Can Time-Reversed Gravitational Waves Be Detected or Recovered?

[georgir]

I’m curious, how can the energy from these waves ever be recovered? How can they be “received”? Is that in any way overlapping with “detected”?
For EM, we have the time-reversed equivalent of emission just as often as we have the emission, but for these gravitational waves that would be absurd… so does that mean mass is just constantly disappearing in the form of unrecoverable and quickly dispersing gravitational waves?

 

[Vanadium 50]

Electromagnetic waves can be absorbed as well as emitted. Gravitational waves can be absorbed as well as emitted. What is the problem?

 

[georgir]

Well, are they absorbed as much as they are emitted?

 

[Dale]

For EM, we have the time-reversed equivalent of emission just as often as we have the emission

I don't think that this is necessarily true. Now that the universe is transparent I think that there are emissions that will never have a corresponding absorption. And as the universe shifted from radiation dominated to matter dominated there must have been more absorption than emission.

 

[Vanadium 50]

Well, are they absorbed as much as they are emitted?

I don't think this question is well-defined enough to answer. Is light? Does light have to be?

 

[georgir]

Ok then, about the other part of my question... What exactly does GW absorption look like? Was the detection of GW in a way absorption of part of its energy?
I did not think EM waves can be detected without also absorbing them, but maybe I am wrong about this too... so can they?
The way I think about it, absorption must be just time-reversed emission. Which works nice for EM which we know can be emitted in single, focused and directed packets, so then there is no problem to also absorb it as such. But for GW, if emission only happens as a spreading spherical wave, how can absorption happen for anything other than an incoming concentrating spherical wave? Or can GW also be emitted in directed, focused packets?

 

[georgir]

I don't think this question is well-defined enough to answer. Is light? Does light have to be?

Regarding this question, I would think that it should be the case, otherwise we'd get infinitely bright sky or something (if the universe was infinite). Or at the very least, increasingly brighter and brighter sky as the universe ages and more and more distant light can reach us...
Though I agree that my opinion on the subject may be very naive and I've nothing to back it up, and I do not intend to argue for it in this thread.

 

[georgir]

Ok then, about the other part of my question... What exactly does GW absorption look like? Was the detection of GW in a way absorption of part of its energy?
I did not think EM waves can be detected without also absorbing them, but maybe I am wrong about this too... so can they?
The way I think about it, absorption must be just time-reversed emission. Which works nice for EM which we know can be emitted in single, focused and directed packets, so then there is no problem to also absorb it as such. But for GW, if emission only happens as a spreading spherical wave, how can absorption happen for anything other than an incoming concentrating spherical wave? Or can GW also be emitted in directed, focused packets?

Bump! Anyone?

 

[PeterDonis]

What exactly does GW absorption look like?

It depends on what is doing the absorbing.

Was the detection of GW in a way absorption of part of its energy?

Of a very small part, yes. Detecting anything involves some kind of change in the detector, which takes energy. That energy has to come from whatever it is that is being detected. In the case of LIGO, the mirrors at the ends of the arms were moved very slightly by the passing GW. That motion took energy, which had to come from the passing GW.

The way I think about it, absorption must be just time-reversed emission.

Only if whatever is doing the absorbing is exactly the time reverse of whatever is doing the emitting. But that is rarely the case, and is sometimes not even possible. For example, the GWs detected by LIGO were formed by the merger of two BHs that spiraled together to form a single BH. The time reverse of that would be a single BH "unmerging" to form two BHs that then spiral apart. But a BH can't split apart, so it would be imposslble to make a GW absorber this way.

 

[PeterDonis]

if emission only happens as a spreading spherical wave, how can absorption happen for anything other than an incoming concentrating spherical wave?

Well, EM waves can be emitted as a spreading spherical wave, but we don't have to detect them as an incoming concentrating spherical wave, do we? We see the Sun, which is emitting spreading spherical waves of light, but we don't see it by concentrating the entire spherical wave it emits to a single point.

 

[PAllen]

Only if whatever is doing the absorbing is exactly the time reverse of whatever is doing the emitting. But that is rarely the case, and is sometimes not even possible. For example, the GWs detected by LIGO were formed by the merger of two BHs that spiraled together to form a single BH. The time reverse of that would be a single BH "unmerging" to form two BHs that then spiral apart. But a BH can't split apart, so it would be imposslble to make a GW absorber this way.

