"It turned out that nature was very kind, and there appear to be many of these black holes in the Universe and we were lucky enough to see one." -Dave Reitze, executive director of LIGO
On September 14th, 2015, just days after turning on, the twin Advanced LIGO detectors detected the first gravitational wave signature: a merger between two black holes, of 36 and 29 solar masses. They inspiraled, they merged, and they lost 5% of their rest mass to gravitational radiation, sending ripples through the fabric of space due to Einstein’s E = mc^2. It raised a whole slew of questions: were these typical black holes? Where were the lighter ones? How many other events would LIGO see? And was this a fluke?
Image credit: NASA, of an inspiral and merger of two massive, compact objects; illustration only.
Today, a second gravitational wave event was announced: GW151226, occurring the day after Christmas, saw a 14 and an 8 solar mass black hole merger together from 1.4 billion light years away. The Universe has always been speaking to us, and thanks to the power of gravitational wave observatories, we’re finally learning how to listen in a whole new way.
Image credit: NASA’s Goddard Space Flight Center.
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@Ethan wrote:
Does this prove gravity is quantum in nature? If I understand correctly, classical mechanics says gravity is just curved space-time. If that were true then the signal would have been shorter because the event horizon wouldn't matter. Gravity can demonstrably escape a black hole. If gravity were purely classical you could gravitationally "see" the in-spiral all the way down.
Instead we have the size of the event horizon playing a role which indicates that while virtual gravitons in a gravitational field can escape an event horizon, real gravitons with real energy like the ones made in a black hole merger cannot escape the event horizon.
Is my thinking flawed here?
WaaHoooo. I can't wait until we have statistics on the mass spectrum of BH binaries.
What was the location/position of each of the black hole collisions?
How common of a thing do we expect these collisions to be, given that these two apparently happened only about 66 days apart (that is, the collisions, not the detection of the resulting gravitational waves)?
@Denier #1: Your thinking here is flawed. The signal for GW151226 lasted longer GW150914 did than because the initial pair of black holes were _lower_ in mass. That means that both (a) they orbit(ed) each other more slowly, and (b) they radiated away less energy per orbit, and hence the inspiral would take longer.
I am not entirely sure what Ethan meant by "the signal was stronger" here. The event was farther away, and for gravitational waves, the amplitude falls off linearly with distance (which is how we can extract the distance, by the way!). The total integrated energy was lower, and combining those two would suggest to me a "weaker" signal (whatever that means).
The nice thing about the total signal lasting longer means you have more data to integrate, so the statistical significance goes up, but it's 5.3 sigma here vs. 5.1 sigma for the 14 Sep event, which is a pretty marginal comparison.
@Deceiver #3: Why not read the papers themselves (or even the abstracts) and learn something for yourself? Or is that too difficult?
https://www.ligo.caltech.edu/page/detection-companion-papers
To Mikey the SLACer #5:
“@Deceiver #3: Why not read the papers themselves (or even the abstracts) and learn something for yourself? Or is that too difficult?”
Why does Ethan write words here on this blog and link to his columns at Forbes, and not instead just give us a list of papers and abstracts to read,
with a parting kiss and a “Have fun! Isn’t science great!”??
I’ll repeat my questions – NEITHER OF WHICH have been answered by Ethan’s material NOR the several OTHER articles I’ve read on this subject:
1)What was the location/position of each of the black hole collisions?
(For example, in *simple terms*: ‘GW151226 emanated from XYZ galaxy which is North of our orbit, and GW150914 emanated from ABC galaxy which is South of our orbit.)
2)How common of a thing do we expect these collisions to be, given that these two apparently happened only about 66 days apart (that is, the collisions, not the detection of the resulting gravitational waves)?
Also, Mikey, for at least the third time now, I’ll ask you
1) Who do you think my “Master” is?
2) Do you believe this “Master” actually exists, is a real being?
The relevant draft did wind up being separated into ApJL and ApJS entries, mind you.
