B 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?

 

[tionis]

OK, so the GWs give the matter they interact with kinetic energy and relativistic mass? Which one is it, or is it both?

I should clarify that here^^ I'm referring to my spaceship moving relativistically as I collide with the GW.

 

[PeterDonis]

so the GWs give the matter they interact with kinetic energy and relativistic mass? Which one is it, or is it both?

"Kinetic energy" is really just part of "energy"; yes, GWs can give energy to matter they interact with. "Relativistic mass" is just another word for "energy".

isn't my relativistic speed enough to make GWs make pairs of matter/antimmater

Pair production is a quantum phenomenon. We don't have a good enough theory of quantum gravity to say whether gravitons, which are the hypothetical quantum particles that correspond to GWs, even exist, let alone whether they can participate in pair production.

More generally, the link between the observed frequency of radiation--whether it's gravitational or electromagnetic--and the energy of that radiation is a quantum phenomenon, and doesn't appear in classical models. For example, if you in your spaceship are moving at relativistic speed towards a source of EM radiation, classically speaking, the amplitude of the radiation that you observe does not change (since EM radiation is transverse, just like GWs), only the frequency and wavelength that you observe change. But classically, the frequency does not affect how much energy the waves can transfer to you. In order to model the frequency change as having any effect at all, you need to use quantum mechanics.

And, as I think has already been said in this thread, the quantum aspect of this is by no means as simple as "higher frequency means more energy transferred". The energy transferred will depend on whether the frequency of the radiation, as you observe it, matches some resonant frequency in the matter of your spaceship. As I commented before, we understand pretty well what determines those resonant frequencies for EM waves, but we don't have any idea how to predict what such resonant frequencies would be for GWs.

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.

That may be, but the only answer is to keep studying the subject until you can.

 

[tionis]

Ok, I'm more or less satisfied with the answers I've received concerning my thought experiment--so I'm done with it. However, I'm not happy that I've come out the other end of this thread more confused about what gravitational waves are. I want to run an analogy by you and see if I can understand it better.

Suppose I have a block or cube made out of Jello representing spacetime or the universe. Embedded at the center of this block are the two black holes that collided. Now let's place the Earth at one corner of the block. When the black holes merge, they send ripples through the Jello in all directions, but the whole of spacetime doesn't change, meaning the block remains the same but with vibrations running through it which eventually reach the Earth at a far corner and go on to infinity. What is wrong with this analogy?

Peter, as an aside question and using the Jello cube: what exactly is dark energy doing to the cube? If the cube is not growing in size, then what is it doing to the geometry of the cube?

 

[PeterDonis]

When the black holes merge, they send ripples through the Jello in all directions, but the whole of spacetime doesn't change, meaning the block remains the same but with vibrations running through it which eventually reach the Earth at a far corner and go on to infinity. What is wrong with this analogy?

You say the Jello represents spacetime, but you're thinking of the ripples as "moving through" it. That's not correct. GWs don't move through spacetime; they are just part of the geometry of spacetime. If the Jello represents spacetime, and you look at it "from the outside", you won't see GW ripples moving through it; you will just see a block that has ripples in it. A given point in the block represents a point of space at an instant of time: and the amplitude of a GW ripple at a given point of space at a given instant of time does not change.

 

[tionis]

GWs don't move through spacetime; they are just part of the geometry of spacetime

So gravitational waves are static, then? And we are the ones moving towards the geometry where they are?

 

[PeterDonis]

So gravitational waves are static, then? And we are the ones moving towards the geometry where they are?

No, no, no.

Please stop and read carefully. Nothing moves in spacetime. Spacetime is a 4-dimensional geometry that just is, it doesn't move. Objects in spacetime are described by curves, or families of curves, in that geometry. Curves don't move; they just are.

This seems to be the core of your mental block, so I really, really think you need to take some time to understand how the 4-d spacetime model works in a simple context, like SR, before you even think about more complex contexts like this one. Describing it in words tends to be tedious and often not very helpful; but we have a better tool, spacetime diagrams. Crack open a basic SR textbook, like Taylor & Wheeler's Spacetime Physics, and look at the spacetime diagrams, and study how they work. That will give you a visual sense of what I said above. Note particularly that time is one of the dimensions of the diagram, and things "moving" relative to each other just means the curves in the diagram that describe those things approach or recede as you go along the time dimension, as a matter of geometry.

 

[Ibix]

I gave this image before, but perhaps with a bit more detail it will make more sense.

