorly constructed argument that starts with an irrelevent ad hominem. What we need to remover about Einstein is he produced some of the most relevant pieces of physics of the 20th century which have been ratified by countless experiments and demonstrated to be true by aspects of our modern world. Paul Dirac, you may of heard of him and your fond of name dropping, said General Relativity was quite possibly the greatest discovery ever made.
Stop doing the equation thing, it’s not a good way of presenting an argument. Use plain English.

Your lack of knowledge on the subject is astounding.
This is the CORIOLIS EFFECT formula:

I'm not the one lacking knowledge on it. You are the one blatantly lying about it.
That formula is the Sagnac effect formula.

Until you show a derivation, from scratch, for a simple ring interferometer, I will agree with my own derivation and that of others showing it is the correct formula.

[skipping your nonsense and looking for where you have addressed the question]

Nope, couldn't find it in that post, maybe your next one.
Still no justification for why you add, meaning the light beam travels along one segment with the rotation, and then magically teleports back to travel along the other segment again with the rotation.

So again, why do you add when the physical situation demands that you subtract?

Can you read basic English?

Yes, can you?
Notice how you switch to fibres, rather than a simple segment? Notice how it uses a PCM, rather than a simple ring?

Here are the initial phase shifts:

Like I said, provide a diagram clearly showing what each section is, because the shifts you calculate require one beam to go forwards along both arcs, which is not the physical reality of it.

You need to reverse one of your phase shifts due to the propagation of the light beams being reversed in the second segment. This leads to the correct Sagnac formula, equivalent to what you wish to pretend is only the Coriolis effect.

So again:
Stop just spouting garbage. Draw a diagram, clearly showing the light path and derive the shift directly from that, noting the time taken for each light beam, rather than trying to treat the 2 arms entirely separately.

Irrelevent.

Einstein FAILED mathematics and physics in high school.

He could not pass a basic engineering exam.

Someone else did his homework for him, while attending university.

Yet, you seem to trust this person when it comes to understanding the universe.

Here is what happens when you do that: a failure on A GRAND COSMIC SCALE.

DARK FLOW, the defiance of the general relativity on a cosmic scale:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1936995#msg1936995


Relativity has had a great impact on modern science and there is tremendous amount of supporting evidence

FAKE SPECIAL RELATIVITY TESTS:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg865008#msg865008

And there is considerable experimental evidence for Einstein's General Relativity too

TOTAL DEMOLITION OF GENERAL RELATIVITY: HOW EINSTEIN FAKED THE 1919/1922 SHIFT EXPERIMENTS AND HOW EINSTEIN FUDGED THE MERCURY PERIHELION EQUATION:

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

By the way your might compare your Sagnac calculations with these General relativistic Sagnac formula revised, Paolo Maraner · Jean-Pierre Zendri

Their result is still the Coriolis effect formula:

4AΩ/c^2

You are embarrassing yourself beyond redemption.

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.

And please show us experimental verification of your claimed sun height of 12 to 20 km above the earth.

ABSOLUTE PROOF THAT THE SHAPE OF THE SUN CANNOT BE SPHERICAL AT ALL:

"The atmospheric pressure of the sun, instead of being 27.47 times greater than the atmospheric pressure of the earth (as expected because of the gravitational pull of the large solar mass), is much smaller: the pressure there varies according to the layers of the atmosphere from one-tenth to one-thousandth of the barometric pressure on the earth; at the base of the reversing layer the pressure is 0.005 of the atmospheric pressure at sea level on the earth; in the sunspots, the pressure drops to one ten-thousandth of the pressure on the earth.

The pressure of light is sometimes referred to as to explain the low atmospheric pressure on the sun. At the surface of the sun, the pressure of light must be 2.75 milligrams per square centimeter; a cubic centimeter of one gram weight at the surface of the earth would weigh 27.47 grams at the surface of the sun."



