Consensus about Van Flandern's ideas on speed of gravity?

[hkyriazi]

Is there any consensus among experimental and/or theoretical physicists about Tom Van Flandern's ideas about gravity propagating (and having to propagate) much faster than the speed of light?

 

[ZapperZ]

How could there be ANY consensus when there are no definitive experimental evidence yet? Let's wait till LIGO starts producing results, why don't we?

Zz.

 

[jtbell]

Van Flandern's ideas have been discussed here before:

http://www.google.com/search?q=flandern+site:physicsforums.com

 

[hkyriazi]

Thanks, JTBell. From those archived discussions, I found a 1999 paper by Steve Carlip, addressing Van Flandern's Physics Letters A article (vol 250, p.1, 1998). (Carlip's article is available at: http://xxx.lanl.gov/abs/gr-qc/9909087.)

It seems to have everything I need. (My interest was in knowing a) whether gravity in general requires multi-light speed of propagation (it does only for Newtonian gravity, and, I guess, any mechanical form of gravity, such as "push gravity"), and b) how general relativity got around this (by the use of velocity-dependent terms).

Now I just need to read and be able to make sense out of Carlip's article, and understand what is meant by "the quadrupole nature of gravitational radiation."

 

[Daverz]

You really don't have to wait for a consensus, because you don't have to be an expert to evaluate Flandern's credibility. See

http://math.ucr.edu/home/baez/RelWWW/wrong.html#speed

 

[Daverz]

"the quadrupole nature of gravitational radiation."

See https://www.physicsforums.com/search.php?searchid=568693

 

[robphy]

Why is this thread in this forum?

 

[pervect]

Why is this thread in this forum?

If the intent is to ask what General relativity has to say about the speed of gravity, the answer is fairly clear - it travels at 'c'. This is a prediction of GR, not yet an experimentally established fact.

If the question is more general, it may belong in some other forum, as robphy has perhaps suggested - though I'm not sure exactly which one.

I believe that Van Flandern has actually been published, so that while his ideas may be full of errors and far away from the mainstream, they are probably "fair game" according to PF guidelines (to discuss only published papers, not personal theories).

 

[MeJennifer]

This is a prediction of GR, not yet an experimentally established fact.

Well obviously if the speed of gravity would not be c then GR would be incorrect. So I would say that GR implies it instead of that it predicts it.

But perhaps I am misunderstood, how does GR predict that the speed of gravity is c?

 

[tehno]

Good question Jennifer!
In Maxwell's theory of EM waves these propagate in vacuum at "speed" determined by two constants,vacuum permeability and permitivity namely.
Why the speed of propagating of a gravity wave,which at first glance has nothing to do with electrical charges,has to be linked with these two electrical constants, in the same manner?

 

[pervect]

I should probably add that the speed of gravity is predicted to be equal to 'c' only for weak fields in a vacuum.

When you linearize the Einstein field equations around a vacuum solution, you come up with a set of linear differential equations. The solution to these linearized equations is a plane wave, just as it is in the case of Maxwell's equations. This plane wave travels at a speed of 1 in geometric units, i.e. it travels at the speed of light, since c=1 in geometric units.

 

[yogi]

I should probably add that the speed of gravity is predicted to be equal to 'c' only for weak fields in a vacuum.

When you linearize the Einstein field equations around a vacuum solution, you come up with a set of linear differential equations. The solution to these linearized equations is a plane wave, just as it is in the case of Maxwell's equations. This plane wave travels at a speed of 1 in geometric units, i.e. it travels at the speed of light, since c=1 in geometric units.

Pervect - can you clarify - are you saying that a plane wave arises from the sudden destruction of matter (conversion to another form such as photons) which is other than gravitational radiation.

 

[tehno]

. This plane wave travels at a speed of 1 in geometric units, i.e. it travels at the speed of light, since c=1 in geometric units.

Only becouse STR is taken as guide in linearization where c=1.
But this fact about EM was found both experimentally,and theoretically.
The claim that gravity wave propagate with c,isn't found experimentally or theoretically...

 

[pervect]

Only becouse STR is taken as guide in linearization where c=1.
But this fact about EM was found both experimentally,and theoretically.
The claim that gravity wave propagate with c,isn't found experimentally or theoretically...

This is incorrect. As I explained earlier, it's a standard textbook exercise to derive the theoretical prediction of the speed of propagation of gravitational waves in GR.

As I re-read your remark, I suppose I should add that GR does presuppose SR is true - it doesn't make any sense to postulate GR without also including SR as a special case.

The result is that according to GR, the speed is equal to 'c'. Just about any GR textbook will go into this, see for instance chapter 18 of MTW's "Gravitation". But if you don't happen to have that textbook handy, pick ANY textbook that covers the topic of gravitational waves.

