Why are the gravitational waves we have detected so faint?

[chaszz]

This is a quote from an article written by a Phd student in physics in the online magazine Aeon (https://aeon.co/ideas/gravitational-waves-will-bring-the-extreme-universe-into-view): "Consider the properties of the September 14 event: the signal was generated by two objects, each roughly 35 times the mass of our Sun, locked in a decaying orbit the size of Switzerland, circling each other 50 times a second. The energy involved was staggering, briefly exceeding that of all the starlight in the Universe, but the signal that reached Earth was among the most imperceptible things that humans have ever measured." I understand that gravity is by far the weakest of the forces, but isn't this rather extreme? How could this signal be so faint when the energy that caused it was so great?

 

[Nugatory]

It's worth playing with the numbers a bit...

The event also happened 1.3 billion light years away. Let's assume for simplicity that the energy was radiated symmetrically in all directions so that by the time it gets to us it is distributed evenly across the surface of a sphere with that radius. If that is case, what fraction of the radiated energy flows through the area covered by the LIGO detectors?

(Be aware that this back-of-the-envelope exercise is hugely oversimplified, but it will give you a feel for the magnitudes involved).

 

[chaszz]

I see. But "...briefly exceeding the energy of all the starlight in the universe." Did we capture the brief moment referred to there? If so, it would seem it should be at least as bright as one ordinary star by the time it got here. Or anyway, not among the most imperceptible things that we've ever measured. Many stars and galaxies are so far away that it takes a very powerful telescope to even see them, but when we do see them, they are not among the most imperceptible of all things we've ever measured, are they?

 

[Vanadium 50]

it should be at least as bright as one ordinary star by the time it got here

The thing is, you have to actually calculate these things. You can't just guess. Do you have such a calculation?

 

[chaszz]

I am a layman who is very interested in physics, but I am neither a physicist nor a physics student. I keep up with the field the best I am able by reading popularizations, and have read hundreds of them. I do not have the math or the aptitude or the technical knowledge to calculate things. I know a great deal less about relativity, quantum mechanics, astronomy, cosmology, the problems facing physics today such as the incompatibility of quantum theory and relativity, dark matter, dark energy, the failure to find new particles or support for supersymmetry at the LHC, the problems with string theory, alternate approaches such as loop quantum gravity and many other physics topics than a professional, but I know a great deal more about these things than my family and friends. Would you say the knowledge I have of these things after 50 years of reading is worthless or meaningless because I work around math? I believe intelligent lay persons provide a good basis and community for public support of science which is not automatic in Congress. For instance I wrote my three Congressional reps in support of the supercollider in Texas which was unfortunately canceled. I assume that the topic in this thread could be described and commented upon in general terms without a calculation. If the site is only for experts, why is it open to the general public? If the site requires calculations to ask questions, I will gladly take my curiosity elsewhere. And I may remember the situation the next time the public is asked to support hard science.

 

[chaszz]

To expand a little more on this...
1. As part of the website purpose on the first page, it says "Our goal is to provide a community for people (whether students, professional scientists, or hobbyists)..."
2. If the site requires questions to be framed or discussed in mathematical terms, why doesn't it say so on that page?

 

[Nugatory]

I do not have the math or the aptitude or the technical knowledge to calculate things.

You may be selling yourself short here - people often don't realize just how much power the math they learned in high school has.

For example, the calculation that I suggested you try requires knowing only the following:
1) How to compute the surface area of a sphere, given the radius.
2) How to compute the surface area of a circle given its diameter.
3) The number of miles in a light-year, so you know how many miles a 1.2 billion light-year radius is.
4) The diameter of the earth, in miles.
#1 and #2 you learned how to do somewhere in or before high school. You may have forgotten the formulas if you haven't needed to use them since then, but that's what google is for. Likewise, #3 and #4 are a google search away if you haven't picked them up in your reading (or, like me, don't bother memorizing numbers that Google will give you any time you need them).

Work this out for yourself, and you will have a deeper understanding of the problem and more power over future problems than you will get from reading one hundred canned answers (which is why we discourage handing out canned answers). We can and will help you with that - "I tried and I'm stuck" gets helpful responses from some very talented teachers who are passionate about explaining this stuff.
(It will also get you some unhelpful noise - this is an internet forum so that happens - but the mentors will try to tamp that down).

