The question is actually quite subtle and I am trying to find the time to write up something on this. First a caveat, I'm not an expert on GR but I had some concerns and have quizzed some professors on the subject and I think now I have worked out the answer.

Typically we are only concerned with what happens in the vicinity of the Solar System and on that scale the answer to your question depends on a choice of coordinates. As you said, this can be "a matter of interpreting abstract spacetime geometry, and there is no single concrete interpretation?"

The usual explanation is based on a coordinate system in which the speed of light is constant and our rulers are defined based on the metre being the distance travelled by light in a given time. The frequency of the light from the laser is always fixed and in those coordinates, the speed of light (and hence the wavelength) is constant. The length of the arms however is varied by the wave. The quadrupole format of the waves means one arm is stretched while the other shrinks hence there is a detectable phase difference produced at the detector.

An alternative description is to use what is called the "transverse traceless gauge" to define the coordinates and in that all the material of the arms maintains a constant length but the coordinate speed of light varies. Again the quadrupole format means the speed increases in one arm while it decreases in the other and the wavelengths are changed by that resulting in the same phase difference at the detector. Since the output is measured by a single photodiode, the signal at that point is invariant, it has the same value whichever coordinate system you choose.

The gravitational signal travels outwards at the speed of light from the source to us. We are lucky "observers".

My understanding is that the (left) tunnel in Fig 1. is squeezed unexpectedly at frequencies that are typically in the audio range (e.g., as an upward chirp and a subsequent ringdown are detected from merging black holes). I think that it would be a transverse vibration on the tunnel length that is detected using laser interferometry. The laser light is just a tool to detect the vibration. The tunnel is long and used multiple times to increase the sensitivity of the measurements. It is underground to help remove confounding terrestrial sources of vibration. 

The length of the tunnel is constant, but the length vibrates unexpectedly. You need only Physics 1 to understand what happens.  The magic is that no other concrete explanation for the observed chirp and ringdown fits except for the very long ago merging of two very distant black holes, where mass (initial masses-final mass) got turned into (gravitational) energy which radiated outwards.

Wikipedia might be helpful to us. See also the legend for the diagram: Figure 1: A beamsplitter (green line) splits coherent light (from the white box) into two beams which reflect off the mirrors (cyan oblongs); only one outgoing and reflected beam in each arm is shown, and separated for clarity. The reflected beams recombine and an interference pattern is detected (purple circle).

Figure 2: A gravitational wave passing over the left arm (yellow) changes its length and thus the interference pattern.

https://en.wikipedia.org/wiki/LIGO#Operation

The light and dark shading of the yellow indicates one squeeze.

https://upload.wikimedia.org/wikipedia/commons/thumb/0/06/Gravitational_wave_observatory_principle.svg/170px-Gravitational_wave_observatory_principle.svg.png

Dear Mr. Kennedy,

I understand what you are saying, but on wikipedia, they are talking about an "effective change" in the tunnel length, which implies that the issue might be more complex. Moreover, if spacetime is changed, does this not also affect the wavelength of light?

Kind regards,

Sascha Grusche

The tunnel is 4 km long, and reused 280 times. Effectively the tunnel is thus like one that is 1120 km long. If the effective length of the tunnel suddenly becomes 1120 km long minus the diameter of an atom, then it has been squeezed (infinitesimally). See the dark yellow in fig 2. If a hundredth of a second later it is effectively 1120 km plus the diameter of an atom, it has been "unsqueezed", and one single, full cycle of gravity variation has been detected. Yes, the tunnel was measured to contract and expand in a hundredth of a second over its effective length. The only complexity introduced was the practical consideration to reuse the measuring path 280 times to keep the lab compact and fundable.

I repeat for clarity. The light is only used as a tool, it comes from our (powerful) earthly laser, not the merging black holes. It is coherent, monochromatic light, unchanging in frequency.

Ignore Wikipedia's entry on spacetime. Forget Startrek. 

"Spacetime" is an English contraction meaning length, breadth, width and time. If the tunnel is pointing at right angles to where the blackholes were merging, the tunnel's breadth and width are constant. Its effective length only vibrates (wiggles / changes) with time over the same duration as the duration of the historical merger.

Gravity variations are not affecting the frequency of the laser's generated light and its wavelength.

Regarding spatial distortions:

As far as I know, gravitational waves are transverse, so if the tunnel is pointing toward the merger, its width and breadth should oscillate. As I understand it, a gravitational wave changes the length of the tunnel if it is orthogonal to the wave direction (or has an orthogonal component).

