[SteelyBob]

He already showed you the assumptions and arithmetic required to arrive at Δt=8ωA/c^2. If you disagree with any of the steps, you'll have to pinpoint them

Is my post not pinpoint enough? If the one term doesn't equal the other, then what follows or precedes it can't be right either, can it? Or am I missing something?

[sandokhan]

I'm curious as to how Sandokhan got to the formula

I have already the provided the link for the derivation of the formula.

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

there's clearly some fairly significant errors along the way

You won't find any. It is a very straightforward derivation.

That looks fundamentally wrong to me - the simplification on the right isn't equal to the term on left. Thoughts?

Work out the term on the left, pretty tedious algebra, and you will arrive at the term on the right.

You also have the classic example from the very simple situation where the center of rotation coincides with the geometrical center:



The formula is correct. What you have to deal with now, are the consequences.

[Pete Svarrior]

For the case of v1=v2, the algebra isn't even particularly tedious.

[sandokhan]

My formula was also obtained by Professor P. Yeh in 1985, using phase-conjugate mirrors:

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

Studies of phase-conjugate optical devices concepts

US OF NAVAL RESEARCH, Physics Division

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



page 152 of the pdf document, section Recent Advances in Photorefractive Nonlinear Optics page 4

The MPPC acts like a normal mirror and Sagnac interferometry is obtained.



Phase-Conjugate Multimode Fiber Gyro

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

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


A second confirmation of the fact that my formula is correct.

Here is the first confirmation:



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)


Exactly the formula obtained by Professor Yeh:

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

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

CORRECT SAGNAC FORMULA:

2(V₁L₁ + V₂L₂)/c²

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


What I did is to derive the formula in the context of the Michelson-Gale experiment and also for ring laser gyroscopes. It is by far the biggest contribution to the field of light interferometry since 1913 when G. Sagnac conducted the first such experiment under strict conditions.

[SteelyBob]

I'm curious as to how Sandokhan got to the formula

I have already the provided the link for the derivation of the formula.

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

there's clearly some fairly significant errors along the way

You won't find any. It is a very straightforward derivation.

That looks fundamentally wrong to me - the simplification on the right isn't equal to the term on left. Thoughts?

Work out the term on the left, pretty tedious algebra, and you will arrive at the term on the right.

You also have the classic example from the very simple situation where the center of rotation coincides with the geometrical center:



The formula is correct. What you have to deal with now, are the consequences.

From your link:



Keep it simple and just look at the first formula - it's just not correct. l/(c-v) - l/(c+v) does not equal 2lv/c²

It's easy to prove by plugging in some numbers - say l=1, c=3 and v=2.

The left hand side would give you 1/(3-2) - 1/(3+2) = 1 - 1/5 = 4/5

The right hand side would give you 2 x 1 x 2 / 3² = 4/9

Always happy to proven wrong, but that doesn't look right to me.

[sandokhan]

No.

c is a fixed constant, O(3x10⁵km/hr).

v is either O(1) or O(30km/hr).

That is, c>>v.

[SteelyBob]

No.

c is a fixed constant, O(3x10⁵km/hr).

v is either O(1) or O(30km/hr).

That is, c>>v.

Ah, thank you - I see what you did now.

[Tom Bishop]

Recall that the device was described as an 'underground seismic observatory'.

The 'rotation of the earth' affects seismic waves:

https://gfzpublic.gfz-potsdam.de/rest/items/item_5005107_3/component/file_5005141/content

SUMMARY

Rotation of the Earth affects the propagation of seismic waves. The global coupling of spheroidal and toroidal modes by the Coriolis force over time is described by normal-mode theory. The local action of the Coriolis force on the propagation of surface waves can be described by coefficients for the coupling between propagating Rayleigh and Love waves as derived by Snieder & Sens-Schonfelder.

....

The rotation of Earth as propagation medium exerts an additional force on moving matter—the Coriolis force. Depending on the angle of the polarization vectors of P and S waves with Earth’s rotation axis, the Coriolis force causes a small transverse component for P waves and a small longitudinal component for S waves. Moreover the Coriolis force causes a slow rotation of the shear wave polarization vector akin to the motion of a Foucault pendulum (Snieder et al. 2016b,a).

The Coriolis force 'causes a slow rotation' and the effect is compared to watching a rotating Foucault Pendulum. In the Foucault Pendulum we allegedly watch the pendulum rotate, not the earth. So the device is observing rotating seismic waves and we are assuming that it is the earth rotating and that the movement isn't coming from the seismic waves rotating, like many other things rotate above us diurnally.