True, but the formal t invariance of GR suggests the amusing possibility that if you could postulate just the right pattern of incoming GW on a boundary (or at lightlike minus infinity), their convegence could split a BH !?

 

[PeterDonis]

the formal t invariance of GR suggests the amusing possibility that if you could postulate just the right pattern of incoming GW on a boundary (or at lightlike minus infinity), their convegence could split a BH !?

Such a solution would be converging GWs splitting a white hole, not a black hole. The time reverse of a black hole is a white hole. And then, of course, you have the problem of explaining where the initial singularity of the white hole came from.

 

[georgir]

Well, EM waves can be emitted as a spreading spherical wave, but we don't have to detect them as an incoming concentrating spherical wave, do we? We see the Sun, which is emitting spreading spherical waves of light, but we don't see it by concentrating the entire spherical wave it emits to a single point.

Well, that was also my point - EM also allows another mode of emission, and hence of absorbtion, so they are no problem to have reasonable EM detectors. This is why I'm wondering if GW can also be emitted in directional packets.

Detecting anything involves some kind of change in the detector, which takes energy. That energy has to come from whatever it is that is being detected. In the case of LIGO, the mirrors at the ends of the arms were moved very slightly by the passing GW. That motion took energy, which had to come from the passing GW.

Um, detecting features of the underlying geometry does not seem to me to require changing it, or taking energy from it. Also, technically the GW did not move the mirrors, it just changed the geometry of the space between them.

Only if whatever is doing the absorbing is exactly the time reverse of whatever is doing the emitting

I do not suggest that a wave can only be absorbed by exactly the time reverse of its emission process. Just the time-reverse of some possible emission process, but not necessarily the exact one that actually originally emitted it. I.e. a photon emitted from an excited electron in an atom may very well be absorbed by anything, even as fancy as reverse annihilation of some particles.

 

[PAllen]

Such a solution would be converging GWs splitting a white hole, not a black hole. The time reverse of a black hole is a white hole. And then, of course, you have the problem of explaining where the initial singularity of the white hole came from.

Ah, right. Then a description would be that the incoming GW 'modulate' the white hole disintegration to produce two WH instead of an 'anti-collapse'. Then, the two WH anti-collapse some time after spiraling away.

 

[PeterDonis]

EM also allows another mode of emission, and hence of absorbtion, so they are no problem to have reasonable EM detectors.

I'm not sure what you mean. If we happened to have a bunch of EM waves in a spherical configuration converging on a single point, we could detect that too. The reason we don't bother building such detectors is that having a bunch of EM waves in a spherical configuration converging on a single point basically never happens. (It would be possible in principle but in practice the kind of configuration of sources that would be necessary never occurs.)

I'm wondering if GW can also be emitted in directional packets.

We probably need to clear up a point here: neither EM waves nor GWs actually get emitted in a perfectly spherically symmetric way. The lowest order EM radiation is dipole, and the lowest order GWs are quadrupole. The reason we often view EM waves or GWs coming from a particular source as spherically symmetric expanding wave fronts is that the source consists of a huge number of dipoles (for EM) or quadrupoles (for GW), and the emission from all of them put together is a spherical wavefront with some very tiny irregularities that we can for most purposes ignore. Then, if we are far enough from the source and looking at a small enough piece of the total spherical wavefront, we can in turn approximate it as a plane wave, which is the easiest kind to model mathematically.

So, if we want to have an emission of waves, either EM or GW, that looks more like a "directional packet", we just need to arrange the little dipole or quadrupole sources differently. With EM wave antennas there are a lot of tricks for doing this to get as much possible beam energy into a narrow solid angle. Similar tricks might work with GWs if we had a way to manipulate huge masses the way we can manipulate electrons in an antenna. But we probably won't have that capability for a long time.

detecting features of the underlying geometry does not seem to me to require changing it, or taking energy from it.

