A Rumors of Gravitational Wave Inspiral at Advanced LIGO | Sept 2015 Launch

[Orodruin]

Right. I have no knowledge of an analysis of lensing for GW; it is a great question. A purely heuristic argument to expect it is that if GW travel at c, and can be treated similar to the EM geometric optics approximation of treating a piece of the wave front as having a world line, then then world line ought to be a null geodesic. Then, the lensing would be basically the same as light. But this is just a general argument - I would not be very confident in it without more analysis or information.

I agree with this. It is my naive expectation as well. Do the math on a Minkowski metric background and the perturbation satisfies the wave equation in flat space. It is a reasonable expectation that doing the perturbation in a curved background you might end up with the wave equation in the curved space. Then again, I have not done the math either.

 

[Borg]

His statement is not about the gravitational lensing. It is about how the GW would interact with matter and dark matter.

Ah, I see the difference. Gravity waves would not be blocked but they still might be lensed. Thanks for your responses.

 

[sanman]

Ah, I see the difference. Gravity waves would not be blocked but they still might be lensed. Thanks for your responses.

So Gravity is able to act like a waveguide for its own waves? Is there any other precedent or analogy for this in nature?

 

[PAllen]

I agree with this. It is my naive expectation as well. Do the math on a Minkowski metric background and the perturbation satisfies the wave equation in flat space. It is a reasonable expectation that doing the perturbation in a curved background you might end up with the wave equation in the curved space. Then again, I have not done the math either.

And indeed, they've already thought of that, and the answer is yes. The references in this paper list similar work as well:

http://arxiv.org/abs/1309.5731

 

[PAllen]

So Gravity is able to act like a waveguide for its own waves? Is there any other precedent or analogy for this in nature?

At the moment, I can't think of any analog. Certainly not EM - a charge does not deflect light.

 

[Dr. Courtney]

Is the speed of gravitational waves a constant?

I mean is there anything analogous to a refractive index that can slow them down, or is their speed truly absolute?

This question came up in a recent meal with my students where I was joking that me trying to hula hoop might be detected by the Livingston facility.

 

[PAllen]

Is the speed of gravitational waves a constant?

I mean is there anything analogous to a refractive index that can slow them down, or is their speed truly absolute?

This question came up in a recent meal with my students where I was joking that me trying to hula hoop might be detected by the Livingston facility.

Well, any time you have path bending you can model it as speed slow down, but, in GR, this is considered a coordinated dependent feature (as are all speeds in GR). What makes the EM case invariant is the ability to compare light through a medium to light through a vacuum on 'nearly the same path'. As with the twin scenario versus coordinate dependent time dilation, the ability to do this comparison is what gives you an invariant effect.

Thus, lensing is not going to provide an answer, as you can't have an unbent and bent GW on the same path.

So, the question boils down to whether, e.g. a dust cloud can slightly slow GW. I haven't heard of this, off the top of my head.

 

[DaTario]

Thank you , Vanadium 50.

How often such apparatus will be able to confirm these measurements?
How often such experimental conditions are fullfilled in nature?

Best wishes,

DaTario

 

[mfb]

I agree that Newton's formula doesn´t have included this principle. But is it plausible to speculate that our calculations with gravity must deal, from now on, with retarded potentials or similar resources ?

Not just from now on. Luckily we already have a theory that can handle this: General Relativity.

Is this equivalent to the annihilation of three solar masses worth of matter in an instant? Was such energy release predicted by present models of BH merger/collision or is this a new phenomenon?

3 solar masses within ~0.2 seconds, with an estimated peak power of 3.6*10⁴⁹ W, more power than the luminosity of all stars in the observable universe combined.

So, while a single measurement is not very constraining, it shows that the speed of gravitational radiation is of the same order as the speed of light.

Right, forgot about that part.

This nature article mentions that other interferometers such as Geo600 in Germany and Virgo in Italy were not operating at the time . Is it known whether Geo600 would have detected the gravitational waves?