Certain other assumptions are made to make this derivation. One assumes that one has a metric n_uv which satisfies Einstein's field equations. G_uv can be written as a compiclated second-order non-linear differential equation of n_uv. It is simplest and usually assumed that n_uv is a Minkowski metric, so that the background space-time is not only a vacuum solution, but it is flat. This is for ease of computation (and ease of interpretation) though, it's perfectly possible (though trickier) to talk about the speed of gravity in a a Schwarzschild vacuum as well as a Minkowski vacuum.

One then assumes a pertubation metric g_uv = n_uv + h_uv, where h_uv is "small". One then linearizes Einstein's field equations, getting LINEAR second order differential equations in terms of the pertubations to the metric h_uv. These equations are found to be the wave equations, and represent gravitational waves. These waves travel at 'c', the speed of light.

While it is incorrect, as I have attempted to explain at length, to say that there is no theoretical foundation for the speed of gravity being c -according to GR (which is I might add, the title of this forum, i.e. this is a GR forum), it is basically correct to say that we currently have no experimental measurements of the speed of gravity. Here we have a few authors such as Kopeikin arguing that they have performed experiments which indirectly measure the speed of gravity and other authors arguing that since one needs to assume some theory other than GR even to talk about the speed of gravity not being c, that the above measurements which assume GR is true in order to interpret the results as a 'speed' have assumed their conclusion rather than actually measuring the speed. I agree with Carlip on this point, and while Kopekin continues to defend his position I don't think he currently has a lot of support (this is a judgement call).

(see for instance http://www.arxiv.org/abs/astro-ph/0302462, http://arxiv.org/abs/gr-qc/0403060, http://arxiv.org/abs/gr-qc/0510048) .

 

[pervect]

Pervect - can you clarify - are you saying that a plane wave arises from the sudden destruction of matter (conversion to another form such as photons) which is other than gravitational radiation.

Analyzing the source of gravitational waves is actually a bit different from the simpler task of determining how fast they move. Conversion of matter to energy is not really the central issue behind creating gravitational waves. A spinning assymetrical bar or plate will, for instance, generate gravitational waves without any such conversion. What's important turns out to be the third time derivative of the quadropole moment of the matter distribution. I'm sorry if that's too technical, I'm not sure how to describe it more simply and still be exact.

But it's basically true that the in order to measure the speed of gravity by accepted defitnions, one wants to create a disturbance "here" and then detect the effects "there", and then compute the propagation speed. So, for instance, while the decay of the orbits of the spinning pulsars (Taylor & Hulse) has provided us with indirect evidence that gravitational waves exist (for which they won the Nobel prize), this smooth decay process doesn't really offer us any "handles" on a way to measure the actual speed of gravitational radiation.

One of the ways that I envision the speed of gravity being measured at some point in the future is for us to observe an binary inspiral or other catastrophic event which emits gravity waves both visually and with gravitational wave detectors such as Ligo, assuming they come on-line and work as expected. This is the sort of experiment that will give us the best information about the "speed of gravity" IMO.

It doesn't appear to be technologically possible in the forseable future to create artiically a gravitational wave disturbance that we can detect, therefore we will have to wait for a catastrophic astrophysical event to occur and measure the waves from it.

Currently, though we've built gravitational wave receivers, they aren't very sensitive, and they have yet to detect any signal at all, much less provide timing information about how fast the signal travels. The former issue (detection of signals) is still expected to change as we improve the sensitivity of the receivers - the lack of detection is not considered to be alarming considering the expected frequency and magnitude of natural sources of gravitational radiation.

 

[tehno]

Certain assumptions are made to make this derivation. One assumes that one has a metric n_uv which satisfies Einstein's field equations. G_uv can be written as a compiclated second-order non-linear differential equation of n_uv. It is simplest and usually assumed that n_uv is a Minkowski metric

So there you go...And what constant,if not "electromagnetic" c ,is fixed in a Minkowski metric?

 

[pervect]

So there you go...And what constant,if not "electromagnetic" c ,is fixed in a Minkowski metric?

And your point is - what, exactly?

It sounds like we might actually agree if you would restrain what appears to be some anti-relativity sentiment. At least that's the way it's coming across to me.

 

[yogi]

Pervect - so the plane wave you were referring to in post 11 is the quadrapole gravitational radiation. Thanks

One more question with regard to your post 15 - if we assume for example a catastrophic event - say electrons combining with positrons to extinquish matter and release photons (a visual event).. is not the total energy of the original particles accounted for in the radiating photon flux - and if so - where is the energy that is conveyed by the gravitational radiation come from?

