The Nanohertz Gravitational-Wave Detection Explained(physics.aps.org)
physics.aps.org
The Nanohertz Gravitational-Wave Detection Explained
https://physics.aps.org/articles/v16/116
71 comments
Excellent illustration. After reading it I thought this looks like the PHD style. And I checked the author, who IS Jorge Cham. About 22 years ago I was reading his Piled higher and deeper, PHD, series and bought several books of his. It is a great feeling to see that he is still doing comics. Thanks Jorge!
What an utterly delightful and eminently understandable presentation of a complex subject!
I know that it would take decades or centuries to gather enough data to make discoveries. But I wonder if one day a scientist will be looking at these results and see something that makes them think "that's odd..." And suddenly our understanding of the universe is turned upside down yet again!
I know that it would take decades or centuries to gather enough data to make discoveries. But I wonder if one day a scientist will be looking at these results and see something that makes them think "that's odd..." And suddenly our understanding of the universe is turned upside down yet again!
Australian scientists vindicated as new pulsar data proves South is up.
I had never heard of "cosmic strings".
https://en.wikipedia.org/wiki/Cosmic_string
https://en.wikipedia.org/wiki/Cosmic_string
I've always wanted to ask this really dumb question, so I'll just ask it here (laugh or answer, your choice):
Would there be gravitational waves so huge that we'd have trouble detecting them? As in, if there was a huge, massive gravitational wave and we were in the process of "riding" it how would we ever know or detect such a thing?
Would this possibly (not plausibly) be an answer to some of the weirdness and contradictions we have observed in astronomy over the past few decades?
Would there be gravitational waves so huge that we'd have trouble detecting them? As in, if there was a huge, massive gravitational wave and we were in the process of "riding" it how would we ever know or detect such a thing?
Would this possibly (not plausibly) be an answer to some of the weirdness and contradictions we have observed in astronomy over the past few decades?
You can see "sensitivity" plots for the various methods we have for observing gravitational waves. The horizontal axis is usually in terms of the frequency of the wave and the vertical axis is how sensitive we are to them. This article is about "nanohertz" waves, which means their wavelength is roughly 10⁹sec × speed of light, i.e. 30ish light years. So, it seems we can detect really "big" gravitational waves. If you look through the aforementioned plots you will see that sensitivity drops off significantly for "more astronomical" wavelengths, so there are definitely scales at which we can not detect, as you suggested.
There might be some interesting ways to introduce very long gravitational waves as solution of current discrepancies in our understanding of cosmology, but they are also probably introducing more discrepancies than they solve. I would guess people have considered these ideas, because "cosmological scale general relativity" is pretty heavily researched and mainstream.
There might be some interesting ways to introduce very long gravitational waves as solution of current discrepancies in our understanding of cosmology, but they are also probably introducing more discrepancies than they solve. I would guess people have considered these ideas, because "cosmological scale general relativity" is pretty heavily researched and mainstream.
> so huge that we'd have trouble detecting them
Gravitational waves can be arbitrarily long because patterns in the cosmic microwave background suggest the early universe had gravitational radiation with wavelengths of arbitrary size, including quite long waves. The metric expansion of space has stretched those "primordial gravitational waves" (PGW), so even short-wavelength-in-early-universe PGW can have periods of many years at about the present size of the universe.
Additionally, most models of cosmic inflation stretch PGW, with some of the stretched wavelengths being made longer than the distance to the cosmic horizon (Initially, before inflation, PGWs can have practically unlimited length or can be almost arbitrarily short, with the shortest winding up not so short once inflation has ended), so at modern times the super-horizon-length primordial waves would have periods of many billions of years.
Any masses in a ~binary orbit (stars to galaxies, down to grains of dust and up to collections of galaxies like in the local group, <https://en.wikipedia.org/wiki/Local_Group>, the "dumbbell" shape is relevant) generates gravitational waves with a frequency comparable to the orbital period. In our sky there are galaxies that appear to be in mutual orbits with orbital periods of many millions of years.
The pulsar timing arrays in the cartoons linked at the top of the page look for gravitational waves with periods of months to years. It takes several orbital periods to be statistically comfortable that a gravitational wave with that period (nanohertz frequency) has been detected. Those are probably generated by supermassive black holes in hard mutual orbits. If we soften such an orbit, increasing the semimajor axis (or radius for a circular orbit), the orbital period grows, so we have to watch the array of pulsars longer (and be more wary of so-called red noise and other long-term signal contamination).
> some of the weirdness and contradictions we have observed in astronomy
Unlikely. Do you have any particular weirdness and/or contradiction in mind?
Gravitational waves can be arbitrarily long because patterns in the cosmic microwave background suggest the early universe had gravitational radiation with wavelengths of arbitrary size, including quite long waves. The metric expansion of space has stretched those "primordial gravitational waves" (PGW), so even short-wavelength-in-early-universe PGW can have periods of many years at about the present size of the universe.
Additionally, most models of cosmic inflation stretch PGW, with some of the stretched wavelengths being made longer than the distance to the cosmic horizon (Initially, before inflation, PGWs can have practically unlimited length or can be almost arbitrarily short, with the shortest winding up not so short once inflation has ended), so at modern times the super-horizon-length primordial waves would have periods of many billions of years.
Any masses in a ~binary orbit (stars to galaxies, down to grains of dust and up to collections of galaxies like in the local group, <https://en.wikipedia.org/wiki/Local_Group>, the "dumbbell" shape is relevant) generates gravitational waves with a frequency comparable to the orbital period. In our sky there are galaxies that appear to be in mutual orbits with orbital periods of many millions of years.
The pulsar timing arrays in the cartoons linked at the top of the page look for gravitational waves with periods of months to years. It takes several orbital periods to be statistically comfortable that a gravitational wave with that period (nanohertz frequency) has been detected. Those are probably generated by supermassive black holes in hard mutual orbits. If we soften such an orbit, increasing the semimajor axis (or radius for a circular orbit), the orbital period grows, so we have to watch the array of pulsars longer (and be more wary of so-called red noise and other long-term signal contamination).
> some of the weirdness and contradictions we have observed in astronomy
Unlikely. Do you have any particular weirdness and/or contradiction in mind?
Thank you for this incredibly informative and detailed answer! It's going to take a few passes (and following some links) to put everything together.
>Do you have any particular weirdness and/or contradiction in mind?
Not in particular or specifically. I was just imagining that if there were such a thing possible, it surely would create some weird anomalies in our measurements.
The idea that something could warp our spacetime so dramatically that we would perceive it as being the normal state of things, even though the "warp" is ultimately temporary, is for some reason incredibly interesting to me.
>Do you have any particular weirdness and/or contradiction in mind?
Not in particular or specifically. I was just imagining that if there were such a thing possible, it surely would create some weird anomalies in our measurements.
The idea that something could warp our spacetime so dramatically that we would perceive it as being the normal state of things, even though the "warp" is ultimately temporary, is for some reason incredibly interesting to me.
"First, [gravitational waves] have really long wavelengths."
Why?
Why?
Not a bad question at all really.
To get a short wavelength requires a high frequency, to get an observable gravity wave requires a very large mass.
We haven't yet seen a Super Massive Black Hole orbiting with (say) an Mercury orbit radius at a thousand times a second.
There is another quote from that wikipedia article:
You'd have to chase the Hawking-Israel paper for their thoughts on short wavelength high frequency gravitational wave sources and how they believe they might plausibly be detected .. I anticipate some devil in the detail.
http://library.lol/main/F92F35CD83F13A6021FC2385BBA171B0
( perhaps wikipedia misquoted that high frequency )
In principle, gravitational waves could exist at any frequency.
