B Transmitting information using gravitational waves

[Agliomby]

<Moderator's note: thread spawned from this previous thread.>

I have a question only loosely associated with any of the above, but that I hope may interest the minds behind this discussion.
Does the apparent discovery and confirmation of gravity waves give us a source of information transmission that does not necessarily depend on light (of any wavelength)? Could we perhaps be on the cusp of a discovery even greater than the understanding of electromagnetism?

 

[Ibix]

I have a question only loosely associated with any of the above, but that I hope may interest the minds behind this discussion.
Does the apparent discovery and confirmation of gravity waves give us a source of information transmission that does not necessarily depend on light (of any wavelength)? Could we perhaps be on the cusp of a discovery even greater than the understanding of electromagnetism?

You mean gravitational waves. Gravity waves are a type of surface waves on water.

Generating gravitational waves is very difficult. As I recall, the gravitational radiation emitted by the Earth moving around the Sun is about the same power level as a lightbulb. We've no way to manipulate the quantity of mass and energy that we would need to throw around to generate measurable gravitational waves.

In principle you can use gravitational waves to communicate, in practice it's far, far beyond our ability to do so. And I can't immediately see a situation where it would be more practical to use gravitational waves than radio or light.

 

[Grinkle]

I can't immediately see a situation where it would be more practical to use gravitational waves than radio or light.

Would gravitational waves tend to retain SNR over distance more robustly than EM waves due to (I think) relatively fewer naturally occurring emitters to contaminate?

Creating a transmitter does seem a daunting task.

 

[PAllen]

Would gravitational waves tend to retain SNR over distance more robustly than EM waves due to (I think) relatively fewer naturally occurring emitters to contaminate?

Creating a transmitter does seem a daunting task.

Equally, or more, daunting is the receiver. A radio burst from a billion light years away that had the energy equivalent of 3 solar masses would be enormously easier to detect than the GW were.

 

[Simon Peach]

Can't quite see why we would bother when we have light that travels just as fast and are a lot easier to propagate and detect

 

[rootone]

Gravitational waves (suggested by Albert), are limited by the speed of light, as is light itself.
Not therefore very useful as an alternative mode of transmitting information.
However some think that we may eventually be able to detect G waves emitted pretty much instantly after the big bang.
That is not possible for light, but whether those waves could reveal anything that could be called information is guesswork at best.

 

[FactChecker]

The gravity wave that was so hard to detect by LIGO was caused by the merging of two objects 36 and 29 times more massive than the Sun which briefly (1/10 second) created more energy than all of the stars in all of the galaxies. That is not an efficient way to transmit information.

 

[PAllen]

The gravity wave that was so hard to detect by LIGO was caused by the merging of two objects 36 and 29 times more massive than the Sun which briefly (1/10 second) created more energy than all of the stars in all of the galaxies. That is not an efficient way to transmit information.

More power. As noted, previously, it created GW with the energy equivalent of 3 solar masses in that 1/10 second.

 

[FactChecker]

Equally, or more, daunting is the receiver. A radio burst from a billion light years away that had the energy equivalent of 3 solar masses would be enormously easier to detect than the GW were.

That brings up a question that puzzled me. Was this event detected in any other way? Why wasn't it really obvious in light and radio waves?

 

[PAllen]

That brings up a question that puzzled me. Was this event detected in any other way? Why wasn't it really obvious in light and radio waves?

Merging BH are not expected to produce any EM radiation if they are 'bare'. To the extent they have accretion disks, the interaction of these would produce EM (but not the merger of the BH per se). Attempts were made to detect a corresponding event, hindered by the very poor localization of the GW direction. One group claimed a possible match, other groups disputed this. Presumably, when a third detector is brought online, direction resolution will be much improved and possible coincident EM signal might be detected.

 

[Paul Colby]

Basically, $16\pi G/c^4=4.15\times 10^{-43}$ seems/is 43 powers of nope as far as human produced GWs is concerned. However, I do question one precept that seems to be common and I'm not convinced is true in general. It is the space components of $T_{\mu \nu}$ or the mechanical stress which radiates GWs. Technically mass need not move to be a gravitational radiation source term. Example of this would be a piezoelectric material electrically driven at a frequency well above or away from resonance. A stress field is generated with essentially no mass movement. This will radiate and by reciprocity will receive.

 

[PAllen]

Basically, $16\pi G/c^4=4.15\times 10^{-43}$ seems/is 43 powers of nope as far as human produced GWs is concerned. However, I do question one precept that seems to be common and I'm not convinced is true in general. It is the space components of $T_{\mu \nu}$ or the mechanical stress which radiates GWs. Technically mass need not move to be a gravitational radiation source term. Example of this would be a piezoelectric material electrically driven at a frequency well above or away from resonance. A stress field is generated with essentially no mass movement. This will radiate and by reciprocity will receive.

