Gravitational Waves @ relativistic speed?

[tionis]

What would happen if I were to fly toward a gravitational wave pulse at relativistic speed? Would I be destroyed by the Doppler-shifted pulse? Would the wave become visible?

 

[rootone]

I don't think anyone has done that yet, so nobody knows.

 

[pervect]

What would happen if I were to fly toward a gravitational wave pulse at relativistic speed? Would I be destroyed by the Doppler-shifted pulse? Would the wave become visible?

The wave would be stronger. I don't see any reason why you'd see it. Being destructive is remotely possible, but would require a very energetic wave and/or an extremely high value of the relativistic velocity / gamma factor.

 

[tionis]

Thx, rootone and pervect. I have so many disjointed thoughts about GWs, that I don't even know where to begin, but I will try.

First, are GWs a distinct form of spacetime, meaning it's a form of spacetime that moves at relativistic speed (curving the geometry of it), whereas normal space (flat) is just sitting there? If so, then, for example, would relativistic bodies such as the protons in the LHC detect in their frame of reference a stronger opposing energy or curvature when encountering a GW that would make them deviate from their trajectory, or perhaps even boost them depending of where the GW pulse came from?

Second, would there be any visible effects that would betray the presence of an approaching GW pulse such as the lensing of background stars or galaxies while approaching the GW pulse at close to c?

 

[tionis]

or perhaps even boost them depending of where the GW pulse came from?

What I'm asking here is that since the LHC proton beam is already going at close to c, wouldn't a GW pulse boost the proton past c? Since it's space that is moving at c, there wouldn't be any violation if the proton were to ride the wave, no?

 

[A.T.]

Second, would there be any visible effects that would betray the presence of an approaching GW pulse such as the lensing of background stars or galaxies while approaching the GW pulse at close to c?

The GW approaches you at c, just like the light from the distant Galaxies. So before the GW reaches you, you also won't see any light that met it.

 

[tionis]

The GW approaches you at c, just like the light from the distant Galaxies. So before the GW reaches you, you also won't see any light that met it.

I'm sorry, I've forgotten that I couldn't see any stars or light because it would have been Doppler-shifted to the invisible part of the spectrum as I approached c. But since GWs are spacetime in motion, it should generate some sort of radiation i.e, Hawking/Unruh, no?

 

[A.T.]

I've forgotten that I couldn't see any stars or light because it would have been Doppler-shifted to the invisible part of the spectrum as I approached c.

You can user other detectors than your eyes. And stars emit frequencies below the visible range, which would be shifted into that range.

 

[tionis]

You can user other detectors than your eyes. And stars emit frequencies below the visible range, which would be shifted into that range.

Very true. I should simplify my scenario:

Suppose space was devoid of any luminous object and it was just me in a spaceship traveling at close to c. Ahead of me, a pulse of gravitational waves goes off and now I'm in a collision course with a GW on steroids (because of the Doppler boost). What effects would I experience? Would my spaceship be tear apart by the tremendous energy of the GW? Or maybe even start moving backwards as it is carried by the GW?

I mean there are bodies in space moving at and close to the speed of light. Surely these bodies encounter GWs all the time. And because they are moving at tremendous speeds, the GWs in their frame of reference have more energy, so there must be an energy contribution. How do, for example, protons going at close to c deal with a boosted GW?

 

[tionis]

I have another question: what is the technical name of the spacetime GWs occur in? Do they occur in curved spacetime and continue to exist in curved spacetime, or as soon as they leave the source they become something else like flat spacetime?

IOW, would it be correct to say that the recently detected GWs occurred in Kerr spacetime (curved) and were detected in Minkoswki (flat) space?

 

[Nugatory]

IOW, would it be correct to say that the recently detected GWs occurred in Kerr spacetime (curved) and were detected in Minkoswki (flat) space?

No. There's only one spacetime in the universe; in some regions it is highly curved and in other regions it is less highly curved. Solutions like the Kerr and Minkowski spacetimes may be more or less good approximations to the local curvature in a particular region, but neither comes even remotely close to describing the curvature in the local neighborhood of two colliding black holes.

