Gravity curvature and graviton

[Nikarus]

Hello all,
I'm new to GR and trying to understand everything in general now...
I was looking at pictures like this one
http://upload.wikimedia.org/wikipedia/commons/2/22/Spacetime_curvature.png
for a very long time. I made two major "experimental" conclusions here:
1. A meter near planet will be longer that a meter far a way from it for observer outside the planet;
2. If two objects travel parallel with same speed and one of them goes near planet, then the one that is closer to the planet will remain behind (if we neglect its trajectory change), but when they come out of the gravity influence, they will have same speed again.
Is that correct?

But I still can't understand, where gravity force comes in action at this picture? I read from Hawking that gravity is curvature. I can only understand it if I add in mind some additional force on the picture directed down that will hold a moving object on this curve - but isn't is stupid?
And where the graviton comes in action here?

 

[bcrowell]

Hi, Nikarus,

Welcome to PF!

1. A meter near planet will be longer that a meter far a way from it for observer outside the planet;

This is not quite right. General relativity does not have a well-defined notion of what it would mean to allow an observer in one location to measure things at a distant location. Curvature is really a local property. For instance, if you make a triangle out of laser beams in your own neighborhood, you will find that the angles don't add up to exactly 180 degres. This is a measure of spatial curvature in that local region.

2. If two objects travel parallel with same speed and one of them goes near planet, then the one that is closer to the planet will remain behind (if we neglect its trajectory change), but when they come out of the gravity influence, they will have same speed again.
Is that correct?

This is correct.

But I still can't understand, where gravity force comes in action at this picture? I read from Hawking that gravity is curvature. I can only understand it if I add in mind some additional force on the picture directed down that will hold a moving object on this curve - but isn't is stupid?

Sounds like you're getting confused by the rubber sheet metaphor. I've pasted a FAQ below that may help.

And where the graviton comes in action here?

The graviton is not part of GR, since GR is a purely classical theory. We don't have a theory of quantum gravity. Even if we did, it would only typically be relevant at the Planck scale.

-Ben

FAQ: The rubber-sheet analogy doesn't make sense to me.

The rubber-sheet analogy says that we can visualize general relativity's description of a the gravitational field of an object such as the sun by imagining that the sun is like a heavy steel ball placed on an initially flat sheet of rubber. The ball makes the rubber sag. The rubber represents curved spacetime. Many people have trouble with this analogy because they then imagine other objects, e.g., the earth, then have to roll around on the sheet as if they were being pulled "downward" by the same external "downward" force that displaced the steel ball downward.

This leads to incorrect results. For instance, it doesn't make it clear why we should expect light rays to be deflected by the sun's field. According to Newton, light isn't affected by gravity, so why should we expect it to have any tendency to roll "downward" into the depression on the rubber sheet under the influence of the external "downward" force?

A better way to imagine this is that we start with a graph-paper grid made of spider silk. The sun is a big beetle caught in the web. The beetle tries to free itself, but the only result of its struggle is that by the time it dies, it has distorted the nearby matrix of the spiderweb. The notion of a straight line has been redefined. Light rays and material objects will now follow paths that are straight as measured by the distorted graph-paper grid. This has non-Euclidean consequences. For instance, two distinct lines can intersect at more than one point, and if these are world-lines of light rays, we interpret the effect as gravitational lensing.

It's also important to realize that what is being described is a distortion of spacetime, not just a distortion of space. If this were not true, then for example an object's motion would not depend on its initial velocity, since two objects starting from the same point and going in the same direction would follow the same line through space.

 

[Nikarus]

Hi bcrowell,
Thank you for the detailed reply!

This is not quite right. General relativity does not have a well-defined notion of what it would mean to allow an observer in one location to measure things at a distant location. Curvature is really a local property. For instance, if you make a triangle out of laser beams in your own neighborhood, you will find that the angles don't add up to exactly 180 degres. This is a measure of spatial curvature in that local region.

Okay, I got your point. I try to give another experiment that will give me same understanding:
If we take a very long and straight stick and put in on surface of massive object, will outside observer see that it is bended because of space curvature? Will the same be with rope?

A better way to imagine this is that we start with a graph-paper grid made of spider silk.
...

Yes, I was trying to imagine it like this before and this seemed more correct. But I'm still confused in dimensions. Above example it is definitely for 2D. Is rubber sheet for 2D also? Then what is on Z axis there?

 

[jtbell]

The "third dimension" in the rubber-sheet analogy doesn't correspond to anything in GR, as far as I know. It's a weakness of this analogy.

 

[bcrowell]

If we take a very long and straight stick and put in on surface of massive object, will outside observer see that it is bended because of space curvature? Will the same be with rope?

There is no meaningful way in GR to define the notion of a distant observer measuring something like this.