Thus the attraction by the solar mass is 10,000 times greater than the repulsion of the solar light. Recourse is taken to the supposition that if the pull and the pressure are calculated for very small masses, the pressure exceeds the pull, one acting in proportion to the surface, the other in proportion to the volume. But if this is so, why is the lowest pressure of the solar atmosphere observed over the sunspots where the light pressure is least?

Because of its swift rotation, the gaseous sun should have the latitudinal axis greater than the longitudinal, but it does not have it. The sun is one million times larger than the earth, and its day is but twenty-six times longer than the terrestrial day; the swiftness of its rotation at its equator is over 125 km. per minute; at the poles, the velocity approaches zero. Yet the solar disk is not oval but round: the majority of observers even find a small excess in the longitudinal axis of the sun. The planets act in the same manner as the rotation of the sun, imposing a latitudinal pull on the luminary.

Gravitation that acts in all directions equally leaves unexplained the spherical shape of the sun. As we saw in the preceding section, the gases of the solar atmosphere are not under a strong pressure, but under a very weak one. Therefore, the computation, according to which the ellipsoidity of the sun, that is lacking, should be slight, is not correct either. Since the gases are under a very low gravitational pressure, the centrifugal force of rotation must have formed quite a flat sun.

If planets and satellites were once molten masses, as cosmological theories assume, they would not have been able to obtain a spherical form, especially those which do not rotate, as Mercury or the moon (with respect to its primary)."


The Sun exhibits a variety of phenomena that defy contemporary theoretical understanding.

Eugene N. Parker


It is not coincidence that the photosphere has the appearance, the temperature and spectrum of an electric arc; it has arc characteristics because it an electric arc, or a large number of arcs in parallel.

British physicist C. E. R. Bruce


It is likely that the problem of the dynamics of the explosions affecting the prominences will only be solved when the electrical conditions obtaining in the chromosphere and inner corona are better understood.

Italian solar astronomer Giorgio Abetti


Observations give a wealth of detail about the photosphere, chromosphere and the corona. Yet we have difficulty in matching the observations with a theory.

Solar Interior & Atmosphere, J.-C. Pecker


The modern astrophysical concept that ascribes the sun’s energy to thermonuclear reactions deep in the solar interior is contradicted by nearly every observable aspect of the sun.

Ralph E. Juergens




PRESSURE: 10^-13 BAR = 0.0000000000001 BAR

The entire chromosphere will then be subjected to the full centrifugal force of rotation, as will the photosphere itself of course.

Completely unexplained by modern science.

Since the gases are under a very low gravitational pressure, the centrifugal force of rotation must have formed quite a flat sun.

NO further recourse can be made for gravity.

Gravity has already balanced out as much as was possible of the gaseous pressure, and still we are left with A VERY LOW PRESSURE.

Solar gravity has balanced out the thermal pressure.

At this point in time the sun will turn into A HUGE GAS CENTRIFUGE WITH NO OUTER CASING, running at some 1,900 m/s.

That is, the solar gases in the photosphere and cromosphere are just standing there, with no explanation by modern science whatsoever.

As if this wasn't enough, we have the huge centrifugal force factor that is exerted each and every second on the photosphere and the cromosphere.

The centrifugal force would cause the sun to collapse into a disk in no time at all.


"However, the gravity is opposed by the internal pressure of the stellar gas which normally results from heat produced by nuclear reactions. This balance between the forces of gravity and the pressure forces is called hydrostatic equilibrium, and the balance must be exact or the star will quickly respond by expanding or contracting in size. So powerful are the separate forces of gravity and pressure that should such an imbalance occur in the sun, it would be resolved within half an hour."


Then, the heliocentrists have to deal with the Nelson effect:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1645824#msg1645824 (the Nelson effect of all the other planets, pulling constantly on the sun's atmosphere, acting permanently, are added to the centrifugal force)

Recourse can be made to the Clayton model equation or even the Lane-Emden equation in order to show that the value for g (computed using the 10^-13 bar value in the chromosphere) is much smaller than the centrifugal acceleration.