Regarding time distortions:

Spacetime is changed. Is it only the spatial dimensions of the tunnel that changes, or does time change (and, hence, frequency), too?

Regarding laser wavelength:

The laser itself is a cavity, so if a gravitational wave passes through the laser, might it not change the length of the laser, and hence the resonant frequency or wavelength of the laser?

Conversely, how do you measure a given wavelength if the length of your measuring stick oscillates due to a gravitational wave?

@Sascha.

1. I corrected my two entries above to change longitudinal to transverse, and direct to right angles. Thank you!

2. I see no reason to believe that the gravity variation need invoke any change in time, only a change with time.

3. Yes, the laser source could be squeezed and "unsqueezed" by the passing gravity variations, but the laser is very much shorter than the 1120 km of the tunnel, and through mirrors, could if required be placed at right angles to the tunnel.

As soon as the laser light is in the tunnel, might its wavelength not be changed, there, (in analogy to gravitational redshift) because space itself is changed by gravity oscillations?

If not, how do you measure a supposedly constant wavelength if the length of the measuring stick changes due to gravitational waves?

If the wavelength of the light somehow got shortened in one direction would it be lengthened by an equal amount on its return path?

https://en.wikipedia.org/wiki/Occam%27s_razor

The question is actually quite subtle and I am trying to find the time to write up something on this. First a caveat, I'm not an expert on GR but I had some concerns and have quizzed some professors on the subject and I think now I have worked out the answer.

Typically we are only concerned with what happens in the vicinity of the Solar System and on that scale the answer to your question depends on a choice of coordinates. As you said, this can be "a matter of interpreting abstract spacetime geometry, and there is no single concrete interpretation?"

The usual explanation is based on a coordinate system in which the speed of light is constant and our rulers are defined based on the metre being the distance travelled by light in a given time. The frequency of the light from the laser is always fixed and in those coordinates, the speed of light (and hence the wavelength) is constant. The length of the arms however is varied by the wave. The quadrupole format of the waves means one arm is stretched while the other shrinks hence there is a detectable phase difference produced at the detector.

An alternative description is to use what is called the "transverse traceless gauge" to define the coordinates and in that all the material of the arms maintains a constant length but the coordinate speed of light varies. Again the quadrupole format means the speed increases in one arm while it decreases in the other and the wavelengths are changed by that resulting in the same phase difference at the detector. Since the output is measured by a single photodiode, the signal at that point is invariant, it has the same value whichever coordinate system you choose.

As per general relativity there is an underlying space time fabric or membrane pervading the universe. When gravitational energy is released, it causes waves in this membrane. So the change in the length of the tunnel, or the wavelength or frequency of light, or the traveling time of light etc. are just the effects.

Dear Vikram Zaveri,

the problem with the space-time fabric is that it is not two-dimensional, but four-dimensional (height, length, width, time). So if this fabric is warped, it takes up five dimensions - which I cannot imagine. So it is hard for me to imagine what the effect of the warping is. 

Moreover, ripples in space time would mean that the shape of the space-time fabric changes as a function of time - but time is part of the fabric. So how can time be the dependent and independent variable simultaneously?

This seems to be the crux of modern physics: We see the phenomena, we use the mathematics, but we are unable to interpret the mathematics in concrete pictures, we can only use simplified and unsatisfying analogies. We need to remember that the analogies are not the same as the phenomena.

The question remains: What exactly changes, and what remains constant? According to George Dishman, there is no single answer because it depends on how you define the coordinates.

Kind regards,

Sascha Grusche 

@ Sasha: One can notice the effect of the warping without seeing it from outside. The Earth is round (``warped'') and we can indeed see it ``from outside'' ever since we could go  into outer space. But could we realise the Earth's roundness before that, even without looking at ships disappearing at the horizon?

The answer is yes: surveyors can, and do, measure the Earth's curvature. The sum of angles of a large triangle can be measured to be larger than 2 right angles. In principle, such purely internal measurements allow to measure all so-called internal curvatures. (There are curvatures you cannot so measure: a cylinder surely looks curved from outside, but cannot be observed to be so from inside, as follows from the fact that you can flatten a cylinder, unroll it, without modifying internal distances).

So 3 dimensional space could be warped, and we could see it using entirely similar techniques. In fact we do: light rays passing close to the Sun are deviated, and this is interpreted to mean that straight lines (which light rays are assumed always to follow) are different according to whether a large mass is nearby or not.