 

[Battlemage!]

So what your saying is, divide the surface area of the Earth by the surface area of a sphere of radius 1.2 billion light years? (or maybe the surface area of a circle the size of LIGO?)

 

[Vanadium 50]

Would you say the knowledge I have of these things after 50 years of reading is worthless or meaningless because I work around math?

No, but I would say that making a quantitative claim based on making stuff up - i.e. without doing the math - is unscientific. Even if you are right, it's unscientific.

 

[jtbell]

divide the surface area of the Earth [...] (or maybe the surface area of a circle the size of LIGO?)

LIGO can't magically "reach out" and detect radiation that passes thousands of miles from it (but still "hits" the Earth), so the latter is a better number to use.

 

[PeterDonis]

If the site requires calculations to ask questions

It doesn't. But if you ask a question that you are probably capable of answering yourself by doing a simple calculation, that might be the kind of response you get. Nugatory explained why we often don't just give canned answers. He also pointed out how simple the calculation actually is; it should be well within the capability of anyone with the background you say you have.

briefly exceeding the energy of all the starlight in the universe

But most of those ordinary stars are closer to us than the black hole merger was--1.2 billion light years is very far away. If you really want to try to compare the apparent brightness of the merger to that of all the ordinary stars we can see, you have to figure out what the effective "average distance" of all those stars is from us, and compare it to that 1.2 billion light-years. I haven't done such a calculation, but the fact that the merger is so faint would indicate that the "average distance" of all the ordinary stars we can see is significantly less than 1.2 billion light years.

 

[PeterDonis]

Many stars and galaxies are so far away that it takes a very powerful telescope to even see them

One other factor to consider, in addition to the "average distance" I referred to in my previous post, is that our powerful telescopes "see" these very distant and faint objects by collecting light from them over an extended period of time. LIGO could not do that; the peak power radiated by the black hole merger was only radiated for a tiny fraction of a second. So when comparing the two, you have to factor in the extremely short "exposure time" for LIGO compared to optical telescopes looking at faint objects.

 

[Nugatory]

LIGO can't magically "reach out" and detect radiation that passes thousands of miles from it (but still "hits" the Earth), so the latter is a better number to use.

Yes, you're right... Another half-dozen or so orders of magnitude to throw on the pile. :)

 

[GeorgeDishman]

You also have to consider the detector "efficiency", how much of the passing power is LIGO able to extract? A visible light telescope is pretty good at utilising the energy that hits the mirror.

 

[chaszz]

I am actually right now involved in packing and moving to a new home, but when I get time will try some calculating along the lines suggested (I did do well in high school math). However, from my original point of view, the response below from PeterDonis, and two others, gave me a good part of the information I was looking for, which I would assume is the purpose of the site. Did these responses, without supporting math, invalidate the assumed site policy of not giving "canned answers?" I knew that telescopes track objects over long periods and didn't make the obvious inference - my fault. But I didn't need math to understand this very clear response and calculating without realizing that wouldn't have helped.

From PeterDonis:
One other factor to consider, in addition to the "average distance" I referred to in my previous post, is that our powerful telescopes "see" these very distant and faint objects by collecting light from them over an extended period of time. LIGO could not do that; the peak power radiated by the black hole merger was only radiated for a tiny fraction of a second. So when comparing the two, you have to factor in the extremely short "exposure time" for LIGO compared to optical telescopes looking at faint objects.

 

[PeterDonis]

Did these responses, without supporting math, invalidate the assumed site policy of not giving "canned answers?"

No, because I didn't give you the answers. I just gave you a general idea of how you would go about calculating the answers. (Similar to what others have posted.) To actually give you the answers I would have had to show you the math, and I didn't do that.

I didn't need math to understand this very clear response

No, but you will if you want to confirm that it's actually correct. I haven't demonstrated that it's correct; I've only suggested it. If you are satisfied with just having it suggested and don't feel the need to confirm it, that's your choice; but you should understand that in that case, you don't really know the answer.

and calculating without realizing that wouldn't have helped.

