Gravitational Waves @ relativistic speed?

[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.

 

[lynchmob72]

Yeah, the whole frame dependency throws me for a loop. But it makes me want to learn more, so thank you for your time. The last quote was me trying imagine light existing in 2 different time frames. 1 where it seemed to exist in a "normal" manner for 1 year, but to me it lasted for many years. That is just me trying to realize more than one time "frame". hmm, i guess i understand the frame thing more than i thought.

 

[PeterDonis]

The last quote was me trying imagine light existing in 2 different time frames.

Things don't "exist in" frames. Frames are just abstractions that we use to describe spacetime and events in it. Different frames are just different descriptions of the same events.

1 where it seemed to exist in a "normal" manner for 1 year, but to me it lasted for many years.

Why do you think it would last many years for you? If you are moving relative to the light source and the Earth (assuming both of those are at rest relative to you), the light will seem to travel a shorter distance and take a shorter time to travel.

 

[lynchmob72]

I had it backwards. Sorry about that. Thanks for your responses.

 

[Dale]

Since gravity affects space/time, then the light from distant objects must be affected.

Yes, this is called cosmological redshift. It is accounted for in current cosmological models and is the reason why the radiation from the surface of last scattering is now so cold. A similar effect called gravitational redshift exists for objects that are close by but very massive (like the Earth or a black hole).

Basically, the effect that I think you are describing is already part of GR.