 

[tehno]

And your point is - what, exactly?

It sounds like we might actually agree if you would restrain what appears to be some anti-relativity sentiment. At least that's the way it's coming across to me.

Impression from the books that "electromagnetic" c sets the "gravitational" c.
Quite comfortably,I would rather say that it's the other way round .
However,I don't think this could be the correct standpoint either.
c must be the universal constant,not exclusively reserved for electromagnetism or gravity.
Beside the fact that it doesn't deal with the gravity,Maxwell's theory cannot be considered as the complete theory.
Covariance:Maxwel's eqs. for empty space stay unchanged if we apply to space-time coordinates linear tranformations->Lorentz transforms.Covariance holds for a transformation composed of more such transformations.Mathematically that's the property of a Lorentz group.Accordingly,from Maxwell's eqs. arise the Lorentz group,but Maxwell's eqs. from the Lorentz group don't arise .The group can be defined independently of these eqs. as the group of linear transforms with c=1 kept constant.
In GR things are even more interesting ,nonlinear transformations must be applied,and Lorentz group aren't generally valid .
But the point is :in electromagnetism where charges oscillates,we find c. In the gravity,where masses oscillate,we will probably verify one day the same velocity c of the field disturbance propagation.
Also the curiosity :A propagating EM wave induces a gravitational field,but a propagating gravitational wave does not induce a magnetic field.

 

[pervect]

Impression from the books that "electromagnetic" c sets the "gravitational" c.
Quite comfortably,I would rather say that it's the other way round .
However,I don't think this could be the correct standpoint either.
c must be the universal constant,not exclusively reserved for electromagnetism or gravity.
Beside the fact that it doesn't deal with the gravity,Maxwell's theory cannot be considered as the complete theory.
Covariance:Maxwel's eqs. for empty space stay unchanged if we apply to space-time coordinates linear tranformations->Lorentz transforms.Covariance holds for a transformation composed of more such transformations.Mathematically that's the property of a Lorentz group.Accordingly,from Maxwell's eqs. arise the Lorentz group,but Maxwell's eqs. from the Lorentz group don't arise .The group can be defined independently of these eqs. as the group of linear transforms with c=1 kept constant.
In GR things are even more interesting ,nonlinear transformations must be applied,and Lorentz group aren't generally valid .
But the point is :in electromagnetism where charges oscillates,we find c. In the gravity,where masses oscillate,we will probably verify one day the same velocity c of the field disturbance propagation.
Also the curiosity :A propagating EM wave induces a gravitational field,but a propagating gravitational wave does not induce a magnetic field.

I'm still not following you - and I have to run.

Basically, though, the point is that one doesn't know what the speed of gravity (I should perhaps say the speed of gravitational radiation) is just by inspecting the Minkowski line element. One actually have to solve Einstein's field equations. When one does so, using the method I sketched earlier, one finds that the speed of gravitational radiation in a vacuum is 'c'. This is a mathematical result, very similar to the way that Maxwell's equations show that the speed of light is equal to 'c' in a vacuum.

Someone has emailed me that I should be more precise on this point, and I will attempt to do so. When I say that the speed of gravitational radiation is 'c', I don't mean the coordinate speed of gravitational radiation is equal to 'c'. That would be rather silly, for the coordinate speed of light is not always equal to c in GR as GR allows arbitrary coordinate systems. What I mean is that the local speed of gravitational radiation, like the local speed of light is equal to 'c'.

 

[rbj]

In Maxwell's theory of EM waves these propagate in vacuum at "speed" determined by two constants,vacuum permeability and permitivity namely.

but these constants are manifestations only of our anthropometric units used to measure them. they are not fundamental properties of the universe. but, even though the numerical value of the speed of E&M propagation is still an anthropocentric number (unless we were to use natural units like Planck units), the quantity of such a speed is fundamental and believed to be universal (and if everyone, including us humans and the aliens on the planet Zog, agree to use Planck units, this speed is always 1 and is the speed reference to measure and describe all speeds against).

That speed is the speed of the disturbance of an E&M field that would happen to a test charge some distance away from a "transmitting" charge that would be accelerated. you disturb a charge at point A and the charge at point B reflects such a disturbance at a time |B-A|/c later as viewed by a distant observer on a line that perpedicularly bisects B-A. now Coulombs law for electrostatic attraction is modeled as instantaneous also, that a change in A would cause an instantaneous change in B, but that doesn't happen. the speed of this ostensibly instantaneous reaction is some universal property we call the "speed of light".

but why would it be reasonable if the speed of propagation of the ostensibly instantaneous electromagnetic action first described as Coulombs law be this finite c and, on the other hand, the speed of propagation of the ostensibly instantaneous gravitational action first described as Newtons law be infinite? i see no good reason to assume this and neither did Einstein.

