I How Many Gravitons Were Detected in Recent Gravity Wave Observations?

[snorkack]

Carrying linear momentum is not the same as delivering it either. An object cannot deliver linear momentum to a detector without delivering power as well.

The rate of change of energy transfer from the light to the mirror.

Cannot quite parse that phrase.
So, consider the case of antenna where perfect reflection occurs. At a suitable frame of reference, the reflected wave has precisely the same frequency and amplitude as the incident wave, just different direction of propagation.Therefore the outgoing energy is precisely equal to incoming energy, and the wave does no work. However, the change of momentum is nonzero and is transferred on the antenna.

Is the change in the momentum of antenna, at constant energy, in principle possible to observe and amplify to a detection event, or is it provably impossible to observe and amplify to a detection because there is zero detected power to amplify?

 

[Paul Colby]

Is the change in the momentum of antenna, at constant energy, in principle possible to observe and amplify to a detection event, or is it provably impossible to observe and amplify to a detection because there is zero detected power to amplify?

These kind of questions can't be answered because too much is missing. What is being detected and exactly how is this detection taking place. For LIGO detection is made using CCDs looking at interference fringe shifts. These shifts are due to work done on the laser beam. You must supply these kinds of details in order for it to even be a question.

 

[PeterDonis]

consider the case of antenna where perfect reflection occurs. At a suitable frame of reference, the reflected wave has precisely the same frequency and amplitude as the incident wave, just different direction of propagation.Therefore the outgoing energy is precisely equal to incoming energy, and the wave does no work. However, the change of momentum is nonzero and is transferred on the antenna.

Again, please show your work. With math.

 

[poor mystic]

So gravitational waves are waves of electromagnetic energy which come from some direction, weakly interact with matter, and move on.
You'd think that a massive sphere (say a planet) would focus gravitational waves much as a glass sphere focuses visible light, so that at some distance a concentration of energies might be found.
?

 

[Ibix]

So gravitational waves are waves of electromagnetic energy

No. They are gravitational waves, not electromagnetic waves. We use their effect on laser interferometers to detect them.

You'd think that a massive sphere (say a planet) would focus gravitational waves much as a glass sphere focuses visible light, so that at some distance a concentration of energies might be found.

I believe that we do expect gravitational lensing of gravitational waves, similar to gravitational lensing of electromagnetic waves, if that's what you are referring to. However, our experimental work is in its infancy and we have no direct experimental confirmation.

 

[Paul Colby]

You'd think that a massive sphere (say a planet) would focus gravitational waves much as a glass sphere focuses visible light, so that at some distance a concentration of energies might be found.

With light/radio waves the refractive index of the material is the ratio of the propagation speed in vacuum to the propagation speed in the material. The higher the index the more refraction that takes place. For a GW the mechanical stiffness, or shear modulus of the material determines the index of GW in the material. If one works it out (one being me so be warned) one gets,

$n(\omega) = \sqrt{1+\left(\frac{\omega_o}{\omega}\right)^2}$

where the characteristic angular frequency is,

$\omega_o = \frac{4}{c}\sqrt{\pi G \Gamma}$

where $G$ is Newton's gravitational constant and $\Gamma$ is the shear modulus of the material (which is assumed isotropic). Assume a solid steel planet $\Gamma\approx 70 GPa$. so $\omega_o \approx 1.0\times 10^{-8} Hz$. For the frequency range of interest, $n(\omega)\approx 1$ to more zeros than is useful IMO.

 

[TeethWhitener]

You'd think that a massive sphere (say a planet) would focus gravitational waves much as a glass sphere focuses visible light, so that at some distance a concentration of energies might be found.

Possibly of interest to you:
http://iopscience.iop.org/article/10.1086/312015/fulltext/985903.text.html

 

[snorkack]

With light/radio waves the refractive index of the material is the ratio of the propagation speed in vacuum to the propagation speed in the material. The higher the index the more refraction that takes place. For a GW the mechanical stiffness, or shear modulus of the material determines the index of GW in the material. If one works it out (one being me so be warned) one gets,

$n(\omega) = \sqrt{1+\left(\frac{\omega_o}{\omega}\right)^2}$

where the characteristic angular frequency is,

$\omega_o = \frac{4}{c}\sqrt{\pi G \Gamma}$

where $G$ is Newton's gravitational constant and $\Gamma$ is the shear modulus of the material (which is assumed isotropic). Assume a solid steel planet $\Gamma\approx 70 GPa$. so $\omega_o \approx 1.0\times 10^{-8} Hz$. For the frequency range of interest, $n(\omega)\approx 1$ to more zeros than is useful IMO.

Shear modulus, not compression modulus?
Then superfluids regardless of stiffness cannot refract gravitational waves.
The superfluid interior of a neutron star would only participate in gravitational, frequency-independent bending of the waves, while the frequency-dependent refraction can only happen in the solid crust of the neutron star?

 

[Paul Colby]

Then superfluids regardless of stiffness cannot refract gravitational waves.

That would be my understanding. Fluids only interact with GW through surface traction forces. I believe this is also true for isotropic solids even though they support shear waves. For a proper acceleration of a bit of matter to occur, a net interatomic force must be developed on the bit. If one looks at the stress developed by a passing GW on a solid, points interior to the solid have no net force due to the GW since the divergence of the stress is zero. All effects must propagate inward from the solids boundary where the stress developed has a divergence.

Of course, the background curvature of the star will effect the propagation just as it does with light as far as I know.

[Edit]

Okay, some clarification. The origin of the refractive index calculation uses the constitutive relation for garden variety solids like steel where the stress tensor is related linearly to the strain tensor. Since shear staining a neutron star leads to no stress, it will not refract a GW IMO.