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Gravitational Waves Discovered

 
 
 
I've read the articles, and I still can't understand where the colliding black holes fit into the discovery process. Did they know about them beforehand, and then find that the gravity wave came from the same direction, or did they somehow extrapolate that the gravity wave could ONLY have been caused by the collision of two black holes?
 
PyramidHead said:
I've read the articles, and I still can't understand where the colliding black holes fit into the discovery process. Did they know about them beforehand, and then find that the gravity wave came from the same direction, or did they somehow extrapolate that the gravity wave could ONLY have been caused by the collision of two black holes?
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The idea of gravity waves are a necessary conclusion of the theory of relativity. If massive bodies deform spacetime as described by relativity then a pair of massive bodies in close orbit will set up a "rhythmic" disturbance in spacetime that will propagate out as gravity waves. We hadn't detected gravity waves and this pair of detectors was essentially a test of the theory of relativity - which it seems to have passed. It doesn't have to be black holes. A pair of neutron stars should do the same but, since they are less massive, the disturbance would be less so more difficult to detect. In fact, planets orbiting sun should create gravity waves but much, much, much less intense. It is the orbiting of the pair of black holes that created the gravity waves but when they merged making one black hole the gravity waves they had been creating stopped - the "chirp".
 
skepticalbip said:
PyramidHead said:
I've read the articles, and I still can't understand where the colliding black holes fit into the discovery process. Did they know about them beforehand, and then find that the gravity wave came from the same direction, or did they somehow extrapolate that the gravity wave could ONLY have been caused by the collision of two black holes?
Click to expand...
The idea of gravity waves are a necessary conclusion of the theory of relativity. If massive bodies deform spacetime as described by relativity then a pair of massive bodies in close orbit will set up a "rhythmic" disturbance in spacetime that will propagate out as gravity waves. We hadn't detected gravity waves and this pair of detectors was essentially a test of the theory of relativity - which it seems to have passed. It doesn't have to be black holes. A pair of neutron stars should do the same but, since they are less massive, the disturbance would be less so more difficult to detect. In fact, planets orbiting sun should create gravity waves but much, much, much less intense. It is the orbiting of the pair of black holes that created the gravity waves but when they merged making one black hole the gravity waves they had been creating stopped - the "chirp".
Click to expand...

I see. So the fact that they were able to detect the signal at all, and that it was 24 times higher than background noise, proves it must have originated from colliding black holes.
 
Does the strain fall off as inverse square? If so, how large would it be at say 1 au from the merger?

Could it do mechanical heating or chemical bond breaking?

Can't find units of the shear modulus of space in response to gravitatonal stress... or any info...
 
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PyramidHead said:
skepticalbip said:
The idea of gravity waves are a necessary conclusion of the theory of relativity. If massive bodies deform spacetime as described by relativity then a pair of massive bodies in close orbit will set up a "rhythmic" disturbance in spacetime that will propagate out as gravity waves. We hadn't detected gravity waves and this pair of detectors was essentially a test of the theory of relativity - which it seems to have passed. It doesn't have to be black holes. A pair of neutron stars should do the same but, since they are less massive, the disturbance would be less so more difficult to detect. In fact, planets orbiting sun should create gravity waves but much, much, much less intense. It is the orbiting of the pair of black holes that created the gravity waves but when they merged making one black hole the gravity waves they had been creating stopped - the "chirp".
Click to expand...

I see. So the fact that they were able to detect the signal at all, and that it was 24 times higher than background noise, proves it must have originated from colliding black holes.
Click to expand...
I would see it a little differently. The fact that it was 24 times background noise would indicate it was a real signal, not noise and the only source we know of with sufficient mass would be black holes. The fact that the signal was periodic with steadily increasing frequency would indicate (assuming the prediction of relativity) that the orbits were decaying, as predicted. The fact that the signal stopped would indicate that the two bodies merged, as predicted. The test didn't "prove" but it was a very good indication that what the theory of relativity describes is accurate.
 
repoman said:
Does the strain fall off as inverse square? If so, how large would it be at say 1 au from the merger?

Could it do mechanical heating or chemical bond breaking?

Can't find units of the shear modulus of space in response to gravitatonal stress... or any info...
Click to expand...

I found this, but I don't understand it, http://web.mit.edu/edbert/GR/gr1.pdf .
 
ryan said:
repoman said:
Does the strain fall off as inverse square? If so, how large would it be at say 1 au from the merger?

Could it do mechanical heating or chemical bond breaking?

Can't find units of the shear modulus of space in response to gravitatonal stress... or any info...
Click to expand...

I found this, but I don't understand it, http://web.mit.edu/edbert/GR/gr1.pdf .
Click to expand...

Vector is a directional derivative. If you have a function of many variables then you choose some directions and see how functions change along this directions. Then you define vector space which is basically if A and B belongs to vector space then aA+bB (a,b are just numbers) belongs to it too. Now concept of basis, basis is just a set of vectors in which all other vectors can be expressed as a linear combination of basis vectors.
Now you can define a linear map which maps vector to a number, interestingly enough that map turns out to be a vector space itself, it's called co-vector space. So co-vector is essentially a map from vector space to R (real or complex numbers). and vector space is the same for co-vector space. What it all means is that if you have vector and co-vector they can be translated/mapped into a simple number. Very neat.
Now about tensors. Suppose you have two vectors, you can form direct product of them, basically multiply components from one vector to another, so if dimension of your space is N then you will have N numbers for one vector and N for another. N*N for direct product. Now you can make linear space of these direct products too. That is called a tensor rank 2. You can do the same for 3 vectors that will have N*N*N components and be called ran 3 tensor. You can do the same for co-vector space and for both too. But you have to remember how many vectors are from vector space and how many for co-vector space.