[SteelyBob]

Recall that the device was described as an 'underground seismic observatory'.

The 'rotation of the earth' affects seismic waves:

https://gfzpublic.gfz-potsdam.de/rest/items/item_5005107_3/component/file_5005141/content

SUMMARY

Rotation of the Earth affects the propagation of seismic waves. The global coupling of spheroidal and toroidal modes by the Coriolis force over time is described by normal-mode theory. The local action of the Coriolis force on the propagation of surface waves can be described by coefficients for the coupling between propagating Rayleigh and Love waves as derived by Snieder & Sens-Schonfelder.

....

The rotation of Earth as propagation medium exerts an additional force on moving matter—the Coriolis force. Depending on the angle of the polarization vectors of P and S waves with Earth’s rotation axis, the Coriolis force causes a small transverse component for P waves and a small longitudinal component for S waves. Moreover the Coriolis force causes a slow rotation of the shear wave polarization vector akin to the motion of a Foucault pendulum (Snieder et al. 2016b,a).

The Coriolis force 'causes a slow rotation' and the effect is compared to watching a rotating Foucault Pendulum. In the Foucault Pendulum we allegedly watch the pendulum rotate, not the earth. So the device is observing rotating seismic waves and we are assuming that it is the earth rotating and that the movement isn't coming from the seismic waves rotating, like many other things rotate above us diurnally.

I'm not really clear what you're suggesting - are you saying that Coriolis is, or isn't a real effect?

It's not really clear what your point is - seismic observations are a major reason why people keep building ever more precise RLGs. They are also interested in slight variations in the earth's rotational axis, amongst other things. But seismic activity manifests as oscillatory motion, whereas as constant rotation is just that - constant rotation. See that graph again:



The earth rate is the constant line, whereas the seismic activity is the oscillatory signal superimposed on it. If not was just seismic activity, the oscillation would be around zero.

[Tom Bishop]

It says that the seismic waves are rotating, like a Foucault Pendulum:

https://inside.mines.edu/~rsnieder/Snieder16Fouc.pdf

Earth’s rotation leads to a slow rotation of the transverse polarization of S waves; during the propagation of S waves the particle motion behaves just like a Foucault pendulum.

The device is watching something rotate, and it is assumed to be caused by the rotation of the earth.

[stack]

It says that the seismic waves are rotating, like a Foucault Pendulum:

https://inside.mines.edu/~rsnieder/Snieder16Fouc.pdf

Earth’s rotation leads to a slow rotation of the transverse polarization of S waves; during the propagation of S waves the particle motion behaves just like a Foucault pendulum.

The device is watching something rotate, and it is assumed to be caused by the rotation of the earth.

The paper referenced  says, "But we know that Earth’s rotation affects Earth’s normal modes [Backus and Gilbert, 1961] and surface waves [Tromp, 1994]. This raises the question: what is the exact imprint of Earth’s rotation on seismic body wave propagation?"

So yes, they are studying Earth’s rotation impact on these waves. What of it?

[Tom Bishop]

The problem is that this is an indirect conclusion, rather than a direct one. If you are floating in a featureless environment in outer space and see an object travel past you at a set speed, you generally could not know whether it is you who was moving or whether it was the object that was moving.

[stack]

The problem is that this is an indirect conclusion, rather than a direct one. If you are floating in a featureless environment in outer space and see an object travel past you at a set speed, you generally could not know whether it is you who was moving or whether it was the object that was moving.

What indirect conclusion?

And who or what is floating in a featureless environment in outer space? We’re talking about earths rotation impacting seismic waves and such, here on earth, not in space. And rlg’s & pendulums and stuff here on or just above earth. What does featureless space have to do with this?

[Tom Bishop]

It has everything to do with it. Look into relative motion. If you are watching something move, you can't tell whether it is you and perhaps your environment that is moving or whether it is the body is moving. This is extremely basic and and I am surprised that you are having trouble understanding this.

[RonJ]

Your referenced article debunks your 'relative motion' statement right from the start.  Scientists that study any seismic activity know that this is a very intermittent phenomenon. The very steady baseline rotation rate on the graph isn’t related to seismic activity at all, it’s the measured rotation of the earth.  You can see that there’s a deviation of the rate both above and below the steady baseline.  The sheer mass of the earth would preclude any sudden changes of the rotation rate like that.  You can take a gyroscope and put it on an airplane, and it will still be influenced by the earth’s rotation but couldn’t be influenced by any seismic activity.