 

[tionis]

OK, Nugatory: what do we call the spacetime region where gravitational waves exist? Do we just call it ''spacetime?''
But as these waves travel, they depart from a flat spacetime, right? IOW, they carry an intrinsic curvature with them. Why doesn't this particular propagating spacetime metric have an assigned name to it?

 

[pervect]

I was thinking about this question more, fleshed it out a bit more, and realized that I didn't know for sure. First let me describe the detailed version of the revised question.

We have a gravitational wave, characterized by a dimensionless strain function h(t), with the peak of h(t) being $10^{-21}$ and "chirps" from 35 to 250 hz, based on what Ligo measured. What hapens when we do an ultrarelativistic boost?

Well, it's a transverse wave, so h(t) shouldn't change. It should still be $10^{-21}$ after the boost. But the chirp frequency should go up, the wavelength should go down. Suppose we assume that we boost the chrip frequency to, say 3.5 - 25 Thz, which if the pulse were electromagnetic, would put it into the visible range at the low end, and well into the ionizing range at the high end. This should put the wavelength of the gravitational wave at the atomic level, where I'd naievly expect the best coupling to atoms. What happens to, say, a target atom in the wave?

I don't know. The effective energy density goes up like $\dot{h}^2$, so we've increased that by $10^{22}$, the $\gamma^2$ dependence I'd expect. But we still have a very small value of h(t), it just happens faster. Do we have enough energy density to potentially do anything? I can't rule it out - I suppose I could do more calculations but I haven't. Would it couple to matter effectively enough to do anything? I don't see how, but I don't feel confident I understand all the potential mechanisms at this point.

Perhaps more to the point is the question - at what value of h(t) would we start to see observable and/or ionizing effects on an atom? Can we calculate this classically, or do we need a theory of quantum gravity?

 

[tionis]

Can we calculate this classically, or do we need a theory of quantum gravity?

Good question. I was hoping for a classical explanation. That is why I boosted the GWs in the thought experiment. Let me ask you another question: can I use the reference frame of the GW pulse to see how my spaceship would look, or is this forbidden--meaning just like the photon, GWs don't have one?

 

[tionis]

I'm trying to workout all the consequences that I would encounter if I were to have a head-on collision with a pulse of GWs at relativistic speed... and it just occurred to me that my time, according to a remote observer, would also be affected not only by my relative speed (close to c), but also by my interaction with the GW pulse. What happens to my clock as viewed by a remote observer? Would I notice anything different happening to time in my ship as the GW pulse hits me?

 

[PeterDonis]

GWs are spacetime in motion

No, they aren't. Spacetime doesn't move; it just is. GWs are just a spacetime geometry that has ripples in it. Remember that "time" in spacetime is just another dimension; it's part of the geometry, not an external parameter.

Why doesn't this particular propagating spacetime metric have an assigned name to it?

It does; it's called a gravitational wave.

 

[tionis]

Hi, Peter. I don't quite understand when you say spacetime doesn't move, but has ripples in it. What is the difference? And these ripples move at c, so it appears that we treat time, when measuring GWs pulses, as an independent parameter, don't we?

Also, would you please address my post #15. I really want to know what happens. Thanks

 

[tionis]

It does; it's called a gravitational wave.

I did a search on Wiki and it appears that the term I'm looking for is 'p-p wave spacetime.' But now I'm not so sure. Is it correct to say that what we detected was a p-p wave spacetime? Is it correct to say that the p-p wave originated in a Kerr spacetime?

Are physicists going to define GWs by the spacetime they originate in? For example: when a GW occurs do to a binary collision of black holes, is the corresponding wave going to be called a Kerr GW? If we detect cosmological GWs, would they be called FLRW GWs?

 

[PeterDonis]

I don't quite understand when you say spacetime doesn't move, but has ripples in it. What is the difference?

Saying that "spacetime is a 4-dimensional geometry" is a simple description. (Not all 4-dimensional geometries have ripples in them; but a spacetime that contains gravitational waves does.) A 4-dimensional geometry is a perfectly well-defined mathematical object. One of the 4 dimensions is "time", so the 4-dimensional geometry of spacetime contains all the information about how things within spacetime "move".

