I'm so busy right now but could you do a semiclassical treatment using a nonrelativistic bouncing ball between plates floating in space where the period of the bounce is faster than the gravitational wave?  This way you could measure the change in the frame of the ball between bounces.  

I should have said the period is much shorter than that of the wave.  

In the PN limit you might be able to make an optical analogy with dielectrics.  Consider this question.  When a gravitational wave passes, does it produce stress in a medium?  Near resonance, does it absorb energy from the wave as it passes?  A static field might just redefine space and time so the medium distortion is not locally discernible to observers but a time changing field creates motions that are not simply a function of the state of the field at the moment so I don't believe such a situation exists.  In the case of a dielectric there is a "ring up" and "ring down" time to equilibrate as the wave enters and leaves.  When the wave leaves this extra energy must be shed so cannot be made invisible to the local observers.  

I knew what you meant. I got to thinking about this in a different way. As the universe expands, wavelengths of light grow longer, but a meter stick, for example, does not. So, i guess the idea is that the size of the experiment does not change although the wavelengths of light do as a gravity wave passes through it. However, this brings up another question that has bothered me a long time but never had the time to really look into it. Why doesn't the meter stick grow longer? Why isn't the spatial dependence of the Coulomb force affected like that of electromagnetic waves, since the Coulomb force is mediated by virtual photons?

You are one of the few physicists I know that is bothered by such questions.  That's why I follow you.  So many of the rest of the physicists push some equations and make pompous statements.  Thank you sir for being interesting.  

Francis,

I believe that interferometer based gravitational wave detectors are fundamentally flawed and will never detect gravitational waves. My reasoning is that the speed of light DOES vary with the stretching and compressing of space. This will result in the two returning light beams always being in phase. This is explained in more detail on my website (which includes supporting computer simulations). You may also be interested in an alternate design of a ‘Time Variance’ GW detector posted on my ResearchGate page. It is based on the principle that a passing GW will cause fluctuations in the rate of flow of time.

http://www3.telus.net/foamyether/introduction-gra.html

Thanks for your input, Peter. Let me elaborate a bit on what i asked. The expansion of the universe is thought to move galaxies farther part, yet orbits stay the same distance as measured by meter sticks that don't expand with space. What is different about the attraction of galaxies for each other compared to objects orbiting each other? Is it just the weakness of the gravitational effect? Is there then some sort of gravitational threshold above which expansion has no effect?

Francis,

This is where (I believe) current cosmology is inadequate. I can only explain expansion using my Foamy Ether Theory (FET). Assuming that the galactic red-shift is caused by an expanding universe is only one explanation. FET states that the only conclusion that we can draw is that space is stretching. Stretching space can be caused by expansion, or it could be cause by the ‘inflow’ that FET proposes (or both). A more detailed explanation of this is available on my website.

http://www3.telus.net/foamyether/expandingunivers.html

There is a threshold for bound states.  The expansion occurs predominantly in the unbound regions. Noerdlinger and Petrosian, Ap. J., 168 1—9 (1971).  

Clifford, i've been busy updating my geology field trips from my last foray into the Chihuahua desert, but i'm now getting back to this. I assume you are referring to bound and unbound gravitational states. I haven't had a chance to look at the ref you cited.

PS, i suppose the answer to the original question is that LIGO is OK so long as meter sticks don't expand as space does. I still don't see why they don't. From what i've read in General Relativity (outside my area) matter held together by electric forces (rigid bodies) remain rigid. This seems like a axiom, but what do i know.

I grew up in that desert.  A fierce place!  Meter sticks do expand with gravity.  I haven't studied this in some time but I think the problem can be thought of in terms of how long the period of the gravitational wave is versus the time for light to traverse the arms.  If it is long then we should get a larger number of wavelengths in one arm than the other.  If it is short then you are right, the wavelengths just get compressed along with the device and there is no effect.  

Crothers, S. J., A Nobel Laureate Talking Nonsense: Brian Schmidt, a Case Study,

16 July, 2015,

http://vixra.org/pdf/1507.0130v1.pdf

I'm not sure I see the connection to the thread but I always like Stephen's work. Nobody calls BS on the current world of theoretical physics like him.  