[SteelyBob]

It says that the seismic waves are rotating, like a Foucault Pendulum:

https://inside.mines.edu/~rsnieder/Snieder16Fouc.pdf

Earth’s rotation leads to a slow rotation of the transverse polarization of S waves; during the propagation of S waves the particle motion behaves just like a Foucault pendulum.

The device is watching something rotate, and it is assumed to be caused by the rotation of the earth.

You've completely changed your position from the start of our discussion here. I'm curious as to whether you've changed your mind - in which case will you change the wiki to reflect this? - or whether you are just adapting your default 'disagree' position to suit what's in front of you. At the start, your argument was all about the noise levels in the rotation graphs. Then, as you realised that, in fact, a lot of the sources you yourself presented did in fact have very accurate, low noise graphs in them, you've pivoted to an argument based on the fact that the gyros are in fact measuring something other than rotation, even though that is precisely what there are designed to do.

Could you very carefully and precisely explain what exactly you think is going on in this graph please?



We have some very obvious seismic activity - clearly oscillatory in nature, superimposed on a flat line that is bang on the generally agreed earth rotation rate. Are you arguing that the flat line is also some kind of seismic activity? And that this activity is somehow a constant, steady state rotation, whose magnitude varies with the sine of the latitude? So it is magically zero on a circle around the monopole North Pole that we call the equator but whose significance is what, precisely, on a flat earth? 

[Tom Bishop]

Actually, the Wiki page accurately says that those types of devices are looking at rotational seismic phenomena right here - https://wiki.tfes.org/Ring_Laser_Gyroscope_-_Seismology

Not sure why you keep reposting that graph. It's not raw data. As you pointed out earlier, the angular rate on that one is faster other graphs we saw which are uncorrected for latitude and this data is reprocessed and visualized. Other visualizations we saw in this thread have radically different views.

GINGERino is not a regular seismograph, it is a special tool which studies "rotational seismology" -

https://physicsworld.com/a/ring-laser-reveals-subtle-seismic-motion/

Seismic shift: GINGERino is deep below these mountains

A laser gyroscope located deep beneath the Gran Sasso mountain in central Italy has made the first deep-underground measurements of the rotational motion that passing seismic waves generate in the Earth’s crust. The ability to make such measurements could boost our understanding of the strain that rocks undergo before an earthquake takes place, say the scientists who carried out the research.

Earthquakes release large amounts of pent-up energy in the form of seismic waves, which propagate in all directions from the quake’s epicentre. When those waves reach the Earth’s surface they can cause the ground to move along one or more orthogonal axes – up and down, back and forth, and side to side. But seismic waves can also generate much smaller rotational motions, in which the ground rotates around one or more of the three axes.

According to Gilberto Saccorotti of Italy’s National Institute for Geophysics and Volcanology (INGV), rotational motion is important to measure for a number of reasons. For one thing, seismologists can determine the speed of a seismic wave – and so better understand the kind of rock it propagates through – by comparing the magnitudes of the rotational and translational motions that it generates. In addition, better measurements of ground rotation during strong earthquakes would allow for more robust building regulations. “Circular motion, like horizontal motion, can be very dangerous,” he says. “Structures haven’t been designed with that in mind but are instead meant to resist vertical forces, i.e. their own weight.”

Frequency shift

Ring-laser gyroscopes, on the other hand, are designed specifically to measure rotational motion. These devices record the very tiny differences in frequency between two laser beams sent in opposites directions around an optical circuit that is fixed rigidly to the ground. The frequency offset reflects the rate at which the ground rotates. Ring lasers in Germany, New Zealand and the US have been detecting earthquakes’ rotational ground movements for about the last two decades, but the fact that these instruments are located at or just below ground level exposes them to disturbances – be they of natural or human origin – that originate close to the Earth’s surface.

In the latest work, Saccorotti and colleagues at the INGV and Italy’s National Institute for Nuclear Physics (INFN) used a ring laser called GINGERino, consisting of four 3.6 m-long sides mounted on a block of granite. Housed 1400 m underground at the Gran Sasso National Laboratory, the device is largely shielded from the tiny variations in air pressure that can trouble ring lasers at shallower depths. It is the forerunner of an experiment called Gyroscopes in General Relativity (GINGER), which will use at least three large ring lasers arranged at right angles to one another to try and measure the very subtle “frame-dragging” effect predicted by Einstein’s general theory of relativity.