Imagine a pond. There is a rock sticking out of it in one corner; this represents the earth. There is a video camera looking down at it. At some time something disturbs the surface of the pond at one point and circular ripples spread out, eventually washing over the "earth" and continuing on. There are little beetles living on the rock who have built a wave detector, which gives a kick as the wave washes past.

This is a model of a 2d universe. There are a number of things wrong with it, in the sense that they do not correspond to the real world, but it'll do for now.

Remember the video camera. It recorded the whole action. If we watch it on a screen we have two spatial dimensions in the screen, and time is... something else. It's not clear quite what it is. Peter called it a parameter.

However, we could take each frame of the video, print it out and stack it on top of the previous one. Now we have two spatial dimensions in the plane of the paper, and time is just the vertical direction in which the sheets are stacked. This model is called the block universe. The "earth" appears at the same place in every frame, so it forms a line in the block universe (called a worldline). Whatever event caused the ripples appears in only one frame - it is a point in the block universe. The ripples are larger circles on each sheet, so form a cone in the block universe. The event where the wave detector kicks also appears in only one frame, the one where the ripples touch the "earth".

The point Peter is trying to make is that you can say that LIGO kicked as the gravitational wave washed over us and went on its way, as if you were watching the video. Alternatively you can say that LIGO kicks at the "point" in spacetime where its worldline crosses the cone shaped surface of the gravitational wave fronts, as if you were looking at the stack of printouts. Note that nothing actually moves in the latter model. Your impression that things change with time would come from your perception of only a slice of the block at a time, and the fact that you remember the past. Either view is fine, but the latter has a lot of advantages for thinking about relativity. You can't mix them, though, which is what you are ending up doing with your jello model.

Obviously the real world has three space-like and one time-like direction rather than 2+1. But that is rather tricky to visualise...

 

[tionis]

I'm not sure if I'm going to be able to fully understand the concept of spacetime not moving, and at the same time able to generate gravitational waves. But it also doesn't make any sense to say that spacetime moves in the form of GWs relative to itself, so I maybe I did learn something.

Unfortunately for me, it's hard to grab a book and assimilate these maths and diagrams easily. Having said that, I think all of you that have participated in this thread have done an excellent job explaining these things, so thank you.

 

[PeterDonis]

I'm not sure if I'm going to be able to fully understand the concept of spacetime not moving, and at the same time able to generate gravitational waves.

In the 4-d spacetime viewpoint, the GWs aren't "generated"; once again, you're incorrectly thinking of time as something outside spacetime. The GWs are simply there. What we would think of, in our ordinary everyday viewpoint, as GWs being "generated", is, in the spacetime viewpoint, just the presence of GWs in a particular region of the spacetime geometry, a region bounded on one end by the GW source.

The key thing to remember in the 4-d spacetime viewpoint is that, if you ever find yourself thinking in terms of something "changing", or any word that implies change (such as "generate"), you're thinking of it wrong.

 

[tionis]

You are passionate, Peter, but you do not persuade. ;-)

 

[PeterDonis]

You are passionate, Peter, but you do not persuade. ;-)

It's not a question of persuasion. I'm telling you what GR says. Whether you believe it or not is up to you; but that's what you said you wanted to know.

 

[lynchmob72]

My question is less technical, and a little bit closer to home. If GW's were to pass by the earth, would we experience time dilation, or would it mess with our own gravity in relation to the sun? I am assuming that Gravity waves are traveling at the speed of light, and that time and space are one.

 

[lynchmob72]

I always wonder if galaxies are truly moving away from us. What if our time is different from the time of those galaxies? Do you think Gravitational Waves might have something to do with that? We all know that gravity has an effect on time. Maybe the super black hole at the center of most galaxies messes with time in a way we don't yet understand.

 

[rootone]

...What if our time is different from the time of those galaxies?

What if 6 = 8 in some other galaxy?, there just isn't any reason to speculate why that could be possible.

 

[lynchmob72]

What if 6 = 8 in some other galaxy?, there just isn't any reason to speculate why that could be possible.

Of course there is. There is a super massive black hole at the center of our galaxy. We know that time is distorted near the center. So yes, 6 may just equal 8 there. But what about galaxies close to us? Maybe 6=6 from our perspective, but maybe 6=8 from it's perspective? Einstein proved that things are weird weather you are looking at them or not. Why does it matter to me? What if the galaxies aren't racing from us? what if it only appears that way to us. The time we enjoy is different than the time between galaxies, the time between stars. I think it's a valid question.