Anyway, 2–53 per year per comoving gigaparsec.
^ "comoving cubic gigaparsec"
This is all pointless, I realize, given that S.N. would object to the unit if he could figure it out in the first place.
Just idly, when did BBH start to take over from BHB?
Oh, man, I needed that after a rough day. Once again, S.N. incoherently blurts out geocentrism.
C'mon, S.N., you already failed the first time around with the "conservation of energy" routine, and you clearly don't understand the instant topic, so let's talk turkey.
What's the difference between a reference frame and a reference system? Shouldn't you just stop wasting electrons and people's time if you're too much of a weakling to actually choose a specific problem with the distance ladder and defend it in your own words?
No supernova yet, when could we expect those to show up?
^ Or, more succinctly, what part of triangulation do you not understand?
About the same time as before.
Re: the question of where the detected BH merger was, here is a map with both detections on it, including various confidence limits. My guess is that the uncertainties have to do with the geometry of the two LIGO sites compared to the origin point when the detection occurs, with more roundish confidence regions on the first event indicating that the US was more "face on" to the first one than the second one.
Hmmm my link doesn't appear to work. Here's the address:
https://www.ligo.caltech.edu/image/ligo20160615b
@eric #14: Nice! In fact, the timing difference tells you more about the orientation.
GW150914 was seen at Livingston about 7 ms before Hanford, which places it in the southern sky, and very roughly "edge on" to the two detectors (because the line of sight between them is somethling like10 ms).
GW151226 had only 1.1 ms delay between the two signals, suggesting a face on view. The error swath is larger because the source could be essentially anywhere on the ring of sky that bisects the two locations.
@eric #15
I wonder what causes the confidence boundaries to be jagged like that and why there's a nose on the Sept 14 merger only in the 90% confidence boundary. Weird.
@16: Ah, thanks for that correction, that makes sense.
@17: I have no idea about the hump. Maybe Ethan can get one of the people who drew it to do a guest post.
To eric #15:
Thanks for the link. But it says only this:
“The APPROXIMATE locations of the two gravitational-wave events detected so far by LIGO are shown on this sky map… the outer purple line defines the region where the signal is predicted to have come from with a 90 percent confidence level; the inner yellow line defines the target region at a 10 percent confidence level.”
How is it that the scientists can be so specific about the collision events (e.g. The first being two large black holes — 36 and 29 solar masses — merging together 1.3 billion light years away; the second being two black holes, 14 and 8 solar masses apiece, merging together from 1.4 billion light years away) yet be so fuzzy on WHERE the collisions happened?
@19
Estimates of the masses and distance are related to characteristics of the waveform detected.
Estimates of event location are related to the difference in wave arrival times and the orientation of the detectors. For more info see, for instance, http://arxiv.org/pdf/0812.4302.pdf
@See Noevo #19: Now this is a very reasonable question. The short answer is that very different data are used for the two kinds of information. This is described in great detail in the published papers, and I try to outline it simply below.
The information about the "collision events" (masses, orbital eccentricity, spins, etc., and even the distance) comes from the detailed shape and structure of the signal itself. General relativity allows us to calculate very precisely what a GW waveform "should look like," given the masses and spins, of the two initial BHs or NSs. That calculation can be inverted, so that given a waveform from the data, you can extract the parameter values needed to fit it.
The information on the location (position on the sky) of the event comes almost exclusively from the relative arrival times of the signals at the two separated detectors. There is a bit of position information in the relative phase of the signals at the two separated detectors, but not a lot.
With just one detector, you don't have any timing information, and so the event could come from _anywhere_ on the sky (does that make sense?). With two detectors, the (signed) time difference in arrival, combined with the known straight-line distance between them, allows you to identify an approximate _direction_ on the sky (a ring around the line connecting the two), and the phase difference can (in some cases) select just a portion of that ring.
