My problem with the relativity representation on gravity.

[jaydnul]

Whenever you see representations of gravity in terms of relativity, you see a planet sitting on a 2d surface of fabric (space) and it is making an indentation, almost as if there another source of gravity pulling it downwards against the fabric. I think this is a poor representation. I mean, let's say the moon is sitting on the inclined fabric that is created by the earth. There is no reason that the moon would slide down this inclination other than a separate source of gravity pulling it downward. Does that make sense? So is there a better way to imagine how warped space is able to pull other objects inward?

 

[ModusPwnd]

This is the case with any analogy or metaphor. You should try to use it to understand rather than try to poke holes in it. Otherwise, get ready to do some math.

 

[sophiecentaur]

Yes - it's a 'model of gravity' which is driven by gravity. Bound to lead to some problems, isn't it? What would you expect?
The better models are progressively harder and harder to understand and are basically Mathematical.

 

[MikeGomez]

Whenever you see representations of gravity in terms of relativity, you see a planet sitting on a 2d surface of fabric (space) and it is making an indentation, almost as if there another source of gravity pulling it downwards against the fabric. I think this is a poor representation. I mean, let's say the moon is sitting on the inclined fabric that is created by the earth. There is no reason that the moon would slide down this inclination other than a separate source of gravity pulling it downward. Does that make sense? So is there a better way to imagine how warped space is able to pull other objects inward?

I agree with you 100% They are doing exactly what you say. They are explaining gravity in term of gravity. It’s stupid, annoying, and does not explain anything.

One example is when they place a bowling ball on a trampoline to explain the effect of gravity. Then they place a marble or something on the trampoline and a falls towards the bowling ball. They think they are explaining gravity!

Another common one is those funnel type graphics they show in outer space supposedly showing how gravity “curves space”. Well let’s take that graphic from space and put in on the surface of the earth. Now it just looks like an ordinary hole in the ground, and that’s because it is. If I tried to explain gravity to someone by showing them a hole in the ground and then dropping something down the hole, they would think I’m nuts.

Here is a youtube video from someone who took the effort to do a more reasonable job. We could poke holes in this one also, but at least he saw the problems with the standard explanations and tried to do a better job. I think he succeeded.

 

[ZapperZ]

Do you also have a problem with Feynman diagrams? After all, space is represented by only ONE dimension!

In trying to explain complex ideas in physics, people often have to resort to either analogies, or simplistic representations. If you don't want that and want something accurate, then study the physics itself!

I'm surprised people are not complaining about those grid lines!

Zz.

 

[ModusPwnd]

They are explaining gravity in term of gravity.

No necessarily. Just imagine some giant cosmic hand pushing the Earth into the sheet if it disturbs you that much.

 

[sophiecentaur]

No necessarily. Just imagine some giant cosmic hand pushing the Earth into the sheet if it disturbs you that much.

An old guy with a beard? Now that's real Physics. HAHA

And where does the "pushing' come from?

 

[Dale]

I think this is a poor representation.

So do most people here.

So is there a better way to imagine how warped space is able to pull other objects inward?

Our forum member A.T. has a series of graphics that are better for understanding the geometry. I suspect he will be along shortly.

 

[ModusPwnd]

An old guy with a beard? Now that's real Physics. HAHA

And where does the "pushing' come from?

The pushing is coming from the hand, and thus the coulomb force. No gravity used to describe gravity (and no body need be attached to the hand). Its an metaphor, you are "supposed" to focus on the parts it purports to explain, not the other stuff...

 

[Nugatory]

This is the case with any analogy or metaphor. You should try to use it to understand rather than try to poke holes in it. Otherwise, get ready to do some math.

I agree with this advice in general... But that rubber sheet analogy is so inadequate and misleading that it's not worth spending time trying to understand it. Better to drop it completely and read MTW's analogy of the ants on the apple, or look at A.T.'s video.