The speed, wavelength, and frequency of a gravitational wave are related by the equation c = λf, just like the equation for a light wave.
For example, the animations shown here oscillate roughly once every two seconds. This would correspond to a frequency of 0.5 Hz, and a wavelength of about 600 000 km, or 47 times the diameter of the Earth.
To get a short wavelength requires a high frequency, to get an observable gravity wave requires a very large mass.
We haven't yet seen a Super Massive Black Hole orbiting with (say) an Mercury orbit radius at a thousand times a second.
There is another quote from that wikipedia article:
Stephen Hawking and Werner Israel list different frequency bands for gravitational waves that could plausibly be detected, ranging from 10^−7 Hz (very slow) up to 10^11 Hz (very very fast).
You'd have to chase the Hawking-Israel paper for their thoughts on short wavelength high frequency gravitational wave sources and how they believe they might plausibly be detected .. I anticipate some devil in the detail.
http://library.lol/main/F92F35CD83F13A6021FC2385BBA171B0
( perhaps wikipedia misquoted that high frequency )
>> The speed, wavelength, and frequency of a gravitational wave are related by the equation c = λf, just like the equation for a light wave [...]
> To get a short wavelength requires a high frequency
For light that is assuming a vacuum. The more general equation is c' = λf where c' is the speed of light in the medium the light is traveling through. c' <= c. Hence, for light, you can get a shorter wavelength without having to raise the frequency if you work with the light in a medium with a lower c'.
Is there anything similar with gravitational waves?
> To get a short wavelength requires a high frequency
For light that is assuming a vacuum. The more general equation is c' = λf where c' is the speed of light in the medium the light is traveling through. c' <= c. Hence, for light, you can get a shorter wavelength without having to raise the frequency if you work with the light in a medium with a lower c'.
Is there anything similar with gravitational waves?
λ = v / f
The velocity (v) is the speed of light for gravitational waves, which is already a really big number. If the frequency (f) is based on the period of the black holes which circle around each other, then I assume one rotation happens over a long period of time. Long period -> low frequency -> small denominator which makes the wavelength (λ) even longer.
The velocity (v) is the speed of light for gravitational waves, which is already a really big number. If the frequency (f) is based on the period of the black holes which circle around each other, then I assume one rotation happens over a long period of time. Long period -> low frequency -> small denominator which makes the wavelength (λ) even longer.
Some rotations are fast. LIGO detects gravitational waves at 200-10000 Hz.
That’s kind of fast. Just imagine a couple of black holes orbiting each other that fast.
That’s kind of fast. Just imagine a couple of black holes orbiting each other that fast.
But the higher frequency waves detected by LIGO are not caused by two bodies orbiting their common center of mass at a distance, but rather by two much smaller masses - a few to a few tens times the mass of our sun - than the ones described in the cartoon. These masses orbits have decayed and they are spiraling into each other merging. The Short waves we detect only occur in the final bit of the spiral and merge - we see only the final milliseconds of the merger, and just a few wave crests.
The idea of something with ten solar masses moving so fast still terrifies me. It's just mind-boggling to think about something at that scale completing an orbit in the blink of an eye.
I am reminded of Randall Monroe taking about the sheer energy of a supernova:
> Which of the following would be brighter, in terms of the amount of energy delivered to your retina:
> A supernova, seen from as far away as the Sun is from the Earth, or
> The detonation of a hydrogen bomb pressed against your eyeball?
> Applying the physicist rule of thumb suggests that the supernova is brighter. And indeed, it is ... by nine orders of magnitude.
https://what-if.xkcd.com/73/
I am reminded of Randall Monroe taking about the sheer energy of a supernova:
> Which of the following would be brighter, in terms of the amount of energy delivered to your retina:
> A supernova, seen from as far away as the Sun is from the Earth, or
> The detonation of a hydrogen bomb pressed against your eyeball?
> Applying the physicist rule of thumb suggests that the supernova is brighter. And indeed, it is ... by nine orders of magnitude.
https://what-if.xkcd.com/73/
[deleted]
I still don't understand what the carrier of gravitational waves is.
How are the waves propagated? Space is not an elastic fabric or water where water molecules transfer potential energy.
Aren't gravitational waves a hint that spacetime is not fundamental, but an emergent property of something else?
How are the waves propagated? Space is not an elastic fabric or water where water molecules transfer potential energy.
Aren't gravitational waves a hint that spacetime is not fundamental, but an emergent property of something else?
Gravitational waves follow because space time and gravity are described by equations that admit waves as solutions. Thinking about what space time is "made of" is contrary to what mathematical physics is about. This was a realization with electromagnetism: early attempts tried to interpret the EM field as something mechanical, but it was eventually realized that math making predictions was what one should focus on, and not try to create some sort of more comfortable interpretation in terms of materials or gears or something.
Not looking for a comfortable interpretation.
The confusing thing here is that spacetime warps in the presence of mass.
But no mass is transmitted in a gravity wave.
So how do the waves travel?
The confusing thing here is that spacetime warps in the presence of mass.
But no mass is transmitted in a gravity wave.
So how do the waves travel?
There are many ways for spacetime to warp, which can be put into two categories. The simpler kind, Ricci curvature, is the only kind of curvature in <4 dimensions and is produced by mass-energy, momentum, pressure, and shear stress, according to general relativity. The other kind, Weyl curvature, only exists in 4 or more spacetime dimensions and can exist in a vacuum.
Gravitational waves are Weyl-curvature distortions of spacetime that propagate in a vacuum according to general relativity.
(Also, gravitational waves do carry a little bit of energy, so they cause a small amount of Ricci curvature, but this is a secondary effect.)
Gravitational waves are Weyl-curvature distortions of spacetime that propagate in a vacuum according to general relativity.
(Also, gravitational waves do carry a little bit of energy, so they cause a small amount of Ricci curvature, but this is a secondary effect.)
I'm not sure why you want to draw attention to non-Lorentzian spacetimes in this context.
> ... that propagate ...
"propagate".
That requires a decomposition of spacetime into space+time, and of course the decomposition of the Riemann curvature tensor, the setting of a background value for the Weyl tensor, and the use of perturbation theory.
But if you're going down that path, why not use the metric tensor? g_munu = eta_munu + h_munu + h.o.t. is standard in post-Newtonian expansion approximations, and in particular https://en.wikipedia.org/wiki/Linearized_gravity (which doesn't track the higher-order terms).
The Weyl curvature tensor C_abcd is useful in understanding that in a spherical region of space (not spacetime, so really we're in the land of extracting 3-Cotton-York C_ab) where a GW is incident suffers not from a volume deficit but from an ellipsoidal stretch-squash. But conceptual understanding of and calculation are... well, not really on speaking terms. Even theorists who take the full covariant theory seriously will decompose further, into e.g. an electrical and magnetic part, and add further structure to match the worldlines to the Raychaudhuri equation in shear and vorticity.
> they cause a small amount of Ricci curvature
???
If nothing else, I think you'd need to choose between explaining this or explaining why "Ricci curvature is produced by [matter but] Weyl curvature ... can exist in a vacuum" (or choose neither).
The sticky bead apparatus is a breaking of the T_munu = 0 vacuum condition.
> ... that propagate ...
"propagate".
That requires a decomposition of spacetime into space+time, and of course the decomposition of the Riemann curvature tensor, the setting of a background value for the Weyl tensor, and the use of perturbation theory.
But if you're going down that path, why not use the metric tensor? g_munu = eta_munu + h_munu + h.o.t. is standard in post-Newtonian expansion approximations, and in particular https://en.wikipedia.org/wiki/Linearized_gravity (which doesn't track the higher-order terms).