It would if you had tried to calculate the peak power of a distant ordinary star observed by a telescope, and then used that to calculate th total energy received from the star, under the assumption that it was only observed for a very short period of time (a small fraction of a second), and realized that it was below the threshold of detection. That would have told you that something was missing from your mathematical model of how distant ordinary stars are observed by telescopes.

 

[PeterDonis]

You also have to consider the detector "efficiency", how much of the passing power is LIGO able to extract?

Another point in this connection is that LIGO does some slick things with the cavities in each of its arms to give it an effective "arm length" that is much larger than its actual physical arm length. So when calculating its effective detection area, you have to use the effective arm length, not the physical arm length.

 

[chaszz]

"No, but you will if you want to confirm that it's actually correct. I haven't demonstrated that it's correct; I've only suggested it. If you are satisfied with just having it suggested and don't feel the need to confirm it, that's your choice; but you should understand that in that case, you don't really know the answer."

I don't need or want to confirm for myself that it's actually correct. That's the whole nub of this argument. I haven't confirmed for myself Special Relativity or any of its effects; I take it as tested and proven (within the limits of a theory) by the testimony of many capable specialists. So do I know the fact or not, that when traveling very close to the speed of light, an object's relativistic mass increases? No, I don't know by how much, but yes, I know it happens and am satisfied to know that. That's what I asked this question for, to get the opinions of more knowledgeable people than I in explaining an apparent issue. Again, if the site is only for specialists, people who want to calculate, or people who agree to be guided in finding their own answers, it would seem it should say so clearly on the first page. And again, if it is, I'll be glad to leave and go searching for another such site. So what is policy on this? And who, one person or a committee, makes it?

 

[PeterDonis]

I take it as tested and proven (within the limits of a theory) by the testimony of many capable specialists.

If that's your approach, of course it's your choice. But then I'm confused about why you didn't take the facts about the LIGO detection, including the fact of it being "among the most imperceptible things that humans have ever measured", as being "tested and proven by the testimony of many capable specialists".

what is policy on this?

If you are satisfied with the answer you got, then there is no problem. You're the one who posted the question. There is no policy that requires you to do calculations you don't want to do.

If you really are not interested in getting into any mathematical details in future threads, it will help if you label your thread as "B" rather than "I". (I have done that with this thread, as you will notice.) An "I" thread indicates that you are willing to deal with at least an undergraduate level of math.

One final note: please use PF's quote feature when quoting other people's posts (as I have done in this post when quoting you). The easiest way to do it is to highlight the text in someone's post that you want to quote; you should then see a little popup with "Quote" and "Reply" buttons. Clicking "Reply" will put the highlighted text into the edit box at the bottom of the page, already enclosed in quote tags.

 

[votingmachine]

But most of those ordinary stars are closer to us than the black hole merger was--1.2 billion light years is very far away. If you really want to try to compare the apparent brightness of the merger to that of all the ordinary stars we can see, you have to figure out what the effective "average distance" of all those stars is from us, and compare it to that 1.2 billion light-years. I haven't done such a calculation, but the fact that the merger is so faint would indicate that the "average distance" of all the ordinary stars we can see is significantly less than 1.2 billion light years.

It is worth pointing out that what we see in the night sky is mostly just black space. There is starlight, but it just barely registers. Most of the stars we see are those in our galaxy. There is WAY more starlight in the universe, but some distant galaxies with more stars than the Milky Way can only be seen with the amplification of telescopes.

And it is not all that useful to compare perception of light by the eye to the perception of gravity by laser interferometry. The perceptible change in laser path length was some mind mind-bogglingly small distance, but while the energy of the collision of these black holes was enormous, it was not an energy to be seen. It happened inside distant black holes and the gravity wave was a wave that propagated from the GRAVITY event that released an energy equal to the stars of the universe.

The distance relationship should be one people recognize. It is clear that the starlight energy of the universe is in the sky every night, and if there is not a nearby light source, or a full moon (or a sun outside), we can still only see a few nearby stars.

 

[Wayne Arthur]

My comment questioning the odds that LIGO detected 1/5th of a second gravitational waves from the collision of 2 theoretical black holes billions of light years away, was not rhetorical. I was wondering if there is a formula for figuring those odds. This is a valid question. This is certainly not a conspiracy theory I've heard anywhere, I came up with the question myself. Please have some respect instead of jumping to conclusions. Why not ask this question? That's what scientists do.