With three or more detectors, you can effectively form multiple such "rings" from each pair, and narrow down the location to where they all intersect on the sky. The next science run (starting in October 2016, I believe) should include both LIGO detectors as well as the VIRGO detector in Italy.
1. Do you have anything resembling a point?
2. Again, what part of triangulation do you not understand? Advanced Virgo isn't on line yet, and LIGO-India is a ways off.
To Michael Kelsey #21:
It sounds like you’re saying we have “not a lot” of information on the “where” because less than three LIGOs were up and running and so they couldn’t triangulate the GW.
I can understand that.
But you also seem to be saying we actually *never detected* the subject black holes, and are only inferring they’re existence and characteristics from a wave and what theorists think the wave “should look like.”
[BTW, speaking of *never detected* (and certainly, *never seen*), do you find images like the second image in Ethan’s Forbes article to be EXTREMELY misleading? I do.]
What I’m NOT understanding is how a single wave can provide such *precise and definite* information on the culprits when the culprits had not otherwise been *detected.*
A SIMPLIFIED ANALOGY might be that I don’t understand how detecting a 16 “Wave” can assure you it’s the result of an 8 “colliding” with a 2. Maybe it’s the result of a 4 x a 4, or a 16 x a1.
SIMPLIFIED ANALOGY continued: Or maybe the 16 “Wave” wasn’t the result of *two* factors (i.e. 8x2 or 4x4 or 16x1) but the degradation of *one*, maybe a 32 “supernova”.
Ditto, and thanks for the added detail.
FTFY.
^ And...
I take it that the same dumb carping would apply in toto to those so-called quarks (PDF).
EpiPete: Estimates of the masses and distance are related to characteristics of the waveform detected.
Estimates of event location are related to the difference in wave arrival times and the orientation of the detectors. For more info see, for instance, http://arxiv.org/pdf/0812.4302.pdf
SN...AFTER EpiPete's explanation:
What I'm not understanding is why you repeat ask the same question after its been answered.
To eric #28:
Me: “What I’m NOT understanding is how a single wave can provide such *precise and definite* information on the culprits when the culprits had not otherwise been *detected.*”
You: “What I’m not understanding is why you repeat ask the same question after its been answered.”
Where was my question answered?
Where did someone here explain how just one wave reveals precisely
-That two (not three or more) things collided/merged, and not instead one thing that, say, exploded,
-That the two things were black holes,
-That one black hole was precisely 36 solar masses and the other was precisely 29 solar masses,
-That the collision/merge occurred 1.3 billion light years away, *even though we don’t know exactly where it was*?
Please cut me some slack, eric. I’m not perfect and I may have missed or forgotten this answer.
Where was my question answered here?
@Deceiver #29: We don't have to cut you any slack, you ignorant, lying, prick. You have been answered multiple times, at a level of detail suitable to your deliberately limited intellect. You have been given pointers to the original papers, which have all of the detail you could ever hope for. You are clearly unwilling and unable to comprehend even the simplest explanation, and unwilling to read through the primary research (unless you're doing to cherry-pick partial and fractured quotes to support your lying and deception).
Go read the paper. If you have specific, concrete questions about specific points described in the paper, come back and ask them. Otherwise, take your ignorance and lies elsewhere.
You realize that even your worthless ass emits gravitational radiation, right? No? Yes? Whatever. Jesus Christ, you "think" that maybe nobody would have noticed 32 freaking SNe in the same goddamned place at z–~ 0.1? Or one?
What happened to your "interest" in the merger rate? Slipped what passes for your mind? "Tl;dr"? Here:
"Since innocent error may attain to the firmest and sincerest conviction, the person's salvation does not seem to be greatly imperilled until good faith turns into bad faith, in which case alone the feeling of pity has no justification.
The basic principle is broadly applicable. The Kingdom of G-d is within you, remember? Protip: You're not competent to invoke "irony." If you accept immanence, you're just doing the equivalent of vomiting in a urinal. But if you insist upon transcendence, you'd have the balls to seek a pastoral evaluation of your on-line conduct.