But saying that the 4-dimensional geometry itself "moves" doesn't even make sense. Where would it move to?

 

[PeterDonis]

these ripples move at c

If we consider the "ripples" as things moving within spacetime, yes, they move at c. But there is another way of viewing them: they are just part of the 4-dimensional geometry of spacetime, and the crests and troughs of the ripples lie along particular kinds of curves (null curves) in that 4-dimensional geometry.

it appears that we treat time, when measuring GWs pulses, as an independent parameter, don't we?

No. "Time" is one of the 4 dimensions; when we say something "moves", we are being sloppy. What we should say, to be perfectly precise, is that the something we are interested in is described by a curve, or a family of curves, in the 4-dimensional geometry. "Time" and "space" are just ways of labeling the points on the curves.

Is it correct to say that what we detected was a p-p wave spacetime?

No. We didn't detect a "spacetime". We detected a particular piece of the geometry of the spacetime we are already in.

Are physicists going to define GWs by the spacetime they originate in?

GWs don't "originate in a spacetime". "Spacetime" means the entire 4-dimensional geometry of the universe--not just the universe at a single instant, but the entire history of the universe. There aren't different spacetimes for different parts of the universe; there is just one spacetime, the entire universe.

 

[PeterDonis]

would you please address my post #15

I think pervect is correct that the GWs would still have the same amplitude, regardless of how you were moving when they passed you. That means that, in general, their effect would still be extremely tiny; you would need extremely sensitive instruments, like LIGO, to detect them. The only difference would be their frequency and wavelength.

I think it is possible, as pervect speculated, that if you were moving relative to the GWs in such a way that their frequency happened to be at a resonance, for example some kind of resonant frequency for atoms, then their effect could be larger. However, I don't know how we could determine what those resonant frequencies would be. They wouldn't be the same as the frequencies of light that are emitted and absorbed by atoms, because those frequencies are determined by the electromagnetic interaction between the electrons and the nucleus, not by anything involving gravity.

 

[tionis]

But saying that the 4-dimensional geometry itself "moves" doesn't even make sense. Where would it move to?

Good question. What about dark energy? Where is the Universe going in such a hurry?

If we consider the "ripples" as things moving within spacetime, yes, they move at c. But there is another way of viewing them: they are just part of the 4-dimensional geometry of spacetime, and the crests and troughs of the ripples lie along particular kinds of curves (null curves) in that 4-dimensional geometry.

OK, so these ''null curves'' are not moving?

No. "Time" is one of the 4 dimensions; when we say something "moves", we are being sloppy. What we should say, to be perfectly precise, is that the something we are interested in is described by a curve, or a family of curves, in the 4-dimensional geometry. "Time" and "space" are just ways of labeling the points on the curves.

And this family of curves don't move?

No. We didn't detect a "spacetime". We detected a particular piece of the geometry of the spacetime we are already in.

But how did we detect it if there is no motion involved? That particular piece of geometry got from there to here, so there must have been some motion, Peter?

GWs don't "originate in a spacetime". "Spacetime" means the entire 4-dimensional geometry of the universe--not just the universe at a single instant, but the entire history of the universe. There aren't different spacetimes for different parts of the universe; there is just one spacetime, the entire universe.

But here you said:

(Not all 4-dimensional geometries have ripples in them; but a spacetime that contains gravitational waves does.)

It looks as if you are describing a completely different spacetime. One that contains GWs. Anyways, I think I'm completely over my head on this spacetime thing lol.

I think pervect is correct that the GWs would still have the same amplitude, regardless of how you were moving when they passed you. That means that, in general, their effect would still be extremely tiny; you would need extremely sensitive instruments, like LIGO, to detect them. The only difference would be their frequency and wavelength.

I think it is possible, as pervect speculated, that if you were moving relative to the GWs in such a way that their frequency happened to be at a resonance, for example some kind of resonant frequency for atoms, then their effect could be larger. However, I don't know how we could determine what those resonant frequencies would be. They wouldn't be the same as the frequencies of light that are emitted and absorbed by atoms, because those frequencies are determined by the electromagnetic interaction between the electrons and the nucleus, not by anything involving gravity.