The Weyl curvature tensor C_abcd is useful in understanding that in a spherical region of space (not spacetime, so really we're in the land of extracting 3-Cotton-York C_ab) where a GW is incident suffers not from a volume deficit but from an ellipsoidal stretch-squash. But conceptual understanding of and calculation are... well, not really on speaking terms. Even theorists who take the full covariant theory seriously will decompose further, into e.g. an electrical and magnetic part, and add further structure to match the worldlines to the Raychaudhuri equation in shear and vorticity.
> they cause a small amount of Ricci curvature
???
If nothing else, I think you'd need to choose between explaining this or explaining why "Ricci curvature is produced by [matter but] Weyl curvature ... can exist in a vacuum" (or choose neither).
The sticky bead apparatus is a breaking of the T_munu = 0 vacuum condition.
I was trying to give a conceptual understanding on the level of the person I was responding to, not instructions for doing actual calculations.
I didn't mean to suggest euclidean metric, I just thought "3+1" would be extra jargon.
The person asking questions was confused because they'd heard that "mass causes curvature" in GR, and that gravitational waves involve curvature. I figured it would help to explain that these are different kinds of curvature.
I think I was totally wrong re: Ricci curvature. I was thinking "oh, GW carry energy and there's nonlinear evolution..." and got carried away, whoops.
If you want to give a more accurate explanation (that makes sense to someone who's never taken a GR class) please do!
I didn't mean to suggest euclidean metric, I just thought "3+1" would be extra jargon.
The person asking questions was confused because they'd heard that "mass causes curvature" in GR, and that gravitational waves involve curvature. I figured it would help to explain that these are different kinds of curvature.
I think I was totally wrong re: Ricci curvature. I was thinking "oh, GW carry energy and there's nonlinear evolution..." and got carried away, whoops.
If you want to give a more accurate explanation (that makes sense to someone who's never taken a GR class) please do!
There is no question that this stuff is hard (and has been cutting edge for decades) and that it is easy to make mistakes.
> give a more accurate explanation (that makese sense to someone who's never taken a GR class)
It's hard to know what level of understanding to aim for on HN. There are non-relativist working physicists here who somewhat casually read other areas of physics (and mathematics) here, for example, rather than e.g. physics SE or looking through literature reviews.
I'm guessing that you have done GR but probably not much with approximations like GEM, nor looked into the history of gravitational waves (e.g. the 1950s-60s work by Bondi with collaborators like Pirani) before the wide availability of powerful computers and observational support for the linearized theory. My goal here is not to nitpick you, but rather to offer a couple of references that might interest you or anyone who is quietly reading along.
> I think I was totally wrong re: Ricci curvature.
R_munu = 0 for one (uncharged) BH, and also for two. Charged BHs are different (Reissner-Nordström's Ricci tensor is R_munu = +- g_munu r_{Q}^2 / r^4 where r_{Q}^2 = \frac{Q^2G}{4 \pi \varepsilon_0 c^4} and ε_0 is the electric constant, all thanks to the electromagnetic stress-energy tensor; the Ricci scalar remains 0).
Superposing two Schwarzschild or Kerr solutions is messy [Krivan & Price 1998 Phys. Rev. D 58, 104003 was a nice overview arxiv html5[*] <https://ar5iv.labs.arxiv.org/html/gr-qc/9806017>, 'two locally Kerr holes, no matter how close they are, will not superpose into a single Kerr hole. Though [this] "failure" of the close limit is physically correct, it is inconvenient [for doing perturbation theory]'] but doesn't change Rmunu = 0.
A charged binary is beyond the scope of this comment.
> I was thinking "oh, GW carry energy ..."
I can recommend two really good papers written at very different times.
Weber & Wheeler 1957 <https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.29....> (it's also on sci-hub) where they struggle with the question of the sense in which GWs are real ("the only well defined way there is to express the influence of [gravitational] radiation [is] in terms of its effect upon invariant space time intervals betwee two test bodies"). I enjoyed seeing the rare \dotequalsdot in eqns 28,30, "geometrically equal to". Also, they lead right into the next suggestion with, "Similarties between gravitational and elecgromagnetic waves thus make it simple to draw a number of reasonable inferences. The significance of these inferences has a much more subtle character in the gravitational case than in the electromagnetic case. Neither field densities nor test particle motions have a meaning independent of the choice of coordinate systems. The simple observable consequences of wave action are instead changes in the separation of nearby test particles -- changes that are related to the covariant components of the curvature tensor R_ijkl."
Goswami & Ellis 2021 <https://iopscience.iop.org/article/10.1088/1361-6382/abdaf3> arxiv html5[*] <https://ar5iv.labs.arxiv.org/html/1912.00591> with the somewhat stentorian title "Tidal forces are gravitational waves". It is really about the Weyl curvature in binaries. The authors explicity consider (for orbital motions of two massive bodies) a decomposition of the Weyl tensor C_abcd into an electric and magnetic part (for which see §III; and eqn 6 repeats the point on R_ab in vaccum), the former compared to Newtonian gravitation and the latter being general-relativistic and encoding the gravitational waves that do not arise in the Newtonian theory. Their focus is on the magnetic part of the Weyl tensor, since (they argue) that is where all the interesting stuff is encoded, and how energy gets from the orbital system to an observer and between the binary partners themselves.
One highlight is a short paragraph summarizing some ~1960 work by Bondi and MacCrae [**], "Through a series of shape changing operations ... one sees that after each rotation, Tweedledum is gaining internal energy as the external tidal force is doing work on him, while Tweedledee is losing energy as she is doing work against the external force. This is an excellent example of how the internal energy of a system can be transferred to another system via gravitational induction, in Newtonian gravity." [emphasis mine].
- -
[*] lost way downpage and heavily downvoted is a HN user pointing out that the page of cartoons linked at the top is not accessibilty-friendly. I accept the point, and make up for it a little with the html5 links here. One can straightforwardly paste the trailing element of the ar5iv into a search engine or whatnot in order to reach a PDF version of each arxived paper above.
[**] The actual Bondi & McCrae paper(s) is(are) proving a bit elusive, but this gives a good overview: §§3-4, Tweedledum and Tweedledee and Energy Transfer (the latter starts with an excellent quote from Bondi in 1957), https://link.springer.com/article/10.1007/s10701-022-00660-z (open access). So this quickly became three papers, and I'll stop now, because I'm fairly sure you can find your way through them if you really want, and figure out how to get help if you get stuck.
> give a more accurate explanation (that makese sense to someone who's never taken a GR class)
It's hard to know what level of understanding to aim for on HN. There are non-relativist working physicists here who somewhat casually read other areas of physics (and mathematics) here, for example, rather than e.g. physics SE or looking through literature reviews.
I'm guessing that you have done GR but probably not much with approximations like GEM, nor looked into the history of gravitational waves (e.g. the 1950s-60s work by Bondi with collaborators like Pirani) before the wide availability of powerful computers and observational support for the linearized theory. My goal here is not to nitpick you, but rather to offer a couple of references that might interest you or anyone who is quietly reading along.
> I think I was totally wrong re: Ricci curvature.
R_munu = 0 for one (uncharged) BH, and also for two. Charged BHs are different (Reissner-Nordström's Ricci tensor is R_munu = +- g_munu r_{Q}^2 / r^4 where r_{Q}^2 = \frac{Q^2G}{4 \pi \varepsilon_0 c^4} and ε_0 is the electric constant, all thanks to the electromagnetic stress-energy tensor; the Ricci scalar remains 0).
