Simple question about warping space

[jaketodd]

Is it true that gravitating bodies actually warp the fabric of space towards them like in this picture? http://www.astronomynotes.com/evolutn/grwarp.gif

 

[CompuChip]

That's a nice analogy, but personally I'd be careful with words like "the fabric of space".

It is true, that light is bent in the direction of gravitational masses. In fact, if the mass is large enough (or more strictly speaking, the mass density) light can be bent so strongly that its orbit is bent into a circle or even more. In that case you have black hole.

Usually, however, the effects are visible near stars. In that case, an object can lie behind a star, like in the lower picture you linked. However, for an observer at the tip of the arrow, the light seems to have originated from somewhere like the far upper corner of the sheet (just draw a tangent line to the last part of the light orbit). This effect has been measured for the sun, as one of the first experimental tests of GR (actually, this effect also exists in Newtonian gravity, but its a factor off which GR gets right) and since it has been seen in action numerous times in so called gravitational lensing, mostly with large clusters and gas clouds.

 

[jaketodd]

Thanks but my question is still unanswered. Is space bent towards a gravitating mass? Or does no one know? What did Einstein think?

Thanks,

Jake

 

[espen180]

I suggest you take a look at the gravitomagnetic field equations, which are a first-order approximation to GR but good enough to give you an idea of what is going on. The effect is similar to the effect due to a magnetic field caused by a moving charge.

"Is space bent towards a mass?" is, I think, a strange question to ask. To properly examine the curvature, you have to take time into account as well. The result of the curvature is that straight lines in space-time appear to be curved toward masses in space.

 

[jaketodd]

I suggest you take a look at the gravitomagnetic field equations, which are a first-order approximation to GR but good enough to give you an idea of what is going on. The effect is similar to the effect due to a magnetic field caused by a moving charge.

"Is space bent towards a mass?" is, I think, a strange question to ask. To properly examine the curvature, you have to take time into account as well. The result of the curvature is that straight lines in space-time appear to be curved toward masses in space.

I appreciate your post. It sounds like I don't need to understand gravitomagnetic field equations. "...straight lines in space-time appear to be curved toward masses..." So the answer to my question seems to be a simple "yes." Right?

Thanks,

Jake

 

[espen180]

I appreciate your post. It sounds like I don't need to understand gravitomagnetic field equations. "...straight lines in space-time appear to be curved toward masses..." So the answer to my question seems to be a simple "yes." Right?

Thanks,

Jake

"...straight lines in space-time appear to be curved toward masses...when isolated in space". You have to take time into account. The fact that space in curved toward something makes little sense to me. The only way to get it right, as far as I know, is to include all four dimensions of space-time.

 

[jaketodd]

Ok, gravitating bodies warp spacetime toward them. Is that correct then? What do you mean by "when isolated in space"?

Thanks,

Jake

 

[prakash kumar]

well I think 'isolated in space' is means that body of certain mass is alone to be observe or in other words it is alone. You can imagine that it is easy to observe the effect when it is only one who shows some deformation in light's straight line path.
prakash0

 

[espen180]

What I meant is that geodesics, which are the straightest possible paths in space-time, sppear curved in space (i.e. not straight lines in space).

What does it mean that something warps spacetime towards it?

 

[starthaus]

Is it true that gravitating bodies actually warp the fabric of space towards them like in this picture? http://www.astronomynotes.com/evolutn/grwarp.gif

Like in http://www.wbabin.net/ntham/todd3.pdf "paper" you just "published" based on what you are learning here.

 

[jaketodd]

Like in http://www.wbabin.net/ntham/todd3.pdf "paper" you just "published" based on what you are learning here.

Is learning here and applying that knowledge to my work against any rules?

 

[TCS]

If you think about space time as a baloon where the stretchiness of the balloon at a spot on its surface is determined by its mass/energy density, then the surface of the balloon will be dimpled. The rate of time and the spatial dimensions are all determined by the radius of the dimple. Motion across the surface of the baloon means that you will be moving through dimples in space time as well as causing a dimple to propagate over the surface.

 

[espen180]

If you think about space time as a baloon where the stretchiness of the balloon at a spot on its surface is determined by its mass/energy density, then the surface of the balloon will be dimpled. The rate of time and the spatial dimensions are all determined by the radius of the dimple. Motion across the surface of the baloon means that you will be moving through dimples in space time as well as causing a dimple to propagate over the surface.

Thank your for that idea. It sparked some of my own.

I guess it works as a 2D analogy of a closed universe, but it doesn't help jaketodd, since inhabitants on the baloon surface cannot experimentally determine the direction of the curvature (positive if on the outside, negative if on the inside, but this is impossible for the 2-dimensional inhabitants to determine).