What happens with gravitational waves? Do they exist forever or can they be absorbed or transformed?

GEO600 wouldn't be sensitive enough for a clear detection, and I doubt it would have seen it at all.
Gravitational waves can be influenced by matter as discussed above, but this effect is tiny. To a very good approximation, they just spread out forever. The wave that passed us in September is now about 5 light months away from us.

How often such apparatus will be able to confirm these measurements?
How often such experimental conditions are fullfilled in nature?

That is one of the questions LIGO tries to anwer. We'll have to wait until more data is available.

 

[vartanieno]

If the amplitude of the discovered gravity waves less than the size of atomic nuclei by the time it reached us, I wonder what the amplitude was at the moment of collision right next to these two black holes.

 

[mfb]

Less than the size of a nucleus over a distance of 4 kilometers.

Right next to the black holes, the deformations were of order 1 - like 1 meter per meter. But there you don't have a nice flat spacetime you could take as baseline, and the deformations don't come from the waves but from the near gravitational fields.

If we go a bit away (like thousands of kilometers), it gets easier: strain at a distance of 1.3 billion light years was 10^-21, and it scales inversely with distance. At a distance of 5,000 km, it was 0.002. Probably enough to be visible in a standard videocamera video with some careful analysis and at least 50 frames per second.

 

[Titan97]

I might sound dumb. But how did LIGO detect the collision of two black holes? I thought it could only detect gravitational waves. How did the scientists conclude that the source was the collision of two black holes?

 

[PeterDonis]

How did the scientists conclude that the source was the collision of two black holes?

By the pattern of the detected waves. Scientists have done detailed numerical simulations of the gravitational wave patterns we should expect from various events. The pattern detected by LIGO from this event matched the pattern the simulations gave for a black hole collision. The patterns for other types of events are different.

 

[strangerep]

At the moment, I can't think of any analog. Certainly not EM - a charge does not deflect light.

An EM field can deflect an EM wave -- an extremely weak QED phenomenon known as Delbruck scattering.

 

[Dave Vrona]

Is production of a GRB expected for this type of event?

If so, was one detected by the satellites?

 

[Haelfix]

By the pattern of the detected waves. Scientists have done detailed numerical simulations of the gravitational wave patterns we should expect from various events. The pattern detected by LIGO from this event matched the pattern the simulations gave for a black hole collision. The patterns for other types of events are different.

This part is actually quite the delicate undertaking. I've been trying to understand the attribution and validation methods and needless to say, it is technically challenging for anyone who isn't an expert.

See the following paper here:

https://dcc.ligo.org/LIGO-P1500218/public/main
Which bases a lot of the numerical work on a set of papers starting with this one:
http://arxiv.org/abs/gr-qc/0507014

What's a little difficult to understand, is how LIGO manage to pinpoint the parameters of the system so well. As far as I can see, they analyze a large amount of different models, each with different assumed parameters (mass, spin, orientation, orbital eccentricity etc (there are 17 parameters in total) and then compute the likeliness of each given the observed data, and then tabulate the best fits through a straightforward Bayesian analysis.

I personally find that the error bars on the analysis, especially on the secondary mass and other inferred parameters which aren't able to be read off in a straightforward manner really quite strong, which indicates a great deal of trust in the numerical methods being utilized... I find this rather remarkable if it holds up to more scrutiny, given how difficult the system it that's being analyzed.

 

[PAllen]

An EM field can deflect an EM wave -- an extremely weak QED phenomenon known as Delbruck scattering.

Very interesting. I was, of course, thinking classically, but anyway wasn't familiar with this.

 

[ProfChuck]

This nature article mentions that other interferometers such as Geo600 in Germany and Virgo in Italy were not operating at the time . Is it known whether Geo600 would have detected the gravitational waves?

What happens with gravitational waves? Do they exist forever or can they be absorbed or transformed?