now, it's just an approximation (for low gravitational fields or nearly flat space-time) but you can imagine a thought experiment where you have two identical infinite and parallel lines of charge moving together along in the direction of the lines at some speed, v relative to some observer. it turns out that, for this observer that the lines are charge are whizzing by that they repel each other more slowly than they appear to repel each other for an observer traveling alongside the moving lines of charge (due to time-dilation). this reduction in repulsive force is identical in direction and quantity to the magnetic force that you would arrive at in classical physics. so the effect of the magnetic field can be thought of as the same as if only the electrostatic field existed, but we took into account the consequences of special relativity.

now apply that same thought experiment to two infinite lines of uncharged mass. they will attract each other, but for the "stationary" observer their rate of attraction will be reduced due to the same time dilation with the same c in the time dilation formula. this reduction of attraction can be thought of as a gravito-magnetic effect and, for the "classical" model formula very similar to Maxwell's equations (called the GEM equations) can be constructed with mass replacing charge, mass density replacing charge density, -G replacing 1/(4 \pi \epsilon_0) but the same c ! if it were a different speed of propagation for gravity, then the time-dilation formula for this second thought experiement, would need a different c to go into it. so different formulae for time-dilation depending on what it is that is moving past an observer? why?

Why the speed of propagating of a gravity wave,which at first glance has nothing to do with electrical charges,has to be linked with these two electrical constants, in the same manner?

those two electrical constants are anthropometric crap. it's the speed of propagation of these ostensibly "instantaneous" effects that is fundamental and is the same for all things instantaneous. then, given your set of units you choose to use, you measure G or \epsilon_0 to come out to be whatever numbers they do.

Only becouse STR is taken as guide in linearization where c=1.
But this fact about EM was found both experimentally,and theoretically.
The claim that gravity wave propagate with c,isn't found experimentally or theoretically...

neither is true.

Sergei Kopeikin and Edward Fomalont have experimental data that the speed of gravity is within +/- 20% of the speed of light: http://arxiv.org/abs/astro-ph/0302294 . also, there is good theoretical reason to expect the same speed for both, which, i think GR is supposed to nail. if the Gravity-Probe B ends up consistent with the predictions of GR, i think that's another nail in the coffin. these frame-dragging or gravito-magnetic effects would have a different magnitude if the speed of gravity was not the same c.

 

[yogi]

Just to clarify what Van Flanderen is saying - gravitational radiation, like electromagnetic radiation, propagates at velocity c. But the field(s) that couple the forces between separated objects (electrical, magnetic and gravitation) is not determined by the same factors. In other words, the force is not coupled by a wave as such, but by some other mechanism. Van Flanderen mistakenly concludes that G acts intantaneously because the Earth is pulled toward the Sun at its Now position rather than its retarded position...Carlip shows this conclusion is unjustified (this has been known for many years - the subject being discussed by Feynman in Vol I published in 1963). So all that can really be said is that Van Flanderen's proof is poof - but the issue of how forces are communicated and whether they differ from c is still uncertain.

 

[pervect]

They way I'd describe Van Flandren's results is that he offers a novel defintion of "speed" that is not compatible with the usual defintion.

Furthermore, by Van Flandren's defintion of "speed", the speed of electromagnetism is greater than 'c'. I gather that Van Flandren has actually admitted as much, but this hasn't deterred him from arguing his point.

The standard defintion of the speed of electromagnetic radiation or of electromagnetic forces insists that you move or wiggle something "over here", and get some sort of physical reaction (a reading on a dial, the movement of a charge) "over there". You can then take the distance divided by the time, and compute the speed as a number. (At least you can once you are able to synchronize your clocks properly, and if you use small distances and small times so you don't get into the local vs global issues I mentioned earlier).

We can sidestep some of these issues about "how to measure speed" and syncrhonize clocks and the entire "local vs global" issue by simply saying that weak-field gravitational radiation travels at the same speed light does.

This still leaves the issue of what strong field gravity does, or the issue of what traveling through media does. I'm pretty sure I recall that the result is that media and strong fields can only slow the propagation speed down, not speed it up. Unfortunately I don't have time to look the issue up further in my textbooks at the moment to confirm this. The place I would start looking is Wald's section on gravity as "a well-posed initial value problem" in his book "General Relativity".