Boy, have i ever been out of the loop while teaching in the boondocks.

have a look to

Physical response of light-time gravitational wave detectors

Michael J. Koop and Lee Samuel Finn

Phys. Rev. D 90, 062002 (2014) - Published 4 September 2014

 find also a critical review of all non sensical question/answers

LIGO, and all its foreign counterparts, are indeed a waste of money. Gravitational energy cannot be localised in General Relativity, and so Einstein's gravitational waves do not exist. General Relativity violates the usual conservation of energy and momentum for a closed system and is therefore in conflict with a vast array of experiments.

The argument for the existence of Einstein's gravitational waves relies upon linearisation of Einstein's nonlinear field equations. The resulting wave equation is coordinate dependent and Einstein merely chose a set of coordinates in order to make the speed of propagation of his waves that of light to satisfy his presumption that they exist and travel at the speed of light. Thus his argument is a vicious circle and therefore invalid.

Moreover, the energy of these alleged waves is calculated by means of Einstein's pseudotensor, which he constructed in order to make his whole theory satisfy the usual conservation of energy and momentum for a closed system so well established by a vast array of experiments. However, his pseudotensor is not a tensor and therefore contradicts his prescription that the equations of physics must be covariant strictly under tensor transformations. According to Einstein and his followers his pseudotensor is admissible because it acts 'like a tensor' under linear transformations of coordinates. Thus it is in fact a coordinate dependent quantity, contradicting again Einstein's fundamental tenet. Assume that Einstein's pseudotensor is mathematically meaningful. Since it acts 'like a tensor' under the above conditions, then it is subject to tensor operations. So contract it. The result is a first-order intrinsic differential invariant. However, the pure mathematicians proved, in 1900, that first-order intrinsic differential invariants DO NOT EXIST! Therefore, by reductio ad absurdum, Einstein's pseudotensor is a meaningless concoction of mathematical symbols, and so it can't be used to represent any physical entity, to model any physical phenomena, or to do any calculations. Yet Einstein and his followers do all three! That's how Einstein's gravitational waves have been created - by wishful thinking, invalid mathematics, and violation of the results of experimental physics. Nonetheless, cosmologists ignore these facts and continue to build fantasy upon fantasy so that today physics and astronomy are intellectually decrepit. This decrepitude is exemplified  by Professor Brian Schmidt, Nobel Laureate (for physics), a prominent spokesman for the cosmologists and their fancies. He again, is Schmidt in action:

Crothers, S. J., A Nobel Laureate Talking Nonsense: Brian Schmidt, a Case Study, 16 July, 2015,

http://vixra.org/pdf/1507.0130v1.pdf

Anybody here is invited to try to defend by scientific argument, Schmidt's versions of mathematics and physics, or to acknowledge his typical errors and falsehoods and the decrepitude of cosmology.  Cosmology is not science - it is mysticism and superstition cloaked in scientific jargon.

I suppose that there is a complementary question: how very often is using the "money system" to accomplish our aims a flagrant waste of human effort? Of course at some point one must begin spending, but there are many problems with these gigantic physics (or astrophysics) projects that need tom be addressed. In the "mythical goldern age" before the Manhattan Project got the physics community into the habit of spending many millions for experiments involving hundreds, or even thousands, a scientist spent much more time (example Einstein) working his own mind (indeed a billion dollar machine!) developing theories and testing hypotheses than he did in joining forces in some kind of macro-physics experiment.

    One of the outstanding mistakes that came out of these attitudes is the many years it took for the physics community to recognize that, in a few dozen pages or so, John Stewart Bell, in 1964,  created the first now dramatic phase of Quantum Mechanics since the Copenhagen interpretation of 1926. Yes, he shook up QT all the way to the rafters, except that his work was virtually ignored for 6 years or more!

This shows that Physics had lost all interest in "thinking" per se, and had become addicted to Cecil B DeMille-type super-productions.