The Clayton model provides us with the g value: g = 0,0000507 m/s^2 which is much lower than the centrifugal acceleration figure:

P(r) = 2πgr²a²ρ²_ce^-x2/3M

where a = (3^1/2M/2^1/24πρ_c)^1/3

a = 106,165,932.3

x = r/a

M = 1.989 x 10³⁰ kg
central density = 1.62 x 10⁵ kg/m³

G = gr²/m(r)

m(r) = M(r/R)³(4 - 3r/R); if r = R, then M = m(r)

Using P(700,000,000) = 1.0197 x 10^-9 kg/m² value, we get:


g = 0,0000507 m/s²


RATIO


a_c/g = 0.0063/0.0000507 = 124.26


Accuracy of the Clayton model:






And you are going to have to explain the radius of the sun paradox, the fact that the Sun has a distinct surface:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2075989#msg2075989 (part I)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2090897#msg2090897 (part II)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2093726#msg2093726 (part III)

That formula is the Sagnac effect formula.

But it is not.

Please read.

Your lack of knowledge on the subject is astounding.

This is the CORIOLIS EFFECT formula:



However, this the CORIOLIS EFFECT formula for light beams.

Full derivation of the above formula using the CORIOLIS FORCE:

https://www.ias.ac.in/article/fulltext/pram/087/05/0071

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

Dr. Silberstein developed the formula published by A. Michelson using very precise details, not to be found anywhere else.

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.

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

Thus A. Michelson knew well in advance that he was going to actually measure the Coriolis effect and not the Sagnac effect.

But Michelson, a Nobel prize winner, claimed that the CORIOLIS EFFECT formula was the SAGNAC PHASE SHIFT formula, thus ensuring that for the next 90 years the RE would always win the debate on heliocentrism vs. geocentrism (not even the proponents of aether theory could not dismiss the MGX since they would have had to explain the fringe shifts measured by Michelson and by every ring laser interferometer since 1925).


Notice how you switch to fibres, rather than a simple segment? Notice how it uses a PCM, rather than a simple ring?

People are laughing at you.

The phase-conjugate mirror is an integral of nonlinear optics.

It has provided breakthroughs which were unimaginable 100 years ago.

Phase Conjugate Mirror

"Let us begin with the properties of a phase conjugate mirror. A phase conjugate mirror is like a mirror, in that it reflects incident light back towards where it came from, but it does so in a different way than a regular mirror.

In a regular mirror, light that strikes the mirror normal to its surface, is reflected straight back the way it came (A). This is also true of a phase conjugate mirror (B). When the light strikes a normal mirror at an angle, it reflects back in the opposite direction, such that the angle of incidence is equal to the angle of reflection. (C)



In a phase conjugate mirror, on the other hand, light is always reflected straight back the way it came from, no matter what the angle of incidence. (D)

This difference in the manner of reflection has significant consequences. For example if we place an irregular distorting glass in the path of a beam of light, the parallel rays get bent in random directions, and after reflection from a normal mirror, each ray of light is bent even farther, and the beam is scattered.



With a phase conjugate mirror, on the other hand, each ray is reflected back in the direction it came from. This reflected conjugate wave therefore propagates backwards through the distorting medium, and essentially "un-does" the distortion, and returns to a coherent beam of parallel rays travelling in the opposite direction."



Steven Lehar


http://www.physics.iitm.ac.in/~cvijayan/opc-review.pdf

Optical phase conjugation: principles, techniques, and applications

Over the last three decades, optical phase conjugation (OPC) has been one of the major
research subjects in the field of nonlinear optics and quantum electronics.

Optical phase conjugation (OPC)1 is a new laser-based technique developed since
1970s. As this technique is feasible for use in many significant applications, the study
of OPC has become one of the most active research subjects in the areas of nonlinear
optics and quantum electronics.

In the area of OPC-related studies, a huge number (more than thousands) of
research papers and conference presentations have been published since 1970s.


So again, why do you add when the physical situation demands that you subtract?

