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Friday, November 16, 2018

New paper claims that LIGO’s gravitational wave detection from a neutron star merger can’t be right


Two weeks ago, New Scientist warmed up the story about a Danish groups’ claim that the LIGO collaboration’s signal identification is flawed. This story goes back to a paper published in Summer 2017.

After the publication of this paper, however, the VIRGO gravitational wave interferometer came online, and in August 2017 the both collaborations jointly detected another event. Not only was this event seen by the two LIGO detectors and the VIRGO detector, several telescopes also measured optical signals that arrived almost simultaneously and fit with the hypothesis of the event being a neutron-star merger. For most physicists, including me, this detection removed any remaining doubts about LIGO’s event-detection.

Now a few people have pointed out to me that the Journal of Cosmology and Astroparticle Physics (JCAP) recently published a paper by an Italian group which claims that the gravitational wave signal of the neutron-star merger event must be fishy:

    GRB 170817A-GW170817-AT 2017gfo and the observations of NS-NS, NS-WD and WD-WD mergers
    J.A. Rueda et al
    JCAP 1810, 10 (2018), arXiv:1802.10027 [astro-ph.HE]

The executive summary of the paper is this. They claim that the electromagnetic signal does not fit with the hypothesis that the event is a neutron-star merger. Instead, they argue, it looks like a specific type of white-dwarf merger. A white-dwarf merger, however, would not result in a gravitational wave signal that is measurable by LIGO. So, they conclude, there must be something wrong with the LIGO event. (The VIRGO measurement of that event has a signal-to-noise ratio of merely two, so it doesn’t increase the significance all that much.)

I am not much of an astrophysicist, but I know a few things about neutron stars, most notably that it’s more difficult to theoretically model them than you may think. Neutron stars are not just massive balls that sit in space. They are rotating hot balls of plasma with pressure gradients that induce various phases of matter. And the equation of state of nuclear matter in the relevant ranges is not well-understood. There’s tons of complex and even chaotic dynamics going on. In short, it’s a mess.

In contrast to this, the production of gravitational waves is a fairly well-understood process that does not depend much on exactly what the matter does. Therefore, the conclusion that I would draw from the Italian paper is that we are misunderstanding something about neutron stars. (Or at least they are.)

But, well, as I said, it’s not my research area. JCAP is a serious journal, and the people who wrote the paper are respected astrophysicists. It’s not folks you can easily dismiss. So I decided to look into this a bit.

First, I contacted the spokesperson of the LIGO collaboration, David Shoemaker. This is still the same person who last year answered my question what the collaboration’s response to the Danish criticism is by merely stating he has full confidence in LIGO’s results. Since the Danish group raised the concern that the collaboration suffers from confirmation bias, this did little to ease my worries.

This time I asked Shoemaker for a comment on the Italian groups’ new claim that the LIGO measurement conflicts with the optical measurements. Turns out that his replies landed in my junk folder until I publicly complained about the lack of response, which prompted him to try a different email account. Please see update below.

Secondly, I noticed that the first version of the Italian group’s paper that is available on the arXiv heavily referenced the Danish group.


Curiously enough, these references seem to have entirely disappeared from the published version. I therefore contacted Andrew Jackson from the Danish group to hear if he has something to say about the Italian group’s claims and whether he’d heard of them. He didn’t respond.

Third, I contacted the corresponding author of the Italian paper, Jorge Rueda, but he did not correspond with me. I then moved on to the paper’s second author Remo Ruffini, which was more fruitful. According to Wikipedia, Ruffini is director of the International Centre for Relativistic Astrophysics Network and co-author of 21 textbooks about astrophysics and gravity.

I asked Ruffini whether he had been in contact with the LIGO collaboration about their findings on the neutron star merger. Ruffini did not respond to this question, though I asked repeatedly. When I asked whether they have any reason to doubt the LIGO detection, Ruffini referred me to (you’ll love this) the New Scientist article.

I subsequently got Ruffini’s permission to quote his emails, so let me just tell you what he wrote in his own words:

“Dear Sabine not only us but many people are questioning the Ligo People as you see in this link: the drama is of public domain. Remo Ruffini”

Michael Brooks, btw, who wrote the New Scientist article knew about the story because I had written about it earlier, so it has now gone around a full circle. After I informed Ruffini that I write a blog he told me that:

“we are facing the greatest dramatic disaster in all scientific world since Galileo. Do propagate this dramatic message to as many people as possible.”