The geometry of spacetime does not "change"; it is a 4-dimensional geometry that just "is". But that 4-dimensional geometry can certainly consist of wavelike "ripples" whose amplitude decreases as you move in spacetime from the vacuum region between the source and a detector, through the region of spacetime occupied by the detector, to the vacuum region beyond the detector. Correspondingly, the matter and energy distribution in the region of spacetime occupied by the detector is different "upstream" of the region where the GW passes through, vs. "downstream" of that region. Geometrically, this is just a particular geometry that is a perfectly good solution of the Einstein Field Equations--the EFE is what makes the connection between the spacetime geometry and the distribution of matter and energy. To us, located near the detector, it would look like a GW passing, being detected by the detector, and giving up some energy to it in the process.

Now consider an alternative geometry, where the GW amplitude did not change at all from the vacuum region before the detector, through the detector, to the vacuum region after the detector. The point I'm making is that, in this case, there would be nothing in the detector region that corresponded to "detecting a GW"; the distribution of matter and energy in the region of spacetime occupied by the detector itself would be exactly what it would have been if no GW had passed through. This is why I said that the only way for a detector to detect a GW is for it to take some energy from it--if there is no exchange of energy, there is nothing in the matter and energy distribution of the detector that is affected by the spacetime geometry of the GW, so no GW is detected.

 

[georgir]

We probably need to clear up a point here: neither EM waves nor GWs actually get emitted in a perfectly spherically symmetric way. The lowest order EM radiation is dipole, and the lowest order GWs are quadrupole. The reason we often view EM waves or GWs coming from a particular source as spherically symmetric expanding wave fronts is that the source consists of a huge number of dipoles (for EM) or quadrupoles (for GW), and the emission from all of them put together is a spherical wavefront with some very tiny irregularities that we can for most purposes ignore.

But what if we do not "average out" the many distinct emissions, but look at just a single one of them? If it is an EM wave from an electron changing its direction or energy we get a single "photon", that when eventually absorbed will give off the entirety of the radiated energy. Is there anything similar happening in the GW case?
[Edit: In other words, I understand you are right for the case of EM waves, but I am not sure about GW.]
[Edit 2: I also understand I'll eventually need to learn the math of it all, as right now all the dipole-quadropole details are just way over my head.]

Now consider an alternative geometry, where the GW amplitude did not change at all from the vacuum region before the detector, through the detector, to the vacuum region after the detector. The point I'm making is that, in this case, there would be nothing in the detector region that corresponded to "detecting a GW"; the distribution of matter and energy in the region of spacetime occupied by the detector itself would be exactly what it would have been if no GW had passed through.

I'm still not convinced by this bit. To have something that corresponded to "detecting a GW" we only need a difference in the time-like region after the GW passing through the detector, not on the null region of the wave itself.
But I concede anyway. In a way, I think the question of whether our "detection" absorbed some GW energy is related to whether forcing a process similar to our detection would emit a GW. I.e. if we force the distance between some objects to change, does that emit a GW? I guess it does, so I see now that our detection must have influenced the GW at least a bit.
Still, it strikes me as odd that the magnitude of this effect should be completely drowned among all the other tiny GW emitted by other variously accelerating objects around the detector.

 

[PeterDonis]

If it is an EM wave from an electron changing its direction or energy we get a single "photon", that when eventually absorbed will give off the entirety of the radiated energy. Is there anything similar happening in the GW case?

If you're asking, are GWs quantized as "gravitons" the way EM waves are quantized as photons, we don't know for sure. It's a reasonable hypothesis, but gravity is so weak compared to the other fundamental interactions that we have no expectation of being able to do experiments any time soon that will test whether it's quantized.

To have something that corresponded to "detecting a GW" we only need a difference in the time-like region after the GW passing through the detector, not on the null region of the wave itself.

You can't have the first without the second. That would violate the Einstein Field Equation.

if we force the distance between some objects to change, does that emit a GW? I guess it does

Not necessarily. It depends on how the distance changes. The lowest order GWs are quadrupole, as I said before; more precisely, in order to radiate GWs, a system needs to have a nonzero third time derivative of the quadrupole moment. So just two masses moving apart and together along a single line won't do it; you need a more complicated motion.

it strikes me as odd that the magnitude of this effect should be completely drowned among all the other tiny GW emitted by other variously accelerating objects around the detector.

Why do you think this is the case? What other objects around the detector do you think are emitting GWs? In the case of LIGO, the various sources of noise that have to be allowed for are not GW sources; they're ordinary vibrations in the air and the supporting structure. One of the reasons for wanting to build LISA, the GW interferometer out in space, is to get rid of those sources of noise and have something much closer to the idealized GW detector that is used in textbooks.