Considering that G waves transport energy, or else LIGOS wouldn't work, they must transfer some of that energy to the objects that they move. however, this question is important from the perspective of possible quantum gravity theories. If gravity is quantized and if gravitons exist then they will not transfer their energy in a continuum but in quanta. This is a whole new area of research enabled by this discovery.

 

[PeterDonis]

If gravity is quantized and if gravitons exist then they will not transfer their energy in a continuum but in quanta. This is a whole new area of research enabled by this discovery.

Even if gravitational waves do transfer energy in quanta, LIGO will not be able to detect this. The quanta are way too small.

 

[mfb]

The gravitational wave had a peak intensity of about 240 mW/m² here on Earth. That is roughly the intensity of artificial light in buildings (as it hits walls, floor and so on).

 

[lpetrich]

The event's peak gravitational strain at the Earth was about 10^-21. Since (strain) ~ 1/(distance), we can extrapolate it back to where it was roughly 1. The distance to the event's source is roughly 1.2*10²⁵ m. So the strain = 1 distance is 10⁴ m or 10 km.

The Sun has a Schwarzschild or black-hole radius of about 3.0 km, and the final black hole thus has one of about 190 km. Thus, the maximum G-wave strain near there was about 1/20.

 

[DaTario]

Not just from now on. Luckily we already have a theory that can handle this: General Relativity.

Ok, it is the Einstein's prediction part, I see. But concerning GR, does it have a well defined prediction for the GW's velocity?

 

[PeterDonis]

concerning GR, does it have a well defined prediction for the GW's velocity?

Yes, it predicts that GWs in vacuum travel at the speed of light.

 

[spacejunkie]

Is there any significance in the spin of the final black hole being 2/3c ? I have a vague recollection of reading that this is a natural limit of some kind but I can't pin it down.

 

[Yashbhatt]

Can anyone explain in simple terms the way in which the LIGO managed to keep the mirrors so still?

 

[mfb]

The event's peak gravitational strain at the Earth was about 10^-21. Since (strain) ~ 1/(distance), we can extrapolate it back to where it was roughly 1. The distance to the event's source is roughly 1.2*10²⁵ m. So the strain = 1 distance is 10⁴ m or 10 km.

The Sun has a Schwarzschild or black-hole radius of about 3.0 km, and the final black hole thus has one of about 190 km. Thus, the maximum G-wave strain near there was about 1/20.

At that distance, you have to include nonlinear near-field effects.

Can anyone explain in simple terms the way in which the LIGO managed to keep the mirrors so still?

The mirrors are suspended by a set of 4 consecutive pendulums, which provide passive damping. In addition, seismic motion is actively canceled by moving the point where they are suspended.

 

[lpetrich]

At that distance, you have to include nonlinear near-field effects.

True, but I was concerned about getting some rough approximation.

I will now consider the question of predictions of alternatives to general relativity. So far, most alternatives to GR have been ruled out because their post-Newtonian predictions disagree with observations. http://relativity.livingreviews.org/Articles/lrr-2014-4/ (Clifford Will, 2014) discusses several of them. The most plausible survivor is the Generalized Brans-Dicke theory, but it contains some parameters that can be adjusted to make it arbitrarily close to GR + (noninteracting scalar field).

Black holes in the Brans-Dicke Theory of Gravitation - Springer by Stephen Hawking.

It is shown that a stationary space containing a black hole is a solution of the Brans-Dicke field equations if and only if it is a solution of the Einstein field equations. This implies that when the star collapses to form a black hole, it loses that fraction (about 7%) of its measured gravitational mass that arises from the scalar interaction. This mass loss is in addition to that caused by emission of scalar or tensor gravitational radiation. Another consequence is that there will not be any scalar gravitational radiation emitted when two black holes collide.