I'd be interested in studying a source for this. Everything I've read relates the radiated power to the third derivative of quadrupole moment, which means (for all practical purposes) mass must move.

 

[Paul Colby]

I'd be interested in studying a source for this. Everything I've read relates the radiated power to the third derivative of quadrupole moment, which means (for all practical purposes) mass must move.

It's a pretty deeply ingrained bias. I've likely read many of the same sources so I got nothing in print. The space and time components of $T_{\mu \nu}$ are related by the conservations laws so it is always possible to blame the time components. However, GW are transverse and only have space components. So in a weak field radiation integral the space components are the ones to radiate just like in EM. That said, the quadrupole formula[1] is correct for what it is applied to.

[1] Another thought. It's like saying the dipole radiation formula for atoms is the end all and be all in radio antenna design. That's just not the case.

 

[PeterDonis]

The space and time components of $T_{\mu \nu}$ are related by the conservations laws

This is equally true of the Einstein tensor, i.e., of spacetime curvature, which is what GWs are made of. In fact, the reason the stress-energy tensor obeys these laws is that the Einstein tensor does because of the Bianchi identities, which forces the SET to as well because of the Einstein Field Equation.

GW are transverse and only have space components

This is only true in a particular coordinate chart (more precisely a restricted set of possible charts, the transverse traceless gauge).

 

[PeterDonis]

Everything I've read relates the radiated power to the third derivative of quadrupole moment

In the case of a binary pulsar, for example, yes, it's the third time derivative of the quadrupole moment of the mass distribution, because that's all that's significant. But consider the case of a black hole merger: there is no mass present (the holes are both vacuum), so what drives the radiated power?

 

[Paul Colby]

This is only true in a particular coordinate chart (more precisely a restricted set of possible charts, the transverse traceless gauge).

This is the confusing bit. For piezoelectric materials the stress and strain are related through a constitutive relation. It appears to be possible for GW to generate a strain in a material with essentially no motion[1]. This will (in principle) generate an electrical signal. This electric signal can't be gauge dependent. If there some some way to write the material constitutive relations in terms of curvature of course my conceptual issue goes away but I don't see a clear way to do this.

[1] the material displacement is unchanging since the divergence of the stress field is zero in the bulk. Off resonance one may neglect the forces on the material boundary.

 

[PeterDonis]

It appears to be possible for GW to generate a strain in a material with essentially no motion

Essentially no average motion of the object as a whole. But individual atoms in the object are certainly moving: that is what "strain" means.

This electric signal can't be gauge dependent

Yes, but the components of the GW are not the same as the electrical signal. It's the same thing as transforming an EM field between frames: for example, a pure E field in one frame will be a combined E and B field in other frames, so the EM field components are frame dependent, but the voltage measured by a particular voltmeter is not frame dependent.

 

[Paul Colby]

Essentially no average motion of the object as a whole. But individual atoms in the object are certainly moving: that is what "strain" means.

My point is the GW need not impart vibrational energy to the crystal for it to generate signal no more than the suspended mirrors in LIGO gain vibrational energy from a passing GW.

 

[PeterDonis]

the GW need not impart vibrational energy to the crystal for it to generate signal

They do if the vibrational energy is what generates the signal, which seems to be what you are describing (the strain within the crystal is what generates the signal). Detection of anything involves transfer of some amount of energy.

no more than the suspended mirrors in LIGO gain vibrational energy from a passing GW

Not vibrational energy internal to the mirrors, but the mirrors do gain energy from the GW, because the GW makes them move when they weren't moving before (and their motion is what generates the signal).

 

[Paul Colby]

Not vibrational energy internal to the mirrors, but the mirrors do gain energy from the GW, because the GW makes them move when they weren't moving before (and their motion is what generates the signal).

My view is that the changing distance between the mirrors does work on the laser beam bouncing between them. Radiation pressure does work on the beam (shifting the frequency of the light) and, by Newton, also does work on the suspended mirrors. No light, no work, no energy transfer.

 

[PeterDonis]

My view is that the changing distance between the mirrors does work on the laser beam bouncing between them

And your view is based on what? Do you have a reference?

 

[Paul Colby]

They do if the vibrational energy is what generates the signal, which seems to be what you are describing. Detection of anything involves transfer of some amount of energy.

Well, then my description isn't working as intended. In piezoelectric materials work done by gravitational strain can be done directly on the EM field. Some of this work will always be transferred to crystal vibration but there are limits were this doesn't appear to be the dominate process.

 

[Paul Colby]

And your view is based on what? Do you have a reference?

No, does that mean I'm automatically wrong?

 

[PeterDonis]

No, does that mean I'm automatically wrong?