Thank you, Peter.

 

[PeterDonis]

What about dark energy? Where is the Universe going in such a hurry?

It isn't going anywhere. Spacetime is not moving; it just is. Dark energy means the 4-d geometry of spacetime has a particular property; it doesn't mean spacetime is going anywhere.

It looks as if you are describing a completely different spacetime.

A "different spacetime" in the sense of a different possible solution of the Einstein Field Equation, i.e., a different possible mathematical model. But only one of all the possible mathematical models is the spacetime that describes our actual universe.

so these ''null curves'' are not moving?

Of course not. Curves don't move; they're just there. They're part of the geometry.

this family of curves don't move?

See above.

That particular piece of geometry got from there to here

No, it didn't. "Here" and "there" are two different small pieces of the 4-d geometry of the universe. They aren't two different places that a geometry can be.

I think I'm completely over my head on this spacetime thing

If you don't understand spacetime as a 4-d geometry in the context of SR, where spacetime is flat and everything is much simpler, I would start there first. Spacetime in SR has the same properties I've been describing here: it's a 4-dimensional geometry, and "time" is just one of the 4 dimensions. Objects are described by curves, or families of curves, in this 4-dimensional geometry; the curves describe the entire history of the object, from its beginning to its end. And so on. Only after you have a good understanding of how all this works in SR would I recommend trying to understand it in the context of GR.

 

[tionis]

Only after you have a good understanding of how all this works in SR would I recommend trying to understand it in the context of GR.

Awesome as always, Peter. Thanks!

I thought I superficially understood the concept of gravitational waves, but after reading just now the reply you gave to georgir:

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.

Reference https://www.physicsforums.com/threads/time-reversed-gw-emission.859974/

and the ones here, I'm definitely sure I don't lol.

Let me impose on your generosity once more and see if at least I can finally have an intuitive grasp of what GWs are. Would it be correct to say that a GW is a change of the configuration of the energy-matter in a particular portion of spacetime without nothing ever traveling in between? If not, then what would be the correct, rigorous, non-mathematical way of describing what a GW is?

Thanks a bunch, Peter.

 

[PeterDonis]

Would it be correct to say that a GW is a change of the configuration of the energy-matter in a particular portion of spacetime without nothing ever traveling in between?

No, for two reasons. First, GWs are spacetime curvature; they're not "made of" energy-matter. Second, the "nothing ever traveling in between" makes it seem like you're describing a violation of energy conservation. GWs can't violate energy conservation any more than anything else can.

what would be the correct, rigorous, non-mathematical way of describing what a GW is?

I don't think there is a rigorous, non-mathematical way of describing anything in physics. If you want the rigor, you need the math. That's why physicists use math to actually do physics (as opposed to describing it to non-physicists). The best short non-mathematical description of GWs is pretty much what I've already said: they are waves of spacetime curvature. But that isn't really rigorous.

 

[tionis]

No, for two reasons. First, GWs are spacetime curvature; they're not "made of" energy-matter. Second, the "nothing ever traveling in between" makes it seem like you're describing a violation of energy conservation. GWs can't violate energy conservation any more than anything else can.

I meant to say that the energy-matter configuration of a a particular portion of spacetime changes when the geometry ripple of the GW passes by, not that spacetime is made of energy-matter. Though now that you mention it, if the ripples of GWs carry the conserved energy of the source: couldn't that energy be converted into matter as per E=mc^2?. Especially, if like the OP proposes, we are traveling at close to c? I think I already asked if I would observe Hawking/Unruh radiation a few posts back but got no answer.

Even after re-reading the answer you gave to georgir, I'm still nonplussed by how ''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," and yet there is no motion whatsoever. I suppose that is my problem, but I would like to understand this.

I don't think there is a rigorous, non-mathematical way of describing anything in physics. If you want the rigor, you need the math. That's why physicists use math to actually do physics (as opposed to describing it to non-physicists). The best short non-mathematical description of GWs is pretty much what I've already said: they are waves of spacetime curvature. But that isn't really rigorous.

Got it. And I thank you for it.

 

[PeterDonis]

if the ripples of GWs carry the conserved energy of the source: couldn't that energy be converted into matter as per E=mc^2?