Clifford Will's paper also agrees. However, papers like [gr-qc/9811012] New Black Hole Solutions in Brans-Dicke Theory of Gravity claim that there do exist nontrivial solutions, those with a varying scalar field.

According to Stephen Hawking and Clifford Will, the recent black-hole merger observation does not distinguish between GR and GBD -- the scalar field is constant. So one has to look to systems with at least one white dwarf or neutron star to test GBD's predictions of gravitational waves.

 

[websterling]

Is there any significance in the spin of the final black hole being 2/3c ? I have a vague recollection of reading that this is a natural limit of some kind but I can't pin it down.

The spin of the final black hole, listed as 0.57 to 0.72, is a dimensionless number known as the spin parameter. It is a measure of the angular momentum of a Kerr (rotating) black hole. It has a range of 0 to 1 with 0 being non-rotating and 1 corresponding to a hole with maximum angular momentum. It is defined as $a = \frac{cJ}{GM^2}$

The is no significance to the value for this event other than it being the result of the spins of the original holes and the dynamics of the inspiral and merger.

 

[Terry Coates]

Surely gravitational waves have been observed from the time of Adam, in that the ocean tides are caused mainly by the gravitation of the moon.
Assuming that gravity waves travel at the speed of light, I make the wavelength of diurnal tides to be 2.682 x 10^13 meters.
Detecting gravitational waves of distant sources is of course quite an achievement

 

[PAllen]

Surely gravitational waves have been observed from the time of Adam, in that the ocean tides are caused mainly by the gravitation of the moon.
Assuming that gravity waves travel at the speed of light, I make the wavelength of diurnal tides to be 2.682 x 10^13 meters.
Detecting gravitational waves of distant sources is of course quite an achievement

Gravity waves and gravitational waves are completely different things. What you refer to is a simple Newtonian effect. Gravitational waves are not an aspect of Newtonian gravity at all. This is unfortunately confusing terminology, but we are stuck with it.

 

[mfb]

Surely gravitational waves have been observed from the time of Adam, in that the ocean tides are caused mainly by the gravitation of the moon.

Those are not gravitational waves. They are the direct gravitational field, which is completely different.

 

[.Scott]

Three solar masses worth of energy were converted to the energy of gravitational waves, which are "invisible" (they interact very weakly).
The "annihilation" as in matter-antimatter reaction would generate electromagnetic radiation (gamma rays), not gravitational radiation.

This is very similar to the subtraction of 3 solar masses from the universe - especially if there is no way to recapture (reconvert) the energy in the gravitational wave.
At Newtonian speeds, a 3 solar mass shell will either exert no net gravitational pull or the same gravitational pull as if the 3 solar masses were concentrated at the center of the shell - depending on whether you are inside or outside the shell. So when the gravitational wave was detected, we crossed from outside the shell to inside the shell - loosing the gravitational pull of those 3 solar masses - perhaps forever.

I'm not sure if that math holds when the shell is expanding at relativistic speeds.

 

[PeterDonis]

This is very similar to the subtraction of 3 solar masses from the universe - especially if there is no way to recapture (reconvert) the energy in the gravitational wave.

The energy can be recaptured; GWs passing through matter can transfer energy to it.

when the gravitational wave was detected, we crossed from outside the shell to inside the shell - loosing the gravitational pull of those 3 solar masses - perhaps forever.

Yes; before the GWs passed us, the gravity acting on us included a 3 solar mass component at the distance of the source--i.e., about a billion light years away. (Note that this is utterly negligible in practical terms; we are only talking about the idealized theory here.) Ideally speaking, as soon as the GWs passed us, the gravity acting on us lost that 3 solar mass component (it still included the rest of the mass of the merged black hole a billion light years away, of course--but that too is utterly negligible in practical terms). Whether that pull is lost "forever" depends on whether any of the energy in those GWs gets absorbed by matter further out, and what happens to the matter afterwards.

 

[.Scott]

The energy can be recaptured; GWs passing through matter can transfer energy to it.