 

[John232]

The graviton and spacetime curvature are two conflicting theories. One says a graviton makes exchanges with other particles giving them mass and the other says objects are attracted to each other because of the curvature of space. Gravitons are used in particle physics and GR in astrophysics. Each theory only works in those fields so there isn't a way to know which one is more correct, I go for the spacetime curvature and I think the graviton is just a set of described interactions that works in particle physics but the particle may not exist.

 

[bcrowell]

The graviton and spacetime curvature are two conflicting theories. One says a graviton makes exchanges with other particles giving them mass and the other says objects are attracted to each other because of the curvature of space. Gravitons are used in particle physics and GR in astrophysics. Each theory only works in those fields so there isn't a way to know which one is more correct, I go for the spacetime curvature and I think the graviton is just a set of described interactions that works in particle physics but the particle may not exist.

Gravitons aren't used in particle physics. Gravitons aren't used in any theory, because we don't have a working theory of quantum gravity. These aren't two conflicting theories. There is only one theory, because we don't have a theory of quantum gravity. If we ever do get a theory of quantum gravity, we still won't have two conflicting theories, because GR will simply be the classical limit of the theory of quantum gravity.

 

[Nikarus]

Thank you for your comments!

There is no meaningful way in GR to define the notion of a distant observer measuring something like this.

I'm a little bit confused here - then what about Gravitational Lensing effect? If you look at this simulation
http://upload.wikimedia.org/wikipedia/commons/c/cd/Black_Hole_Milkyway.jpg
and imagine a stick (inf length would be more correct I think) "sucking" into black whole, I think that it should definitely look curved. I think that the best effect will be if the stick will be at some angel to the blackwhole and positioned a little bit behind it - then its lower part should come closer to the blackwhole event hor making a curve.

The "third dimension" in the rubber-sheet analogy doesn't correspond to anything in GR, as far as I know. It's a weakness of this analogy.

Okay, now it is clearer. Why then do we need to make this hollow under the object? Spider silk analogy looks more correct. Actually isn't it what we will see if we will look straight down on the rubber sheet?

First time when I saw the rubber sheet I was imagining that 2D space is curved to 3D meaning that in our life space is curved to 4D. Do I understand it right that it is not correct to talk about 4D in GR?

 

[jtbell]

In GR (as in SR) spacetime is 4D to begin with.

 

[Nikarus]

Are you talking about time as 4th dimension?
I'm talking about 4th spatial dimension.

 

[bcrowell]

I'm a little bit confused here - then what about Gravitational Lensing effect? If you look at this simulation
http://upload.wikimedia.org/wikipedia/commons/c/cd/Black_Hole_Milkyway.jpg
and imagine a stick (inf length would be more correct I think) "sucking" into black whole, I think that it should definitely look curved. I think that the best effect will be if the stick will be at some angel to the blackwhole and positioned a little bit behind it - then its lower part should come closer to the blackwhole event hor making a curve.

Just because an object looks a certain way based on measurements of light rays, that doesn't mean you have an absolute notion of measuring an object from a distance.

 

[Passionflower]

Just because an object looks a certain way based on measurements of light rays, that doesn't mean you have an absolute notion of measuring an object from a distance.

This is what Nikarus wrote:

Hi bcrowell,
If we take a very long and straight stick and put in on surface of massive object, will outside observer see that it is bended because of space curvature? Will the same be with rope?

Clearly he wants to know what an object looks like based on what the observer sees. That is a good and valid question.

It appears that the only person talking about "an absolute notion of measuring an object from a distance", whatever that is supposed to mean, is actually you.

 

[pervect]

I don't think Nikaru's question is clear enough to have any definite answer, alas. The question is phrased as if "an outside observer" was unique. But there are lots of different "outside observers", who will all be at different points along the long rod.

Furthermore, and more to the point that bcrowell was trying to make, even if you did specify, exactly, the worldline of some particular observer, that STILL might not provide enough information to answer the question. When Nikaru's asks what they "see", I would guess that he would want not what they would photograph, but rather a notion of the object with the light-speed delays removed, i.e. a description of the object in some coordinate system. Though perhaps not, it's really hard to say, the word "see" is a bit ambiguous in this regard.

Let's assume for now the former, i.e. that the OP is interested in a representation of the object with the lightspeed delays removed, and not a photograph. While specifying the worldline of an observer specifies a unique coordinate system in the local region. close to the object, it's clear that the O.P. wants information about the object in distant regions. And there are several different ways that "an observer" could extend their coordinate system to extend out from the local region into distant regions.

It is for reasons like this that many authors suggest that the notion of "an observer" has outlived its usefullness in GR.

 

[bcrowell]

I think pervect's #13 is an excellent summary.

 

[closet mathemetician]

Thank you for your comments!