 

[PeterDonis]

If GW's were to pass by the earth, would we experience time dilation

No one experiences time dilation relative to themselves. Different objects that are affected by a gravitational wave could, in principle, see each other's rates of time flow as different, because they are moving relative to each other, but for waves of the sort detected by LIGO, this effect would be extremely small.

or would it mess with our own gravity in relation to the sun?

Gravitational waves are fluctuations in tidal gravity, and such fluctuations are superimposed on whatever gravity is already there.

I always wonder if galaxies are truly moving away from us.

No one has been able to construct a model of the universe in which they aren't, that accounts for our observations. That's why cosmologists believe that they are, with high confidence.

What if our time is different from the time of those galaxies?

"Time" is relative anyway, so this doesn't really have any well-defined meaning. You're going to need to be more specific about the model you have in mind.

There is a super massive black hole at the center of our galaxy. We know that time is distorted near the center.

What do you mean by "time is distorted"? How does this affect what we expect to observe? How does it affect the light emitted by objects close to the hole, when it is seen by us?

I think it's a valid question.

Not the way you're asking it; it's too vague. Einstein didn't just say "time works differently in different places". He gave very specific rules for how time works differently. To apply those rules, you need to have a specific model. Just saying "what if time works differently in other galaxies" is not a specific model.

 

[rootone]

... what if it only appears that way to us...

That is assuming there is another way

 

[lynchmob72]

I kind of understand how time dilation works. I realize that i would never see it happening. I still wonder if it would happen. So GW's just ride over top of existing gravitational forces...got it. thanks!
So, i was thinking that light from a distant galaxy is affected by time. Since gravity affects space/time, then the light from distant objects must be affected. Light travels at a constant speed, but time can alter that. I don't have a model for my idea, i apologize. I am not that intelligent. I just have thoughts that i wish to either collaborate, or disprove.
Let's say, under "normal" circumstances light from a star 1 light year away takes 1 light year to reach earth.
Lets say now, that that star is close to the super massive black hole . The light from that star travels at a constant 165 thousand miles per second or whatever it is. But that's how we measure it in "Normal" time. What happens to that light in space/time that is affected by a super massive black hole? How do we perceive that light here on Earth? Is that light traveling faster than the speed of light from our point of view It existed for 1 yr, but we saw it for many years.

 

[lynchmob72]

That is assuming there is another way

That is what I'm saying... kind of. We see what we see, and we measure it with the tools we have. Light from the Andromeda Galaxy is measured with what we know. Light speed is constant, so if it takes X amount of time to reach us, that's how far away it is. What i am suggesting, is that some of that lite may be manipulated by time. maybe we see x light years, but it's actually Y light years because of the time difference. There isn't much gravity in deep space (maybe dark matter) so wouldn't light move faster than what we think is light speed because of the difference in time?

 

[PeterDonis]

under "normal" circumstances light from a star 1 light year away takes 1 light year to reach earth.

But both the distance and the time are frame-dependent; there is no absolute sense in which the star is 1 light-year away and takes 1 light-year to reach Earth. That's only true in one particular frame--you probably implicitly intended it to be true in a frame in which Earth is at rest. In a frame in which Earth is moving, the light source will not be 1 light-year away from Earth and the light will not take 1 year to travel to Earth.

Also, as soon as gravity is involved, spacetime is curved, and you can no longer deduce the light travel time from the distance or vice versa; it's more complicated than that. See below.

What happens to that light in space/time that is affected by a super massive black hole?

Locally, i.e., when measured by an observer as the light is passing him, light travels at $c$, no matter where in spacetime it is.

Globally, it depends on what frame you choose. See above.

This is an instance of what I was saying before: you need to be more specific about what model you are using. Who are you assuming is observing the light? Where are they relative to the black hole, and how are they moving?

How do we perceive that light here on Earth?

If we assume that Earth is at rest relative to the black hole, and that the light source is also at rest relative to the hole (but much closer to it), then the light will appear redshifted to us when we observe it on Earth. Also, the light will take longer to reach us than it would if the hole were not present; in other words, the light will take longer, in the frame in which Earth and the hole are at rest, to cover the distance from the light source to Earth than light in flat spacetime (i.e., with no gravity present) would take to cover the same distance. But, as above, this time (and the distance) are frame-dependent.

Is that light traveling faster than the speed of light from our point of view It existed for 1 yr, but we saw it for many years.

I don't understand what this means.