That was not the case in the LIGO experiment, but more generally one would expect that work could be extracted from that wave. For example, as it passed across a planet, you would think that the planet would minutely warm.

But that implies that something about the planet was able to change the gravitational wave - leaving it a bit weaker than before the interaction.

How exactly would that happen? Would it depend on the mass of the planet? Perhaps the mass and shape? But not of the mechanical strength and structure?

 

[PeterDonis]

That was not the case in the LIGO experiment

Sure it was. If no energy were transferred from the GWs to the LIGO detector, the detector would not have detected a signal. Detectors aren't magic; there needs to be energy transfer for them to work.

How exactly would that happen?

Consider the simple example from MTW that I think I mentioned earlier in this thread. (Or maybe it was in another of the recent LIGO threads, there have been several.) You have two masses connected by a spring, with the spring unstressed and the masses at rest relative to each other, oriented transverse to a passing GW. The GW will induce oscillations of the masses; i.e., energy will be transferred from the GW to stored energy in the oscillations (i.e., the total energy of the spring + masses is larger when the masses are oscillating than when the system is at rest in equilibrium).

Of course a large object like the Earth is more complicated than two masses on a spring, but the general principle is the same: any time GWs pass through a material where you have atoms (or particles or whatever) with an interaction between them that provides a restoring force if the atoms are moved from their equilibrium positions, the GWs will transfer energy to the material by inducing oscillations of the atoms. From a macroscopic viewpoint, it will look like the object has heated up.

 

[.Scott]

Sure it was. If no energy were transferred from the GWs to the LIGO detector, the detector would not have detected a signal. Detectors aren't magic; there needs to be energy transfer for them to work.

So the mirrors were accelerated relative to one another, and that caused some of the GW energy to be absorbed.

Consider the simple example from MTW that I think I mentioned earlier in this thread. (Or maybe it was in another of the recent LIGO threads, there have been several.) You have two masses connected by a spring, with the spring unstressed and the masses at rest relative to each other, oriented transverse to a passing GW. The GW will induce oscillations of the masses; i.e., energy will be transferred from the GW to stored energy in the oscillations (i.e., the total energy of the spring + masses is larger when the masses are oscillating than when the system is at rest in equilibrium).

Of course a large object like the Earth is more complicated than two masses on a spring, but the general principle is the same: any time GWs pass through a material where you have atoms (or particles or whatever) with an interaction between them that provides a restoring force if the atoms are moved from their equilibrium positions, the GWs will transfer energy to the material by inducing oscillations of the atoms. From a macroscopic viewpoint, it will look like the object has heated up.

That makes sense. It's the simple mechanical motion of mass that transmits the signals and it's the same mechanisms that absorb the energy.
At the minuscule, these waves probable affected the orbit of the moon around the Earth - and similarly, gravity waves are generated by that orbital motion tending to reduce the moon's orbital energy.

So any type of mass, especially a large one, will absorb some of the GW energy. The elasticity of the mass would change how the energy was converted after being absorbed, but it wouldn't affect the amount of energy absorbed. It would also seem that the amount of energy absorbed would be proportional to the strength of the GW. So until quatization becomes a factor, the GW would only loose a portion of its strength with each interaction.

 

[mfb]

So until quatization becomes a factor, the GW would only loose a portion of its strength with each interaction.

Sure.

I would expect this value to be tiny, but now I got confused:
As a rough estimate, a slow uniform stretching of Earth by 10^(-21) needs tens of GJ (the 30 GPa are a guess). We have to deform Earth multiple times.

The total amount of gravitational wave energy that passed through Earth is 450 GJ.

 

[PAllen]

Sure.

I would expect this value to be tiny, but now I got confused:
As a rough estimate, a slow uniform stretching of Earth by 10^(-21) needs tens of GJ (the 30 GPa are a guess). We have to deform Earth multiple times.