Nevertheless, the baloon analogy is exellent for demonstrating that asking in what direction spacetime curves is nonsense. We can see that on the balloon, spacetime is embedded in 4 dimensional space (2 spatial dimensions, 1 temporal dimension and a fourth dimension into which spacetime also curves). By analogy we can see that we would need a 5-dimensional space in which to embed our 4-dimensional spacetime for us to be able to ask in which direction spacetime curves, and even then it would be a question of definiton.

 

[TCS]

Thank your for that idea. It sparked some of my own.

I guess it works as a 2D analogy of a closed universe, but it doesn't help jaketodd, since inhabitants on the baloon surface cannot experimentally determine the direction of the curvature (positive if on the outside, negative if on the inside, but this is impossible for the 2-dimensional inhabitants to determine).

Nevertheless, the baloon analogy is exellent for demonstrating that asking in what direction spacetime curves is nonsense. We can see that on the balloon, spacetime is embedded in 4 dimensional space (2 spatial dimensions, 1 temporal dimension and a fourth dimension into which spacetime also curves). By analogy we can see that we would need a 5-dimensional space in which to embed our 4-dimensional spacetime for us to be able to ask in which direction spacetime curves, and even then it would be a question of definiton.

I like the balloon analogy because it allows me to visulaize masss/energy density as the thickness of the rubber and also that we are part of space time, were part of the fabric that holds the universe together.

 

[jaketodd]

We can see that on the balloon, spacetime is embedded in 4 dimensional space (2 spatial dimensions, 1 temporal dimension and a fourth dimension into which spacetime also curves). By analogy we can see that we would need a 5-dimensional space in which to embed our 4-dimensional spacetime for us to be able to ask in which direction spacetime curves, and even then it would be a question of definiton.

You don't necessarily need a 5th dimension. Imagine, instead of a dimple, spacetime stretched toward a massive object without curving into a 5th dimension. However, the question remains: What force or tendency makes objects go into regions of stretched spacetime?

 

[TCS]

You don't necessarily need a 5th dimension. Imagine, instead of a dimple, spacetime stretched toward a massive object without curving into a 5th dimension. However, the question remains: What force or tendency makes objects go into regions of stretched spacetime?

Objects are like wave packets in space time, where the the medium of oscillation is the energy density. Greater energy density changes the elasticity and causes time to slow down. When the localized energy in a wave packet enters a high energy density region, the rate of energy transmission through space slows down. Accordingly, the wave energy is trapped in the slowed down area of space and since the location of the object is based upon the location of the energetic portion of its wave function, the object goes into the higher energy region of space time.

 

[A.T.]

What force or tendency makes objects go into regions of stretched spacetime?

It is the tendency to move on straight lines in spacetime:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

 

[jaketodd]

It is the tendency to move on straight lines in spacetime:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

That explains why something in motion would follow stretched spacetime or a dimple in spacetime, but it doesn't explain why something starting from rest, relative to a massive object, starts falling toward the massive object.

 

[A.T.]

http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

but it doesn't explain why something starting from rest, relative to a massive object, starts falling toward the massive object.

Yes it does:

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_time.gif

The "falling object" here is initially at rest in space : it advances initially only along the (proper)time dimension. But It starts moving in space towards the massive object ("more stretched spacetime"), just by advancing locally straight in spacetime.

 

[jaketodd]

If the "falling object" mirrored the path of the proper time in the graphic, then it would stay at the top of the house.

 

[A.T.]

If the "falling object" mirrored the path of the proper time in the graphic, then it would stay at the top of the house.

It wouldn't be a free falling object then, because it's path through spacetime(worldline) wouldn't be a straight line anymore. In order to keep the object at the top of the house, you have to bend it's worldline by applying an upwards force on the object.

 

[jaketodd]

In the graphic, why doesn't the object have to mirror the axis of proper time? What causes it to deviate from that path?

 

[TCS]

If the "falling object" mirrored the path of the proper time in the graphic, then it would stay at the top of the house.

In the four dimensional model of space time, you are never stationary. In uncurved space, you are moving at a constant velocity in the direction of time. When space curves, some of your velocity is in the other three dimensions.

However, I think that five dimensional models provide a more intuitive picture of space time.

 

[jaketodd]

In the four dimensional model of space time, you are never stationary. In uncurved space, you are moving at a constant velocity in the direction of time. When space curves, some of your velocity is in the other three dimensions.

However, I think that five dimensional models provide a more intuitive picture of space time.

So you're saying inherent temporal velocity is transferred to spatial velocity in the environment of warped spacetime? There still needs to be something that chooses which spatial direction to go in. And if you bring a 5th dimension into it, there needs to be a force that pulls things into a dimple of spacetime.

 

[A.T.]

In the graphic, why doesn't the object have to mirror the axis of proper time?

Because there is no real force acting on it (it is in free fall), it advances on a straight line trough spacetime.