Yo.

Update: Here is the response from Shoemaker that Google pushed in the junk folder (not sure why). I am sorry I complained about the lack of response without checking the junk folder - my bad.

He points out that there is a consensus in the community that the gravitational wave event in question can be explained as a neutron-star merger. (Well, I guess it’s a consensus if you disregard the people who do not consent.) He also asks me to mention (as I did earlier) that the data of the whole first observing run is available online. Alas, this data does not include the 2017 event that is under discussion here. For this event only a time-window is available. But for all I can tell, the Italians did not even look at that data.

Basically, I feel reassured in my conclusion that you can safely ignore the Italian paper.

2nd Update: The non-corresponding corresponding author of the Italian paper has now popped up after being alerted about this blogpost. He refuses to comment on his co-author’s claims that LIGO is wrong and the world needs to be told. Having said this, I wish all these people would sort out their issues without me.

45 comments:

  1. They correspond through published papers. It's excruciatingly slow, but it's public (if you pay...) and we get to see all the gory details. What we need next as a blogger expert in all the covered areas and good as you when explaining it!

    Perhaps you'd have more luck with a common post between you and some astrophysicist blogger that know about these stars (whether white dwarf or neutron star) and is interested.

    ReplyDelete
  2. My understanding of the danish groups claim is that they find small correlations that are not explained by the gravitational models, but also to my understanding the models used by LIGO are quite simplified using something on the order of 10 parameters, which I imagine come from angular velocities of each black hole the angular velocity of the orbit, the angular position of the merger, and the masses of the objects. Do you know if that’s correct? I’m basing this understanding on what I’ve read in the popular press.

    I don’t imagine the models account for matter distributions in the accretion disks, so it wouldn’t be surprising that there are unexplained small correlations in the data. But it also wouldn’t be surprising that I’ve misunderstood the danish groups claims by only reading the popular science accounts.

    ReplyDelete
  3. dlb,

    If you think they correspond through published papers, you have not been following. The issue is exactly that this is *not* happening. There are just some people putting out criticism and a collab who thinks it's beneath them to respond. That's not how communication works. And the people who are criticizing them don't seem to communicate among each other either.

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  4. Jan,

    You must have misunderstood this. If you use correlations between two detectors to identify a signal then there should be no correlations left after you've removed the signal, regardless of how well your model fits onto the signal. And in any case, there certainly should not be correlations in periods without a signal (ie, in what's supposedly "noise").

    ReplyDelete
    Replies
    1. Thanks for the reply. I guess it goes to show, science communication is hard and one must be careful relying solely on the popular press. So instead of relying on the popular press, I’ve started reading the original danish group article and this line in the introduction seems to be what I had read second hand: “Clearly, the more general presence of correlations with time delay τGW would significantly reduce the ability to identify and measure gravitational wave signals with a similar time delay. In fact, after subtracting the best-fit GW template from the cleaned data, the remaining signals in the two detectors are also maximally correlated for the same time lag. Since similar effects are also found for the GW151226 and GW170104 events, this suggests the presence of unwanted systematic effects.“

      I haven’t read beyond the introduction yet, but this seems to be what I was saying. They matched a best fit GW model and found there were still correlations left, but it doesn’t seem at all surprising that the GW model would not be perfectly accurate (e.g. not modelling accretion disks) and hence there are gravitational wave components being measured that are not predicted by the simplified binary black hole/ neutron star models and hence turn up after removing the best fit gravitational wave model. this would be along the lines of your criticism of neutron star modelling.

      I have to admit it’s still unclear from the paper, but it seems like this quote is the thrust of their argument. Do you think there’s another interpretation of their statement?

      I’m going to try to work my way through to where they actually perform the best fit and see if my interpretation is correct or not.

      Delete
  5. Sorry if I missed something, but I still don't know what the fabric of space-time is made of.If really unkwown yet I think that alternative explanations are worth to be taken into account.

    ReplyDelete
  6. Is the code that computes gravitational waves from neutron star mergers in the public domain?

    ReplyDelete
  7. On correlations: we have seen many instances of random correlations (there is or used to be a Google function that would search for correlations among unrelated events; at Andrew Gelman's blog there is a recent post about some). So I don't understand how removing a physical signal from noise should remove all random correlations--unless you mean the random correlations become part of the signal, but then the signal would not be just the physical signal and would not match theory.