And you demonstrably don't. You're neither more nor less than 190-proof Bad Faith, unless you want to take refuge in some sort of mangled Sartrean hilarity.
^ "z ~ 0.1"; I wanted an 'nbsp', but motor memory served up 'ndash' instead, and SB preview is as likely as unicorns boarding the Ark.
The answer was given before you asked it: because the data needed to determine 'the collision events' comes from the waveform detected, while the data needed to determine location comes from the timing and orientation of the signal compared to the detectors. Two separate types of data from the same event; if one type is precise and the other isn't, then our understanding of 'the collision events' will be more precise than our understanding of location.
Some imperfect analogies: hearing a roar and being able to tell it comes from a lion but not where the lion is. Or being able to tell that a radio station you're picking up plays rock n' roll but not where the radio transmitter is. Wave content data (frequency, amplitude, etc.) is a different thing from signal direction.
To Mikey the SLACer #30:
“You have been answered multiple times… You are clearly unwilling and unable to comprehend even the simplest explanation…”
And what would be the “SIMPLEST EXPLANATION” to a “Deceiver, ignorant, lying, prick” for…
HOW just one wave reveals precisely
– That two (not three or more) things collided/merged, and not instead one thing that, say, exploded,
– That the two things were black holes,
– That one black hole was precisely 36 solar masses and the other was precisely 29 solar masses,
– That the collision/merge occurred 1.3 billion light years away, *even though we don’t know exactly where it was*?
Please provide that simplest explanation, Mikey.
Who knows, maybe it would even help OTHER readers here.
To eric #33:
Me: “Where was my question answered?”
You: “The question we’re discussing was “How is it that the scientists can be so specific about the collision events…yet be so fuzzy on WHERE the collisions happened?” The answer was given before you asked it…”
Answered? I don’t think so.
The FULL question was: “How is it that the scientists can be so specific about the collision events **(e.g. The first being two large black holes — 36 and 29 solar masses — merging together 1.3 billion light years away; the second being two black holes, 14 and 8 solar masses apiece, merging together from 1.4 billion light years away)** yet be so fuzzy on WHERE the collisions happened?”
And I’ll repeat the question, with a little more specificity:
HOW does just one wave reveal precisely
– That two (not three or more) things collided/merged, and not instead one thing that, say, exploded,
– That the two things were black holes,
– That one black hole was precisely 36 solar masses and the other was precisely 29 solar masses,
– That the collision/merge occurred 1.3 billion light years away, *even though we don’t know exactly where it was*?
Where was THIS FULL question answered here?
SN @35
Scientists have developed a model of what the gravitational wave from a BH coalescence would look like here at earth.
The model has various parameters, that when varied will produce different looking GW waveforms.
To characterise a detected waveform, the parameters can be adjusted until the waveform they produce matches the detected waveform. For this event, the best matching parameters were, one black hole with 14 solar masses and the other with 8 solar masses, at a distance of 1.3 BLY. BTW, nowhere do they say "precisely". In fact, the mass of the larger black hole is reported as 14.2 +8.3, -3.7.
I'm not sure what you're trying to get at with your line of questioning. If you're curious about the whole detection process take a look here: https://labcit.ligo.caltech.edu/~ajw/IntroPapers/Camp-annurev.nucl.54.0…
There you go, SN, Ep Pete has given you the reference. Go. Learn.
To eric #37:
“There you go, SN, Ep Pete has given you the reference. Go. Learn.”
From EpiPete’s link I learned that
1) “The relative weakness of the gravitational force makes detection extremely challenging” and
2) That this field of gravitational wave detection and interpretation is “theoretical and experimental.”
In thinking some more about what I’ve read so far, it seems that theoretical models - models of what black hole gravitational waves (BHGW) *might* or *should* look like – were tweaked to match what *appears* to be an actual BHGW.
What could possibly be wrong with this picture?