 

[georgir]

Well, I give up. I don't know what to think anymore.
To me absorption is still the time-reverse of emission, and due to time-reverse symmetry of most laws actually also the same as emission itself, just with an opposite phase so the result is waves cancelling each other out.
So if you say the passing GW changed some distances between some mirrors here in some specific way and lost some of its energy, it should be true that making the mirrors change distances in a similar (or reversed) way should emit that same energy as a GW.

And it's not just the distance between the mirrors that got affected by the GW, even though that's the one we noticed. All particles of all matter that the GW passes through are affected in exactly the same way as the mirrors were. If they did take a portion of the GW's energy, wouldn't it add up to a much more pronounced effect? Yet from what I read about GWs, they are (mostly?) unaffected by matter they pass through.

 

[PeterDonis]

To me absorption is still the time-reverse of emission

You are confusing yourself by insisting on stating this in a way that makes it seem like a simple fact, when it is actually glossing over a lot of complexities.

It is true that the fundamental laws of EM, and the fundamental laws of GR, are time symmetric. Here is what that means: given any solution of the fundamental equations, there will be another solution that is the time reverse of that one. So, given a particular solution that describes the emission of a wave, there will be another solution that is the time reverse of that one.

However, that does not at all imply that the time reversed solution must occur the same number of times as the original one, nor does it imply that the time reverse of a solution describing the usual process of emission of a wave, is a solution corresponding to the usual process of absorption of a wave (or vice versa). To take one example that has already been discussed: suppose we have a solution that, to a good approximation, describes a source of EM radiation emitting outgoing spherical wavefronts that take away energy from the source. (They won't be exactly spherical wavefronts, for reasons that have already been discussed, but we can arrange a macroscopic source to contain a very large number of small dipoles whose combined radiation can be modeled as outgoing spherical wavefronts to a good approximation.) What is the time reverse of this solution? It is a solution describing a "sink" of EM radiation that just happens to have a series of incoming spherical wavefronts converging exactly on it, in just the right way to deliver energy to the source. This time reversed solution will obviously be much, much rarer than the original one, since it requires an extremely precise arrangement of the incoming spherical wavefronts and of the charges inside the source, which is extremely improbable.

Consider another example: an EM absorber consisting of a material with little charges in it that are made to oscillate when an EM wave passes through. A small piece of a spherical wavefront emitted by a source very far away can be idealized as a plane wave, and the little charges will oscillate when the plane wave passes, transferring a small portion of the energy carried by the wave to the charges. (Note that as the charges oscillate, they also generate EM waves, and in a fully rigorous analysis we have to take those into account as well; the net energy absorbed by the charges will be the energy taken from the incoming EM waves, minus the energy re-radiated as other EM waves. We'll see why that's relevant in just a moment.) What is the time reverse of this solution? It is a solution where a plane wave is passing through the material in the other direction, and the material contains charges that are already oscillating in a very particular way; and the combined effect is to make the charges stop oscillating in exactly the right way to draw energy from the charges inside the material and transfer it to the waves. (Note that for this to happen, the charges must themselves radiate EM waves as they stop oscillating, and the energy re-radiated must be larger than the energy absorbed by the incoming wave.) Again, this latter situation will be much, much more improbable than the original one.

Similar remarks apply to the case of GWs. Consider the BH merger that produced the GWs detected by LIGO. The time reverse of this, as I pointed out in my response to PAllen, would be converging GWs that hit a white hole and split it in two, so that, as PAllen said in his response to my response, you would have two white holes "exploding" and sending out matter and radiation, instead of one. But we don't even think that a solution with one white hole is physically realistic, let alone one with a white hole being split in two by GWs.

Now consider the process by which LIGO detected the GWs. A very tiny fraction of an already very tiny amount of energy carried by the GWs was deposited in the LIGO detector during the detection process by making the mirrors start oscillating. (Note that, by analogy with the EM case, the LIGO detector will re-radiate GWs--containing a still tinier amount of energy, so that there is a net energy transfer from the GWs to the detector.) The time reverse of this would be GWs coming through LIGO in the other direction, and the LIGO detector mirrors oscillating, both in just the right way to cause the LIGO detector mirrors to stop oscillating and re-radiate GWs that took net energy away from the detector. This is, again, much, much more improbable than the original solution, describing LIGO detecting GWs and absorbing energy from them, would be.