 

[1977ub]

I prefer these:

https://www.physicsforums.com/showpost.php?p=3629987&postcount=22

http://i.ytimg.com/vi/DdC0QN6f3G4/0.jpg

 

[Nugatory]

I prefer these:

https://www.physicsforums.com/showpost.php?p=3629987&postcount=22

http://i.ytimg.com/vi/DdC0QN6f3G4/0.jpg

Yep, that's the stuff that I (and likely DaleSpam in #8) was referring to. I've wondered if it would be worth incorporating into the FAQ, as the rubber sheet silliness shows up fairly often.

 

[A.T.]

I prefer these:

https://www.physicsforums.com/showpost.php?p=3629987&postcount=22

http://i.ytimg.com/vi/DdC0QN6f3G4/0.jpg

Here the animated version:

https://www.youtube.com/watch?v=DdC0QN6f3G4

 

[jaydnul]

Thanks for all the replies guys. What I am getting out of all this is that the only way to fully understand it, you got to do the mathematics. Seems like a reoccuring theme haha

 

[A.T.]

What I am getting out of all this is that the only way to fully understand it, you got to do the mathematics.

You can understand the geometric concepts without doing the math. Check out this links:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.relativitet.se/spacetime1.html

 

[ikjyotsingh]

I'm sorry, but the interpretation here is slightly off.

The diagrams you are referring to of planets weighing down and indenting rubber sheets are not an idealization, but an Euclidean space embedding of the Schwarzschild geometry.

Recall, that according to Birkhoff's theorem, any spherically symmetric static solution is necessarily the Schwarzschild solution. Now, from a physical perspective, the Schwarzschild metric models any isolated mass. Any "particle" that enters the gravitational field of this isolated mass moves along a geodesic. With respect to our solar system, the moon moves around a geodesic around the earth, the Earth moves around a geodesic around the Sun, etc.

The embedding diagram comes from embedding the Schwarzschild metric in polar coordinates, precisely, embedding constant time slices in the equatorial plane in polar coordinates. The resulting equation is a paraboloid surface which is the rubber sheet diagram that is commonly shown. Although, because the latter is never explained properly, some think that this diagram is science fiction, and as you can see it is not.

Hope this helps.
Thanks.
Ikjyot Singh Kohli

 

[Dale]

The diagrams you are referring to of planets weighing down and indenting rubber sheets are not an idealization, but an Euclidean space embedding of the Schwarzschild geometry.
...
The embedding diagram comes from embedding the Schwarzschild metric in polar coordinates, precisely, embedding constant time slices in the equatorial plane in polar coordinates.

That statement may be consistent with the drawings, but it is inconsistent with the descriptions that generally accompany such drawings. Typically it is described that a marble or something else representing a satellite will roll along the curved surface and be pulled in towards the gravitating mass. If they were actually using the drawing as "embedding constant time slices in the equatorial plane" then the marble would have an infinite velocity.

 

[Thinker007]

Yes - it's a 'model of gravity' which is driven by gravity. Bound to lead to some problems, isn't it? What would you expect?

For me, the problem with the rubber sheet model lies mostly in the description that accompanies the model. There is typically a confusing assumption that the gravity that made the indentations is also what causes the marble to move along its curved path.

When I use that indented sheet model (and everyone seems to know about it) I like to ask the listener to imagine that the sheet is some sort of plastic surface that was heated, then cooled, so it retains its indented shape. Now I tell them that a toy car is rolled along the surface. The toy car always tries to move straight. Imagine a spring driven toy car that has sticky wheels, and put the whole sheet into outer space - removing the "gravity" that originally caused the sheet to assume its indented shape.

The sticky wheels cause the car to always stay in contact with the surface. Or you can describe an ant crawling "straight" along the sheet surface - but still in a weightless environment. The car or ant or whatever follows the same path as the rolling marble usually referred to in this model, but all this happens without the "gravity" that is so confusing.

Once it becomes clear that it's the shape of the indented sheet that is important to the path of the moving car/ant/marble and not the gravity, the rest of the discussion becomes easier.