Any questions?
 
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I meant more like Young's Modulus, but for spacetime.

E = young's modulus

YM_03.JPG

young-modulus-3.jpg

of course, I would imagine the spacetime stress/strain modulus would be a lot more complicated than Young's modulus. Also, maybe even the units are totally different.

Wow, I found a 1969 paper about gravitational wave detection written by Freeman Dyson (he credits J. Weber):
http://articles.adsabs.harvard.edu//full/1969ApJ...156..529D/0000529.000.html

I am super rusty, but equations 2.28 and 3.19 look interesting.

He is saying that the small strain is partly from the fact that the speed of light and speed of the shear wave through the earth don't match well and leads to a very poor power transfer from the gravitational waves. Is the term "coupling" useful here? As in gravitational waves poorly couple with terrestrial density materials.

The paper may actually answer my questions, but I am too innumerate now to understand it.
 
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So if this discovery of gravity waves is not a false alarm like the last time, over enthusiasm, does it confirm inflation theory?
 
DBT said:
So if this discovery of gravity waves is not a false alarm like the last time, over enthusiasm, does it confirm inflation theory?
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I don't think so. Not that inflation need any confirmation. And gravitational waves have been indirectly observed before.
 
repoman said:
I saw this one tweet related to a science conference saying that spacetime has a modulus of 10^24 GPa. I can't find more info.
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The speed of a wave in an elastic medium is the square root of the modulus of elasticity divided by the density. Since gravity waves propagate at the speed of light, that would appear to be equivalent to saying that spacetime has a density of 1013 kg/L, like neutron star material. It's not clear what it would mean for spacetime to have a density.
 
The journal paper:
Phys. Rev. Lett. 116, 061102 (2016) - Observation of Gravitational Waves from a Binary Black Hole Merger
Its abstract:
On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10^−21. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410+160−180 Mpc corresponding to a redshift z=0.09+0.03−0.04. In the source frame, the initial black hole masses are 36+5−4 M⊙ and 29+4−4 M⊙, and the final black hole mass is 62+4−4 M⊙, with 3.0+0.5−0.5 M⊙c^2 radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.
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It was detected with the two detectors of  LIGO, one at Hanford, WA, and the other at Livingston LA. The similar signals observed at both sites helped rule out the hypothesis that the observed signal was noise. The Europeans'  VIRGO interferometer was not operating at the time, but it should be later this year. It is a single detector near Pisa, Italy, and it will be operated in collaboration with LIGO.

Since only two detectors "saw" it, the delay between them constrains the source direction to a circle in the sky. It may be possible to get a further constraint from the relative intensities of the signals, but I'm not sure if the LIGO team did that. However, one may get some combination of (source direction) and (source orientation).

Now that this detector evidently saw something, I think that that will make it easier for other G-wave research teams to get support for their efforts. There's already an under-construction one in Japan (KAGRA) and a proposed one in India (INDIGO).

Here's a table of results:
What | Mass (Msun) | Spin (relative)
Primary | 36 +5-4 | < 0.7
Secondary | 29 +4-4 | poorly constrained
Final | 62 +4-4 | 0.67 +0.05-0.07
About 3 +0.5-0.5 solar masses of energy was radiated as G-waves.

Its peak G-wave luminosity was (3.6 +0.5−0.4)×10^56 erg/s, equivalent to 200 +30−20 solar masses / second. The Sun has a luminosity of 3.9 * 10^26 watts in the electromagnetic spectrum -- that gives about 10^23 solar luminosities for this event, or somewhere around the combined luminosity of every star in the observable Universe.

The progenitors of those two black holes were likely very massive stars with relatively weak stellar winds, meaning that they retained much of their original mass before collapsing. Their metallicity or heavy-element content was likely <~ 1/2 that of the Sun. "Heavy" being everything heavier than helium. So their protostellar nebula(e) was not as enriched as the Sun's was. This is consistent with their being very old stars whose black holes then spiraled in over the lifetime of the Universe. Or else with much younger ones that formed in a metal-poor galaxy with star formation (there are some such galaxies).

The observation suggests an event rate somewhere within various estimates of the rates of mergers of massive black holes. It is only one observation, so it will be necessary to observe more events to get a better fix.

Identifying the event's home galaxy will be more difficult, since it will likely require G-wave detectors in outer space outside of low Earth orbit. That's what's necessary to get a good baseline to get a good fix on an event's position.
 
repoman said:
Does the strain fall off as inverse square? If so, how large would it be at say 1 au from the merger?

Could it do mechanical heating or chemical bond breaking?

Can't find units of the shear modulus of space in response to gravitatonal stress... or any info...
Click to expand...
Energy per square meter presumably falls off as inverse square, which would imply amplitude falls off as the reciprocal of distance. Based on lpetrich's numbers, that suggests an object 1 au from ground zero (sky zero?) would be stretched and compressed by one part in ten million. I'm guessing neutrinos would do more damage.
 
So, strain of 10^-7 is what would happen to an earth at that distance. But does earth like material not couple efficiently with the wave? Is spacetime strained a lot more?
 
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