  ( I don't deny that the discovery of the Higgs Boson was remarkable and impressive!)

https://en.wikipedia.org/wiki/Bell%27s_theorem

I am a fan of GR but not the dominant geometrodynamic approach.  I think it is a big puzzle why the equations come out as those of differential geometry.  Einstein was not the promoter of this point of view so much as Wheeler.  It is not necessary to view them that way and one can reformulate it in an equivalent nontensorial form whereby one does have strict global conservation laws.  My view is that the field interactions lead to a nonlinearity that must be "geometric" in that the local causal future of each particle tends to align through these couplings.  I sketched this out in a paper but it needs much more attention.  If one constrains oneself to the purely tensorial and geometric picture one never sees this.  I like some of Crothers' work and sympathize with his poor treatment by some of the egotists of physics.  Eventually, I think his view and mine will be seen as opposite sides of the same coin and the geometric point of view will fall out of favor in a valid unification theory.  I doubt we will live to see it though.

Reading Crothers' answer raised the following question in my mind. Didn't the work of Taylor and Hulse on the double pulsar establish strong evidence for gravitational waves?

yes absolutely;in addition to the Hulse and Taylor observation, General Relativity has passed with flying colors all tests in the dynamics of the Solar system;

Crother handwaving arguments get just the opposite answers when treated properly with basic GR; allow me to insist > please read the paper I quoted before; it is the most accurate and general in solving this long standing issue;

also consider that your GPS navigator would go bananas in a few minutes if not constructed according to basic GR

Massimo Cerdano,

You are not being honest. The points I made in my previous post are correct. Since you contend that my arguments are 'handwaving' then put up a scientific rebutal instead of your handwaving. For instance, give us your proof that Einstein's pseudotensor is not a meaningless concoction of mathematical symbols. Or give us your proof that GR does not violate the usual conservation of energy and momentum for a closed system, and therefore not in conflict with a vast array of experiments. And by the way, how many experiments suffice to prove a theory invalid? One will do! 

The Taylor-Hulse observations are of a binary system. So give us Massimo, a set of Einstein field equations for two comparable masses, and then give us your solution to that set of field equations, bearing in mind that there are no known solutions to Einstein's field equations for two or more masses and no existence theorem by which it can even be asserted that his field equations have the capability of dealing with two or more masses.

I am honest and you are on a  wrong track (the reason why is in the last sentence of the answer); here in simple words how the matter stands; but this is not handwaving, because I am describing in words accurate calculations performed with basic GR (without use of any pseudotensor)

Q:  Can we detect them ? (if space shrinks/stretches under the gravitational wave and the light does the same, maybe the effects compensate and nothing can be detected…)

A: Yes, we can. Nowadays the leading method consists in measuring phase shifts of light in Michelson like interferometers. A formal answer is the following. In the weak field approximation of the Einstein equations, the Riemann tensor is gauge invariant and gives directly the second derivative of the phase shift, which is the invariant measurable quantity. One calculates the GW induced phase shifts in a convenient gauge, finds it non-zero and that’s it. The experimentalist answer takes some more explanation. She/he may like to use the Fermi gauge. In such a “laboratory” gauge three gyroscopes sit in free fall at the origin, and give the three directions of the Cartesian coordinates. The Michelson interferometer has the arms on two of the axis and the beam splitter is at the origin. In the approximation – appropriate for both ground and space based detectors – that the GW wavelength is much larger than the arm length, in turn much larger than the wavelength of the laser light, the picture is simple . The coordinate distance of the end mirror in each arm stretches and shrinks – in counter phase to the other arm – but light is not affected at lowest order. So light travel time and the corresponding phase shifts give a measure of the GW amplitude. Does such a “coordinate” description give the actual gauge invariant physics? Yes, in fact the coordinate arm length approximates well the proper length and this oscillates as the Riemann GW tensor induces a “geodetic deviation” of the end mirror in respect to the front mirror. And to double check one can use the so called Transverse Traceless gauge, within which the approximation of “short” arms is not even needed, to get the same phase shift when recombining the light beams from the arms. Notice how the TT description is different: in TT the mirror coordinates do not change, while it is rather the light, which gets an oscillating GW dependent effective “refractive index”. Of course if one uses both the coordinate descriptions at the same time then gets the (wrong) intuition given in the question above. Beyond the above, for a most illuminating, gauge independent, discussion of GW detection [see ref given]

now the binary pulsars: they are wonderful laboratories for testing GR from weak to moderate field intensities (not only waves); tests come OK within expertimental errors at high orders of approximation;    in any case here a summary concerning gw's (notice that it answers also the question of energy and angular momentum conservation):

Q: Did we have already detection?