 

[pervect]

Thanks for all the replies guys. What I am getting out of all this is that the only way to fully understand it, you got to do the mathematics. Seems like a reoccuring theme haha

Well, the first thing you have to do is understand special relativity. If you jump into trying to understand General Relativity without correctly understanding Special Relativity, you'll wind up very confused.

Once you understand special relativity, a conceptual understanding of GR isn't that hard. The starting point is understanding, conceptually, how the space-time diagrams of SR work,

Space time diagrams represent the very abstract entity called "space-times" by replacing the time dimension with a spatial one, so that we can visualize the abstraction.

Then GR just says that these space-time diagrams can't be drawn properly on a flat sheet ot paper, it must be drawn on a curved sheet of paper.

A proper understanding of "curvature" is a very advanced topic, but I think the basics are intuitive enough that one can get a reasonable conceptual understanding of curvature without too many of the mathematical details.

The surface of the Earth is curved. The surface of a plane is not curved. Just as it's not possible to draw a scale map of the Earth on a flat sheet of paper, it's not possible to draw a scale map of space-time around a large mass on a flat sheet of paper.

And that's pretty much the basics. If you don't understand space-time diagrams well, the illustrations of AT and others about "geodesic deviation" may not make much sense. There are also important issues to understand from SR such as the "relativity of simultaneity", or why there is no universal now.

Though on second thought, understanding "curvature" may be where the difficulty is. It seems natural to understand intrinsic curvature to me by now, but I can imagine someone intuitively undersanding curvature to , for example, always be extrinsic curvature, in which case some of the points would get lost along the way.

A good understanding of curvature requires the Riemann tensor - still, there's a lot one can do by adding up angles of triangles and such, so it may not be hopeless to get a reasonable understanding of curvature without all the math.

 

[ikjyotsingh]

A clarification

That statement may be consistent with the drawings, but it is inconsistent with the descriptions that generally accompany such drawings. Typically it is described that a marble or something else representing a satellite will roll along the curved surface and be pulled in towards the gravitating mass. If they were actually using the drawing as "embedding constant time slices in the equatorial plane" then the marble would have an infinite velocity.

No. It is important to note, that the constant time slices constitute a foliation of the spacetime manifold. The geodesics are not to be considered in this context, as they would be purely space like, which are not physical. The timelike geodesics show that particles necessarily move at less than the speed of light and not infinite velocity.

Also, because of the general problem of manifolds, we can't actually visualize spacetime uniquely. All we can do is visualize spacetime as an embedding in our Euclidean space.

 

[Dale]

The geodesics are not to be considered in this context

But they are, almost without exception.

 

[pervect]

I'm sorry, but the interpretation here is slightly off.

The diagrams you are referring to of planets weighing down and indenting rubber sheets are not an idealization, but an Euclidean space embedding of the Schwarzschild geometry.

Recall, that according to Birkhoff's theorem, any spherically symmetric static solution is necessarily the Schwarzschild solution. Now, from a physical perspective, the Schwarzschild metric models any isolated mass. Any "particle" that enters the gravitational field of this isolated mass moves along a geodesic. With respect to our solar system, the moon moves around a geodesic around the earth, the Earth moves around a geodesic around the Sun, etc.

The embedding diagram comes from embedding the Schwarzschild metric in polar coordinates, precisely, embedding constant time slices in the equatorial plane in polar coordinates. The resulting equation is a paraboloid surface which is the rubber sheet diagram that is commonly shown. Although, because the latter is never explained properly, some think that this diagram is science fiction, and as you can see it is not.

Hope this helps.
Thanks.
Ikjyot Singh Kohli

While the spatial embedding of the Schwarzschild metric is useful for some things (such as how space is distorted by gravity, or perhaps even the "extra" deflection of light), it's not terribly useful for explaining where gravity comes from.

What you'd want, conceptually, to explain gravity would embed the r-t plane, not the r-theta plane.