What causes it to deviate from that path?

In GR you don't need a cause to advance straight in spacetime - it the default behavior of all objects. You need a cause (force) to deviate from that straight line.

There still needs to be something that chooses which spatial direction to go in.

By moving locally straight you always tend towards the area of increasing distances (more stretched spacetime). This is dictated by geometry as shown in the pictures.

And if you bring a 5th dimension into it, there needs to be a force that pulls things into a dimple of spacetime.

No, moving locally straight is enough.

 

[jaketodd]

Because there is no real force acting on it (it is in free fall), it advances on a straight line trough spacetime.

Since the graphic defines the proper time as curved, then an object with no forces on it would mirror that curved path. It would be following the curvature of time in spacetime. The movement of the object as presented in the graphic would be like taking a shortcut straight across a dimple in the time part of spacetime.

 

[A.T.]

Since the graphic defines the proper time as curved, then an object with no forces on it would mirror that curved path.

No. The graphic shows how GR models gravitation, and in GR force free objects advance locally straight in spacetime. Maybe you are confusing GR with a different (your own?) theory.

 

[jaketodd]

No. The graphic shows how GR models gravitation...

...gravitation...

gravitation

Finally, a force that makes things move in spacetime and can lead to the straight line in the graphic.

 

[jaketodd]

Because there is no real force acting on it (it is in free fall), it advances on a straight line trough spacetime.

In GR you don't need a cause to advance straight in spacetime - it the default behavior of all objects. You need a cause (force) to deviate from that straight line.

As you can see, before you where claiming no force on the object.

 

[A.T.]

gravitation

Finally, a force...

Where did I say "force" ? "Gravitation" refers to the general phenomena, not a specific model.

...that makes things move in spacetime

No. In GR you don't need a force to make things advance in spacetime. All objects advance in spacetime by default.

and can lead to the straight line in the graphic.

No. In GR you don't need a force to advance locally straight in spacetime. It is the default behavior of force free objects.

As you can see, before you where claiming no force on the object.

Yes, in GR within inertial frames, free falling objects are force free.

 

[jaketodd]

Also, the graphic shows the object taking a path shorter than the curved, proper time dimension. This is incorrect because an object would take longer than the proper time since its motion causes time dilation. So its path should be longer than the proper time curve between the two end points of the object's path.

 

[jaketodd]

Where did I say "force" ? "Gravitation" refers to the general phenomena, not a specific model.

No. In GR you don't need a force to make things advance in spacetime. All objects advance in spacetime by default.

No. In GR you don't need a force to advance locally straight in spacetime. It is the default behavior of force free objects.

Yes, in GR within inertial frames, free falling objects are force free.

So objects fall according to what? The curvature of spacetime? What pulls them into a dimple? I guess you could say objects move by default to less dense areas of spacetime. But that brings up the question of what is the difference between tendency and force?

 

[A.T.]

Also, the graphic shows the object taking a path shorter than the curved, proper time dimension.

No idea what you compare here, A dimension doesn't "take a path of a finite length",

This is incorrect because an object would take longer than the proper time since its motion causes time dilation. So its path should be longer than the proper time curve between the two end points of the object's path.

Time dilation in this diagram means the object advances less along the proper time dimension. This might help you to understand the diagram better:
http://www.adamtoons.de/physics/relativity.swf
Set: intial speed : 0, gravity : 1.0 to simulate a free fall from rest towards a mass somewhere to the right.

So objects fall according to what? The curvature of spacetime?

Yes

What pulls them into a dimple?

You could just as well ask "What bends a cricle?". It is simply a geometrical consequence of the mathematical model (geodesics on curved manifolds).

I guess you could say objects move by default to less dense areas of spacetime.

You can say a lot of things. But the things GR says also fit the observation quite well.

 

[jaketodd]

I'm done debating this. We're going in circles or at least this thread as a whole is. I wish one of the people who have been recognized by the forum to be an authority would set the record straight.

 

[Dale]

I guess it works as a 2D analogy of a closed universe, but it doesn't help jaketodd, since inhabitants on the baloon surface cannot experimentally determine the direction of the curvature (positive if on the outside, negative if on the inside, but this is impossible for the 2-dimensional inhabitants to determine).

Actually, the curvature of the balloon surface is positive regardless of which "side" of the surface you are talking about. In fact, the concept of "inside" or "outside" the surface is only valid in the 3D embedding space and is meaningless within the 2D surface itself.

The curvature is an intrinsic property defined entirely within the surface itself. Experimenters within the surface can determine the positive curvature of a balloon by measuring the sum of the interior angles of a triangle and determining that it is greater than 180º. A 2D surface with negative curvature would be saddle-shaped in 3D, and again the "side" would have no bearing on the curvature. The sum of the interior angles of a triangle would be less than 180º.