A: Yes (indirectly somebody says…): neutron stars in binary systems spiralize one onto the other, because of the energy loss due to the emission of gravitational waves.

In some NS-NS binaries, one or even both are pulsars delivering their regular ticking to us. Thus the dynamics of the system can be recorded, with secular augmentation of the precision of the measured orbital features. The pulsar PSR 1913+16 is observed since 1974, and gives unequivocally that it is part of a binary system of almost equal mass neutron stars, which is losing energy and angular momentum due to GW emission. The GW emission is just that predicted by the classic 1916 Einstein quadrupole formula - Hulse & Taylor, Nobel 1993

We seem to have a bit of a controversy here. In spite of that, i have had some thoughts that i'd like to toss out and then jump back over the fence before they get trampled. I'm thinking that perhaps a better way to think of the cosmological redshift is as a gravitational redshift. (This may be equivalent to thinking about the "stretching" of space. I'm not an expert in GR.) The universe is getting less dense as it expands, so shouldn't there be a gravitational redshift? And, shouldn't that mean that the energy lost by the photons goes to increase gravitational energy? Then, i'm thinking that real and virtual photons both respond to this redshift; however, virtual photons are emitted and absorbed on such a small time scale that the redshift has essentially no effect on them. If so, this is why meter sticks stay rigid, as they are held together by electromagnetic forces. However, real photons that travel thousands of light years do show gravitational redshift effects. The equipment in LIGO is held together by the exchange of virtual photons which are so ephemeral they won't respond to the spatial undulations of a gravity wave. However, real photons in the experiment will so long as their existence is long enough so that they are affected to a measurable degree by the gravity wave. So, i change my mind. LIGO can measure gravity waves theoretically.  OK, have at as you will. I'm outta here!

Jumping back in for a millisecond to add a PS. I think Clifford Chafin may have a similar comment if i understood him correctly.

I was playing with some simple models to see if I can understand this in some way other than a perturbation expansion.  The bouncing ball down two perpendicular arms while keeping track of the times measured at the ends of the device was one.  To get back to the optical standing wave case closer to the experiment, consider that waves trapped between mirrors have a pretty short lifetime due to damping.  This waves are continually created by the laser source and the equilibrated over the limbs of the device on a much shorter time than the period of the gravitational waves.  

Assuming a monochromatic wave, the frequency of the relaxed solution will then be at frequency omega locally at every location.  Different spacetime directions will now give different wavelengths (but still of integer number) in each direction.  This seems to suggest that there would be no interference observed for long gravitational wave periods.  I seem to have talked myself into a corner.  Not sure how seriously to take this argument.  

I agree. If the photon relaxation time is very much smaller than the gravity wave period, the interference might not be be detected. Assuming a gravitational wave has a wavelength on the order of the sun and travels at the speed of light, then it would have a period on the order of 4 seconds. Could such a wave be detected? If i understand how LIGO works, the maximum photon relaxation time is on the order of one millisecond. Couldn't that be detected by the precision inherent in interferometry? On the other hand, aren't you detecting photons with a range of travel times? Would this blur the signal?

Yes.  Blur the signal.  I haven't decided how to estimate this best.  It seems someone would have done this but there have been crazy oversights before.  

I finally did something intelligent and actually looked at the LIGO website instead of relying on memory. They say the arms of the interferometer will change in length as a gravity wave goes by. This was how i remembered it and i thought the light wavelengths should change as well. Given my comment above (if valid) on thinking of a gravity wave as modulating the gravitational redshift as it passes, that would seem to imply that the arms stay the same length while the light wavelengths would change. I'm still confused.

I was thinking the dynamics of the system must be playing a role.  The deviations from the flat space metric is usually solved for in the traceless gauge so that time oscillations vary oppositely to the spatial ones.  I think this is important to generate extensions that are not the same for the coordinates and the em waves.  The case of a an oscillating parir of masses on a spring is a more mechanical probe and we can solve the solutions that give the predictable resonance damping solutions.  This is not LIGO but does show how the alternating h_xx and h_tt oscillations transfer energy to the masses.  If your argument was valid then this would not happen either.  