Superposing two Schwarzschild or Kerr solutions is messy [Krivan & Price 1998 Phys. Rev. D 58, 104003 was a nice overview arxiv html5[*] <https://ar5iv.labs.arxiv.org/html/gr-qc/9806017>, 'two locally Kerr holes, no matter how close they are, will not superpose into a single Kerr hole. Though [this] "failure" of the close limit is physically correct, it is inconvenient [for doing perturbation theory]'] but doesn't change Rmunu = 0.
A charged binary is beyond the scope of this comment.
> I was thinking "oh, GW carry energy ..."
I can recommend two really good papers written at very different times.
Weber & Wheeler 1957 <https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.29....> (it's also on sci-hub) where they struggle with the question of the sense in which GWs are real ("the only well defined way there is to express the influence of [gravitational] radiation [is] in terms of its effect upon invariant space time intervals betwee two test bodies"). I enjoyed seeing the rare \dotequalsdot in eqns 28,30, "geometrically equal to". Also, they lead right into the next suggestion with, "Similarties between gravitational and elecgromagnetic waves thus make it simple to draw a number of reasonable inferences. The significance of these inferences has a much more subtle character in the gravitational case than in the electromagnetic case. Neither field densities nor test particle motions have a meaning independent of the choice of coordinate systems. The simple observable consequences of wave action are instead changes in the separation of nearby test particles -- changes that are related to the covariant components of the curvature tensor R_ijkl."
Goswami & Ellis 2021 <https://iopscience.iop.org/article/10.1088/1361-6382/abdaf3> arxiv html5[*] <https://ar5iv.labs.arxiv.org/html/1912.00591> with the somewhat stentorian title "Tidal forces are gravitational waves". It is really about the Weyl curvature in binaries. The authors explicity consider (for orbital motions of two massive bodies) a decomposition of the Weyl tensor C_abcd into an electric and magnetic part (for which see §III; and eqn 6 repeats the point on R_ab in vaccum), the former compared to Newtonian gravitation and the latter being general-relativistic and encoding the gravitational waves that do not arise in the Newtonian theory. Their focus is on the magnetic part of the Weyl tensor, since (they argue) that is where all the interesting stuff is encoded, and how energy gets from the orbital system to an observer and between the binary partners themselves.
One highlight is a short paragraph summarizing some ~1960 work by Bondi and MacCrae [**], "Through a series of shape changing operations ... one sees that after each rotation, Tweedledum is gaining internal energy as the external tidal force is doing work on him, while Tweedledee is losing energy as she is doing work against the external force. This is an excellent example of how the internal energy of a system can be transferred to another system via gravitational induction, in Newtonian gravity." [emphasis mine].
- -
[*] lost way downpage and heavily downvoted is a HN user pointing out that the page of cartoons linked at the top is not accessibilty-friendly. I accept the point, and make up for it a little with the html5 links here. One can straightforwardly paste the trailing element of the ar5iv into a search engine or whatnot in order to reach a PDF version of each arxived paper above.
[**] The actual Bondi & McCrae paper(s) is(are) proving a bit elusive, but this gives a good overview: §§3-4, Tweedledum and Tweedledee and Energy Transfer (the latter starts with an excellent quote from Bondi in 1957), https://link.springer.com/article/10.1007/s10701-022-00660-z (open access). So this quickly became three papers, and I'll stop now, because I'm fairly sure you can find your way through them if you really want, and figure out how to get help if you get stuck.
A simple point that might clear up the confusion is: note that the electromagnetic field warps in the presence of charge, yet no charge is transmitted in an electromagnetic wave either.
Explanation: the wave is the warping itself. If a charge or mass exists, the field is (permanently) warped to contain it, in a way that doesn't propagate (although it can be mathematically described as an exchange of particles). But if the charge or mass accelerates, then the warping changes, and the information about that acceleration propagates away. Basically the wave is other charges/masses 'finding out' about a distant change in the velocity of a charge.
Explanation: the wave is the warping itself. If a charge or mass exists, the field is (permanently) warped to contain it, in a way that doesn't propagate (although it can be mathematically described as an exchange of particles). But if the charge or mass accelerates, then the warping changes, and the information about that acceleration propagates away. Basically the wave is other charges/masses 'finding out' about a distant change in the velocity of a charge.
Water & sound waves don't transmit any mass, either, but just energy. In fact, that's pretty much the definition of a wave: An oscillation in space and time that transports energy.
Yes, but what energy is transported here?
Gravitational energy.
Necessary disclaimer: Gravitational energy / energy in General Relativity is notoriously difficult to define and the story of energy conservation is even worse. In general, you can no longer expect energy to be conserved globally. Locally yes, due to the 4-divergence of the energy-momentum tensor vanishing, but globally you can have effects such as cosmic expansion that causes all photons to lose energy as they travel through the universe and, as far as we know, that energy is simply lost.
A few references:
https://en.wikipedia.org/wiki/Conservation_of_energy#General...
https://en.wikipedia.org/wiki/Mass_in_general_relativity
Necessary disclaimer: Gravitational energy / energy in General Relativity is notoriously difficult to define and the story of energy conservation is even worse. In general, you can no longer expect energy to be conserved globally. Locally yes, due to the 4-divergence of the energy-momentum tensor vanishing, but globally you can have effects such as cosmic expansion that causes all photons to lose energy as they travel through the universe and, as far as we know, that energy is simply lost.
A few references:
https://en.wikipedia.org/wiki/Conservation_of_energy#General...
https://en.wikipedia.org/wiki/Mass_in_general_relativity
The "carrier" is the metric tensor. Roughly, at every infinitesimal point in a spacetime like ours there is a tensor value which encodes the distance from that point to its neighbours along all four orthogonal dimensions. "The metric" of a spacetime is usually taken to mean an integration of the metric tensor values at each point along some set of points.
Let's draw a supermassive black hole binary. In the rough <https://en.wikipedia.org/wiki/Minkowski_diagram> schematics below, each equal-mass black hole is an O and we show an observer ("y" for "you") who sees the binary's circular orbit edge-on. The y axis is time, oriented with the future towards the start of this comment. The x axis is one spatial dimension. The diagram-angle from the binary to the observer is meant to be 45 degrees, representing a null aka lightlike separation.
Let's consider two snapshots of the binary's mutual orbit:
1.
"y" is at a spatial remove. But "y" is drawn a couple of lines up because of the finite propagation speed c. The orientation OO...y or 8...y is not felt by y at the time, but later. A null curve connects the binary "at the time" with the "but it's felt later at" observer.
We then integrate all the infinitesimal points along the null curve between y and the centre of mass ("COM") of the binary and find that the null curve in diagram 1 is shorter* than the null curve in diagram 2, because there is more mass between y and the COM in the first diagram.
Above, "y" is pointlike and y would free-fall towards the centre of mass. In y's proper time the free-fall would be faster during orientation 1 than during orientation 2. Since the binary is in a mutual orbit, there is a speeding-up and slowing-down of the free-fall measured by y in y's proper time.
Now we consider some extended-body stuff. Things above and below the SMBHB orbital plane will tend to fall towards the plane. If "y" has some height and the binary isn't treated as practically pointlike, the various parts of now line-like y want to free-fall to the black hole closest to them. In orientation OO the top and bottom of the y will squash inwards. In orientation 8 the top and bottom of the y will stretch up and down. Interpolate through the orientations between OO and 8. The "height" here is along one axis in the plane perpendicular to the binary's orbital plane; a "y" with "width" would be extended in that plane in the orthogonal axis. In orientation 8 there is a stretch along that axis compared to OO.