Because if you substract you are going to get the Coriolis effect.

If you add the phase shifts, you get the Sagnac effect.

Nope, couldn't find it in that post, maybe your next one.
Still no justification for why you add, meaning the light beam travels along one segment with the rotation, and then magically teleports back to travel along the other segment again with the rotation.

EXPERIMENTAL PROOF (right from scratch, as required by the RE):

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)

Dr. P. Yeh
PhD, Caltech, Nonlinear Optics

Principal Scientist of the Optics Department at Rockwell International Science Center
Professor, UCSB

"Engineer of the Year," at Rockwell Science Center

Leonardo da Vinci Award in 1985

Fellow of the Optical Society of America, the Institute of Electrical and Electronics Engineers

The first phase-conjugate Sagnac experiment on a segment light path with an external pump configuration.



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.

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


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

The very same formula derived by me:

Δt = (l₁ + l₂)/(c - v₁ - v₂) - (l₁ + l₂)/(c + v₁ + v₂) = 2[(l₁v₁ + l₂v₂)]/c²


To obtain the correct Sagnac effect for two separate segments (which feature different lengths and different speeds) of an interferometer which is located away from the center of rotation, one has to add (not substract) the two distinct components.


FULL JUSTIFICATION FOR THE ADDITION OF THE PHASE SHIFTS HAS JUST BEEN GIVEN.


MATHEMATICAL/THEORETICAL PROOF

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 = 4π(V1L1 + V2L2)/λc


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.

The Coriolis effect means that the phase shift will be caused by the physical modification of the light paths (inflection and deflection due to the Coriolis force effect on the light beams).


l₁/(c - v₁) - l₂/(c - v₂) (we combine the terms which feature c - v_1,2)

(l₁c - l₁v₂ - l₂c + l₂v₁)/(c² - cv₂ - cv₁ +v₁v₂)

Factoring out c and observing that the terms l₁v₂/c, l₂v₁/c and v₁v₂/c can be neglected, we obtain:

(l₁ - l₂)/(c - v₂ - v₁)

Since l₁ ~= l₂, we can see that the velocity addition equations for the true Sagnac effect, c + v and c - v (in this case c + v₁ + v₂ and c - v₁ - v₂) are not applicable to the Coriolis effect situation.

The Coriolis effect is caused by the physical deflection/inflection of the light beams, not by the modification of the velocities.


Let us proceed now exactly as Professor Yeh did in the phase conjugate mirror experiment described above:

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

2[(l₁v₁ + l₂v₂)]/c²

Now, we have the correct, true Sagnac effect formula valid for an interferometer which is located away from the center of rotation.

Averaging (v₁ + v ₂)/2 = v, and (l₁ + l₂)/2 = l, v₁ ~= v₂ = v, l₁ ~= l₂ = l, we obtain:

4lv/c²

Moreover, we can see that now the velocity addition equations are valid:

(l₁ + l₂)/(c - v₂ - v₁)

To obtain the Coriolis effect phase shift, we substract the phase differences for each separate segment.

This formula is proportional to the area and the angular velocity.

To get the Sagnac effect phase shift, we have to add the phase differences for each separate segment

This formula is proportional to the linear velocity (and the radius of rotation), and will feature the addition of the two separate speeds and segment lengths. We can average the lengths and the velocities, to get a final formula which features one length and one velocity.

This is the great omission in the calculation done by A. Michelson.

Here are the initial phase shifts:

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

For each separate segment/arm of the interferometer, each with a slightly different length and a slightly distinct velocity, the calculations proceed as follows:

l₁/(c - v₁) - l₁/(c + v₁) = 2l₁v₁/c²

l₂/(c - v₂) - l₂/(c + v₂) = 2l₂v₂/c²

The phase differences have already been obtained.