 

[tehno]

but these constants are manifestations only of our anthropometric units used to measure them. they are not fundamental properties of the universe. but, even though the numerical value of the speed of E&M propagation is still an anthropocentric number (unless we were to use natural units like Planck units), the quantity of such a speed is fundamental and believed to be universal ...

now apply that same thought experiment to two infinite lines of uncharged mass. they will attract each other, but for the "stationary" observer their rate of attraction will be reduced due to the same time dilation with the same c in the time dilation formula. this reduction of attraction can be thought of as a gravito-magnetic effect and, for the "classical" model formula very similar to Maxwell's equations (called the GEM equations) can be constructed with mass replacing charge, mass density replacing charge density, -G replacing 1/(4 \pi \epsilon_0) but the same c ! if it were a different speed of propagation for gravity, then the time-dilation formula for this second thought experiement, would need a different c to go into it. so different formulae for time-dilation depending on what it is that is moving past an observer? why?...



those two electrical constants are anthropometric crap. it's the speed of propagation of these ostensibly "instantaneous" effects that is fundamental and is the same for all things instantaneous. then, given your set of units you choose to use, you measure G or \epsilon_0 to come out to be whatever numbers they do.

I don't know why do you feel to write at length about set/system of units?
I don't rise that question up becouse I don't find it an issue at all.
I didn't say permeability,permitivity are fundamental units of the universe.
Matter of fact,I expressed my opinion about c being universal constant not reserved exclusively for electromagnetism or gravity.
Hmm...

Sergei Kopeikin and Edward Fomalont have experimental data that the speed of gravity is within +/- 20% of the speed of light: http://arxiv.org/abs/astro-ph/0302294 . also, there is good theoretical reason to expect the same speed for both, which, i think GR is supposed to nail. if the Gravity-Probe B ends up consistent with the predictions of GR, i think that's another nail in the coffin. these frame-dragging or gravito-magnetic effects would have a different magnitude if the speed of gravity was not the same c.

In the paper it's only interpretation of the experiment that speed of gravity is close to the speed of light .But that is far from being the measurment of speed of gravity (gravity waves namely).
What is Gravity-Probe B?I don't find it in the paper.

 

[jtbell]

What is Gravity-Probe B?I don't find it in the paper.

http://www.google.com/search?q="gravity+probe+b"

 

[tehno]

Thanks jtbell.
Stupid me:)
Why they need so much time to process the data gathered from the experiment?

 

[Garth]

What is Gravity-Probe B?

Thanks jtbell.
Stupid me:)
Why they need so much time to process the data gathered from the experiment?

Gravity Probe B is not directly concerned with the question of the speed of gravity and is not directly testing for it.

You may find the following threads interesting: Alternative theories being tested by Gravity probe B, Gravity Probe B mission ends, which explains why it takes so long to process the data, and of course the GP-B website.

I hope these help.

Garth

 

[rbj]

I don't know why do you feel to write at length about set/system of units?
I don't raise that question up becouse I don't find it an issue at all.
I didn't say permeability,permitivity are fundamental units of the universe.

but you said

In Maxwell's theory of EM waves these propagate in vacuum at "speed" determined by two constants,vacuum permeability and permitivity namely.
Why the speed of propagating of a gravity wave,which at first glance has nothing to do with electrical charges,has to be linked with these two electrical constants, in the same manner?

i guess you qualified that as "in Maxwell's theory", but the implication that i got from what you wrote was that it was curious why these two electrical constants (that combine in some way to be c) would have anything to do with the speed of gravity. isn't that the question you asked?

and my answer to that is that those two constants are just numbers we get as a consequece of the units we use. the speed of a propagating gravity wave, which has nothing do do with electical charges, has nothing per se to do with \epsilon_0 and \mu_0, except that both the speed of E&M propagation and gravity has something to do with c which has something to do with \epsilon_0 = 1/(4 \pi k_C) and \mu_0 = 1/(c^2 \epsilon_0).

but could also be related in a similar manner to \epsilon_G = 1/(4 \pi G) and \mu_G = 1/(c^2 \epsilon_G) = (4 \pi G)/c^2. now if the results from these different experiments like LIGO or GP-B seem to indicate a lesser gravitomagnetic effect than predicted by GR, then \mu_G = (4 \pi G)/c^2 might be thunk of as smaller and the speed of gravity as bigger than what GR predicts. or the GEM model might be completely no good to begin with, even in flat spacetime.

Matter of fact,I expressed my opinion about c being universal constant not reserved exclusively for electromagnetism or gravity.

and that could very well be the case.

 

[tehno]

The intensive gravitational wave radiation should happen during
supernovae events.Right?
If I'm not mistaken ,that would be the most suitable for direct observation of both :existance of GWs and comparing their speed with speed of light.
Question:
In 1987 ,there was registered a powerful 1987 A supernova event.
Did they detect any gravitational radiation from it?Wasn't there interferometer antenae back in 1980s too?
Gravitational radiation is extremely weak but I wonder wasn't instruments sensitive enough 20 years ago to detect it from that cosmic event.