 

[votingmachine]

My comment questioning the odds that LIGO detected 1/5th of a second gravitational waves from the collision of 2 theoretical black holes billions of light years away, was not rhetorical. I was wondering if there is a formula for figuring those odds. This is a valid question. This is certainly not a conspiracy theory I've heard anywhere, I came up with the question myself. Please have some respect instead of jumping to conclusions. Why not ask this question? That's what scientists do.

It is not that it is a rhetorical question ... it s just an insult to the scientists involved. You think they faked the data, which is about the worst thing you can accuse a scientist of.

There were MANY people involved in collecting the data and analyzing the results. And they were high level scientists ... not really depending on the funding of this experiment. Your question is: did the data get faked, to make an argument for further research funding?

That is a highly offensive question. It seems appropriate to jump all over you for that.

 

[votingmachine]

My comment questioning the odds that LIGO detected 1/5th of a second gravitational waves from the collision of 2 theoretical black holes billions of light years away, was not rhetorical. I was wondering if there is a formula for figuring those odds. This is a valid question. This is certainly not a conspiracy theory I've heard anywhere, I came up with the question myself. Please have some respect instead of jumping to conclusions. Why not ask this question? That's what scientists do.

To calculate the odds:
1. Determine the frequency of detectable events that occur.
2. Divide the length of time observing by that.

So if the events occur at one-per-10-years, a random observation period of 10 years has a decent chance, if the events are distributed randomly in time and space.

But I don't think anyone yet knows the frequency of black hole collisions. the LIGO apparatus is the first way to look. Maybe they are very common ...

 

[Orodruin]

My comment questioning the odds that LIGO detected 1/5th of a second gravitational waves from the collision of 2 theoretical black holes billions of light years away, was not rhetorical. I was wondering if there is a formula for figuring those odds. This is a valid question. This is certainly not a conspiracy theory I've heard anywhere, I came up with the question myself. Please have some respect instead of jumping to conclusions. Why not ask this question? That's what scientists do.

Your entire premise is flawed. LIGO was not operating at the same level of sensitivity for 10 years without seeing anything. (If you are near sighted and look at the night sky you will not see stars, regardless of how long you look). It underwent enhancement in order to increase its sensitivity (when you put your prescribed glasses on, you will see the stars at night). In fact, the reverse is true, it is likely that the first event was seen sooner than one would expect based on the rate we now observe (more events have been reported since).

 

[Isaac0427]

My comment questioning the odds that LIGO detected 1/5th of a second gravitational waves from the collision of 2 theoretical black holes billions of light years away, was not rhetorical. I was wondering if there is a formula for figuring those odds. This is a valid question. This is certainly not a conspiracy theory I've heard anywhere, I came up with the question myself. Please have some respect instead of jumping to conclusions. Why not ask this question? That's what scientists do.

It is not that it is a rhetorical question ... it s just an insult to the scientists involved. You think they faked the data, which is about the worst thing you can accuse a scientist of.

There were MANY people involved in collecting the data and analyzing the results. And they were high level scientists ... not really depending on the funding of this experiment. Your question is: did the data get faked, to make an argument for further research funding?

That is a highly offensive question. It seems appropriate to jump all over you for that.

I find this to be a very valid question. The answer of course, is that the observations by LIGO are most likely reliable. I am not the one to answer this question, but I believe what @Wayne Arthur is getting at is that these results are very, well, odd. Why should we trust these results? What about how LIGO ran the experiment makes these results valid? These are something that people should know about an experiment instead of blindly trusting scientists (this is not accusing the scientists of anything, but just as it has been mentioned in this very thread, trusting things without the calculations, or in this case the details, is not full understanding). I know there are very good sources out there, but I'm afraid my knowledge on the subject is limited, and I could not tell the good ones from the bad/oversimplified ones.

 

[Orodruin]

I find this to be a very valid question.

It is not. The premise is flawed. Please read my post.