By substracting these phase differences, one is actually going to derive the Coriolis effect formula:

https://www.ias.ac.in/article/fulltext/pram/087/05/0071

Spinning Earth and its Coriolis effect on the circuital light beams

Since the phase differences have already been calculated, one has to ADD them in order to get the final, total Sagnac effect:

2[(l₁v₁ + l₂v₂)]/c²

This fact has never been observed to the present day.

For a Sagnac interferometer, located away from the center of rotation, one has to ADD the separate phase differences in order to obtain the full Sagnac effect:

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


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.


Sagnac formula for an interferometer whose center of rotation coincides with its geometrical center:

Δt = l/(c - v) - l/(c + v)

Sagnac formula for an interferometer located away from the center of rotation (different radii, different velocities):

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

A beautiful generalization of the Sagnac formula for interferometers which are located away from the center of rotation.

Proven by Dr. Yeh's experiment.

Proof:

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

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)

φ = -2(φ₂ - φ₁) = 4π(R₁L₁ + R₂L₂)Ω/λc

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


l₁/(c - v₁) + l₂/(c - v₂) = (l₁c - l₁v₂ + l₂c - l₂v₁)/(c² - cv₁ - cv₂ + v₁v₂)

l₁/(c + v₁) + l₂/(c + v₂) = (l₁c + l₁v₂ + l₂c + l₂v₁)/(c² + cv₁ + cv₂ + v₁v₂)

Since we have already added the correct Sagnac differences, corresponding to the (l₁ + l₂)/(c - v₁ - v₂) and (l₁ + l₂)/(c + v₁ + v₂) terms, now the final phase difference can be correctly derived:

(l₁c - l₁v₂ + l₂c - l₂v₁)/(c² - cv₁ - cv₂ + v₁v₂) - (l₁c + l₁v₂ + l₂c + l₂v₁)/(c² + cv₁ + cv₂ + v₁v₂) = 2[(l₁v₁ + l₂v₂)]/c²

The Coriolis effect formula by contrast is just the physical effect of the Coriolis force upon the light beams, a modification of the paths of the light beams leading to a final formula where the effect is directly proportional to the area and to the angular velocity.

The Sagnac effect is an electromagnetic effect, the modification of the velocities of the light beams, c + v₁ + v₂ and c - v₁ - v₂, leading to the final formula where the Sagnac effect is directly proportional to the linear velocity (radius of rotation x angular velocity) and the length of the segments of the interferometer.

Irrelevent.
Einstein FAILED mathematics and physics in high school.

Totally incorrect, Mr Sandokhan! You fail, as usual!

Read:

Rare Historical Photos, Albert Einstein’s matriculation certificate, 1896

Albert Einstein’s matriculation certificate, aged 17, 1896. It’s a myth that Einstein was bad at math.

This puts to rest that urban legend that Einstein was a “bad student”, although he received a three in French. He did, apparently, receive straight sixes in algebra, geometry, physics, and – history! Young Einstein knew what was important, it seems. Perhaps the legend is founded in the fact that the Swiss school system has a 6 as best grade, and 1 as poorest, while the German is the other way round. In his certificate of qualification for university matriculation the lessons which he was less interested in can easily be detected. But the average grade in his certificate was a 5, i.e. the grade “good”.

From: Rare Historical Photos, Albert Einstein’s matriculation certificate, 1896.

Read this again, " He did, apparently, receive straight sixes in algebra, geometry, physics, and – history" and a siz in Switzerland was the highest possible grade!

Please do your homework properly Mr Sandokhan!

By the way
    The dimensions of a sacred cubit are simply length and 2/π is dimensionless so it is quite invalid to equate them!
    The dimensions of g are length/time² and again π² so again is dimensionless so it is quite invalid to equate them!

    Any comments on another of your horrendous and far-reaching blunders.

This page is worthy of downloading, so i am going to do it right now...
Thanks Sanodkhan!

Irrelevent.

Einstein FAILED mathematics and physics in high school.

He could not pass a basic engineering exam.

Someone else did his homework for him, while attending university.

Yet, you seem to trust this person when it comes to understanding the universe.