    Also, re correlations in periods without a signal, how does one know there is no signal? Among noise there could always be low-level signals, it seems to me.

    Probably there are details which I am not aware of, so I am really asking for more explanation (which there may not be time for in your busy schedule).

    In any case, this is a very important blog post. I understand the main point which is lack of communication. In Tommaso Dorigo's book (which I heard about here), he tells about some severe and emotional disagreements within a team of scientists. They were only solved by referring them to the head of the project for an authoritarian resolution. Unfortunately there is no higher authority to refer to, nor any objective third-party that all sides will defer to, in this case.

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  8. Reminds me of the CAGW debacle.

    It would seem that a pitfall for any organized body (in any discipline) is that being a part of the "in group" is so valuable that it's worth working for -and defending- regardless of the result.

    Manufacturers spend enormous amounts of money to take clique behaviors out of their culture. I imagine those who receive grants instead of purchase orders don't have cash allocated for that.

    ReplyDelete
  9. Ms Hossenfelder, I believe you will find that I did send you several emails if you look in e.g., spam folders or just a bit more carefully in your Inbox. I copy the opening section of a little handful from last week.

    From: David Shoemaker
    Subject: Re: GW170817
    Date: 2018-11-04 at 04:52:55 EST
    To: Sabine Hossenfelder

    Sabine, greetings. I’ll look (again) at the paper a little later today (Europe daytime, on my way to Marseille for a LISA meeting), and have something back to you on the astrophysical arguments in that paper....

    From: David Shoemaker
    Subject: Re: GW170817
    Date: 2018-11-04 at 12:36:46 EST
    To: Sabine Hossenfelder
    Cc: David Shoemaker

    Sabine, do understand that my specialty is building the instruments, not doing the astrophysics. Again, I recommend you ask of astrophysicists — in and outside of the collaborations involved in the measurements — to get a more complete and arguably more objective perspective. With that preamble, ...

    From: David Shoemaker
    Subject: Re: GW170817
    Date: 2018-11-09 at 06:49:25 EST
    To: Sabine Hossenfelder

    Sabine - curious! I know I composed a response. I am with my phone now but in half hour or so will have my computer and see what happened to it.

    D.

    On 9 Nov 2018, at 12:41, Sabine Hossenfelder wrote:

    Hi again David,

    I understand you are busy but please allow me to explain that
    the reason for me contacting you is that you are listed on the
    LIGO website as the acting spokesperson. If you do not answer
    my question, I will have to write that the LIGO spokesperson did
    not respond to my inquiry. With best regards,

    Sabine


    From: David Shoemaker
    Subject: Fwd: GW170817
    Date: 2018-11-09 at 07:40:34 EST
    To: Sabine Hossenfelder

    Sabine, It looks like this email went out, in fact — I hope you do not have a problem with your email!...

    Begin forwarded message:

    From: David Shoemaker
    Subject: Re: GW170817
    Date: 2018-11-09 at 07:44:58 EST
    To: Sabine Hossenfelder
    Cc: David Shoemaker

    and whether I wrote it in my last note or not, allow me to stress:

    The data for the gravitational-wave events is available to the public, and I would appreciate if you would point those who read your blog to the Gravitational Wave Open Science Center at https://www.gw-openscience.org/ where not only the data from our published signals can be found but also the entire O1 data set, as well as both tutorial programs and pointers to the actual software we use, and workshop materials for those who would like to learn about analyzing gravitational wave data. ...

    Begin forwarded message:

    From: David Shoemaker
    Subject: Re: GW170817
    Date: 2018-11-10 at 16:01:54 EST
    To: Sabine Hossenfelder
    Cc: David Shoemaker

    In some measure similar to your request that I respond, do indicate that you have received my emails.

    thanks

    David


    ReplyDelete
  10. I didn't write what I was actually thinking, sorry about that.

    When two parties communicate and argue over something, they can address each other's criticism and try to converge to the essence of their disagreement. Verbally or in writing.

    In the case of this debate over signals detected by LIGO, all parties write down their argument but don't respond to criticism. Yes, that's miscommunication, but it least they write papers, and we can judge with whatever expertise we have on the subject who's right and who's wrong.