While such embeddings do exist, see for instance http://arxiv.org/abs/gr-qc/9806123 , Marolf's "Space Time Embedding Diagrams for Black Holes", for pedagogical purposes it is generally simpler to use diagrams such as AT's that illustrate the concept of geodesic deviation without taking care to model the details of the Schwarzschild geometry.

 

[ikjyotsingh]

Corrections and Clarifications

I would like to point out some corrections in your reply.

Well, the first thing you have to do is understand special relativity. If you jump into trying to understand General Relativity without correctly understanding Special Relativity, you'll wind up very confused.
This is actually not true. In fact, learning SR first, can often confuse one as to how GR works. GR should be learned first, and then SR as a "special" case follows quite naturally.


A proper understanding of "curvature" is a very advanced topic, but I think the basics are intuitive enough that one can get a reasonable conceptual understanding of curvature without too many of the mathematical details.
curvature is actually not a very advanced topic at all. Curvature is defined as whether the second derivative of vector fields commute. Take two paths of particles moving in space. If the particles remain parallel to one another throughout their evolution, then the space is flat. If the particle paths diverge or converge due to the geometry of the space alone, the space is curved. One measures the curvature using the Riemann curvature tensor, but the curvature tensor intrinsically employs the aforementioned arguments.

The surface of the Earth is curved. The surface of a plane is not curved. Just as it's not possible to draw a scale map of the Earth on a flat sheet of paper, it's not possible to draw a scale map of space-time around a large mass on a flat sheet of paper.
Well, I'm not sure how good of an example this is. You can't draw a spacetime in general, because, there is no way to visualize a manifold without some type of Euclideam embedding. But, this is visualizing just one neighbourhood of a point in the manifold to Euclidean space.

 

[ikjyotsingh]

Reply

But they are, almost without exception.

Yes, but that doesn't mean they're correct. This is why I always say to study differential geometry before GR. too many people follow Carroll and Weinberg, and think GR can be learned in one shot, like Electromagnetism. The majority of confusions arise because people don't understand the differential geometry well.

 

[ikjyotsingh]

A reply

While the spatial embedding of the Schwarzschild metric is useful for some things (such as how space is distorted by gravity, or perhaps even the "extra" deflection of light), it's not terribly useful for explaining where gravity comes from.
Well, no one really understands where gravity comes from! Nothing in GR explains where gravity comes from. In fact, GR says that gravity is just a manifestation of spacetime curvature.

What you'd want, conceptually, to explain gravity would embed the r-t plane, not the r-theta plane.
Be careful, here. You can't explain gravity using GR. In fact, I assume you're talking about the Schwarzschild vacuum metric still, in that case, the solution is static, so embeddings of the rt plane would look the same in every slice, so this embedding wouldn't tell you anything.

 

[Nugatory]

Be careful, here. You can't explain gravity using GR.

Dunno... I've had a fair amount of success explaining gravity to the satisfaction of my [STRIKE]victims[/STRIKE] explainees using notions of GR and curvature. The two key ideas that mass curves space-time and objects want to travel in a straight line through space-time are not truly explained by GR (or anything else, for that matter) but they're intuitive enough to be readily accepted. And it's easy enough to explain how curvature and straight-line travel in a N-dimensional spacetime can present as a force in the N-1 dimensional space.

 

[ikjyotsingh]

A reply

Dunno... I've had a fair amount of success explaining gravity to the satisfaction of my [STRIKE]victims[/STRIKE] explainees using notions of GR and curvature. The two key ideas that mass curves space-time and objects want to travel in a straight line through space-time are not truly explained by GR (r anything else, for that matter) but they're intuitive enough to be readily accepted. And it's easy enough to explain how curvature and straight-line travel in a N-dimensional spacetime can present as a force in the N-1 dimensional space.

My comment was a reply to the other user of the forum, I meant to say you can't explain the ORIGIN of gravity using GR or anything else. It's not mass that curves space-time rather the existence of mass-energy through the energy-momentum tensor. Objects only travel in a straight line in spacetime for which the christoffel symbols vanish and the geodesic equation becomes trivial. The concept of force (rather the gradient of the gravitational potential) and inertia comes out of the geodesic equation, where the christoffel symbols represent forces. This is the weak equivalence principle.