The magic is all in the orientation of the observer/gravitational-wave-detector to the two mutually-orbiting bodies, and the integration of the metric tensor between every part of the observer and every part of the binary. This is ... generally analyitically intractable, so one does numerical methods ("NR", numerical relativity) or one works in the approximation known as linearized gravity. Most non-specialists, and even many members of the LIGO/Virgo/KAGRA et al collaborations who have encountered the mathematics of gravitational waves did so in the context of linearized gravity, and only sometimes encounter NR and (assuming they aren't writing the NR codes) even then don't think too hard about how the "block universe" spacetime described by the field equations are split into 1+3 dimensions.
So, in summary, the crucial thing is the length of the null curves connecting every part of the y with every part of the binary. The periodic rotation of the binary causes the lengths and angles of those curves to oscillate, shortening and spreading or lengthening and narrowing. Looking closely at a large number of such null curves at once, one can successfully model them in bulk as obeying the massless wave equation, even though nothing actually propagates (the whole spacetime-filling metric tensor field is solved all at once; it only "evolves" or "propagates" when we think in terms of the initial values formalism or a 1+3 formalism).
Finally, here is an pulsar-timing-array astrophysicist (<https://www.aoc.nrao.edu/~tcohen/>) doing an intepretive dance (after a bit of explanation):
https://www.youtube.com/watch?v=uH91gSI4ELs&t=0s
(there are further links in the video description).
- --
* someone is bound to pounce on "shorter" given that the interval of a null curve is always 0 (thus the name and from that flows crazy wrong ideas about "photons experience no time"), but we can use the very much timelike worldlines of the (components of the) binary and observer and retarded time to construct a notion of the length of the null curves connecting them. Eric Poisson has gory technical details for anyone actually interested, in the context of the self-force formalism which is more suitable than linearized gravity for high-mass-ratio binaries, especially as the binary hardens.
PS. "Fabric of spacetime" is a cliché that causes me to grit my teeth. I grit harder when someone who has worked with the Einstein Field Equations writes or says it. It's not only overused, it's misleading to non-experts (and sometimes even to experts). Spacetime is not a substance. It does not "distort", a solution to the EFEs is what it is; "distortions" imply comparing the solution to some alternative that one likes better (e.g. the spacetime without any matter, despite any non-zero stress-energy in the solution). It is at best a mathematical container for coincidences ("events" where two objects at the same point in spacetime can have e.g. their velocities usefully compared) and interactions like collisions, scatterings or the formation of molecular bonds.
Unfortunately, colloquially or informally it's very hard to talk about gravitational waves without talking about the stretching and squashing of some region of space (not spacetime), because people (even experts) internalize "fabric" and similar metaphors, because formalisms and approximations to general relativity used in studying inspiralling-binary sources of gravitational waves split spacetime into space + time, and don't invite the consideration of solutions of the geodesic equation (for tractability reasons).
Let's draw a supermassive black hole binary. In the rough <https://en.wikipedia.org/wiki/Minkowski_diagram> schematics below, each equal-mass black hole is an O and we show an observer ("y" for "you") who sees the binary's circular orbit edge-on. The y axis is time, oriented with the future towards the start of this comment. The x axis is one spatial dimension. The diagram-angle from the binary to the observer is meant to be 45 degrees, representing a null aka lightlike separation.
Let's consider two snapshots of the binary's mutual orbit:
1.
y
OO
y
8
"y" is at a spatial remove. But "y" is drawn a couple of lines up because of the finite propagation speed c. The orientation OO...y or 8...y is not felt by y at the time, but later. A null curve connects the binary "at the time" with the "but it's felt later at" observer.
We then integrate all the infinitesimal points along the null curve between y and the centre of mass ("COM") of the binary and find that the null curve in diagram 1 is shorter* than the null curve in diagram 2, because there is more mass between y and the COM in the first diagram.
Above, "y" is pointlike and y would free-fall towards the centre of mass. In y's proper time the free-fall would be faster during orientation 1 than during orientation 2. Since the binary is in a mutual orbit, there is a speeding-up and slowing-down of the free-fall measured by y in y's proper time.
Now we consider some extended-body stuff. Things above and below the SMBHB orbital plane will tend to fall towards the plane. If "y" has some height and the binary isn't treated as practically pointlike, the various parts of now line-like y want to free-fall to the black hole closest to them. In orientation OO the top and bottom of the y will squash inwards. In orientation 8 the top and bottom of the y will stretch up and down. Interpolate through the orientations between OO and 8. The "height" here is along one axis in the plane perpendicular to the binary's orbital plane; a "y" with "width" would be extended in that plane in the orthogonal axis. In orientation 8 there is a stretch along that axis compared to OO.
The magic is all in the orientation of the observer/gravitational-wave-detector to the two mutually-orbiting bodies, and the integration of the metric tensor between every part of the observer and every part of the binary. This is ... generally analyitically intractable, so one does numerical methods ("NR", numerical relativity) or one works in the approximation known as linearized gravity. Most non-specialists, and even many members of the LIGO/Virgo/KAGRA et al collaborations who have encountered the mathematics of gravitational waves did so in the context of linearized gravity, and only sometimes encounter NR and (assuming they aren't writing the NR codes) even then don't think too hard about how the "block universe" spacetime described by the field equations are split into 1+3 dimensions.
So, in summary, the crucial thing is the length of the null curves connecting every part of the y with every part of the binary. The periodic rotation of the binary causes the lengths and angles of those curves to oscillate, shortening and spreading or lengthening and narrowing. Looking closely at a large number of such null curves at once, one can successfully model them in bulk as obeying the massless wave equation, even though nothing actually propagates (the whole spacetime-filling metric tensor field is solved all at once; it only "evolves" or "propagates" when we think in terms of the initial values formalism or a 1+3 formalism).
Finally, here is an pulsar-timing-array astrophysicist (<https://www.aoc.nrao.edu/~tcohen/>) doing an intepretive dance (after a bit of explanation):
https://www.youtube.com/watch?v=uH91gSI4ELs&t=0s
(there are further links in the video description).
- --
* someone is bound to pounce on "shorter" given that the interval of a null curve is always 0 (thus the name and from that flows crazy wrong ideas about "photons experience no time"), but we can use the very much timelike worldlines of the (components of the) binary and observer and retarded time to construct a notion of the length of the null curves connecting them. Eric Poisson has gory technical details for anyone actually interested, in the context of the self-force formalism which is more suitable than linearized gravity for high-mass-ratio binaries, especially as the binary hardens.
PS. "Fabric of spacetime" is a cliché that causes me to grit my teeth. I grit harder when someone who has worked with the Einstein Field Equations writes or says it. It's not only overused, it's misleading to non-experts (and sometimes even to experts). Spacetime is not a substance. It does not "distort", a solution to the EFEs is what it is; "distortions" imply comparing the solution to some alternative that one likes better (e.g. the spacetime without any matter, despite any non-zero stress-energy in the solution). It is at best a mathematical container for coincidences ("events" where two objects at the same point in spacetime can have e.g. their velocities usefully compared) and interactions like collisions, scatterings or the formation of molecular bonds.
Unfortunately, colloquially or informally it's very hard to talk about gravitational waves without talking about the stretching and squashing of some region of space (not spacetime), because people (even experts) internalize "fabric" and similar metaphors, because formalisms and approximations to general relativity used in studying inspiralling-binary sources of gravitational waves split spacetime into space + time, and don't invite the consideration of solutions of the geodesic equation (for tractability reasons).
>Space is not an elastic fabric
Space is an elastic fabric, if Einstein's explanation of a spacetime dimension is correct. This would mean that gravity is the warping and stretching of this dimension.