 

[Ibix]

I think I must have missed a post. But here is a possibly helpful analogy. Imagine a bead floating on the surface of a pond, threaded onto a fixed wire. This detects surface waves when the bead bobs up and down. (It's a gravity wave detector )

Somebody is throwing stones into the water at random. Sometimes they make big waves, sometimes small ones. Sometimes they are close to our detector, sometimes not. But the waves always wash over our detector eventually. What are the odds it will detect something?

In one sense, odds isn't the right word. If our detector can detect waves that are at least 1mm in amplitude (for the sake of argument) then there's a fairly straightforward calculation that gives you the maximum distance from the detector that a stone thrown in with a certain energy can be detected. If an event happens within that radius then it will be detected. Full stop.

Where the question of odds comes in is in how long we expect to have to wait for a detectable wave. How often do stones thrown with sufficient energy land in that critical radius? That, of course, depends on the way the stones are being thrown in.

Back to LIGO. If a black hole merger of a certain energy level happens within a critical radius of the Earth, it will be detected (this is a slight overstatement due to polarisation issues, but it'll do). The only place "odds" comes into the question is at what rate detectable events occur. As far as I'm aware there's no answer to that - the only data we have comes from LIGO.

So, really, asking "what are the odds" isn't going to be a fruitful line of enquiry. Orodruin's point about the upgraded capabilities of LIGO explains why we didn't detect any signals before and now we do. And now that we are detecting events the only odds-related question is the frequency of detectable events, which we don't know except for how often LIGO detects them.

 

[Battlemage!]

I find this to be a very valid question. The answer of course, is that the observations by LIGO are most likely reliable. I am not the one to answer this question, but I believe what @Wayne Arthur is getting at is that these results are very, well, odd. Why should we trust these results? What about how LIGO ran the experiment makes these results valid? These are something that people should know about an experiment instead of blindly trusting scientists (this is not accusing the scientists of anything, but just as it has been mentioned in this very thread, trusting things without the calculations, or in this case the details, is not full understanding). I know there are very good sources out there, but I'm afraid my knowledge on the subject is limited, and I could not tell the good ones from the bad/oversimplified ones.

Did you notice the part about upgraded sensitivity? Perhaps that will shed some light on that question.

I fear the people who asked it have ran off convinced that the scientific community is closed minded or "in on it" simply because they (those that asked) refused to read the simplest explanations of/ answers to their questions.

 

[votingmachine]

I find this to be a very valid question. The answer of course, is that the observations by LIGO are most likely reliable. I am not the one to answer this question, but I believe what @Wayne Arthur is getting at is that these results are very, well, odd.

That is entirely an assumption. The results are a set of gravity waves, detected by a new method. There seems to be nothing odd about that. As an analogy, if a trees fall in the forest and there is nothing to detect the falling, how do we know? If we build a way to detect the trees falling, is it suddenly very a odd result to say a tree fell?

Why should we trust these results? What about how LIGO ran the experiment makes these results valid? These are something that people should know about an experiment instead of blindly trusting scientists (this is not accusing the scientists of anything, but just as it has been mentioned in this very thread, trusting things without the calculations, or in this case the details, is not full understanding).

Results always are dependent on the materials and methods. You don't trust a measurement made with an imprecise instrument, or a measurement that does not have some validation. In this case, the entire method is well documented, and I think it is a robust detection method with reliable validation.

I know there are very good sources out there, but I'm afraid my knowledge on the subject is limited, and I could not tell the good ones from the bad/oversimplified ones.

There is absolutely no way to help if you cannot tell good from bad. But given that starting point, I can tell you to not bother to make the assumption that the results are odd. We ALL have no way of knowing how rare or how common this was.

We know trees fall in the forest. We see the trees laid out on the ground. But I haven't seen a tree fall ... I had one fall on my house in a storm, but I didn't see it. I cannot say with certainty the odds of a tree falling, or a tree falling on my house. I can say it happened, and the broken stump, and tree thru the roof was adequate proof for the insurance company.

The odds requires more numbers. The reason we can talk about a "100-year flood" is because we have a frequency distribution of flood event severity, built up over many floods. Perhaps this was a "1000-year black hole event" ... but it might also be a "1-year black hole event" ... until we have a frequency distribution of gravity wave events, there is no way to say what the odds are. (Unless there is some other method of calculating black hole collision event frequencies).