No, but it means I can't really discuss your claim, because I don't know what it's based on. I suggest doing some research to see how the case in question is actually modeled.

 

[PeterDonis]

In piezoelectric materials work done by gravitational strain can be done directly on the EM field.

Reference, please? My understanding of piezoelectricity is that it is a direct relationship between mechanical stress/strain and electric field. So in order to create an electrical signal in such a material, you have to first create a mechanical strain, which means moving some atoms.

 

[Paul Colby]

I suggest doing some research to see how the case in question is actually modeled.

Always sound advice. <general vague comment> With most things there are multiple views one may take. Often the one "true" description can be translated into equivalent forms sometimes informative forms</general vague comment> Is it worth trying to do this in this case?

 

[PeterDonis]

the one "true" description

There might not be one, at least in the sense you are using the term. For example, in a GW detector like LIGO, the only "true" description (in the sense of being the same no matter what other choices we make in description) is the overall output signal. If we ask whether that signal is due to the mirrors moving, or due to the speed of light changing between the mirrors while the mirrors stay fixed, there isn't really a "true" answer; it depends on how you choose your coordinates. AFAIK the usual coordinate choice for the LIGO scientists is one in which the speed of light is constant and the mirrors move.

 

[Dale]

Is it worth trying to do this in this case?

Only if you wish to discuss it here. If you don't wish to discuss it here then there is no reason to go through the effort, but if you make a claim here then you need to be able to show that it is consistent with the literature.

 

[Paul Colby]

Reference, please?

I have no really good reference and I've searched. "Piezoelectric Crystals and Their Application to Ultrasonics" by Mason is a quaint book but not very accessible IMO. The basic form of the constitutive relations appear in many places. They are,

$T_{i j} = C_{i j k l} S_{k l} - d_{i j k} E_k$
$D_i = d_{ijk} S_{j k} + \epsilon_{i j} E_j$​

where, $T_{i j}$ is the mechanical stress, $S_{k l}$ the strain, $D_i$ the electric displacement, and $E_i$, the electric field. To these one must add the equations of motion which are,

$\rho \ddot{u_i} = T_{i j, j}$
$D_{i,i} = 0$
​

Clearly one must solve the dynamical problem (which I've done for a toy configuration. However, $S_{i j}=0$ with $E_J \ne 0$ will generate stress.

 

[rootone]

The gravity wave that was so hard to detect by LIGO was caused by the merging of two objects 36 and 29 times more massive than the Sun

Isn't that right at the extreme end of the scale for stellar mass BH?
If so then such objects should be very rare, and collisions even more rare.

 

[PeterDonis]

the equations of motion which are,
$$
\rho \ddot{u}_i = T_{ij,j}
$$

What is $u$?

$S_{i j}=0$ with $E_J \ne 0$ will generate stress.

But stress is an input, not an output. The question is whether an applied stress can result in a pure electric field with zero strain. I think you need to solve the equations of motion to know whether that is possible.

 

[PeterDonis]

Isn't that right at the extreme end of the scale for stellar mass BH?

What scale are you referring to?

 

[rootone]

What scale are you referring to?

A scale including all black holes that would have originated as the result of a very large stars collapsing, (or merging)
I guess that means all except the supermassive ones in galaxy cores.
I thought the typical estimated mass for those is usually in the region of 10x solar mass, and 20x or more would be very unusual.

 

[PeterDonis]

I thought the typical estimated mass for those is usually in the region of 10x solar mass, and 20x or more would be very unusual.

I've seen different estimates from different sources; I don't know that we have a very good understanding of what the expected range actually is.

 

[FactChecker]

Basically, $16\pi G/c^4=4.15\times 10^{-43}$ seems/is 43 powers of nope

Ha! -- "43 powers of nope". I like that.

 

[Paul Colby]

What is $u$?

$\ddot{u}$ is the $a$ in $F=ma$ for linear elastic materials. $S_{i j} = \frac{1}{2}(u_{i,j}+u_{j,i})$ in this case. The $T_{i j,j}$ is the divergence of the stress tensor. Note that $T_{i j,j}=0$ implies that $\ddot{u}=0$. This is at least in part the origin of all the wrong sounding off resonance comments I'm making.

 

[Paul Colby]

But stress is an input, not an output. The question is whether an applied stress can result in a pure electric field with zero strain. I think you need to solve the equations of motion to know whether that is possible.

I have solved the dynamical problem. If there is interest I can post it here. In the time harmonic case the strain, $S_{i j}$, and the stress, $T_{i j}$ and the circuit current, $I$ (yet to appear) are all proportional. The proportionality constants are all frequency dependent. So technically yes, there will not be zero strain for a given stress however, depending on the drive circuit and impedance match one may generate considerable stress with little resulting strain.