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

I still don't clearly see why LIGO works though.  It seems like there would be an integer number of wavelengths in each arm and I don't see how this would change.  

You have made a good point. My interpretation of the gravitational redshift for a passing gravitational wave, which emphasizes the spatial variance  does not address the time variance. It's been 25 years since i sat in on Prof Rindler's GR class, and I'm guessing it is showing.

Francis, the solution is again in my comments anbove; see this

"the arms of the interferometer will change in length as a gravity wave goes by"  correct this comes out making the calculations in the Fermi coordinates

 my comment above (if valid) on thinking of a gravity wave as modulating the gravitational redshift as it passes, that would seem to imply that the arms stay the same length while the light wavelengths would change"  again correct !  you are calculating ib I'm still confused

" I'm still confused" you should not > you got it !

the matter is that in GR coordinates are arbitrary and you are not supposed to attach them a physical mening unless you make with them a gauge invariant statement; what you shoud never do is to use arguments from  both coordinates at the same time

Thanks, Massimo. I'm going back to Rindler's textbook (actually the new one) and reeducating myself.

Gravity waves found! Final answer, apparently.

Well folks, gravity waves were detected by Russell and Hulse in 1978 through studying the decay in the orbiting of a pulsar star around another. Various other hypotheses were rejected and the "gravity wave" interpretation deemed the best one in an article by Taylor and Weisberg in 1989. Finally ,Taylor and Hulse won the Nobel prize in 1993 for this achievement!

It has been said that this result was "indirect". Consider: The proof by the school of Pythagorus 2500 years ago, that the square root of 2 is irrational, was indirect, the first recorded indirect proof in mathematical history. Was this discovery, though indirect, any less true than the assertion than the direct calculation that 2+2 = 4!

  Yes, indeed, LIGO was a "waste of money" if this ends up being its onlym discovery. We hope that this amazing instrument will make hundreds of other important discoveries. My favorite is the following: we know that Dark Matter, which comprises 84% of all matter in universe, has gravity; in fact thats all we know about it. However, by Einstein's equations, when there is gravity there must be gravity waves! How can we "indirectly"(!) detect the gravitational radiation from dark matter. Wobbles in the galaxies, perhaps

  What the LIGO result shows is that LIGO works!

they not only wasting money but also forcing us to follow blindly their filmy stories.....

these people (LIGO, string theory, etc) killing physics by telling beautiful stories.......

It appears to me just from reading popular accounts that the signals received by LIGO are compared with what mathematical models based on the G Th of R predict for the convergence of black holes. I don't know how else they could come up with the masses they claim for the black holes. This raises the question of just how well the signals match the predictions. If the match is good enough, then they are likely correct. I don't have the time to do this, so i have to trust the peer reviewers to have done their job.

My opinion is that money is not wasted.  However I like to state that LIGOs detected electromagnetic waves created by two giant objects.  This is a great achievement.  Some details may be found the article attached with this post.

Article LIGOs Detected Magnetic Field Waves; not Gravitational Waves

It is common to find answers to this question about as follows: "Even though the wavelength deforms (stretches or compresses) along with the material of the arm, this doesn't matter. What causes the interference pattern is the different TIMES required for the light beams to return (due to the G-Wave-induced changes in arm length and constant propagation speed").

[See, e.g., https://stuver.blogspot.com/2012/09/q-if-light-is-stretchedcompressed-by-gw.html ]

Curiously, to my knowledge, nobody ever provides a PICTURE of this. I think it's because a logically consistent picture shows the stretched or compressed wavelengths (in proportion to the stretched or compressed arms) in the perpendicular beams returning at the SAME time (no interference). The speed of light remains = c in the deformed state because measured distance per time doesn't change. Only by juxtaposing an undeformed (imaginary) coordinate system against the deformed (physical) one do we infer a time offset (interference).

The validity of this juxtaposition is questionable. It is achieved by appealing to "Riemann tensor phase shifts" in conjunction with the TT gauge. It is perhaps mathematically interesting. But if you can't draw a logically consistent picture of what supposedly happens, I remain suspicious. I still suspect hand-waving.