I'm a little bit confused here - then what about Gravitational Lensing effect? If you look at this simulation
http://upload.wikimedia.org/wikipedia/commons/c/cd/Black_Hole_Milkyway.jpg
and imagine a stick (inf length would be more correct I think) "sucking" into black whole, I think that it should definitely look curved. I think that the best effect will be if the stick will be at some angel to the blackwhole and positioned a little bit behind it - then its lower part should come closer to the blackwhole event hor making a curve.


Okay, now it is clearer. Why then do we need to make this hollow under the object? Spider silk analogy looks more correct. Actually isn't it what we will see if we will look straight down on the rubber sheet?

First time when I saw the rubber sheet I was imagining that 2D space is curved to 3D meaning that in our life space is curved to 4D. Do I understand it right that it is not correct to talk about 4D in GR?

I think another weakness of the rubber sheet analogy is to picture a ball rolling along the sheet. A ball is an object with an existence separate from that of the sheet. So now you need something to hold the ball on the sheet.

I like to think of it this way: take a deflated balloon and draw a small circle on the side. Now, stretch the surface on either side of the circle which gets distorted into an ellipse because of the distortion of the surface of the balloon. This is what gravity does. It "stretches" space and time. So if you are the circle, YOU get stretched as well.

 

[Passionflower]

It is for reasons like this that many authors suggest that the notion of "an observer" has outlived its usefullness in GR.

As far as I am concerned an observer is still an observer in curved spacetimes.

Care to back your statement up with textbook references? Who are those 'many authors' you speak of?

 

[pervect]

re: banishing observers

The reference that comes immediatly to mind is a paper, not a textbook:
http://arxiv.org/abs/gr-qc/9508043

A method for making sure that the relativity effects are specified correctly
(according to Einstein’s General Relativity) can be described rather briefly.
It agrees with Ashby’s approach but omits all discussion of how, historically
or logically, this viewpoint was developed. It also omits all the detailed
calculations. It is merely a statement of principles.
One first banishes the idea of an “observer”. This idea aided Einstein
in building special relativity but it is confusing and ambiguous in general
relativity. Instead one divides the theoretical landscape into two categories.
One category is the mathematical/conceptual model of whatever is happening
that merits our attention. The other category is measuring instruments
and the data tables they provide.

Some historical context. There was some debate going on as to how to calculate the GR effects for the Global Positioning Satelites back in the days when it was new. This was Misner's response, to try to clear up some of the issues involved.

BTW, my personal position isn't that it's impossible to define an observer - though it often winds up involving some wrangling and cross discussion to make sure everyone's defined it in the same way. Questions like "what defintion of simultaneity did you use" and "what curve was the distance measured over" - I'm sure you've seen me ask them before :-).

 

[Nikarus]

I'm sorry for giving you the confusion, probably I don't understand something.
I am looking at the light rays as at the ultimate measurer of curvature. As photon does not have weight, then it should move exactly like space is curved. So this means that if we see a curved object then we see exactly how it is curved relatively to us. If we are near BH event horizon then all objects near looks okay but all things far away should look curved.
Then

Curvature is really a local property.

is not very clear for me. I'd say that it is not correct to talk about "locality" of this effect. Please correct me where I'm wrong.

About spider silk analogy, I drew it:

[PLAIN]http://xmages.net/storage/10/1/0/e/9/upload/f60ad99a.jpg

Lets say that this blue thing is a star.
So(if I understand everything right), if you image an object passing near, then it will first come closer to the star and then will be thrown away

So, then I imagined opposite picture that seemed to be more real, that closet mathemetician also described (thanks for that! :) ):

[PLAIN]http://xmages.net/storage/10/1/0/e/9/upload/4a0ef92e.jpg

You can see my curved long rod as well :)
So here, the object passing by will orbit the star(at least). This looks more correct to me. As closet mathemetician said, the material stretches the space creating gravity. So gravity is result of material and space interaction.
Is this correct understanding? :)

 

[Jonathan Scott]

Neither picture is correct if the lines are meant to represent "straight lines in space" as distorted by gravity. Lines should all be curved towards the central mass for their whole length, and the curvature increases as you get closer to the mass. This means lines which are parallel on one side of the mass would not be parallel on the other. Lines close to the mass would converge and cross on the other side (eventually - the curvature in cases such as the solar system is almost undetectable) and lines further away would be less affected but would still converge a bit. It's not possible to use a grid representation to show this, as a grid is effectively a map of flat space, regardless of how it is distorted.

Photons follow the same rules under gravity as other objects, the only difference being that their speed is c. A brick traveling at nearly c will follow the same path as a photon. An object traveling tangentially to a gravitational field g will be accelerated by g (1+v²/c²) where the v²/c² term is due to the ordinary curvature of space and the 1 is due to the curvature of space with respect to time. This means that anything traveling near c is effectively accelerated twice as much as a static object.