GWs that pass through matter can certainly deposit some of their energy in that matter, which would count as converting the GW energy to matter. I don't think, however, that it's possible for GW energy to be converted into matter in an empty region of space where there is no matter already. But I don't know for sure; I haven't seen any proof one way or the other.

I think I already asked if I would observe Hawking/Unruh radiation a few posts back

I don't think so. Hawking radiation comes from a black hole horizon, which is a very different piece of spacetime geometry from a GW. Unruh radiation is observed by someone who has a very large proper acceleration; that has nothing to do with any particular spacetime geometry, it happens even in flat spacetime.

I'm still nonplussed by how ''The geometry of spacetime does not "change"; it is a 4-dimensional geometry that just "is".

Because, without realizing it, you are still thinking of "time" as something outside spacetime, instead of just as one of the dimensions within spacetime. Once again, I strongly recommend starting with SR and flat spacetime and understanding how time is one of the dimensions within spacetime in that context. For example, look at a spacetime diagram in an SR text. One of the dimensions of the diagram is time. "Change" just means that the relationships between the curves describing different objects can be different at the top of the diagram than at the bottom (i.e., at different places in the "time" dimension). But the geometry of spacetime is the geometry of the whole diagram; that doesn't change at all, it just is.

 

[Ibix]

OP: Here's a light cone: https://en.m.wikipedia.org/wiki/File:World_line.svg

Ignore the lower cone - it's not relevant here. The point of the upper cone is the two black holes colliding. As time goes on the gravitational waves spread out from that point, making ever larger circles - which form a cone. Think of a video of ripples on a pond. Then print each frame of the video and stack them on top of each other.

You are thinking of the video of the circles getting bigger. Peter is (approximately!) thinking of the frames stacked on top of each other making a cone, which doesn't change.

How literally you take either view is up to you. Either is a reasonable interpretation of the maths, but Peter's is one of the easiest ways to visualise it as a whole.

 

[tionis]

GWs that pass through matter can certainly deposit some of their energy in that matter, which would count as converting the GW energy to matter. I don't think, however, that it's possible for GW energy to be converted into matter in an empty region of space where there is no matter already. But I don't know for sure; I haven't seen any proof one way or the other.

I don't think so. Hawking radiation comes from a black hole horizon, which is a very different piece of spacetime geometry from a GW. Unruh radiation is observed by someone who has a very large proper acceleration; that has nothing to do with any particular spacetime geometry, it happens even in flat spacetime.

OK, so the GWs give the matter they interact with kinetic energy and relativistic mass? Which one is it, or is it both? Also, in my thought experiment, isn't my relativistic speed enough to make GWs make pairs of matter/antimmater, forgetting about Hawking/Unruh radiation?

[Because, without realizing it, you are still thinking of "time" as something outside spacetime, instead of just as one of the dimensions within spacetime.

That is most definitely the truth, Peter, but I also think that you are divorcing spacetime from gravitational ripples somehow. I understand this is do to my ignorance, but I can't shake that feeling.

 

[tionis]

OP: Here's a light cone: https://en.m.wikipedia.org/wiki/File:World_line.svg

Ignore the lower cone - it's not relevant here. The point of the upper cone is the two black holes colliding. As time goes on the gravitational waves spread out from that point, making ever larger circles - which form a cone. Think of a video of ripples on a pond. Then print each frame of the video and stack them on top of each other.

You are thinking of the video of the circles getting bigger. Peter is (approximately!) thinking of the frames stacked on top of each other making a cone, which doesn't change.

How literally you take either view is up to you. Either is a reasonable interpretation of the maths, but Peter's is one of the easiest ways to visualise it as a whole.

Ibix, I've never been able to understand lightcones, though I wish I could because they hold so much information that I'm missing on. For example, I read somewhere that as you approach a black hole, lightcones start tipping over and that is such a cool thing I wish I could understand. But getting back to your post: where am I in the top part of the lightcone you gave a link to? I see a wiggly line moving from left to right, but I don't know what that means. You said that where the lines converge (bottom part) is where the black holes are, and the waves expand from there, but where is my location in that lightcone?