Here is what happens when you do that: a failure on A GRAND COSMIC SCALE.

DARK FLOW, the defiance of the general relativity on a cosmic scale:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1936995#msg1936995


Relativity has had a great impact on modern science and there is tremendous amount of supporting evidence

FAKE SPECIAL RELATIVITY TESTS:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg865008#msg865008

And there is considerable experimental evidence for Einstein's General Relativity too

TOTAL DEMOLITION OF GENERAL RELATIVITY: HOW EINSTEIN FAKED THE 1919/1922 SHIFT EXPERIMENTS AND HOW EINSTEIN FUDGED THE MERCURY PERIHELION EQUATION:

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

By the way your might compare your Sagnac calculations with these General relativistic Sagnac formula revised, Paolo Maraner · Jean-Pierre Zendri

Their result is still the Coriolis effect formula:

4AΩ/c^2

You are embarrassing yourself beyond redemption.

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.

And please show us experimental verification of your claimed sun height of 12 to 20 km above the earth.

ABSOLUTE PROOF THAT THE SHAPE OF THE SUN CANNOT BE SPHERICAL AT ALL:

"The atmospheric pressure of the sun, instead of being 27.47 times greater than the atmospheric pressure of the earth (as expected because of the gravitational pull of the large solar mass), is much smaller: candy o i need you sunday dress ruby rings candy o i need you so could you help me in purple hum, assorted cards razor lights, you bring and all to prove you're on the move and vanishing candy o i need you so candy o i need you so the edge of night distract yourself obstacles don't work homogenize, decentralize it's just a quirk different ways to see you through all the same in the end peculiar star that's who you are do you have to win  the pressure there varies according to the layers of the atmosphere from one-tenth to one-thousandth of the barometric pressure on the earth; at the base of the reversing layer the pressure is 0.005 of the atmospheric pressure at sea level on the earth; in the sunspots, the pressure drops to one ten-thousandth of the pressure on the earth.

The pressure of light is sometimes referred to as to explain the low atmospheric pressure on the sun. At the surface of the sun, the pressure of light must be 2.75 milligrams per square centimeter; a cubic centimeter of one gram weight at the surface of the earth would weigh 27.47 grams at the surface of the sun."



Thus the attraction by the solar mass is 10,000 times greater than the repulsion of the solar light. Recourse is taken to the supposition that if the pull and the pressure are calculated for very small masses, the pressure exceeds the pull, one acting in proportion to the surface, the other in proportion to the volume. But if this is so, why is the lowest pressure of the solar atmosphere observed over the sunspots where the light pressure is least?

Because of its swift rotation, the gaseous sun should have the latitudinal axis greater than the longitudinal, but it does not have it. The sun is one million times larger than the earth, and its day is but twenty-six times longer than the terrestrial day; the swiftness of its rotation at its equator is over 125 km. per minute; at the poles, the velocity approaches zero. Yet the solar disk is not oval but round: the majority of observers even find a small excess in the longitudinal axis of the sun. The planets act in the same manner as the rotation of the sun, imposing a latitudinal pull on the luminary.

Gravitation that acts in all directions equally leaves unexplained the spherical shape of the sun. As we saw in the preceding section, the gases of the solar atmosphere are not under a strong pressure, but under a very weak one. candy o i need you sunday dress ruby rings candy o i need you so could you help me in purple hum, assorted cards razor lights, you bring and all to prove you're on the move and vanishing candy o i need you so candy o i need you so the edge of night distract yourself obstacles don't work homogenize, decentralize it's just a quirk different ways to see you through all the same in the end peculiar star that's who you are do you have to win  Therefore, the computation, according to which the ellipsoidity of the sun, that is lacking, should be slight, is not correct either. Since the gases are under a very low gravitational pressure, the centrifugal force of rotation must have formed quite a flat sun.

If planets and satellites were once molten masses, as cosmological theories assume, they would not have been able to obtain a spherical form, especially those which do not rotate, as Mercury or the moon (with respect to its primary)."