If it is not then the other solution is in quantum field theory, which would state that gravity is a field with a messenger particle, the graviton, in which case we are just detecting a group of gravitons as they pass by.
Space is an elastic fabric, if Einstein's explanation of a spacetime dimension is correct. This would mean that gravity is the warping and stretching of this dimension.
If it is not then the other solution is in quantum field theory, which would state that gravity is a field with a messenger particle, the graviton, in which case we are just detecting a group of gravitons as they pass by.
The confusing thing here is that space time warps in the presence of mass.
But no mass is transmitted in a gravity wave.
So what is the fabric made of?
But no mass is transmitted in a gravity wave.
So what is the fabric made of?
Spacetime warps in the presence of mass, yes. But the full answer is that spacetime warps in the presence of energy/momentum; Einstein's field equations make no mention of mass specifically, except that via E=mc^2 masses are energy.
So, once you get a gravitational wave going (by shaking masses) the warping of spacetime itself at one place sources warping for a nearby place which sources warping for a nearby place which ... is what we call a gravitational wave.
So, once you get a gravitational wave going (by shaking masses) the warping of spacetime itself at one place sources warping for a nearby place which sources warping for a nearby place which ... is what we call a gravitational wave.
That would also mean Earth moving around the sun would create such waves?
Indeed it does. But the Earth is so light and the orbit so long that the power emitted is very very low. The sun will explode long before the Earth's orbit will be noticeably modified due to energy loss by gravitational radiation. The distortion effects are not noticeable on experimental scales we have the technology to probe.
The mechanism can noticeably modify orbits, however. In fact the first (indirect) observation of gravitational waves was using exactly that effect.
https://en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_pulsar
The mechanism can noticeably modify orbits, however. In fact the first (indirect) observation of gravitational waves was using exactly that effect.
https://en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_pulsar
When you move mass around - the spacetime curvature responds with light-speed delay. I thought gravitational waves are just that - delayed change of curvature of space-time in response to the mass distribution changing in one place?
No mass is transmitted in a gravity wave, just the same way that no mass is transmitted when the Sun's gravity pulls on the Earth.
And just the same way that no cell phone towers are transmitted when you use your phone.
It's entirely correct to say that the electromagnetic field warps in the presence of moving charges, sending out EM waves like in wireless communication. And the EM waves can travel without any medium, even in hard vacuum. What is the electromagnetic field made of?
And just the same way that no cell phone towers are transmitted when you use your phone.
It's entirely correct to say that the electromagnetic field warps in the presence of moving charges, sending out EM waves like in wireless communication. And the EM waves can travel without any medium, even in hard vacuum. What is the electromagnetic field made of?
We use words to describe abstractions which try to model reality as we observe it.
In case of "space time warps in the presence of mass" it's important to understand that this is just a model. Another way to explain it that there is no space-time per se, only masses (with special case of photon et al) and masses interact. What we mean by space-time is that if there was a tiny mass in this given point, it would experience given force. Or, again, modeled differently, travel along given path.
But if there is nothing to interact with, there is no "space-time" per se in this point, after all, it is an abstraction to describe interactions.
So, to sum up, masses interact, space-time is an abstraction to conveniently describe how they interact. Gravitational wave is two massive masses rotating and shaking third small mass as a result of distance changes.
In case of "space time warps in the presence of mass" it's important to understand that this is just a model. Another way to explain it that there is no space-time per se, only masses (with special case of photon et al) and masses interact. What we mean by space-time is that if there was a tiny mass in this given point, it would experience given force. Or, again, modeled differently, travel along given path.
But if there is nothing to interact with, there is no "space-time" per se in this point, after all, it is an abstraction to describe interactions.
So, to sum up, masses interact, space-time is an abstraction to conveniently describe how they interact. Gravitational wave is two massive masses rotating and shaking third small mass as a result of distance changes.
Space is the fabric.
Moving electric charges produce electromagnetic waves (light). No charge is transmitted with light, but it can cause charges to move. Space is also the fabric for electromagnetic waves.
Moving electric charges produce electromagnetic waves (light). No charge is transmitted with light, but it can cause charges to move. Space is also the fabric for electromagnetic waves.
Space is like a fabric, it's a literal compression and stretching of space as the wave propagates through it. The distances physically get shorter and longer as the wave passes by.
It doesn't necessarily mean that spacetime cannot be fundamental, as there's no rule that says that space itself must emerge from some sort of underlying medium (eg the way fabric is made of threads).
It doesn't necessarily mean that spacetime cannot be fundamental, as there's no rule that says that space itself must emerge from some sort of underlying medium (eg the way fabric is made of threads).
What is stretching/compressing it?
Spacetime is warped by mass but no mass is transmitted. So what exactly is being carried along?
Spacetime is warped by mass but no mass is transmitted. So what exactly is being carried along?
Are you perhaps mis-applying how we say that photons carry the electromagnetic force?
If so, for now we believe that gravity is simply the result of the warping of spacetime, with no known carrying particle. That's kind of the hurdle between uniting gravity with the quantum world.
If say, it turns out that there is such a thing as a graviton - which carries gravity, then gravitational waves would be a bunch of gravitons.
If so, for now we believe that gravity is simply the result of the warping of spacetime, with no known carrying particle. That's kind of the hurdle between uniting gravity with the quantum world.
If say, it turns out that there is such a thing as a graviton - which carries gravity, then gravitational waves would be a bunch of gravitons.
The surface of water is warped by a rock thrown into a pond, but no rock is transmitted by the waves. The electromagnetic field is disturbed by accelerating charges but no charges are transmitted by the EM waves.
In any case, mass is not the only thing that warps spacetime. The components of the stress–energy tensor [1] include energy (which includes mass) density, energy flux, momentum density, and momentum flux, the latter of which is composed of pressure and shear stress components.
[1] https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor
In any case, mass is not the only thing that warps spacetime. The components of the stress–energy tensor [1] include energy (which includes mass) density, energy flux, momentum density, and momentum flux, the latter of which is composed of pressure and shear stress components.
[1] https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor
You're essentially asking the same question after it's been answered. Space-time is the carrier that acts like a fabric, and some large cosmological mass is distorting that fabric.
The distortion of the fabric of space-time ripples throughout the entire universe at the speed of light, and spreads it's effect proportional to the inverse square related to distance.
The distortion of the fabric of space-time ripples throughout the entire universe at the speed of light, and spreads it's effect proportional to the inverse square related to distance.
I don't think they are a hint that spacetime is not fundamental. But I do think spacetime has to be some kind of real physical reality.
The modifications of spacetime that we see as effects of gravity are relative changes to our immediate surroundings or reference frame.
Similarly how you can't tell who is actually stationary and who is moving when two objects are in freefall and all you can note is the relative speed between the two, it would be equally valid to say the objects inside spacetime are getting distorted relative to spacetime.
The modifications of spacetime that we see as effects of gravity are relative changes to our immediate surroundings or reference frame.
Similarly how you can't tell who is actually stationary and who is moving when two objects are in freefall and all you can note is the relative speed between the two, it would be equally valid to say the objects inside spacetime are getting distorted relative to spacetime.
So forget about waves for a second. Forget about spacetime. Forget about general relativity.
The force of gravity is correlated to the mass of the object divided by the square of the distance to the object. The higher the mass, the lower the curvature. The larger the distance, the lower the curvature.
The force of gravity doesn't change instantaneously. The speed is the speed of light. If you move the Sun around using Sufficiently Advanced Technology, (SAT) the orbit of the Earth won't change until 8 minutes later, when the gravity has had time to propagate from the Sun to the Earth.