The total amount of gravitational wave energy that passed through Earth is 450 GJ.

The following has sections on interaction of GW with matter, and suggests that the above 'hand wave' is inaccurate by orders of magnitude. The first order change in dimension is not the scale at which attenuation/energy transfer occurs. See section 5, on interaction of GW with matter and EM fields.

https://www.lorentz.leidenuniv.nl/lorentzchair/thorne/Thorne1.pdf

 

[mfb]

Great, thanks.

 

[S.Daedalus]

GR has long been validated at low energies, but remains problematic at high energies. It is at high energies that theories are still needed to complete GR and the standard model.

True, but aren't there also theories that change the low energy/long distance behavior of GR? Like TeVeS or Modified Gravity or other attempts to give a relativistic formulation of MOND? I doubt any of these would yield any difference to vanilla GR in LIGO experiments, but if somebody knowledgeable on the subject could confirm/refute that hunch, I'd be grateful.

Also, what about theories with propagating torsion, such as Einstein-Cartan gravity? Again, I suppose LIGO couldn't see torsional effects (or rather, differences to metric waves, if there are any), but any pointers are appreciated.

I'm going to disagree a little with mfb on point (2). He's correct that this experiment doesn't measure the speed of gravity. However, there is still information. The speed of gravity has to be less than the distance between Richland and Livingston, which is about 1850 miles, divided by the difference in time, which is less than 10 ms. So that gives as a ballpark estimate of within a factor of a few of 185,000 miles per second.

So, while a single measurement is not very constraining, it shows that the speed of gravitational radiation is of the same order as the speed of light.

And indeed, somebody has already spun that observation into a paper: On constraining the speed of gravitational waves following GW150914. They arrive at a speed for gravitational waves $\lesssim 1.7 c$, which is actually a better constraint than I would have expected.

 

[Buzz Bloom]

Those are not gravitational waves. They are the direct gravitational field, which is completely different.

Hi mfb:

It has occurred to me that there is a similarity in the effect of (1) the Newtonian gravity of a moving mass on another mass, and (2) the GW effect. Here is a thought experiment.

Imagine three pendulums A, B and C, each consisting of a spherical weight of the same mass suspended by string of the same length (and therefore A, B, and C all have the same period) in an environment with a gravitational force that is constant (not varying with height or location). Assume that the test environment is a vacuum, and that there are no electric charges on any of the materials. Assume the the points of suspension of A, B, and C are in a line and that the distance between A and B is the same as the distance between B and C. Assume every thing is frictionless.The initial dynamics is that the three weights are stationary.

The A weight is moved away from B as let go.

I am guessing that GR would predict the start of a Gravitational Wave that would cause B and C to move. (If this is wrong, and someone can explain why, I will modify the thought experiment accordingly.) Newtonian Gravity would also predict that the time variable position of A would cause motion in B and C.

As I understand the difference, the NG force moves with infinite velocity, while the GW moves at velocity c. The implication is that both NG and GW produce repetitive motion in B and C with a period equal to (or related to) the pendulum period, but the difference in velocity will produce a relationship in the phase of A's motion and B's motion that would be different with respect to NG and GW.

Is this correct.

 

[mfb]

Assuming B and C are not astronomically far away, B and C would move due to the quasistatic field of A which changes slowly over time. You get nearly the same result for Newtonian gravity.
There is also an emission of gravitational waves, but that effect is tens of orders of magnitude (!) smaller for typical pendulum parameters. This effect does not exist at all in Newtonian gravity.

 

[PeterDonis]

As I understand the difference, the NG force moves with infinite velocity, while the GW moves at velocity c.

No. Any change in spacetime curvature propagates at the speed of light.

 

[Buzz Bloom]

As I understand the difference, the NG force moves with infinite velocity, while the GW moves at velocity c.

No. Any change in spacetime curvature propagates at the speed of light.

Hi Peter:

I am sorry for the confusion. "NG" means Newtonian Gravity.