It would be one thing if a phenomenon was seen and even experienced like, say, an earthquake, and subsequently models and detection equipment are developed to detect and measure the phenomenon.
But it’s another thing to develop models and detection equipment for a phenomenon that has never been seen or experienced like, say, the collision/merging of two black holes, and then claim the phenomenon happened because your models and detection equipment say so.
It reminds me a bit of the movie “Field of Dreams.”
You know, “If you build it, he will come.”
But here it’s “If you build the detection equipment - for about $620 million – what you want to detect will come.”
I read elsewhere that the GW was about “1/100,000 of a nanometer, about the width of an atomic nucleus.”
I just hope we’re not making a mountain out of a mole hill.
Because this Field of Dreams mole hill *may* have a mountain of other problems, including
“Non-repeatability and non-verifiability; External pressure to produce results; Lack of accuracy; Questionable laser isolation; Questionable mirror isolation; Insufficient mirror tolerances; Lack of third-party environmental monitoring; Gravitational wave angle limitations; Biased and skewed pattern matching; Misleading audio; Objects are far beyond detection range; Detection occurred before official observations began”.
http://www.skepticforum.com/viewtopic.php?t=26639
It's truly amazing that S.N. has elected to make an ass out of himself at tedious length with no other content than failure to grasp the basic notion that scientific theories make testable predictions.
On the other hand, the content of the Nicene Creed is a sure thing.
@Daran #13
LIGO should already be able to detect Supernovae, its a bit strange that they aren't showing up yet. They should be the best proof that LIGO works as we would get an second observational signal from the gamma rays. Now with the Blackholes merger we only have the signal, and we're attaching a paricular event to it without any further proof. I certainly acknowledge the simultanious 'sound' recordings, but the origin of the signal is still out of sight.
See Noevo @38
"In thinking some more about what I’ve read so far, it seems that theoretical models – models of what black hole gravitational waves (BHGW) *might* or *should* look like – were tweaked to match what *appears* to be an actual BHGW.
What could possibly be wrong with this picture?"
Clearly you see this process as "changing the theory to fit the facts", but that is not what is being tweaked. Perhaps you also see a "wave" as a simple up-down transition? The recorded wave from these events has many pulses of varying amplitude and frequency. Think of the behaviour of the pen one of those chart recorders beloved of earthquake/volcano disaster movie makers.
There is an infinite number of possibilities as to how two black holes can merge. Okay, QM may turn "infinite" into "a product of at least four incredibly large numbers" Each of the two black holes has a near infinite variability in mass. At some defined "start" of a merger there is a near infinite variability their separation, and a near infinite variability the angular momentum of the system. It is those parameters that are being tweaked in the model, not the underlying theory. The research team run huge numbers of simulations, refining those parameters each time until the predicted waveform matches the one measured by the detectors. The theory effectively predicts the starting conditions from the observed result. If you asked the team they could put your alternate hypothesised starting points in the model and show how the wave pattern predicted would be totally unlike the wave pattern measured.
Michael Kelsey @4
I think Ethan's comment about the signal being stronger stems from the increased sensitiviy of the LIGO detectors at the frequencies involved in this case.
SN @38
It's not a model that are being adjusted, it is the input to the model. Assume we make a model of the frequency, harmonics, and amplitude made by a violin string based only on the length of the string, the material it's made of (natural or synthetic, for instance), and the force used to bow it. We don't have any strings to observe so we develop the model using what we know about materials science, acoustics, etc.
As we change the parameter for string length in the model, the frequency the model outputs changes accordingly. longer length -> lower frequency, or different material -> different harmonics
Then we get a recording of an unknown sound and observe the waveform. We can take an _output_ of the model with a particular value for the length, material, and bow strength and see if it matches the waveform from the unknown sound. If it matches, then we know what we've got. If it doesn't match, we vary the string length, for instance, and check again.
We are not changing the relationship between string length and frequency in the model (shorter is still higher in frequency) we are changing the parameter for string length.
