Gravitational waves (split from The speed of propagation of gravity)

[Dagl1]

This may require a split, but I have two questions that came up when reading this thread:

Are gravitational waves affected by gravitational lensing, I found some random (not very sciency) websites talking about how gravitational waves will affect light (by changing the amounts of gravitational lensing). However I was wondering, will these waves also change 'apparent' direction (light goes in a straight path but it is space-time that is curved, which we see as 'apparent' curved paths, right?)?

@Markus Hanke Could you attempt to explain how  wave-tails emerge from non-linear interactions (at 1.5 post newtonian?). I looked up some articles about it, but realise this is currently quite far outside what I can easily understand. https://arxiv.org/abs/1607.07601 

Thanks in advance!
Dagl

[swansont]

35 minutes ago, Dagl1 said:

This may require a split, but I have two questions that came up when reading this thread:

!

Moderator Note

For everyone's awareness: In general, questions not directed at the OP should be in a new thread, especially when the thread is in speculations.

 

[Dagl1]

Thanks Swanson, 

Just to be sure, in general I should, open a new thread myself if I feel like it will require it to be split?

Sorry for being lazy hahaha;p 

[swansont]

1 hour ago, Dagl1 said:

Thanks Swanson, 

Just to be sure, in general I should, open a new thread myself if I feel like it will require it to be split?

Sorry for being lazy hahaha;p 

Yes, that's what people should do. When you have questions not directed at the OP, unless it's simple clarification of someone's answer, it's likely that it needs a new thread.

 

[Markus Hanke]

19 hours ago, Dagl1 said:

Are gravitational waves affected by gravitational lensing

Gravitational waves are affected by the background curvature of spacetime, and you can get many of the same effects that light would be subjected to, such as deflection, frequency shift etc. However, the actual dynamics of gravitational waves are potentially much more complicated than those of light, because gravity is non-linear, unlike electromagnetism; this means that such waves also interact with each other and with themselves.
Can you construct an arrangement that acts like a lens for gravitational waves? Yes, you certainly could, but depending on what exactly it is you are trying to achieve, this may be a very complex problem (both mathematically and practically).

19 hours ago, Dagl1 said:

Could you attempt to explain how  wave-tails emerge from non-linear interactions (at 1.5 post newtonian?).

This is a very complex topic, and truthfully speaking I have not done (or even seen) the exact maths of how this comes about. The general idea is that you start with a wave pulse (i.e. a more or less sharply defined packet of wave fronts) and send this through a region of spacetime that has substantial background curvature due to the presence of some gravitational source, e.g. a black hole. What happens then is that the wave pulse, as it travels through this region, backscatters off the background curvature, which leads to its shape and polarisation to change in some very specific manner. The deformation is such that a “tail” is produced behind the travelling pulse, and that wave tail propagates at less than the speed of light. 

My understanding (someone more expert at this particular detail please correct me if I am wrong) is that the wave tail travels at below c due to its own gravitational self-interaction - which is a non-linear process.

 

[Dagl1]

Thanks! That sounds really cool (and currently way too complex to really understand. There is something specific I can work towards to understand).

If anyone else comes along and wants to add some information, I find it quite interesting that gravity waves could travel at a speed lower than c (even if the wave interacts with itself, shouldn't whatever (particle??, graviton?) the wave is, travel at c at all times since is mass-less(?). Even light in a medium only has 'apparent' reduced speeds due to interaction/absorption with atoms right? 

Thanks again for the interesting answer!

-Dagl
 

[MigL]

Well it may help to consider that photons interact with the electrons in the medium they are traversing, and that leads to an 'effective' speed reduction. But actually, between each interaction, they still travel at c .

Gravity is self-interacting, so one could assume massless gravitons travel at c also, except when they interact with themselves to reduce their effective speed. These would be the 'tails' Markus refers to

[Mordred]

21 hours ago, Dagl1 said:

Thanks! That sounds really cool (and currently way too complex to really understand. There is something specific I can work towards to understand).

If anyone else comes along and wants to add some information, I find it quite interesting that gravity waves could travel at a speed lower than c (even if the wave interacts with itself, shouldn't whatever (particle??, graviton?) the wave is, travel at c at all times since is mass-less(?). Even light in a medium only has 'apparent' reduced speeds due to interaction/absorption with atoms right? 