So one must specify a distance in space. Gravitational waves involve a modification in time of these distances. So we need to describe distances between points, and to that end, we first must describe points in space time, that is, events. To do this, we must introduce some coordinates, in a way which is in general quite arbitrary. Anything which depends on the choice of coordinates cannot really correspond to a physical phenomenon.

So when we talk of ``lengths changing'' or speeds or wavelengths changing'' we are using concepts that do not correspond to unique phenomena. The phenomenon observed is that light leaks out of a system during a finite time. Which changes in the system led to this leak will vary according to your favourite way of describing the world.

A possible elementary analogy: let a cyclist travel from west to east, that is, in the direction of the Earth's rotation. We may all agree that this cyclist is lifted by an upward apparent force: he exerts less weight on the Earth's surface than if he were at rest. Now let me ask: is this force a centrifugal force or a Coriolis force? Different point of view lead to different answers, and discussion on such issues is fruitless.

Dear F. Leyvraz,

so you would agree that the answer to the question depends on the reference frame or choice of coordinate system. If we choose a coordinate system where the length of the tunnel is measured to be oscillating, shouldn't the wavelength of light vary accordingly, simply because it is some type of length?

Kind regards,

Sascha Grusche

The issue is rather complicated. If you do the maths, you find there is a non-zero effect which is independent of coordinates, just as you do for my cyclist. How that comes out is beyond what can easily be explained, at least by me. If there is such a non-zero effect, and that is what the maths says, it does not matter whether you look at it as a change in length of the arms or a change in the speed of light, just as it does not matter whether the cyclist experiences a centrifugal or a Coriolis force.

As to the argument that ``all lengths should scale in the same way'' it does not work quite that way, because it is not only space distances which are affected, but the time coordinate as well, so that everything varies in a complicated manner. There certainly is no trivial error in the computation that leads to the existence of a non-zero effect, but I would recommend waiting for George's work to understand it.

Dear F. Leyvraz,

so, in summary, no matter how one looks at it, the detection of gravitational waves is not easy to describe because time and space seem to be related to each other in a self-reflexive manner. This reminds me of the basic motto of general relativity: Mass tells spacetime how to curve, and curved spacetime tells mass how to move. It is so intertwined that a causal explanation and teasing out of constants and variables seems hard. Indeed, I am excited about the visualisation George Dishman is working on.

Kind regards,

Sascha Grusche

I agree with the explanations of Prof. F. Leyvraz.

Regards

SM Najim

Most of the debates on interpretation of the measurements from Laser Interferometer Gravitational Waves Observatory (LIGO) are based on a simple linear theory where the metric tensor is approximated as the sum of a flat time space Minkowski tensor and a small perturbation. The elementary derivation of the corresponding linear wave equation is presented by Beyersdorf (2001) in sections 2.1 and 2.2.

http://nlo.stanford.edu/system/files/dissertations/peter_beyersdorf_thesis_january_2001.pdf

The perturbation of metric due to the action of Gravitational Waves (GW) in the framework of linear theory is given by eq. (2.2) in section 2.1.

Analyzing eq. (2.2), we can say that the metric is distorted by GW and since the speed of light in the local inertial frame of reference is constant, the beams in two arms will acquire a phase difference because of the difference of length of both arms.

Beyersdorf (2001) (text on page 12 just below Fig. 2.1) presents slightly different interpretation: "The beams will acquire a phase difference due to the gravitational wave modulating the "refractive index" of the vacuum in the arms"

A nice review of the all aspects of linear theory is presented in the deck of slides by Glampedakis

http://webs.um.es/bussons/GW_lecture_KG.pdf

The linear theory of GW is often questioned. A very convincing and concise presentation with excellent historical notes is presented by A. Loinger in the paper posted in arXiv

https://arxiv.org/pdf/astro-ph/9810137.pdf

Please note a reference to the paper by Einstein and Rosen (1937). The commentary about the opinion of Einstein on GW has been recently posted in arXiv by Galina Weinstein

https://arxiv.org/pdf/1602.04674.pdf

This is a fascinating text and it should be disseminated widely.

After considering all the above references, I believe that the answer to the original question posted by Sascha Grusche is as follows

1. If we accept the linear theory, what we will measure is the phase shift

2. Otherwise it is not clear whether or not GW actually passes through the apparatus and additional theoretical studies are necessary.