This is not to say that we never change our models, but that happens when we have new evidence that provides us with better understanding of the physical processes underlying our models. It doesn't happen in the middle of an analysis run.
Finally, our models could be wrong. Maybe how fast the string is bowed is important, and that's not in our model. But no model is exactly correct, and there's not even a need for that. If we waited until we had perfect (whatever that means) models we wouldn't have the technology that allows us to even have this conversation.
It appears to me that, in general, you purposefully misunderstand the particular science in Eathan's posts. If you have an argument to make about how science comes to know things (and this is a big, interesting, and important topic) find a blog where that is what they discuss. If you have sincere question about the science Ethan discusses, then ask here.
To Paul Dekous #40:
“LIGO should already be able to detect Supernovae, its a bit strange that they aren’t showing up yet.”
And as I asked in #3, which no one has responded to,
how common of a thing do we expect these collisions to be, given that these two apparently happened only about 66 days apart?
@Paul Dekous #40: The problem with SNe detection is that you need a large quadrupole moment (that is, anisotropy in two orthogonal directions) to generate gravitational waves. A dipole anisotropy (like the opposed jets/bubbles you can see in SN 1987a) won't generate GW.
So the question about Type II (core collapse) SNe detection rates hinges almost entirely on how asymmetric they can be. If the majority of Type II SNe are close to spherically symmetric, then we aren't going to see them. If the majority have a large quadrupole moment, then we might start seeing them.
@See Noknowledge #43: If only you could read! Ethan wrote in the very post that you're hijacking here, "If what we’ve seen so far is representative of what’s actually present in our Universe, we might expect a black hole-black hole merger as frequently as once every month or two in the LIGO detectors."
The LIGO collaboration itself, in the various papers you refuse to read, has computed a "true" (i.e., accounting for detector efficiency, threshold, etc.) rate of between 6 and 400 per cubic gigaparsec per year.
@Paul Dekous #40: Besides SNe, the other, probably better, source with an electromagnetic counterpart is binary neutron star mergers. These had been suggested as the most likely "first signal" in LIGO, because they should be more common than binary black holes (it's expected to be easier for binary star systems to both become neutron stars over time, than both become black holes).
The downside to NS-NS mergers is the masses are substantially lower than for black holes (that pesky Chandrasekhar limit :-), which means the signal will be lower in amplitude than for a BH-BH merger at the same distance.
To Epi Pete #42:
“It’s not a model that are being adjusted, it is the input to the model.”
Even IF so, they are at least tweaking the inputs until the output of the *theoretical* model matches the *real* phenomenon, or apparently real phenomenon.
............
“Assume we make a model of the frequency, harmonics, and amplitude made by a violin string based only on the length of the string, the material it’s made of (natural or synthetic, for instance), and the force used to bow it. We don’t have any strings to observe so we develop the model using what we know about materials science, acoustics, etc.”
Or you could develop the model based on what even the modelers have “seen (or heard) and even experienced”, namely, the sound of someone playing a violin.
(But I can sympathize with your trying to come up with an analogy for something no one has seen, heard or experienced.)
Comments 8 and 9, genius.
To Mikey the SLACer #45:
“If only you could read! Ethan wrote in the very post that you’re hijacking here, “If what we’ve seen so far is representative of what’s actually present in our Universe, we might expect a black hole-black hole merger as frequently as once every month or two in the LIGO detectors.”
I’ll modify my question to make clearer what I was getting at:
“How common of a thing *DID* we expect these collisions to be, given that these two apparently happened only about 66 days apart?”
In other words, WERE the scientists SURPRISED by the short time between the two black hole GWs?
(I might also ask if they’re surprised they have NOT yet detected GWs from supernovae.)
This is very different from what Ethan is saying.
So, in your state of epistemological constipation, the proper understanding of the Theremin should have awaited one's being observed in nature?
Oh, and one other thing, Mikey,
about “Ethan wrote in the very post that YOU’RE HIJACKING here”,
What’s the definition of “hijacking a post/thread”?