So what does it feel like if you're on the Earth and somebody is using SAT to wiggle the Sun around? The force felt from the Sun will go up and down. The math that you would use to quantify this changing force is the same math you'd use to characterize sound waves, or water waves, or electromagnetic waves. So we call this changing tidal acceleration 'gravitational waves'.
That's how gravitational waves were described in the 19th and early 20th century, before general relativity. Not long after Einstein published his paper on General Relativity, he adapted the same process via which gravitational waves propagate in Newtonian F = m1 m2 G / r^2 gravity to General Relativity/curvature of spacetime gravity. The math is nasty, and it wasn't really ironed out until decades later, but the theoretical predictions of what gravitational waves will look like in any given detector was worked out well before we actually went and detected them.
> Space is not an elastic fabric
It's a 4D/(3,1) Lorentzian manifold. If you want a better analogy than the stretched elastic fabric analogy, unfortunately the next step is to grab a textbook and slog through the math.
The force of gravity is correlated to the mass of the object divided by the square of the distance to the object. The higher the mass, the lower the curvature. The larger the distance, the lower the curvature.
The force of gravity doesn't change instantaneously. The speed is the speed of light. If you move the Sun around using Sufficiently Advanced Technology, (SAT) the orbit of the Earth won't change until 8 minutes later, when the gravity has had time to propagate from the Sun to the Earth.
So what does it feel like if you're on the Earth and somebody is using SAT to wiggle the Sun around? The force felt from the Sun will go up and down. The math that you would use to quantify this changing force is the same math you'd use to characterize sound waves, or water waves, or electromagnetic waves. So we call this changing tidal acceleration 'gravitational waves'.
That's how gravitational waves were described in the 19th and early 20th century, before general relativity. Not long after Einstein published his paper on General Relativity, he adapted the same process via which gravitational waves propagate in Newtonian F = m1 m2 G / r^2 gravity to General Relativity/curvature of spacetime gravity. The math is nasty, and it wasn't really ironed out until decades later, but the theoretical predictions of what gravitational waves will look like in any given detector was worked out well before we actually went and detected them.
> Space is not an elastic fabric
It's a 4D/(3,1) Lorentzian manifold. If you want a better analogy than the stretched elastic fabric analogy, unfortunately the next step is to grab a textbook and slog through the math.
I think you’re looking for a ‘ether’? Many people have asked similar questions about all sorts of physical phenomena over the years.
https://en.wikipedia.org/wiki/Aether_theories
https://en.wikipedia.org/wiki/Aether_theories
Along similar lines, I wonder if gravitational waves can be focused.
They should be focusable by objects with mass, just as light is. A difference is that gravitational waves could be focused by the Sun's core, and so would come to a focus closer to the Sun than light would be, which would have to be focused by the entire Sun (as any light passing through the Sun itself is blocked.)
Yes, foreground massive objects can magnify gravitational waves emitted by a background source (the foreground objects can also induce a beating pattern on the background waves, or split the background waves into multiple wavefronts). The "foreground" emitter in a massive cluster of thousands of galaxies can be deep inside the cluster, and those are probably the gravitationally-lensed gravitational-wave sources we will identify first [more below at [1]].
A good starting point for a non-specialist is probably <https://astrobites.org/2021/05/25/gw-lensing/>.
(You could compare a specialist paper <https://www.aanda.org/articles/aa/full_html/2020/11/aa38730-...> which describes the lensingGW software package https://gpagano.gitlab.io/lensinggw/ ).
- -- [1] When a candidate gravitational wave (GW) detection is found at LIGO et al., an electromagnetic (EM) detection may follow. Neutron stars collide explosively, generating a huge burst of very high-frequency (gamma ray) EM. Black holes don't explode but their accretion structures can interact very strongly producing high-frequency (X-ray) EM. These bright high-frequency EM flashes decay into a glow that can last for many days after a merger. Consequently they are looked for, as part of the overall project of multi-messenger astronomy (where EM and GW are two "messengers"; neutrinos and so forth make it "multi-").
Close to the source, peak EM tends to lag a bit behind the merger, mostly because of how the EM is produced at some distance outside merged black holes. Additionally, EM scatters/refracts/etc with dust and gas that one finds deep inside galaxies, which are more transparent to GW than to EM. Consequently in general GWs will be detected before EMs from the same source. Candidate GW detections provoke searches across the electromagnetic spectrum, since EM may arrive hours or even days later.
GW from an inspiral and merger in general have much much longer wavelengths than the X-rays from the gas around the merging objects. Black holes merge roughly when their horizons touch, and horizon size is proportional to mass. GW wavelength is proportional to the orbital diameter, which must be larger than the sum of horizon radiuses, so supermassive black hole binary (SMBHB) mergers have much longer-wavelength GW than stellar-mass black hole binary mergers.
The relatively short wavelengths of electromagnetic radiation will follow the laws of geometrical optics and in particular will experience Shapiro delay. GW wavelengths, being much longer, will not. This explains a further delay on EM from SMBHB mergers that are deep within a massive galaxy or cluster of galaxies.
Foreground lenses (e.g. massive galaxies that the source does not live within) will further increase the delay suffered by EM produced by the merger that sourced the GW. Moreover, since foreground lenses can split the wavefronts of the GW and EM, there may be ~four detections, at different times, of the same merger in GW and EM. Alternatively, the foreground lens can magnify the source merger, but with the delays described above and geometric optics vs not, the focal point for GW and for EM will differ.
All of this is active research, close to cutting edge, so sadly is mostly to be found via a literature search on Einstein lensing of gravitational waves. AFAICT most "pop sci" attempts to summarize some of the academic literature is simply awful. Hopefully I'm merely just not great above. :-/
A good starting point for a non-specialist is probably <https://astrobites.org/2021/05/25/gw-lensing/>.
(You could compare a specialist paper <https://www.aanda.org/articles/aa/full_html/2020/11/aa38730-...> which describes the lensingGW software package https://gpagano.gitlab.io/lensinggw/ ).
- -- [1] When a candidate gravitational wave (GW) detection is found at LIGO et al., an electromagnetic (EM) detection may follow. Neutron stars collide explosively, generating a huge burst of very high-frequency (gamma ray) EM. Black holes don't explode but their accretion structures can interact very strongly producing high-frequency (X-ray) EM. These bright high-frequency EM flashes decay into a glow that can last for many days after a merger. Consequently they are looked for, as part of the overall project of multi-messenger astronomy (where EM and GW are two "messengers"; neutrinos and so forth make it "multi-").
Close to the source, peak EM tends to lag a bit behind the merger, mostly because of how the EM is produced at some distance outside merged black holes. Additionally, EM scatters/refracts/etc with dust and gas that one finds deep inside galaxies, which are more transparent to GW than to EM. Consequently in general GWs will be detected before EMs from the same source. Candidate GW detections provoke searches across the electromagnetic spectrum, since EM may arrive hours or even days later.
GW from an inspiral and merger in general have much much longer wavelengths than the X-rays from the gas around the merging objects. Black holes merge roughly when their horizons touch, and horizon size is proportional to mass. GW wavelength is proportional to the orbital diameter, which must be larger than the sum of horizon radiuses, so supermassive black hole binary (SMBHB) mergers have much longer-wavelength GW than stellar-mass black hole binary mergers.
The relatively short wavelengths of electromagnetic radiation will follow the laws of geometrical optics and in particular will experience Shapiro delay. GW wavelengths, being much longer, will not. This explains a further delay on EM from SMBHB mergers that are deep within a massive galaxy or cluster of galaxies.