Dear Sascha Grusche:

You have a valid point. I prefer to consider space time of general relativity as imaginary artifacts that solves many problem. But I also think that there is something real about the underlying fabric or membrane. Such a membrane can support the instantaneous action of gravity at astronomical distances. In following theory I have replaced the space time by wavelengths and periods of the particle waves. Here a periodic invariant is defined and space time invariant of special relativity appear as a special case of this periodic invariant. Time is no longer linear like in general relativity but you can only define period between two events. Thus time is no longer independent but you can keep the imaginary time independent for convinience. What is part of the fabric is the period of the wave and the wavelength. Due to ripples in the fabric, these wavelengths and perods of the matter particles change This can change the length of the tunnel, or the wavelength or frequency of light, or the traveling time of light. But the imaginary time and length standard remain constant.

Article Periodic relativity: Basic framework of the theory

@Aleš Kralj:

I am aware that the Pioneer anomaly is explained. But it is not through the Cassini data as you say. See the New York Times Report (July 23, 2012).

The anomalous acceleration of the Pioneer 10 and 11 spacecraft is due to the recoil force associated with an anisotropic emission of thermal radiation off the vehicles.

Phys. Rev. Lett. 108, 241101 (2012)

https://arxiv.org/abs/1204.2507

Dear Sacha, you are asking an important question. This is seriously addressed and answered in a satisfactory way in the following paper by M. Koop and L. Finn (I quote the arXiv number: 130.2871) and add their abstract (to attract your curiosity):

"Gravitational wave detectors are typically described as responding to gravitational wave metric perturbations, which are gauge-dependent and — correspondingly — unphysical quantities. This is particularly true for ground-based interferometric detectors, like LIGO, space-based detectors, like LISA and its derivatives, spacecraft doppler tracking detectors, and pulsar timing arrays de- tectors. The description of gravitational waves, and a gravitational wave detector’s response, to the unphysical metric perturbation has lead to a proliferation of false analogies and descriptions regarding how these detectors function, and true misunderstandings of the physical character of gravitational waves.

Here we provide a fully physical and gauge invariant description of the response of a wide class of gravitational wave detectors in terms of the Riemann curvature, the physical quantity that describes gravitational phenomena in general relativity. In the limit of high frequency gravitational waves, the Riemann curvature separates into two independent gauge invariant quantities: a “background” curvature contribution and a “wave” curvature contribution. In this limit the gravitational wave contribution to the detector response reduces to an integral of the gravitational wave contribution of the curvature along the unperturbed photon path between components of the detector. The description presented here provides an unambiguous physical description of what a gravitational wave detector measures and how it operates, a simple means of computing corrections to a detectors response owing to general detector motion, a straightforward way of connecting the results of numerical relativity simulations to gravitational wave detection, and a basis for a general and fully relativistic pulsar timing formula."

(By the way: Sam Finn is one of the best known former PhD students of Kip Thorne.)

The arXiv reference in Norbert Straumann's post (the last on the preceding page) should be 1310.2871 as linked below.

https://arxiv.org/abs/1310.2871

historical comment to F. Leyvraz (in early morning): The circumference of the Earth (and thus its curvature) was first determined by Eratosthenes astonishing accurately around 240 BC, in a scientific manner, based on the angle of elevation of the Sun at noon on the summer solstice in Alexandria and on Elephantine Island near Syene (modern Aswan).

@ Norbert Straumann: Indeed. But I did not mention this remarkable triumph, because it was not clearly what you might call an internal curvature measurement, which is what I was trying to describe.

I meant the curvature of the surface of the Earth. Eratosthenes was convinced that this is a sphere. Unfortunately, Columbus did nor know his result.

Dear Sascha Grusche,

I am sure that you know the response to your question. Why do you not tell it?

Dear László-Attila Horváth,

if I knew the response, I would not pose the question here. I am interested in serious discussion of the question because I hear contradictory answers. I am trying to resolve the (apparent) contradictions.

Kind regards,

Sascha Grusche

Dear Sascha Grusche,

Excuse me for my mistake! I will give you an answer and waiting with big interest your reasoning… You have right when you are saying that here are existing contradictory answers!...- that is why you also know something in this subject… and you know well!

My simply response: the gravitational waves are changing of gravity field! So they are causing changing of the gravity field!

Best regards,

Laszlo  

Dear László-Attila Horváth,

I agree that gravitational waves change the gravitational field. How does this affect the LIGO detector? From a classical standpoint, everything should periodically become lighter and heavier, but how would this explain the changes in the interference pattern?