    One can spend time responding to criticism, or perform actual work on data instead. If LIGO think their position is strong enough (as I think it is), I can't really blame them for not wasting energy on this. Let the critics dig their own grave.

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  11. I'm not an expert, but there have been several papers explaining what a beautiful fit the optical spectra of GW170817 are to the expected light curves from NS-NS mergers (and the basic features of these light curves were predicted prior to the event), see, for example, https://arxiv.org/abs/1710.05456

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  12. Ughh, Sounds like a male ego pissing contest. Too bad this has to become public. Knowing almost nothing about it, maybe it would be nice if Ligo shared more of their computational details.

    ReplyDelete
  13. "The biggest drama I can see here is a complete breakdown of scholarly communication"
    Physics has become a publishing house of theory yelling at theory. Electromagnetic observation supports LIGO - that reported first.

    Build a third LIGO in the Western Australia Desert, such as GPS -32.2, 125.0 or -28.5, 130.72. That is as near the antipodes of Livingston (30.562894, -90.774242) and Hanford (46.455144, -119.407656) LIGOs as land extends. Stop arguing and trilaterate.

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  14. @Arun: according to the GW170817 announcement paper [ https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.161101 ], the binary NS waveforms were caught using a post-Newtonian template bank. These are actually analytical (but very complicated) waveforms that get close to --- but don't encompass --- the final stage of the merger.

    There *are* openly available codes to calculate the complete merger of black holes & neutron stars, but the detailed result depends on the precise form of the neutron star equation of state. The pre-merger part of the resulting gravitational waveforms agrees well with the post-Newtonian waveforms used above. Here's a large open-source community code that can do this, if you can supply a realistic starting point for the evolution:

    https://einsteintoolkit.org/

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  15. Some doubt the reality of the event, others calculate additional details from it, deriving that the merger resulted in a very massive neutron star:
    https://ras.ac.uk/news-and-press/research-highlights/gravitational-waves-merged-hyper-massive-neutron-star
    At least the raw data for such an analysis seem to be available - whether one believes it or not.

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  16. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.091601
    … Physical theory is saved (arXiv:1804.09606) with fractionally charged and possibly strongly interacting massive gravitinos.

    ReplyDelete
  17. Well, I guess it’s a consensus if you disregard the people who do not consent.

    Consensus is not unanimous; there’s always someone who disagrees. Always will be.

    Thanks for the update; we’ll have to see how this soap-opera turns out.

    sean s.

    ReplyDelete
  18. Neutron stars are complicated objects. They have an iron crust in a degenerate state, with the next layer being nuclei and neutrons in a complicated mixture o, then a neutron liquid, followed if the star is large enough by a quark-gluon plasma at the core. Two neutron stars that collide will then in a way splash such that the scattering material cools into heavy nuclei. Heavy metals are thought to come from this.

    Now, how can we distinguish whether the observed event GRB 070201 was a neutron star or white dwarfs? We can estimate something without a lot of fuss. The potential for a quadupole is Q_{ij}n_in_j/r^3, which is the lowest moment we expect for the emission of gravitational radiation. So we can make some estimates by just looking at the relative magnitude of two white dwarfs at the point of impact and the same for neutron stars. White dwarfs are on the order of 10^4km in radius while neutron stars are on the order of 10km. So the relative magnitude of gravitational radiation produced would then be

    (d_w/d_n)^3 = 10^{12}.

    That is a sizable difference!

    The GRB 070201 event was placed 1.4x10^8 light years distant at NGC 4993, an elliptical galaxy in the constellation Hydra. So with the relative power one might expect of a white dwarf collision, which in its own right would be of some interest, and the neutron star it seems implausible there is a problem with the LIGO assessment.

    ReplyDelete
  19. "Alas, this data does not include the 2017 event that is under discussion here. For this event only a time-window is available."
    And does our dear Shoemaker provide a reason for why data for this most important event is lacking, while it is available for others?

    "For most physicists, including me, this detection removed any remaining doubts about LIGO’s event-detection."
    The detection for which the data is lacking convinced most physicists, you included and "removed any remaining doubts"? There can be no doubt that EM waves were emitted by the event, as confirmed by independent telescopes. EM could affect LIGO in ways not accounted for and could result in a "detection", but such a "detection" would not match their gravitational wave templates.