 

[Dale]

Yes, but that doesn't mean they're correct.

Yes, that is my point. Even if they show a correct graphic the description is not correct.

You seem to think that this is a discussion about embedding diagrams. It is not. It is a discussion about the rubber sheet analogy. Even if the rubber sheet analogy is presented with an accurate graphic of an embedding diagram, it remains a deeply flawed analogy, and the embedding diagram is irrelevant to the analogy.

 

[sophiecentaur]

One of the big problems with thr rubber sheet analogy is that it does not explicitly stress the fact that the object being studied is progressing along a line and not just sitting there, waiting to 'roll in' towards the nearby massive object. The fact that the rubber sheet is a graph of space and time is mostly lost in translation. If those points aren't shouted loud then the analogy is lost.

 

[A.T.]

The fact that the rubber sheet is a graph of space and time...

It isn't. The rubber sheet represent purely spatial geometry.

 

[sophiecentaur]

It isn't. The rubber sheet represent purely spatial geometry.

Really? Then all it can be showing is the effect of a gravitational potential well, albeit with the wrong slope. How can it represent anything about GR if it doesn't include time?
I can't believe it is much use at all if all it does is to show, roughly, how a star will affect the trajectory of a passing planet.

 

[A.T.]

Really?

Well, which of the two sheet dimensions is supposed to be time?

How can it represent anything about GR if it doesn't include time?

Exactly.

 

[1977ub]

Generally a dotted line is drawn to indicate a 2nd object's path, or else it is seen moving in an animation.

 

[pervect]

Be careful, here. You can't explain gravity using GR. In fact, I assume you're talking about the Schwarzschild vacuum metric still, in that case, the solution is static, so embeddings of the rt plane would look the same in every slice, so this embedding wouldn't tell you anything.

I don't quite understand why you say that. While any embedding is ultimately a visual aid or tool, you can learn a lot from this one - see the original paper by Marolf for details. There are simpler illustrations out there, though, which I would continue to reocmmend - the feature that makes Marolf's embedding particularly interesting is that it does model the entire Kruskal geometry (including the Schwarzschild geoemtry as one part), and that it does include time.

 

[sophiecentaur]

It isn't. The rubber sheet represent purely spatial geometry.

I am confused. The rubber sheet model is frequently used in conjunction with discussions about GR, in which it's used to show the concept of "space/time" being distorted in the presence of mass. Which bit of the model represents time and how does the model portray anything other than a 'simple', classical 2D potential well? If time is involved then an animation could be misleading (we don't normally animate simple xy graphs). Perhaps I am just having a problem with interpretation.

 

[pervect]

I am confused. The rubber sheet model is frequently used in conjunction with discussions about GR, in which it's used to show the concept of "space/time" being distorted in the presence of mass. Which bit of the model represents time and how does the model portray anything other than a 'simple', classical 2D potential well? If time is involved then an animation could be misleading (we don't normally animate simple xy graphs). Perhaps I am just having a problem with interpretation.

I think this is a poor representation.

So do most people here.

Add me to the list of people here (many of which are science advisors, and/or PF mentors) who think the diagram is unusually poor.

The reasons for the poorness have mostly been discussed, and a few better alternatives have been mentioned.

So while you may or may not be misinterpreting it, even if you did interpret it correctly, it would, unfortunately, do little to actually aid you in understanding general relativity.

Amongst diagrams I can somewhat recommend are the "parable of the apple", which you can find in http://www.eftaylor.com/pub/chapter2.pdf, which is a publically downloadable chapter from "Exploring Black Holes" by E F Taylor. You can find a similar diagram in Misner, Thorne, and Wheeler's textbook "Gravitation". In fact, you can see it on the front cover :-).

https://www.amazon.com/dp/0716703440/?tag=pfamazon01-20

minus the explanatory text - and unfortunately it doesn't make that much sense without the explanation.