Kind regards,

Sascha Grusche

Dear Sascha Grusche,

You have right! To this last question I do not know the response! Example exist another question to: how they determined the distance of source… another: how they determined the objects type which caused gravity waves?... Exist other 13 question…

Best Regards,

Laszlo

P.S. My main question: Do we accept the LIGO’s discovery like a real discovery?

LAH: how they determined the objects type which caused gravity waves?

The signal is a sine wave that gets a bit distorted near the merger. The frequency and the rate of change can easily be measured and the ratio of those tells us the chirp mass, a number that depends on the two masses. The final frequency tells us how far apart the bodies were just before they merged.In the case of GW150914, the masses were around 30 times that of the Sun but their final separation was much smaller than the size of a star. It is therefore inferred that they were black holes.

LAH: how they determined the distance of source

Knowing the masses means we know the intensity of the waves emitted, the "luminosity". They decrease as the inverse of the distance and we know the luminosity observed hence it is trivial to calculate the "luminosity distance".

Dear DH,

Thank you for explanation.

Exist in math a very simple law at set:

A not= B and B=C then A not=C   (1)

 using from the: A=B and B=C , Then A=C

 (1)  Using like an analogy in the next:

If somebody is able to contradict a theory (example: GR), which predict something (“model” of discovery of gravity waves), Then he will be able to contradict the mentioned discovery too… For this I tell you he will negate your explanation too.. They are only explanation of someone imaginations!  (only in one case you can prove it if  you have direct proves)… Example you can tell:  how the asteroids of inner asteroid belt was formed; because they can be accepted like direct analysed objects… Another example: Plate tectonics Subduction! If an actual accepted science cannot prove this process… How we can accept the LIGO discoveries? and accept your explanation!

Best Regards,

Laszlo

P.S,

Dear colleague

Gravitational waves give us another way to observe space. For example, waves from the Big Bang would tell us a little more about how the universe formed. Waves also form when black holes collide, supernovae explode, and massive neutron stars wobble. So detecting these waves would give us a new new insight into the cosmic events that produced them.

Finally, gravitational waves could also help physicists understand the fundamental laws of the universe. They are, in fact, a crucial part of Einstein's general theory of relativity. Finding them would prove that theory and could also help us figure out where it goes astray. Which could lead to a more accurate, more all-encompassing model, and perhaps point the way toward a theory of everything.

Regards 

Exciting replies interesting, I agree with the answers and explanations above.

Dear Saeed Al Rashid,

thank you for your explanation of how gravitational waves change our worldview. But what do they change physically, that is, which physical quantities are affected?

Kind regards,

Sascha Grusche

The answer is that what changes is the curvature of the metric. To convert that into say distances between the test masses or the wavelength of the laser requires a choice of coordinate system, but the phase difference between the beams acquires a variation which is independent of that choice.

There is no "out of plane" component as long as you define the plane correctly. The waves emanate from the binary system and produce two wave cycles per rotation of the binary so a section through the orbital plane showing the strain as colour coding looks like the first linked video. You can follow the waves moving radially outwards but the phase relationship means that a crest looks like a spiral. The plane of the wavefront is a tangent to the spiral, not to the radial line, although the difference is negligible for all practical situations.

I'm currently working towards a note on this subject as I think some of the web explanations can be a bit misleading even though not wrong. Taking the Wikipedia page illustration, which is typical of many, and extending it in a ribbon centred on the binary system gives a simple picture, illustrated in the second linked video. Watch any single rectangle on the surface and you'll see it behave in the same fashion as the Wikipedia illustration.

This is shown in a coordinate system chosen such that the speed of light is isotropic on the surface. It works locally but causes some curious effects when considered globally. It's too complex to explain here but I hope to write it up over the coming months.

https://vimeo.com/157321123

https://vimeo.com/157730717

Hint for Sascha Grusche:

Since you are also interested im pedagogical aspects connected to your question, the following suggestion may interest you: In November 1915 we organised at ETH the symposium "100 years General Theory of Relativity" for a general audience, with background in physics, mathematics or related fields. In the audience we had lots of retired people who are interested in scientific progress. (Only two talks on first evening were for people close to the field.) We had excellent speakers, who tried their best to present their subject in an understandable pedagogical manner (without equations). One of them was Sam Finn, who concentrated on gravitational waves (before the LIGO event was announced). You can see his talk (and also some of the other speakers)) as video on the following address:

     einstein.phys.ethz.ch

Very important topic and very interesting answers by dear professors and colleagues who covered almost every aspect of it. I agree with most of them.