Prior to this post, I had 13 of the 49 posts, a little over a quarter.
Or is “hijacking” similar to the definition of “trolling” here? “Trolling”, as in posting comments which *challenge or contradict* the point of view of the author and other sheep, I mean, other commenters?
You are trolling sn, for a variety of reasons
- you are intentionally misrepresentating what you've been told
- you are failing to read the references you've been givenjoying
- you are asking questurns with no intention of working to understand the answers
- you are repeatedly whoring yourself as some type of victim
^ I suppose it's also completely unpossible to infer anything from the observation of strong gravitational lensing based on the theory that predicted it.
Here, S.N.
Gee, S.N., if your level of asshurt is leading to this level of moronic screeching, perhaps you need a change of scene. This seems to be crying out for your insight.
So challenging.
To Naked Bunny with a Whip #55:
And on YOUR side, we have something more like this
(it’s even science-y!):
https://www.youtube.com/watch?v=1qQEsVl0wkQ
Protip, S.N.: A hallmark of Eternal September is making too many ignorant assumptions.
^ Dammit (missed opening quote).
If one traces back S.N.'s perhaps* randomly G—led link, it leads to one "Shannon Sims," of plasma-dot-pics. Draw your own conclusions.
* It also appears to have dropped this at WUWT.
Mike, the difference between 5.1 and 5.3 sigmas is bigger than 0.2 sigmas.
My first thought was just that signal to noise was higher for the longer lasting process. So I suspect this is what Ethan meant.
"What I’m not understanding is why you repeat ask the same question after its been answered."
See Nowt doesn't understand, doesn't WANT to unerstand and won't STOP not understanding, because while they remain in their comforting incomprehension, they can keep JAQing off and complaining that you MUST be wrong because see nowt doesn't understand.
ALL of which would be lost if it made any successful effort to understand, and, since that effort would be done knowing it was wasted, is not even tried by See Nowt.
Just treat it the same as sn's "AFAIK". Who cares what it knows or doesn't? How can we tell it's warranted or manufactured? SN needs to define for us before we can begin to care which it is.
"It appears to me that, in general, you purposefully misunderstand the particular science in Eathan’s posts"
Bingo!
@Wow #60: I presume you're referencing my #4, where I wrote, "5.3 sigma here vs. 5.1 sigma for the 14 Sep event, which is a pretty marginal comparison."
Well, let's compare the two marginal populations (i.e., how much of the Gaussian integral is outside N sigma). 5.1 sigma corresponds to a "P-value" of 3.4e-7, while 5.3 sigma is 1.16e-7. The difference between those two is superficially a factor of two, but both of them are way, way out on the tails.
My experience (and yours, I'm sure) is that assuming perfectly Gaussian behaviour for any detector system on the tails is a pretty stupid move :-)
Without some really solid assurance that all of LIGO's systematics are perfectly Gaussian, I would not claim that 5.1 vs. 5.3 sigma is internally significant. Both of them are equally, and highly, significant compared to the null hypothesis (i.e., random background), but comparing the two on this basis isn't a very useful exercise, I think.
W against T, reference required. #conspiracyofscience
"The difference between those two is superficially a factor of two"
The deifference between them IS (actually MORE THAN) two, mike.
Really that's End Of Story.
I'm much much stronger than an ant, and I'm probably quite a bit stronger than you. The fact that we're both out on the tail of strength when including each living entity on the planet is really rather unimportant unless that's somehow essential to your thesis.
"My experience (and yours, I’m sure) is that assuming perfectly Gaussian behaviour for any detector system on the tails is a pretty stupid move"
But generally, because reality is limited whilst the model for gaussian is infinite, it's generally that the further off the tail you are, the more wrong gaussian is.
But like I said, when something is twice as likely as another, then that's quite a big difference between those two things.
Since nobody had mentioned a third option, let alone the entire spectrum of possibilities, it's really rather irrelevant to compare them.