So an ordinary, common process of absorption is not just the time reverse of an ordinary, common process of emission, and you are confusing yourself by talking as though it is.

 

[PeterDonis]

All particles of all matter that the GW passes through are affected in exactly the same way as the mirrors were.

No, they're not, any more than all charges in any piece of matter are affected in exactly the same way by an EM wave as the charges in a piece of matter that is specifically designed to be an EM wave detector. The LIGO apparatus has to be set up in a very precise way in order for it to absorb a detectable amount of energy from the GW.

 

[RockyMarciano]

No, they're not, any more than all charges in any piece of matter are affected in exactly the same way by an EM wave as the charges in a piece of matter that is specifically designed to be an EM wave detector. The LIGO apparatus has to be set up in a very precise way in order for it to absorb a detectable amount of energy from the GW.

I don't understand this bit. Sure, they won't be affected in in exactly the same way, but it seems naive that the passing GW transfers to matter crucially different amounts of energy through the Ligo set up than through the rest of the earth. I would venture that it would transfer more than through the vacuum of space, of most of the last 1.3 bly, though.
One thing I don't know how to interpret is if you take a look at the pictures of the superposed waveforms from the two locations in the main paper of Ligo's september detection, is that even just by eye it looks evident the amplitude decrease in the signal from Washington to Louisiana. If we think about the distance travelled(1.3 bly) by the GW and the fact that it is not supposed to interact but slightly with matter, how can about a thousand miles of flight produce an amplitude decrease so noticeable?

 

[Ibix]

The detectors are oriented differently, so have different sensitivities, much as the motion of a wooden bead on a straight wire will depend on the orientation of the wire with respect to a passing water wave. Which is, I think, an illustration of Peter's point about different bits of matter absorbing different amounts of energy from the gravitational wave.

 

[PeterDonis]

it seems naive that the passing GW transfers to matter crucially different amounts of energy through the Ligo set up than through the rest of the earth

We actually don't know how much energy the GW transferred to the Earth as a whole; there's no way to measure that. So it's possible that the total energy transferred was not "crucially different" for LIGO than for a similarly sized piece of matter elsewhere in the Earth. I believe a LIGO physicist would say LIGO is more sensitive than a random piece of matter of a similar size, so it would have more energy transferred, but I don't know that they would say it is "crucially more".

What we do know, at least to a pretty good approximation, is that both of those energies--the energy transferred to the LIGO detectors, and the energy transferred to a random piece of matter of a similar size--are very tiny compared to the total energy carried by the GWs that passed through the Earth, which is itself extremely tiny compared to the total energy released as GWs at the source--the BH merger. That is what people mean when they say that GWs aren't affected much by passing through matter.

 

[PeterDonis]

even just by eye it looks evident the amplitude decrease in the signal from Washington to Louisiana.

That's because those two detectors were oriented differently with respect to the plane wave fronts, as was discussed in one of the recent LIGO threads--the angle between the plane of the detector and the plane of the wave fronts affects the amplitude that is detected. It has nothing to do with attenuation of the GW by matter.

 

[georgir]

...[long post]...

You're still explaining me the large-scale picture, and I understand that and agree - the reversed direction is much more unlikely, entropy, arrow of time, all that jazz. But that's not what I'm interested in here. I want to understand the small scale, the basic interactions, i.e. single electron case or just 2 small point masses in a fraction of their orbital arc, not black hole mergers.

No, they're not, any more than all charges in any piece of matter are affected in exactly the same way by an EM wave as the charges in a piece of matter that is specifically designed to be an EM wave detector. The LIGO apparatus has to be set up in a very precise way in order for it to absorb a detectable amount of energy from the GW.

But it doesn't seem like so. An EM wave detector is made just like an EM wave emitter. What we did for GW detector was more like if we just got a voltmeter and watched for the changes in voltage in order to detect EM waves - and the better the voltmeter quality, the less current would it need and so the less would it affect the wave. I doubt anyone would describe such a measurement as absorbing EM wave energy...

