Gravitational wave's velocity

[calinvass]

In flat Minkowski spacetime, everything that travels at c, relative to some observer, it travels the same speed relative to any observer. If we refer to gravitons as bosons through this flat spacetime, it is clear they can be defined as traveling at c. And you can even some classical non-quantised wave as gravitational wave through spacetime to describe gravity in a classical framework. This way you remain in the context of SR. However, in GR spacetime is distorted and only local speed of light applies. I understand, light can even appears to travel at infinitesimal velocity relative to an observer outside a Black Hole, for example, even though locally it is still at the same c.
It is thought and confirmed that gravitational waves travel at c. It is not clear to me how can you apply a principle from SR for propagating waves of spacetime itself. Let me give you another example. Imagine some gravitational wave traveling towards the event horizon from inside a Black Hole. It seems confusing to me. Does the same local speed apply?

 

[PeterDonis]

you can even some classical non-quantised wave as gravitational wave through spacetime to describe gravity in a classical framework. This way you remain in the context of SR.

No, you don't. Gravitational waves are waves of spacetime curvature. You can't treat them "in the context of SR", because in SR spacetime is flat.

It is thought and confirmed that gravitational waves travel at c.

No, what is "thought and confirmed" is that gravitational waves travel on null worldlines, just like EM waves do. That works fine in curved spacetime.

It is not clear to me how can you apply a principle from SR

That's not what's being done. See above.

Imagine some gravitational wave traveling towards the event horizon from inside a Black Hole

You can't; gravitational waves inside a black hole must travel towards the singularity, just like everything else.

 

[calinvass]

Thank you.
I mean in SR (and we imagine we don't know anything about GR) you can treat gravity as a regular force, generated by a field around massive objects and have waves in that field similarly to the electromagnetic field. But it's only an example that if gravity was like that it would have been easier to explain. But the best explanation for gravity is as spacetime curvature.

I understand waves can travel on null worldlines. But I can't picture spacetime distortions traveling also on worldlines.

In my example I can replace the BH with some very massive object and waves as generated by some smaller colliding objects (or some accelerating craft) near its surface. Some distant observer would see light escaping the gravity of the massive object, slower than it normally would, if I'm not wrong. In that case the gravitational waves would do the same.

 

[PeterDonis]

in SR (and we imagine we don't know anything about GR) you can treat gravity as a regular force

No, you can't. Such a theory predicts aberration for gravity similar to the observed aberration for light; but we don't observe that.

generated by a field around massive objects and have waves in that field similarly to the electromagnetic field

Now you appear to be referring to a different model, which is treating gravity as a spin-2 field on flat spacetime. (This is not the same as "treating gravity as a regular force" unless by "force" you really mean "a quantum field interaction".) This theory turns out to be equivalent to GR--i.e., the effects of this spin-2 field are equivalent to spacetime curvature. In other words, the flat "background" spacetime of this theory is unobservable.

I understand waves can travel on null worldlines. But I can't picture spacetime distortions traveling also on worldlines.

Actually, "worldlines" is a misstatement in both cases. A more accurate statement would be that the wave vector and the surfaces of constant phase are null in both cases. In the case of gravitational waves, the waves are waves of changes in the metric coefficients, so the metric is the "field" analogous to the EM field in the case of EM waves.

Some distant observer would see light escaping the gravity of the massive object, slower than it normally would

If "normally" means "in flat spacetime", then yes, this is a reasonable description of what the distant observer would see, and it's fine as long as it's only treated as a description of what the distant observer would see.

In that case the gravitational waves would do the same.

Yes.

 

[Dale]

I mean in SR (and we imagine we don't know anything about GR) you can treat gravity as a regular force, generated by a field around massive objects

No, you cannot. That is the whole reason for developing GR in the first place. No treatment as you describe winds up being self consistent.

One thing that might help you is to think of linearized GR. You have a metric that is close to flat spacetime, with some small perturbations. Then you can talk about the propagating perturbations on top of the flat background.

 

[calinvass]

Thank you.
But my example is not important anyway. I was only an example of some concept that is easier to explain which of course it doesn't apply to our reality. But the concept of a graviton can be taken into consideration. Even gravitons through a flat spacetime are simpler to understand than gravitational waves in curved spacetime because they are not part of spacetime.

Yes, with linearised GR in the end, I see the same problem because the perturbation is still of spacetime, not other fields.
I think I need to follow a complete course of GR until thinking about this.

 

[PeterDonis]

gravitons through a flat spacetime are simpler to understand than gravitational waves in curved spacetime because they are not part of spacetime.

Huh? Gravitons are the quantum aspect of gravitational waves. If gravitational waves are made of spacetime curvature, so are gravitons.

 

[calinvass]

Thank you. I thought quantum graviton models gravity so that it gives the same effect for macroscopic objects but not manipulating spacetime curvature but by considering gravitons force carriers similar to photons as force carriers of the electromagnetic field.
Quantisation of spacetime curvature seems to me way more complex.

 

[PeterDonis]

I thought quantum graviton models gravity so that it gives the same effect for macroscopic objects but not manipulating spacetime curvature but by considering gravitons force carriers similar to photons as force carriers of the electromagnetic field.

"Quantum graviton" is the spin-2 field model I described in post #4. In other words, it's equivalent to the spacetime curvature model.

Quantisation of spacetime curvature seems to me way more complex.

It is. That's why it's so hard to come up with a theory of quantum gravity.

 

[calinvass]

I've seen some analogies trying to explain gravity to general public using as a model water flowing towards a sink hole in the place of some massive object. I've also seen scientist talking about simulations using air instead of water for a 3d effect, and sound waves.
Sometimes close to gravitons, I think can be the the particles or molecules that the fluids are made of, acting as quanta.

 

[Ibix]

If I understand right (and I may not) gravitons are more closely analogous to phonons than atoms in that analogy.

 

[PeterDonis]

Sometimes close to gravitons, I think can be the the particles or molecules that the fluids are made of, acting as quanta.

No, they can't. The models you're referring to only work for static or stationary spacetimes, like Schwarzschild spacetime; but no gravitational waves are present in such spacetimes.

If I understand right (and I may not) gravitons are more closely analogous to phonons than atoms in that analogy.

Not even to phonons; the analogy doesn't work at all. See above.

 

[Ibix]

Peter, can you recommend a good intro to quantum gravity? I suspect I've got a lot of work to do to get to understanding it, but I'd like to do so.

 

[PeterDonis]

can you recommend a good intro to quantum gravity?

It depends on what kind.

For quantum field theory in curved spacetime, which is really semi-classical (or as John Baez once defined that term, "half-assed") quantum gravity, Wald has an excellent monograph, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (which unfortunately I have not been able to find online, I have a print copy that I came across years ago and snapped up). That book is an "intro" only in the sense that you are not assumed to know about quantum field theory in curved spacetime when you start reading it--but you certainly need to have a good thorough knowledge of quantum field theory, and curved spacetime, as separate topics before you start.

For the various candidates for a full theory of quantum gravity--string theory, loop quantum gravity, and whatever else is out there--I don't know of a good introductory reference that discusses them all. String theory has tons of "review" papers at this point--it's a good thing most of them are on arxiv because if they were printed out, they would probably outweigh a copy of Misner, Thorne, and Wheeler (of which it is said that anyone copy is at risk of undergoing gravitational collapse and becoming a black hole itself). Carlo Rovelli has a good review paper about loop quantum gravity that is on arxiv somewhere, but I don't have a link handy at the moment.