    The data they got with the neutron star event possibly did not match their gravitational wave templates, and so they do not want to release the data.

    Providing all the data should be the ideal way to completely remove doubts in physics.

    ReplyDelete
  20. Unless the schedule has slipped, full public data release for LIGO's O2 data will be in 2019Q1, i.e. one year after the end of O2. As with the schedule of O1's public data release this has not changed for years as far as I know and that information was publically available.

    Also, I don't fully get why the full data set is really necessary for analyzing a relatively short event. Granted, the full data set helps understanding the long-term behavior and significance levels, but to my understanding all data and software necessary to confirm this event are published and described in papers as well as on https://www.gw-openscience.org/events/GW170817/

    ReplyDelete
  21. Ashish,

    But the data *is* availabe, as I point out in the very sentence you quote. What is not available is the larger time-series around the event and (so my understanding) the template. In any case, the Italians didn't look at it. Best,

    B.

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  22. Sean,

    How large do you think a fraction of people who disagree is allowed to be? Where do you get the number from? And have you checked your number with the actual number? In which group? Why this group? And how does it even matter? Whoever said that scientific evidence should be rated by head counts?

    I think this insistence of US-Americans to argue by way of "consensus" is toxic for science.

    ReplyDelete
  23. Jan,

    As they say in section 3.3 "To provide a rough estimate of this uncertainty, we have also considered the possibility of a free ±10% scaling of the templates... The results are nearly identical to those of Fig. 7. Considering that the residual noise is significantly greater than the uncertainly introduced by the family of templates, this is not surprising. It would appear that 7 ms time delay associated with the GW150914 signal is also an intrinsic property of the noise."

    Please also note that the gravitational wave signal is dominated by the massive parts. A disk would be relevant for the electromagnetic signal, but it doesn't carry much weight (literally). Besides this, I'd expect the disk to have become unstable long before the merger. Best,

    B.

    ReplyDelete
  24. Sabine,

    Thanks for clarifying. From the data that *is* available for the neutron star event, can one analyse if there is "similar" correlation found in detector noise?

    "Similar" term is referenced from (quoting from my comment on your "Story about LIGO noise resurfaces in New Scientist"):
    The Danish group's paper "On the time lags of the LIGO signals" says: "With special focus on GW150914, we report correlations in the detector noise ... the other two events, GW151226 and GW170104, exhibits similar behavior."

    ReplyDelete
  25. This text was very enlightening, both in dismissing the italian paper claims and exposing how (some bad) scientists deal with the controversy, which should be the fuel of their researching instead of some kind of personal offence.

    Prof. Ruffini is reputed as 'saying to have a genial idea per minute' among the HE atrophysicists, and making 'groundbreaking' affirmations without the will to give more than lazy responses to the following reactions does not help him with that.

    ReplyDelete
  26. My comment is about the 2nd update: "The non-corresponding ... He seems somewhat unhappy about his co-author’s statements...". For the transparency of the readers I would like to tell that the blog author and I exchanged few emails in which I alerted the incorrectness of astro and technical aspects of the blog when summarizing the results of our paper (and other about basic physics). The attentive reader that have followed the blog main text evolution could have noticed that some corrections have been applied. The blog author instead of pointing out in the 2nd update that I enter into contact for these reasons that led to a correction of the text (never mentioned) pointed out an update more appropriate for a gossip blog. For the people interested I can make public the emails I sent to the blog author so yourselves can check whether the 2nd update corresponds or not to reality.

    ReplyDelete
  27. So now you add "investigative journalist" to your philosophy of science credentials!

    ReplyDelete
  28. "event. (The VIRGO measurement of that event has a signal-to-noise ratio of merely two, so it doesn’t increase the significance all that much.)"

    There's certainly something I'm not understanding. The 1/2? s/n ratio. Since gravity wave signal displacement is on the order of 1/2 a proton diameter, I'd think ambient noise world swamp discrimination software.

    Is it possible to explain in.the proverbial 15 words or less how such a discrimination is made, in light of overpowering ambient noise? I've had little success researching an answer.
    Thx.

    ReplyDelete
  29. Ashish,

    Similar to what? I'm afraid I don't understand the question.

