Dispersion of gravitational waves

[bcrowell]

The LIGO paper https://dcc.ligo.org/LIGO-P150914/public puts limits on the dispersion of gravitational waves, which can be interpreted as an upper limit of 10^-22 eV on the mass of the graviton. We all know that low-amplitude gravitational waves are supposed to propagate at c according to the Einsten field equations, although proving this is a bit of work and not entirely transparent. Clearly if gravitational waves have some fixed velocity, it has to be c, because there is no other invariant velocity. I guess if the graviton had a mass, there would have to be some other unitful constants in the field equations besides G and c, since you can't build anything with units of mass out of G and c.

But is there any simple way of looking at the field equations and seeing that they predict no dispersion for gravitational waves? By "simple" I mean something simpler than linearizing them and showing that the solutions propagate at c.

There was a time about 10 years ago when Lee Smolin was pushing the idea that LQG predicted dispersion of light, and he claimed that there were prospects for testing and confirming that prediction soon. Turns out that he was wrong on theoretical grounds. I wonder if this limit on dispersion of gravitational waves puts any constraints on LQG or any other theories of quantum gravity.

 

[ProfChuck]

Verification of the existence of gravitational waves is important but not really unexpected. Einstein's field equations predict (assume?) that G Waves will propagate at light speed which suggests that Maxwell's relationship between the characteristic impedance of free space and c extends beyond electromagnetic radiation and that gravitational waves are subject to the same underlying space-time structure. The logic is sound but the propagation velocity of G waves has never been measured. Such a measurement would provide yet another validation of general relativity. It is possible that the LIGOS interferometer can support such a measurement. The Abbot paper on G Wave observation is consistent with Vg=c but I am not sure that their discovery rises to the level of confirmation.

 

[Buzz Bloom]

The logic is sound but the propagation velocity of G waves has never been measured.

Hi ProfChuck:

You may want to look through the other threads about LIGO. Unfortunately I don't remember which one, and my search effort was not successful.

One of the posts calculated the speed of the detected wave as it moved from the Washington site to Texas (or vise versa). It was slightly slower than c, and the the difference was within the measurement error.

Regards,
Buzz

 

[fresh_42]

#144 in https://www.physicsforums.com/threads/advanced-ligo-detection.836670/page-8

 

[ProfChuck]

The frequency of the G waves is low, a few hundred hz, and the light time separation between the two sites is about 10ms It is difficult to measure Vg with high accuracy under these conditions. The measurement results are consistent with Vg=~c but, like the equivalence principal it would be nice to have a more accurate measurement.

 

[mfb]

Just by the time difference, a single event does not allow to set a lower limit on speed - the wave could be very slow if its propagation is nearly perpendicular to the line between the two detectors. More events will rule out that option, and a careful analysis of the polarization and relative amplitudes helps as well. Also, a speed notably slower than c without dispersion would be really odd.

 

[ProfChuck]

Hi ProfChuck:

You may want to look through the other threads about LIGO. Unfortunately I don't remember which one, and my search effort was not successful.

One of the posts calculated the speed of the detected wave as it moved from the Washington site to Texas (or vise versa). It was slightly slower than c, and the the difference was within the measurement error.

Regards,
Buzz

If it turns out that Vg is differeng

Just by the time difference, a single event does not allow to set a lower limit on speed - the wave could be very slow if its propagation is nearly perpendicular to the line between the two detectors. More events will rule out that option, and a careful analysis of the polarization and relative amplitudes helps as well. Also, a speed notably slower than c without dispersion would be really odd.

Any speed other than c would require a serious examination of the Einstein field equations and general relativity. Proving that Vg=c would provide additional confirmation to GRT. If Vg does not = c then that would suggest new physics.

 

[Buzz Bloom]

Just by the time difference, a single event does not allow to set a lower limit on speed - the wave could be very slow if its propagation is nearly perpendicular to the line between the two detectors.

Hi mfb:

From http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.061102
With only two detectors the source position is primarily determined by the relative arrival Time and localized to an area of approximately 600 deg² (90% credible region).

I think this implies that the calculation of the speed of the wave between Washington and Texas was used to calculate the 600 deg² value.

Regards,
Buzz

 

[ProfChuck]

Hi mfb:

From http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.061102
With only two detectors the source position is primarily determined by the relative arrival Time and localized to an area of approximately 600 deg² (90% credible region).

I think this implies that the calculation of the speed of the wave between Washington and Texas was used to calculate the 600 deg² value.

Regards,
Buzz

In summation: Do gravity waves exist? Yes. Does Vg=c? Insufficient data.

 

[mfb]

@Buzz Bloom: that localization assumed light-speed propagation.

 

[Buzz Bloom]

that localization assumed light-speed propagation.

Hi mfb:

Thank you for clarifying. That was what I guessed, but i wasn't sure.

Regards,
Buzz

 

[ProfChuck]

A pivotal question: "Do gravitational waves constructively interfere?" If so it may be possible to construct a device that generates a coherent monochromatic beam of gravitational radiation that is powerful enough to be detected by a LIGOS interferometer.

 

[mfb]

A pivotal question: "Do gravitational waves constructively interfere?" If so it may be possible to construct a device that generates a coherent monochromatic beam of gravitational radiation that is powerful enough to be detected by a LIGOS interferometer.

If you have 10¹⁵ massive spinning objects, maybe. That's about the amplification factor you would need. So if we convert Earth into a huge array of spinning objects, ...

 

[ProfChuck]

If you assume constructive interference and the gravitational equivalent of a traveling wave amplifier it might just be doable. I am looking at the math. The machine would be huge and would push materials science but the rewards would be significant. Among other things it would provide a direct measure of Vg which would be another GTR confirmation. Fantastic? Yes, Impossible? Maybe not. Think of a dynamic version of the Cavendish experiment.

 

[mfb]

I am looking at the math.

So what do you need as source?

A direct measurement of the speed of gravitational waves will come once more detectors are in operation.

 

[ProfChuck]

Actually, what I have in mind is more of a traveling wave gravitational oscillator than amplifier. It would produce a bidirectional coherent beam of gravitational radiation at a selectable frequency. Unfortunately, my initial calculations suggest that in order to produce G waves detectable by LIGO the machine would need to be over 200 km long with several hundred rotors with diameters over 80 meters. Difficult but, in principal, not impossible. Hmmm.

 

[ProfChuck]

It would also require several tons of depleted uranium to act as mass couple pairs. I can't imagine that anyone would be willing to fund such a thing.

 

[Vanadium 50]

If you can build it at all, you certainly don't need Uranium. Tungsten is both denser and cheaper.

The bigger problem is the power. To be as loud at 900 miles as the gravitational wave source was at 1.3 GLy, you need a power in the gravitational spectrum of 750 MW. Since only a tiny fraction of the power will go into gravitational radiation, you need a huge power source - probably more than the entire power generation of Earth, which is only about 15 TW,

Where are you a professor?

 

[ProfChuck]

Yes, Tungsten would work. I agree, with the parameters you mention it is impractical. Just a fun exercise. But the same thing was said about
Alcubierre drive. New numbers have moved it from the impossible to the really really hard.
I am retired now. I worked at NASA/JPL as a research scientist and pilot for 40 years and taught astronomy and physics at several different colleges as a visiting professor.

 

[Vanadium 50]

But the same thing was said about Alcubierre drive.

I don't see one of those either.

 

[PeterDonis]

the gravitational equivalent of a traveling wave amplifier

Which would be what, exactly?