Thanks again for the interesting answer!

-Dagl
 

Well truth of the matter is it would be extremely difficult to simplify how tails result from nonlinear aspects of curved spacetime. I've studied a few examples in the past but the mathematics are not trivial. Even if I were to post those mathematics without bring familiar with the quadrupole moments of linearized equations a reader wouldn't understand the nonlinear equations.

 A good way to understand tails is to think of backscatterring with curved spacetime. The backscatterring causes delays to reach the detector. It's a simplification to describe monopole - monopole - quadrupole interaction moments which isn't the same as interaction with a medium. 

The interaction is with spacetime itself but only the non linearity conditions such as curved spacetime. Which is different than photons interacting with a medium (though fields can give medium like relations )

it's best to never think of spacetime as a medium. 

Probably the most accurate analogy I can think of is to use the example of signal propogation delay in electrical signals. If you take a signal wire and lay it parallel to a power line the delay is negligible from the cross talk between the signal wire and power wire. However if you were to lay the signal wire perpendicular to the power wire you can induce a propogator delay due to the EM field crosstalk between the two wire field lines.

The tails is very similar to this analogy it is the non linear cross interactions of the GW waves with the local nonlinear spacetime curvature that causes the signal propogation delay of the GW wave. This analogy doesn't require any association with a medium as your simply involving field interactions which is the cases when dealing with spacetime. (It also provides the right direction to apply the relevant mathematics). Those mathematics will involve polarity states Ie a quadrupole has 4 polarity states while the EM field is Dipolar with two polarity states. These states are needed to model tails. (Hence part of the complexity)

 

Now onto the massless graviton. If the the graviton has mass then gravity would not have infinite range. Much like the photon as the propogator for the EM field. The effective range of a force is a function of the mass term of the mediator boson. For example the mass term of the W and Z bosons limit the range of the weak force. In order for a force to have infinite range it's mediator boson must be massless.

[latex] ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/latex]

[latex]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex]

Now the above is an example of linearized spacetime. We haven't got any curvature terms so you wouldn't get tails from the above. The above is also how GW waves are derived. Those two above equations are where the polarizations [math]h_+[/math] and [math]h_x[/math] are derived from.

However let's look at a rotating Neutron star (we will get nonlinear terms from the Sagnac effect.)

Spacetime in a rotating frame would look like this.

[latex]g_{\mu\nu}=\begin{pmatrix}1-\frac{w^2r^2}{c^2}&0&\frac{wr^2}{c^2}&0\\0&1&0&0\\\frac{w^2r^2}{c^2}&0&r^2&0\\0&0&0&1\end{pmatrix}[/latex]

So in this spacetime the relation between worldtime and proper time (tau for proper)

[math]d\tau=\sqrt{1-\frac{w^2r^2}{c^2}dt}[/math] in essence time goes slower in a rotating frame.

This situation can lead to tails. Hope that helps

 

 

 

Edited January 23, 2020 by Mordred

[Dagl1]

5 hours ago, MigL said:

Well it may help to consider that photons interact with the electrons in the medium they are traversing, and that leads to an 'effective' speed reduction. But actually, between each interaction, they still travel at c .

Gravity is self-interacting, so one could assume massless gravitons travel at c also, except when they interact with themselves to reduce their effective speed. These would be the 'tails' Markus refers to

Thanks! The big one of that is the self-interacting part, I had trouble imagining it (and now that I see the answer, once again, I should go and study the maths for a real answer).
 

@Mordred Thank you very much for this gem of information! Like always, I understand about half. But I also don't understand the mechanism by which two cables interfere with each other (I never stood still by that, but always assumed it was because both wires induce a magnetic field and that (for whatever reason) 'annoys' the signal that is travelling through both). 

From your explanation I think I do get that I can't think of the self interaction as turbulence. The wave itself changes the curvature of spacetime and that is why it pulls on/interacts with itself? 

Thanks again everyone!
Dagl

[MigL]

Thanks for putting the 'meat on the bones' of our understanding, Mordred.