Regards

SM Najim

Dear Sascha Grusche,

I am ready with my article.

https://www.researchgate.net/publication/313632704_AZ_ELMELETI_TUDOMANY_KENYES_JELENSEGE

The English Resume is in the comment...

Best Regards,

Laszlo.

P.S.

Intuitionally I have realised what they did! Why? What was their purpose

Research AZ ELMÉLETI TUDOMÁNY KÉNYES JELENSÉGE

Dear László-Attila Horváth,

I have read your English summary. Are you saying that the detection of gravitational waves is an illusion because the method is not appropriate?

Do you mean that the change in the light interference pattern in the detector is not due to gravitational waves?

Kind regards,

Sascha Grusche

Dear Sascha Grusche,

Thank you for you made effort and read my poor English Resume (I am only played after Chinese clothes selling, the East Hungarian village people become more poor after 1990…-that is an economical-political story )

Become to your recent post:

I do not saying anything, because this part I have accepted discussion of W.W. Engelhardt:

https://www.researchgate.net/publication/304581873_Open_Letter_to_the_Nobel_Committee_for_Physics_2016 [13]

“13. A szóban forgó felfedezést olyan tartományban történő mérésekhez kötik, amelyekre a LIGO műszerei képtelenek [13].  — „A gravitációs hullámok 4×10 ^-18 m dimenziójú változást okoztak a mérőműszerekben, 456-szor kisebbet, mint a proton sugara.”-The mentioned discovery  was happened in such a measuring scale that the LIGO measurements tools cannot reach  [13] (The W.W. Engelhardt letter) — “the gravitational waves causing 4×10 ^-18 m changing in tools, 465 smaller than the proton radius”… This not my filed put I can ask something for those who are working in your Field: Why behave light like particle (made from photon)?...

The next: “Do you mean that the change in the light interference pattern in the detector is not due to gravitational waves?”- your question: Why the LIGO’ Scientist was not able to measure gravity waves when the source is the “Gutenberg discontinuity” (contact of inner mantle and outer core) the real source gravitation of Earth which has gravity changing in time of Earthquakes and daily ordinary tides- these processes also can be interpreted like gravity waves!!!) I will translate this article If somebody help me to put in a correct English text!

Yesterday in time of selling clothes, when I did not have costumer I have had a brainstorm: what was the aim of “LIGO’s Discovery”…

Best Regards,

Laszlo

Data Open Letter to the Nobel Committee for Physics 2016

LAH: these processes also can be interpreted like gravity waves!

Unfortunately in English we use similar names for different things, "gravity waves" are completely different from "gravitational waves".

https://en.wikipedia.org/wiki/Gravity_wave

https://en.wikipedia.org/wiki/Gravitational_wave

AK: In this way, earthquakes or other more localised sources could have been rejected as possible sources of erroneous measurement.

Seismic disturbances are at lower frequencies and are isolated by the suspension system.

AK: Calibration could be done post measurement.

Calibration is done continuously by injecting specific test frequencies at known levels, you can see the resulting spectral lines in the sensitivity plot that is displayed in the centre of the control room. See the bottom of page 39 of the linked LIGO magazine.

http://www.ligo.org/magazine/LIGO-magazine-issue-8.pdf

@George Dishman, I like your comment, it is quite stimulating.

We can add also that the minuscule variations of the gravitational field of our planet are used to perform continuous monitoring of the changes taking place in the atmosphere as well as for recording of the seismic activity.

The precise Sagnac interferometers are also used in monitoring of many environmental processes. I suspect even that they hold some answers to the questions of extended range weather prediction. The construction of the apparatus which could be used for this purpose is described at

https://arxiv.org/pdf/1007.1861.pdf

In general it is quite surprising that there are so many links between the very different concepts of "gravity waves" and "gravitational waves".

If we approach the problem of gravity waves in their stratified atmosphere on the ellipsoidal Earth written in the tensorial 4-D form we see a lot of mathematical similarities to the equations in GR despite of the different physical principles involved.

Thank you all for your in-depth answers. To summarize, what changes during the detection of gravitational waves is a matter of perspective. Depending on the reference frame, one might say that what changes is the wavelength or frequency of light, the speed of light, the length of the tunnel, or a complicated combination of those.