 

[yogi]

Einstein's reason for asserting gravitational radiation is based upon energy conservation. As between two masses undergoing acceleration changes, energy will be lost because their gravitational force(s) of attraction are postulated to travel at a finite velocity (c). My question is: Is it correct to extrapolate the quadrapole transverse wave to a situation that involves a sudden conversion of matter to em energy as would be the case in a supernova. Perhaps the propagation mechanism might be different (e.g., longitudinal) in the latter case. Or alternatively - perhaps all the energy of the supernova event is converted to em radiation - there being nothing left over to produce gravitational wave flux.

 

[pervect]

The first LIGO science run was in 2002. http://www.ligo-wa.caltech.edu/ligo_science/P030045-B.pdf

so 1987 was way too early for Ligo.

As far as other detectors go:

Google finds http://adsabs.harvard.edu/abs/1987STIN...8814922A which says that while some sort of glitch was detected in one particular detector, it probably wasn't due to the supernova. Google also finds http://adsabs.harvard.edu/abs/1987STIN...8814922A (but I don't know what's it says!).

Because stars rotate, supernova are expected to generate gravitational waves - people are starting to try and predict the details (amplitudes and wave spectrum/wave shape).

The rotation is important because according to GR, non-rotating spherical collapse shouldn't generate any gravity waves.

 

[quantum123]

Not true, have you heard of the Weber bar?

A Weber bar is a device used in the detection of gravitational waves first devised and constructed by physicist Joseph Weber at the University of Maryland. The device consisted of multiple giant aluminium cylinders, 2 meters in length and 1 meter in diameter, antennae for detecting theoretical gravitational waves.

Around 1968, Weber collected what he concluded to be "good evidence" of the theorized phenomenon. However, his experiments were duplicated many times all with a null result.

Such experiments conducted by Joseph Weber were very controversial, and his positive results with the apparatus have since been largely discredited. Criticism of the study focuses on Weber's data analysis and his incomplete definitions of what strength vibration would signify a passing gravitational wave.


http://prola.aps.org/abstract/PRL/v20/i23/p1307_1

 

[tehno]

Uh,huh!In 1968-1970 Weber said his ancient detector system found something
on a several occassions but ,latter, much more sophisticated antenae devices found nothing.How come?
Perhaps earthquakes were more common in Webber's area/time ..

 

[yogi]

The first LIGO science run was in 2002. http://www.ligo-wa.caltech.edu/ligo_science/P030045-B.pdf


Because stars rotate, supernova are expected to generate gravitational waves - people are starting to try and predict the details (amplitudes and wave spectrum/wave shape).

The rotation is important because according to GR, non-rotating spherical collapse shouldn't generate any gravity waves.

Thanks for clarifying that point pervect. Now, how would you treat a situation where one of two nearby non rotating massive bodies disintegrates - causing an abrupt decrease in the mutual gravitational attraction - or if you choose - in the local spacetime curvature. In either case, the surviving object will be affected - if the change is not communicated by gravitational radiation - what is the nature of the wave is involved?

 

[pervect]

Thanks for clarifying that point pervect. Now, how would you treat a situation where one of two nearby non rotating massive bodies disintegrates - causing an abrupt decrease in the mutual gravitational attraction - or if you choose - in the local spacetime curvature. In either case, the surviving object will be affected - if the change is not communicated by gravitational radiation - what is the nature of the wave is involved?

A body can't suddenly disappear, but it could be exploded. To approximate the gravitational wave emission, you'd have to calculate the quadropole moments for the system - and calculate the third time derivative of the quadropole moments.

The quadropole moment might be more familiar to you as the moment of inertia tensor. Actually, one subtracts some constant times an identity matrix from the moment of inertia tensor to get the "traceles part" of this tensor, i.e. so that the sum of the diagonal elements of the resulting tensor is zero. This gives Q_jk, the reduced quadropole moment - Q_jk has a trace of zero (the sum of its diagonal elements is zero) - it is the "traceless part" of the moment of inertia tensor.

Take the third time derivate of Q_jk, and square it - i.e calculate
\sum_{j,k=1..3} \left< Q'''_{jk} Q'''_{jk} \right>

The <> represents the process of taking a "time average" over a complete cycle.

This result is proportional to the total power of emitted gravitational radiation. In geometric units, the proportionality constant is 1/5 according to my textbook.

 

[quantum123]

Ever since the Weber bar, there have been a lot of gravitational waves detectors all around the world: LIGO, VIRGO, GEO 600, and TAMA etc that promise to demonstrate gravitational waves. So far the result has been null. This reminds me of psychics who always claim to be able to detect harmful vibrations. Yes, neat mathematics, but what are we talking about here?