 

[RockyMarciano]

That's because those two detectors were oriented differently with respect to the plane wave fronts, as was discussed in one of the recent LIGO threads--the angle between the plane of the detector and the plane of the wave fronts affects the amplitude that is detected. It has nothing to do with attenuation of the GW by matter.

Yes, the detectors' arms are oriented at different planes due to the Earth's curvature, but note that unfortunately we cannot model exactly the effect that inclination has on the amplitude since we are lacking information about the polarization of the GW, 4 detectors would be necessary to have a precise knowledge about it.
In any case I guess you are right that this should explain the amplitude loss rather than attenuation.

 

[PeterDonis]

What we did for GW detector was more like if we just got a voltmeter and watched for the changes in voltage in order to detect EM waves - and the better the voltmeter quality, the less current would it need and so the less would it affect the wave. I doubt anyone would describe such a measurement as absorbing EM wave energy...

But the voltmeter would still be absorbing some energy from the EM wave--just a very tiny amount compared to the total energy in the wave. Exactly as I described the amount of energy absorbed by LIGO as compared to the total energy in the GW. It's impossible to make a voltmeter that absorbs zero energy from an EM wave and still detects it; there must be some energy transfer if there is an interaction at all. Similar remarks apply to a GW detector.

 

[georgir]

But the voltmeter would still be absorbing some energy from the EM wave--just a very tiny amount compared to the total energy in the wave. Exactly as I described the amount of energy absorbed by LIGO as compared to the total energy in the GW. It's impossible to make a voltmeter that absorbs zero energy from an EM wave and still detects it; there must be some energy transfer if there is an interaction at all. Similar remarks apply to a GW detector.

Ok, I see your point that some energy transfer is unavoidable in any interaction.
So it could gain energy from the wave, yes. But it could also lose energy and add to the wave, if it's current were accidentally timed just right. I'd guess it could also balance out at zero over time, especially if the gain/loss probability is a cointoss. The point is that transfer of energy is not the core mechanism behind the measurement. The detector does not rely on gaining energy from the wave, and is actually designed to minimize that transfer, unlike an antenna that was designed to resonate at the exact frequency and absorb as much energy from the wave as possible.
Anyway, I'll drop this part of the discussion.

Now, how about the GW emitted by a system of masses along a very small portion of their orbits? Is that still spherically symmetric? Or does the spherically symmetric part come from averaging emissions along entire orbits?
[I'm trying to remember where I came up with this impression that GW are always emitted as spherical waves, but can't so far. I guess that's just me misinterpreting something and causing me all this headache for nothing.]
[And actually, wouldn't it make more sense for the energy to be released in the orbital plane only?]

 

[PeterDonis]

it could gain energy from the wave, yes. But it could also lose energy and add to the wave, if it's current were accidentally timed just right. I'd guess it could also balance out at zero over time, especially if the gain/loss probability is a cointoss.

All of these are possible, but only the first corresponds to a detection of the wave. The second corresponds to emission of a wave by the object. The third corresponds to nothing happening on average.

The point is that transfer of energy is not the core mechanism behind the measurement.

I think you need to take a step back and think carefully about what you are saying. A "detection" of a wave is a particular kind of interaction between the wave and the detector, and any interaction transfers energy. So it's impossible to have a detector where transfer of energy is not "the core mechanism", because transfer of energy is "the core mechanism" of any interaction whatever. And, since we live in a quantum universe, it is impossible to make the energy transfer arbitrarily small; that is particularly important since you say you are interested in what's happening on the scale of fundamental particles, not large numbers of them.

how about the GW emitted by a system of masses along a very small portion of their orbits? Is that still spherically symmetric?

First of all, it doesn't really make sense to think of a GW being emitted by a system of masses along a very small portion of their orbits. Just as it doesn't really make sense to think of an EM wave being emitted by an oscillating dipole along a very small portion of its oscillation. Those concepts only make sense if at least one complete oscillation is included (actually even more than that, multiple oscillations are needed if you want to have a well-defined waveform). The "oscillation" in the GW case is a complete orbit of the system of masses.

So we really should think about the GW emitted by a system of masses during a small number of orbits. The simplest possible such system would be two masses mutually orbiting each other. As I've said, the lowest order GW is quadrupole--it's driven by the third time derivative of the quadrupole moment. So the GW emitted by the simplest possible system would be quadrupole in nature.