I was saying that Newton's Laws did not include a finite speed for light or for any other "action at a distance", like gravity. The assumption was that all action at a distance was instantaneous. I was making the interpretation that for this thought experiment, that the difference between Newton and GR was the difference in how long it takes for a change to propagate from one point to another.

I gather from @mfb post #192 that the GR involvement in the thought experiment only involves gravitational waves as a very much smaller effect than the speed of action difference.

Regards,
Buzz

 

[PeterDonis]

I was saying that Newton's Laws did not include a finite speed for light or for any other "action at a distance", like gravity.

Actually, Newton's Laws were consistent with a finite speed of light. They did, however, assume that gravity was an instantaneous action at a distance. Thanks for clarifying what you meant.

 

[aabottom]

I'm going to disagree a little with mfb on point (2). He's correct that this experiment doesn't measure the speed of gravity. However, there is still information. The speed of gravity has to be less than the distance between Richland and Livingston, which is about 1850 miles, divided by the difference in time, which is less than 10 ms. So that gives as a ballpark estimate of within a factor of a few of 185,000 miles per second.

So, while a single measurement is not very constraining, it shows that the speed of gravitational radiation is of the same order as the speed of light.

Hummmm, thinking about the geometry of the two measurements in Livingston, LA and Hanford, WA, the time delay between the two can be anywhere between 0 ms and 10 ms. If the source of the gravitational wave is collinear with Livingston and Hanford, then the time delay would be +10 ms or -10 ms, depending on the direction of the source. But if the source is perpendicular to that line, then the time delay would be 0 ms. This is just using high school geometry.

I'm not sure how or if the LIGO team is getting the directions of the source. But if it's from the time delay and the geometry of the two LIGO detectors, Then they can't say much about the speed of gravitational waves. It seems that we need at least 3 non-coplanar detectors to get information on the speed of gravitational waves.

For example, assume 2 things: 1) source of the gravitational wave is collinear with Livingston and Hanford; 2) speed of gravitational waves is 1.4 c. Then the time delay would be 7 ms, consistent with the LIGO measurement.

Is there some shape or characteristic of the two temporal waveforms (other than the time delay) that the LIGO team can use to determine the source direction?

Thoughts anyone?

 

[mfb]

They can set a hard upper speed limit based on the time delay alone - if the waves would be much faster than the speed of light, there is no way to get the observed delay. Yes, the upper limit is higher than the speed of light, but not so much. In addition, they observed a chirp, so a range of frequencies. That gives a really good upper limit on dispersion. And we know that there can only be one universal speed that would not lead to any dispersion, unless you want to give up Lorentz invariance completely.

Adding the relative amplitude (and therefore polarization information) allows to make better estimates, but I didn't study in detail which polarization would appear in which way where.

 

[aabottom]

...
And indeed, somebody has already spun that observation into a paper: On constraining the speed of gravitational waves following GW150914. They arrive at a speed for gravitational waves $\lesssim 1.7 c$, which is actually a better constraint than I would have expected.

Thanks for that. This paper discusses my idea in #196 in much more detail. They consider the minimal value of the time delay within two-sigma deviation from the mean. They get
cgw <= 1.7 c
instead of my rough estimate of cgw <= (c 10 ms)/(7 ms) = 1.429 c.

 

[Davephaelon]

Assuming the magnitude of oscillating displacement of matter is proportional to the inverse square of the distance to this 410 megaparsec distant black hole merger, I did a quick back-of-the-envelope estimate of of the amount of stretch (and shrink) we would have experienced, had this merger occurred only 8 kiloparsecs away, at the center of our Milky Way galaxy. The number I came up with is .0026 meters, or about 1/10th of an inch.

 

[mfb]

The displacement is proportional to the inverse distance. You would have to be much closer for such a huge amplitude.
The energy density is proportional to the amplitude squared, so this drops with the inverse squared distance.