 

[rbj]

Ever since the Weber bar, there have been a lot of gravitational waves detectors all around the world: LIGO, VIRGO, GEO 600, and TAMA etc that promise to demonstrate gravitational waves. So far the result has been null.

or, at least, not exceeding noise from geologic, tidal phenomema, whatever.

which has more gravitational effect on you? the semi-truck passing by or a super-nova on the other side of the Milky Way?

 

[quantum123]

That sounds awfully familiar - yes, the Michelson Interferometer and the ether.

 

[Hans de Vries]

Ever since the Weber bar, there have been a lot of gravitational waves detectors all around the world: LIGO, VIRGO, GEO 600, and TAMA etc that promise to demonstrate gravitational waves. So far the result has been null. here?

The trend of ever more sensitive detectors will likely continue.

Advanced LIGO:

http://www.ligo.caltech.edu/advLIGO/scripts/summary.shtml

"The Advanced LIGO interferometers proposed here promise an improvement over initial LIGO in the limiting sensitivity by more than a factor of 10 over the entire initial LIGO frequency band. It also increases the bandwidth of the instrument to lower frequencies (from ~40 Hz to ~10 Hz) and allows high-frequency operation due to its tunability. This translates into an enhanced physics reach that during its first several hours of operation will exceed the integrated observations of the 1 year LIGO Science Run. These improvements will enable the next generation of interferometers to study sources not accessible to initial LIGO, and to extract detailed astrophysical information. For example, the Advanced LIGO detectors will be able to see inspiraling binaries made up of two 1.4 M neutron stars to a distance of 300 Mpc, some 15x further than the initial LIGO, and giving an event rate some 3000x greater. Neutron star - black hole (BH) binaries will be visible to 650 Mpc; and coalescing BH+BH systems will be visible to cosmological distance, to z=0.4."


The original target sensitivity was reached last year after some 3 to 4 years
of steady improvements, Time to take the next step. Stronger lasers (200W
instead of 10W) Larger and heavier test masses (34 cm vs. 25 cm,
40 kg vs. 11 kg) and much more.Regards, Hans

 

[pervect]

That sounds awfully familiar - yes, the Michelson Interferometer and the ether.

Given Taylor & Hulse's 1993 Nobel prize winning observations, it would be *extremely* surprising if gravitational radiation did not exist, as the measured decay of the pulsar orbits is within .5 percent of the value expected due to gravitational radiation.

 

[Stingray]

Ever since the Weber bar, there have been a lot of gravitational waves detectors all around the world: LIGO, VIRGO, GEO 600, and TAMA etc that promise to demonstrate gravitational waves. So far the result has been null. This reminds me of psychics who always claim to be able to detect harmful vibrations. Yes, neat mathematics, but what are we talking about here?

The fact that gravitational waves have not been observed yet by these detectors was expected. There are theoretical estimates of the gravitational wave strengths from various astrophysical phenomena. Given what we know about how common these events are, nothing currently running was given a significant chance of detecting anything.

I am most familiar with LIGO, so I'll give you the story there. The current design has a sensitivity right on the edge of what might be useful. It was considered possible but unlikely that it would see anything within a few years. A major upgrade ("advanced LIGO") was always planned, and that is expected to detect a signal fairly quickly.

Advanced LIGO was not built directly because it would have been too hard. The current detector - while inadequate - was still extremely difficult to design and build. Even after a very careful design, it took several years for people to figure out how to remove all of the unexpected noise sources from the working instrument. The experience gained in first building something simpler was considered essential before proceeding. There have also been various technological advances which make certain upgrades much simpler (and cheaper) now.

 

[tehno]

More interesting example

Thanks for clarifying that point pervect. Now, how would you treat a situation where one of two nearby non rotating massive bodies disintegrates - causing an abrupt decrease in the mutual gravitational attraction - or if you choose - in the local spacetime curvature. In either case, the surviving object will be affected - if the change is not communicated by gravitational radiation - what is the nature of the wave is involved?

Yogi,how about of central collision of two identical mass black holes approaching each other with same acceleration and terminal speed with regard to the distant observer?

 

[yogi]

Yogi,how about of central collision of two identical mass black holes approaching each other with same acceleration and terminal speed with regard to the distant observer?