Using GINGERino, the INFN-INGV group was able to record a magnitude-seven earthquake that occurred under the Atlantic Ocean during a week of data-taking in June 2015. The researchers say that although their data exhibit a poor signal-to-noise-ratio, they were still able to detect rotational motion generated by the earthquake’s seismic waves in the rock surrounding the lab.

Potential earthquake precursors

According to Saccorotti, the result shows the feasibility of installing a long-term experiment in the Gran Sasso lab – be it GINGER or a single, larger ring laser. Such a device would systematically record rotational ground motions over a two- to four-year period. This would allow the detailed study of the elastic deformation of rock caused by the gradual build-up of energy across a geological fault ahead of an earthquake. “That deformation can include rotational motion, so having a very sensitive device in a low-noise environment opens up interesting possibilities for studying a potential earthquake precursor”, he says, pointing out that Gran Sasso is in one of the most seismically active regions of Italy.

Ulrich Schreiber of the Technical University of Munich, who collaborates with the Italian group, points out that the field of “rotational seismology” is now quite well established, thanks to the availability of improved ring-laser gyroscopes. But he nevertheless praises the latest work. “GINGERino is a prototype instrument that has still to mature a fair bit before reaching its full potential,” he says. “But being able to observe rotational motion from remote earthquakes in a deep-underground laboratory is an important step forward.”

It's a new field of "rotational seismology" which is "able to observe rotational motion from remote earthquakes".

[Iceman]

Wait, this whole time the vague mentions of rotational seismic phenomena/rotating seismic waves were just describing Rayleigh surface waves?

Is your argument now that RLGs cant measure long period rotation of the earth because they're also measuring very small rotational movements associated with short-lived elliptical oscillations during seismic wave propagation?

[RonJ]

The ring laser gyros in question must be firmly attached to the ground as per the attached article.  They do, indeed, measure rotation from some source.  It has been implied that the source of the rotation is seismic waves.  Most gyroscopes in operation are NOT attached to the ground in any way and still measure a steady 15 degrees per hour rotation.  What are they measuring? I submit that they are measuring the steady rotation of the earth.  The gyroscopes I had access to also measured a change in the z axis while moving from location to location that wouldn’t be seen on a flat earth.  The ring laser gyro argument that it’s just measuring some constant, steady, rotating seismic phenomenon is thus debunked.

[SteelyBob]

Actually, the Wiki page accurately says that those types of devices are looking at rotational seismic phenomena right here - https://wiki.tfes.org/Ring_Laser_Gyroscope_-_Seismology

Nobody is saying the devices aren't used for seismology. They absolutely are. They are extremely sensitive, and can measure tiny rotations, several orders of magnitude less than the earth's rotation. They are also using them for studying variations in the earth's axis of rotation, amongst other things.

Not sure why you keep reposting that graph. It's not raw data.

I keep posting it for several reasons. Firstly, it's from a site that you linked to. Moreover, it clearly shows earth rate, with far less noise than the apparently unacceptable amount in the examples you have cherry picked for use in the wiki. You kept saying that the amount of noise rendered the various other examples meaningless, but now here we have one with fa less noise, and you've pivoted to some nebulous claim about it measuring seismic activity. You aren't clear though on what, precisely, it is measuring. Seismic activity is, by it's nature, oscillatory. The graph in the example clearly shows a steady state rotation. If it's a steady state rotation, then it must be rotating.

Your request for 'raw data' is also curious, as when you had raw data, such as from the Canadian Honeywell test, you didn't understand what it was, despite it actually demonstrating earth rate, if you knew what to do with the data.

As you pointed out earlier, the angular rate on that one is faster other graphs we saw which are uncorrected for latitude and this data is reprocessed and visualized. Other visualizations we saw in this thread have radically different views.

GINGERino is not a regular seismograph, it is a special tool which studies "rotational seismology" -
...
It's a new field of "rotational seismology" which is "able to observe rotational motion from remote earthquakes".

Yes, it absolutely is. Rotational motion...because it's a highly sensitive rotation detector. Which is why the graph I've shown you, from the site that you linked to, clearly shows oscillatory seismic activity superimposed on the steady state earth rotation.

I suppose the ultimate question really is: 'what RLG data would convince you that the earth was actually rotating?'

You seem to be rejecting every piece of data for a variety of reasons...eg too much noise in a simple device, but then an ultra sensitive device with much less noise must be detecting something else other than earth rate, despite it clearly measuring earth rate.