 

[Paul Colby]

AFAIK the usual coordinate choice for the LIGO scientists is one in which the speed of light is constant and the mirrors move.

My description is relative to this choice of coordinates. They are consistent with how LIDARs are modeled.

 

[PAllen]

In the case of a binary pulsar, for example, yes, it's the third time derivative of the quadrupole moment of the mass distribution, because that's all that's significant. But consider the case of a black hole merger: there is no mass present (the holes are both vacuum), so what drives the radiated power?

In my view there is mass, but not matter. A BH has adm mass, bondi mass, and mass according to the various formulations of quasi local mass. Especially the quasilocal formulations allow definition of quadrupole moment for the system.

 

[PeterDonis]

$\ddot{u}$ is the $a$ in $F=ma$ for linear elastic materials.

Ah, got it.

Note that $T_{i j,j}=0$ implies that $\ddot{u}=0$.

But $i$ and $j$ here range only over the spatial indices, not the time index. So even though conservation laws require that $T_{\mu \nu, \nu} = 0$ (in the limiting case where spacetime is flat, at least to a good enough approximation), where we are including all four indices (space and time), that does not mean that we must have $T_{ij, j} = 0$.

 

[PeterDonis]

In my view there is mass, but not matter. A BH has adm mass, bondi mass, and mass according to most variants of quasi local mass. Especially the quasilocal formulations allow definition of quadrupole moment for the system.

Ah, ok.

 

[PeterDonis]

My description is relative to this choice of coordinates.

But in these coordinates, the GW does work on the mirrors. The laser beams have no work done on them; their frequency does not change. All that changes is the distance they cover in each arm.

They are consistent with how LIDARs are modeled.

Do you have a reference? I'm not familiar with how LIDARs are modeled, so I am curious.

 

[Paul Colby]

Do you have a reference? I'm not familiar with how LIDARs are modeled, so I am curious.

Arguably any elementary book on interferometers should cover this material.

https://www.arm.gov/publications/tech_reports/handbooks/dl_handbook.pdf

 

[Paul Colby]

But in these coordinates, the GW does work on the mirrors. The laser beams have no work done on them; their frequency does not change. All that changes is the distance they cover in each arm.

Interesting. The phase difference between the arms changes as a function of time. How do you modulate the phase in time without changing the frequency of the light ever so slightly. Do you have a reference?

 

[Paul Colby]

that does not mean that we must have $T_{ij,j}=0$.

Don't recall saying that. However, when discussing illumination by GW isn't this the case when the wavelength is much larger than the crystal? The gravitational stress is nearly constant over the volume. When discussing transmission the stress and strain vary as sine and cosine through the crystal thickness. The stress term also has a component which is essentially constant arising from the applied field. The strain lacks this term.

 

[PeterDonis]

How do you modulate the phase in time without changing the frequency of the light ever so slightly

By changing the distance between the mirrors.

Do you have a reference?

A typical description is on the LIGO site at Caltech, here:

https://www.ligo.caltech.edu/page/what-is-interferometer

See the "How does it work?" section.

I thought I had links to more technical references that describe the math underlying the description given there, but I can't seem to find them at the moment. I know MTW discusses GW detection by interferometers and gives a simple model of this type. I can't remember whether Wald does.

 

[Paul Colby]

By changing the distance between the mirrors.

Wow, that seems to violate basic mathematical facts? In phase modulated radio transmissions the carrier develops side bands. One need only Fourier transform $cos(\omega t +\phi(t))$ to see this. No sidebands no information transmission. In optics it's very much the same situation or at least that's what I was lead to believe. Well, all snark aside it should be possible for me to dig this out of your reference, thanks. [edit] I think a more complete description would include what I'm discussing. I expect LIGO looks for modulation in the phase difference and that this is an important detail.

 

[Paul Colby]

I know MTW discusses GW detection by interferometers

I have a dent in my chest from where I rest this book when I read it in bed.

 

[PeterDonis]

that seems to violate basic mathematical facts?

I don't see how. The GW moves the mirrors. Moving the mirrors changes the round-trip travel time of the light beams, and does so differently in the two arms (stretch in one arm, squeeze in the other). Changing the relative round-trip travel time changes the relative phase of the beams when they come back together.

I expect LIGO looks for modulation in the phase difference

I think that's what I described just above, yes. [Edit: but see a caveat in my next post.]

 

[PeterDonis]

phase modulated radio transmissions

I don't think this is a good analogy, because the phase modulation in this case is at the source, whereas in the case of LIGO it's at the detector (and "phase modulation" might not even be a good term in the LIGO case if it connotes modulation at the source). Nothing at all is done to the laser beams themselves; their source emits them in an unchanging state.