Foreground lenses (e.g. massive galaxies that the source does not live within) will further increase the delay suffered by EM produced by the merger that sourced the GW. Moreover, since foreground lenses can split the wavefronts of the GW and EM, there may be ~four detections, at different times, of the same merger in GW and EM. Alternatively, the foreground lens can magnify the source merger, but with the delays described above and geometric optics vs not, the focal point for GW and for EM will differ.
All of this is active research, close to cutting edge, so sadly is mostly to be found via a literature search on Einstein lensing of gravitational waves. AFAICT most "pop sci" attempts to summarize some of the academic literature is simply awful. Hopefully I'm merely just not great above. :-/
Thanks a lot for all the answers! Many of them are outside of my math skills but I appreciate the different ways this was explained. Thanks!
[deleted]
Really great explainer!
Naive question: how do we know it is gravity specifically distorting space? Could there be other forces or phenomena not related to mass?
Naive question: how do we know it is gravity specifically distorting space? Could there be other forces or phenomena not related to mass?
The theory of general relativity says that "gravity" and "distorted space(-time)" are one and the same phenomenon. So it's a question of whether you believe that theory is correct.
We've known for a long time that GR predicts that when black holes and/or neutron stars collide, they should emit gravitational waves with a very specific shape. The LIGO and Virgo observatories detected faint signals that seem to match this shape, which gives us confidence that the theory is a correct explanation of the data.
This adds to the mountains of other evidence for GR, and complements it by showing that GR still holds in environments where space-time curvature is extremely strong.
Technically, we don't know for sure that it's impossible for GWs to be produced by other sources than moving masses, but we have neither theory nor evidence to suggest such a thing is possible.
We've known for a long time that GR predicts that when black holes and/or neutron stars collide, they should emit gravitational waves with a very specific shape. The LIGO and Virgo observatories detected faint signals that seem to match this shape, which gives us confidence that the theory is a correct explanation of the data.
This adds to the mountains of other evidence for GR, and complements it by showing that GR still holds in environments where space-time curvature is extremely strong.
Technically, we don't know for sure that it's impossible for GWs to be produced by other sources than moving masses, but we have neither theory nor evidence to suggest such a thing is possible.
If gravitational waves can be detected by looking at pulsars, then what is the purpose of LIGO and ground-based gravitational wave observatories? Is there any difference in the waves detected by LIGO and those from observing pulars?
As mentioned in the sibling comment, different frequencies means probing different things.
I found this talk[1] rather nice to explain the NANOGrav experiment, and at 6:45 there's a very nice plot that shows where NANOGrav fits in compared to the other gravitational wave experiments and which type of sources the various experiments can probe.
[1]: https://pirsa.org/20100068
I found this talk[1] rather nice to explain the NANOGrav experiment, and at 6:45 there's a very nice plot that shows where NANOGrav fits in compared to the other gravitational wave experiments and which type of sources the various experiments can probe.
[1]: https://pirsa.org/20100068
LIGO detects gravitational waves in the frequency range of hundreds of Hertz (10^2 Hz), which are produced in the last moments of the in-spiraling of merging neutron stars or blackholes.
Nanohertz are 10^-9 Hz which relate to a rotational period of decades of years.
https://en.wikipedia.org/wiki/Gravitational-wave_astronomy
Nanohertz are 10^-9 Hz which relate to a rotational period of decades of years.
https://en.wikipedia.org/wiki/Gravitational-wave_astronomy
For one we didn't have a way to measure the speed of gravitational waves before [1].
[1] https://physics.stackexchange.com/questions/622729/did-ligo-...
[1] https://physics.stackexchange.com/questions/622729/did-ligo-...
Those two methods observe waves of much different wavelength/frequency, and the mechanisms that create such different wavelengths are assumed to be different. So cosmologists are studying different things by looking at different wavelengths.
I don't have a deep understanding of physics and would have no chance at understanding the details of this if it was in a traditional academic paper, and not presented so well. This is absolutely fantastic!
Fantastic explainer. The illustrations are both charming and helpful.
It's reminiscent of other excellent multi-modal "explainers", e.g. Julia Evans (https://jvns.ca), https://betterexplained.com, Randall Munroe (https://xkcd.com), http://inception-explained.com ...
And on this topic of mixing text with imagery, I highly recommend Nick Sousanis's amazing "Unflattening" (https://archive.org/details/unflattening0000sous)
It's reminiscent of other excellent multi-modal "explainers", e.g. Julia Evans (https://jvns.ca), https://betterexplained.com, Randall Munroe (https://xkcd.com), http://inception-explained.com ...
And on this topic of mixing text with imagery, I highly recommend Nick Sousanis's amazing "Unflattening" (https://archive.org/details/unflattening0000sous)
Is there a similar illustration to the Quantum Entanglement phenomena?
Something I yet to have to fully understand how that is possible?
Say your car and another car got in a crash, but you both panicked and drove away(that is, you did not inspect the damage.)
You get home and finally summon the courage to look at your car. It's busted. With that information you can infer that the other car is busted too, and you don't need to ever come in contact again with the other car to know this fact only that at some point in the past your car and theirs interacted.
You get home and finally summon the courage to look at your car. It's busted. With that information you can infer that the other car is busted too, and you don't need to ever come in contact again with the other car to know this fact only that at some point in the past your car and theirs interacted.
This explanation infers a hidden variable, which is not how quantum entanglement works.
IE - it sounds like the damage occurs at the time of impact, and you just decided to look at a later point in time. But that isn’t what happens with quantum entangled particles. The particles will have opposite spin when the entangled state collapses, but measurement will affect the angle of the spin in a way that proves spin is not preselected when the particles were initially entangled and local to one another.
In your story, looking at your own car would have an observable effect on the entangled car, even though it is far away. But you also cannot even tell it was entangled with the other car without comparing the two over more traditional channels!
Edit: Since a graphic was requested, I found this image hosted by JPL, which shows a related phenomenon (quantum teleportation) to what I described, and hopefully dispels the car crash explanation which doesn’t imply “spooky action at a distance”.
https://www.jpl.nasa.gov/news/researchers-advance-quantum-te...
IE - it sounds like the damage occurs at the time of impact, and you just decided to look at a later point in time. But that isn’t what happens with quantum entangled particles. The particles will have opposite spin when the entangled state collapses, but measurement will affect the angle of the spin in a way that proves spin is not preselected when the particles were initially entangled and local to one another.
In your story, looking at your own car would have an observable effect on the entangled car, even though it is far away. But you also cannot even tell it was entangled with the other car without comparing the two over more traditional channels!
Edit: Since a graphic was requested, I found this image hosted by JPL, which shows a related phenomenon (quantum teleportation) to what I described, and hopefully dispels the car crash explanation which doesn’t imply “spooky action at a distance”.
https://www.jpl.nasa.gov/news/researchers-advance-quantum-te...
outstanding delivery
Very well done
So pulsars are not regular at the tick level as they can spin faster and slower but have 100 nanoseconds accuracy (Way worse than an atomic clock) when doing an average profile -
https://astronomy.swin.edu.au/cosmos/p/Pulsar+Timing
This is a cool line -
"In effect this allows changes in the relative distance between the pulsar and Earth to be computed to an accuracy of 30 metres (~100 feet)"
So pulsars are not regular at the tick level as they can spin faster and slower but have 100 nanoseconds accuracy (Way worse than an atomic clock) when doing an average profile -
https://astronomy.swin.edu.au/cosmos/p/Pulsar+Timing
This is a cool line -
"In effect this allows changes in the relative distance between the pulsar and Earth to be computed to an accuracy of 30 metres (~100 feet)"
It would be nice if there was a plain-text version for accessibility.