The Sun exhibits a variety of phenomena that defy contemporary theoretical understanding.

Eugene N. Parker


It is not coincidence that the photosphere has the appearance, the temperature and spectrum of an electric arc; it has arc characteristics because it an electric arc, or a large number of arcs in parallel.

British physicist C. E. R. Bruce


It is likely that the problem of the dynamics of the explosions affecting the prominences will only be solved when the electrical conditions obtaining in the chromosphere and inner corona are better understood.

Italian solar astronomer Giorgio Abetti


Observations give a wealth of detail about the photosphere, chromosphere and the corona. Yet we have difficulty in matching the observations with a theory.

Solar Interior & Atmosphere, J.-C. Pecker


The modern astrophysical concept that ascribes the sun’s energy to thermonuclear reactions deep in the solar interior is contradicted by nearly every observable aspect of the sun.

Ralph E. Juergens




PRESSURE: 10^-13 BAR = 0.0000000000001 BAR

The entire chromosphere will then be subjected to the full centrifugal force of rotation, as will the photosphere itself of course.

Completely unexplained by modern science.

Since the gases are under a very low gravitational pressure, the centrifugal force of rotation must have formed quite a flat sun.

NO further recourse can be made for gravity.

Gravity has already balanced out as much as was possible of the gaseous pressure, and still we are left with A VERY LOW PRESSURE.

Solar gravity has balanced out the thermal pressure.

At this point in time the sun will turn into A HUGE GAS CENTRIFUGE WITH NO OUTER CASING, running at some 1,900 m/s.

That is, the solar gases in the photosphere and cromosphere are just standing there, with no explanation by modern science whatsoever.

As if this wasn't enough, we have the huge centrifugal force factor that is exerted each and every second on the photosphere and the cromosphere.

The centrifugal force would cause the sun to collapse into a disk in no time at all.


"However, the gravity is opposed by the internal pressure of the stellar gas which normally results from heat produced by nuclear reactions. candy o i need you sunday dress ruby rings candy o i need you so could you help me in purple hum, assorted cards razor lights, you bring and all to prove you're on the move and vanishing candy o i need you so candy o i need you so the edge of night distract yourself obstacles don't work homogenize, decentralize it's just a quirk different ways to see you through all the same in the end peculiar star that's who you are do you have to win  This balance between the forces of gravity and the pressure forces is called hydrostatic equilibrium, and the balance must be exact or the star will quickly respond by expanding or contracting in size. So powerful are the separate forces of gravity and pressure that should such an imbalance occur in the sun, it would be resolved within half an hour."


Then, the heliocentrists have to deal with the Nelson effect:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1645824#msg1645824 (the Nelson effect of all the other planets, pulling constantly on the sun's atmosphere, acting permanently, are added to the centrifugal force)

Recourse can be made to the Clayton model equation or even the Lane-Emden equation in order to show that the value for g (computed using the 10^-13 bar value in the chromosphere) is much smaller than the centrifugal acceleration.

The Clayton model provides us with the g value: g = 0,0000507 m/s^2 which is much lower than the centrifugal acceleration figure:

P(r) = 2πgr²a²ρ²_ce^-x2/3M

where a = (3^1/2M/2^1/24πρ_c)^1/3

a = 106,165,932.3

x = r/a

M = 1.989 x 10³⁰ kg
central density = 1.62 x 10⁵ kg/m³

G = gr²/m(r)

m(r) = M(r/R)³(4 - 3r/R); if r = R, then M = m(r)

Using P(700,000,000) = 1.0197 x 10^-9 kg/m² value, we get:


g = 0,0000507 m/s²


RATIO


a_c/g = 0.0063/0.0000507 = 124.26


Accuracy of the Clayton model:






And you are going to have to explain the radius of the sun paradox, the fact that the Sun has a distinct surface:

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2075989#msg2075989 (part I)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2090897#msg2090897 (part II)

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg2093726#msg2093726 (part III)