    ReplyDelete
  30. The change I made is to exchange "optical" for "electromagnetic" and to remove two words referring two the strength of the signal because Jorge pointed out, correctly of course, that the signal would be in a different frequency range for white dwarfs and that statement was therefore confusing. As these are irrelevant minor changes I didn't see the use in noting them down.





    ReplyDelete
  31. Matthew,

    As you can tell, it's no fun...

    ReplyDelete
  32. APEppink,

    The snr is 2, not 1/2. You can find this in the original paper (page 2, bottom row). The ratio does not directly transfer to the size of the displacement, it refers to how well the whole signal could be extracted from the background.

    ReplyDelete
  33. Sabine,

    I have put the word "similar" in bold and repeated my comment below. Very interesting continued analysis of LIGO issue at your blog, but am trying to find out if there is correlation in detector noise in neutron star event, "similar" to that in black hole events. The answer does not seem to be available, and is this because LIGO has not made all the data available for the neutron star event?
    ----

    Thanks for clarifying. From the data that *is* available for the neutron star event, can one analyse if there is "similar" correlation found in detector noise?

    "Similar" term is referenced from (quoting from my comment on your "Story about LIGO noise resurfaces in New Scientist"):
    The Danish group's paper "On the time lags of the LIGO signals" says: "With special focus on GW150914, we report correlations in the detector noise ... the other two events, GW151226 and GW170104, exhibits similar behavior."

    ReplyDelete
  34. Ashish,

    I don't know if anyone has looked at that.

    ReplyDelete
  35. On consensus, there is never unanimous agreement. Serious people do not believe in the infinite, and so discount Cantor diagonalization. And sometimes the almost unanimous consensus is wrong - the three circles of maximal area inscribed in a given triangle had an incorrect solution for centuries.

    Still, we do what we can.

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  36. Sabine, Shoemaker, Rueda,

    In the interest of everybody and the scientific world, organize a two-day conference to discuss the papers. Invite LIGO, Danish and Italian groups to present their cases. Invite Sabine to report the outcome to the media and public. I’m sure Caltech, Kavli Institute, AAS or RAS would like to host this conference.

    ReplyDelete
  37. It is not true that the EM signal observed from the NS merger GW170817 was inconsistent with coming from a neutron star merger. In fact, its exactly what you expect. The gamma-ray burst observed was previously hypothesized (given strong circumstantial evidence) to come from neutron star mergers. The observed optical wavelength signal also matched remarkably well the predictions from our paper in 2010 for the fading glow produced by the radioactive decay of isotopes synthesized in the neutron-rich merger ejecta by the rapid neutron capture process (http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1001.5029). You can see a comparison of the observed light curve to the first model presented in our 2010 paper in Figure 1 here of my mini-review on GW170817: https://arxiv.org/abs/1710.05931 . A white dwarf merger would not be expected to ejecta such neutron-rich material and thus I do not see how it could explain the observed event. Furthermore, the observed signal was unlike that of any previously observed astrophysical transient - how likely is it that LIGO would be able to point astronomers to such a rare thing if it were not a real event. To me, the evidence is overwhelming that the neutron star merger was real.

    ReplyDelete
  38. Hi Sabine, I see sometimes you do "Ask Dr. B" posts. I do not understand how gravitational wave detectors work. If the radii of the atoms in the mirrors in the interferometer are 10^-10 meters then how can they use them to detect signals on the order of 10^-18 meters? The answer is I usually see is, "Statistics!!!," but that is not a satisfying answer to me. Can you explain how these detectors work?

    ReplyDelete
  39. Jonathan,

    I don't know why you think this has something to do with the radii of the atoms to begin with. What's this got to do with anything? You measure the presence/absence of an interference pattern. I don't like to explain things that have been explained in thousands of other places.

    ReplyDelete
  40. Unknown (a.k.a. Shoemaker)

    Why don’t you explain that to the Danish and Italian groups in the conference room? Writing comments in somebody else’s blog with unknown name is singing November Rain in the bathroom.

    ReplyDelete
  41. Baryonic matter and electrons in the intergalactic medium effectively increase the refractive index of the medium, creating frequency and phase distortion which results in decrease of the velocity of propagation that varies with frequency. What is the chance that the velocity of propagation of gravity waves would fortuitously match the EM waves, a one percent difference in arrival time for an event at 10^9 light years would be 10^7 years.

    Curious
    Barry

    ReplyDelete

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