I have always had the feeling that gravitational radiation might not be adequate to explain all the circumstances which can be proposed - Einstein himself had doubts while considering the problem. So When the subject comes up on these boards I try to tease answers out of pervect and others. In doing so I try to break the problem down into a simple physical situation - for example, the total conversion of the engery contained in a positron and electiron that combine to create two gamma ray photons - all the energy is accounted for in the product - the gravitatinal field of the electron and positron is extinquished - how is this reported to an external observer - I see this as analogous to the interaction of two black holes

Pervect stated that, in the cases of massive bodies, w/o rotation, theory predicted no gravitational radiation - but the destruction of the G field for an electron and positron is a reality which is communicated to outside observers (other masses). Interestingly - positrons and electrons do have an inherent spin h bar/2 - but this angular moment is picked up by the photon spin - so I still can't find anything left over to fund the collapse of the gravitational field

 

[tehno]

When two black holes "central collide",with all identical parameters of mass and speed,obviously they create new stationary black hole.
(Part of) The difference of energy prior and after the event being converted into?

 

[pervect]

A body can't suddenly disappear, but it could be exploded. To approximate the gravitational wave emission, you'd have to calculate the quadropole moments for the system - and calculate the third time derivative of the quadropole moments.

Let me go into this in more detail.

Suppose we have two bodies, both with mass m, and positions as a function of time of f(t) and -f(t) (so that the center of mass is at the origin). We further assume that y=z=0 for both bodies.

If we want to apply the approximation I mentioned previously, first we calculate

Ixx = 2*m*f(t)^2

We then reduce this so that the trace is zero

Qxx = (4/3)*m*f(t)^2
Qyy = -(2/3)*m*f(t)^2
Qzz = -(2/3)*m*f(t)^2

Take the third time derivative, squaring, and collecting terms, I get radiated power proportional to:

<br /> {\frac {32}{3}}\, \left( 3\, \left( {\frac {d f}{dt}}<br /> \right) {\frac {d^{2} f}{d{t}^{2}}} +f \left( t<br /> \right) {\frac {d^{3} f}{d{t}^{3}}} \right) ^{2}<br />

I don't think I've seen this particular result in a textbook anywhere, hopefully I've carried out all the steps correctly.

It looks like we have on term that's proportional to velocity * acceleration, and another term that's proportional to distance * rate of change of acceleration. These terms are added together and squared.

 

[tehno]

Differential equations of motion for such problems can not be solved explicitely.Even in the case of classical mechanics when the energy of the system is conserved.Even worse,we would have sort of damping
due to energy loss of gravitational radiation here.

 

[yogi]

.Even in the case of classical mechanics when the energy of the system is conserved.Even worse,we would have sort of damping
due to energy loss of gravitational radiation here.

Isn't that what pervect derived - the damping consequent to the radiated power. The loss of gravitational energy to space is manifested by radiation reaction forces that dampen the motion within the system. While it is true that the quadrapole energy flux formula does not come from an exact solution of Einstein's equation - the approximations are consistent with the observations.

But I still wonder about my original query - in a matter system that by definition does not lead to gravitational radiation (because of symmetrical destruction, with no velocity or unbalanced acceleration or rotational components) there will nonetheless be an information signal heralding a diminution in the gravitational field experienced by nearby masses.

 

[quantum123]

The fact that gravitational waves have not been observed yet by these detectors was expected.

Yes, they were expected but was never announced in the first place. If it were announced, do you think the project would have been given a go-ahead? Lots of promises are given everytime in the attempt to get money. And such words are given only after the project fails to give any results. There is a feeling of deception.

 

[Stingray]

Yes, they were expected but was never announced in the first place. If it were announced, do you think the project would have been given a go-ahead? Lots of promises are given everytime in the attempt to get money. And such words are given only after the project fails to give any results. There is a feeling of deception.

There was no deception. If you go into the relevant papers, it was always made clear how hard it would be to detect gravitational waves. I've also spent the last 8 years or so around people heavily involved with LIGO. They have always emphasized that it would be surprising if the 1st generation machine detected anything interesting.

 

[pervect]

Differential equations of motion for such problems can not be solved explicitely.Even in the case of classical mechanics when the energy of the system is conserved.Even worse,we would have sort of damping
due to energy loss of gravitational radiation here.

I'm not sure if I mentioned it in this thread or another, but formulas I gave earlier are the gravitational equivalent of the Lamor radiation formulas for electromagnetism. The goal is to get a reasonable approximate answer in analytical form.

People can and do get better results with numerical simulations of black hole collisions directly from the Einstein field equations - but you won't find that sort of detail in a PF post, you'll have to go to the source papers. Attempting to insure that these sorts of numerical simulations are accurate is a difficult task. I gather that there has been a lot of progress in the field of how to make "good" numerical simulations in General Relativity, but I don't know much about the details.

I don't think there are many numerical simulations of "head on" collisions however, that would be a rather unlikely scenario and given the amount of effort involved, the researchers are interested in simulating events that might actually happen. Most of the simulations I've heard of are various forms of inspirals.