 

[Dale]

The rubber sheet model is frequently used in conjunction with discussions about GR, in which it's used to show the concept of "space/time" being distorted in the presence of mass. Which bit of the model represents time

None.

how does the model portray anything other than a 'simple', classical 2D potential well?

It doesn't.

 

[sophiecentaur]

Well, now I can rest easy at nights chaps.

 

[ikjyotsingh]

Once again, the rubber sheet analogy is ALWAYS used to represent the Schwarzschild solution. It is not used for any other solution in G.R. You can only have an isolated mass bending spacetime in a static, spherically symmetric setting, this spacetime is then asymptotically flat. If you take the Schwarzschild vacuum metric, and take constant time slices and embed that into cylindrical coordinates, you get the equation of a surface, which is a paraboloid, which represents the "dimple" in spacetime that is caused by an isolated mass. Any particle moving in the vicinity of this mass moves along a geodesic assuming there are no non-gravitational forces.

The rubber sheet analogy (which is a mathematically correct analogy), only applies to the Schwarzschild metric.

 

[ikjyotsingh]

Rubber sheet model

I am confused. The rubber sheet model is frequently used in conjunction with discussions about GR, in which it's used to show the concept of "space/time" being distorted in the presence of mass. Which bit of the model represents time and how does the model portray anything other than a 'simple', classical 2D potential well? If time is involved then an animation could be misleading (we don't normally animate simple xy graphs). Perhaps I am just having a problem with interpretation.

Hello. As I explained in my other post, the rubber sheet model is not a general model in G.R., and is a visualization of only ONE solution in G.R., a solution that is static and spherically symmetric, that is, it has one time-like and 3 space-like Killing vectors, and by Birkhoff's theorem, this can only be the Schwarzschild metric.

Time plays no role in THIS class of solutions, as the solution is static, and asymptotically flat, more precisely, it is time-symmetric.

In general, you cannot show the concept of spacetime, as spacetime is a 4D pseudo-Riemannina manifold, these are impossible to visualize in the way we are used to visualizing geometry. You must embed these manifolds in Euclidean geometry to get a good visualization of them.

Also, more generally, the idea of evolving a spacetime in time is not trivial, the whole field of numerical relativity and 3+1 dynamical relativity is built upon this. One must essentially break apart the space-time symmetry to consider a foliation of spatial slices moving in time. It is how the curvature of those spacelike slices evolve in "time" that determine the dynamics of the model. In the Schwarzschild/rubber sheet visualization, each spatial slice is constant in time, which is what you would expect.

Hope this helps.
Ikjyot Singh Kohli

 

[ikjyotsingh]

It is about embedding diagrams

Yes, that is my point. Even if they show a correct graphic the description is not correct.

You seem to think that this is a discussion about embedding diagrams. It is not. It is a discussion about the rubber sheet analogy. Even if the rubber sheet analogy is presented with an accurate graphic of an embedding diagram, it remains a deeply flawed analogy, and the embedding diagram is irrelevant to the analogy.

This is a discussion about embedding diagrams, no one seems to realize it, that's why there is so much confusion! The rubber sheet analogy which is an Euclidean embedding of the Schwarzschild vacuum metric only applies in this metric. You cannot have the rubber sheet analogy in any other context in G.R. It only applies for a static, spherically symmetric, vacuum, and asymptotically flat metric. Embed the S-metric into Euclidean space and you get the rubber sheet, there is simply no other context in G.R. which can produce the rubber sheet analogy.

The Schwarzschild solution, perhaps due to the prediction of black holes is the most popular solution in G.R. (other than FLRW), that's why these rubber sheet diagrams have taken on so much momentum, but they only apply in the S-metric case.

The idea then, is not flawed at all, and the embedding diagram is where the analogy comes from!

 

[Dale]

This is a discussion about embedding diagrams, no one seems to realize it, that's why there is so much confusion! The rubber sheet analogy which is an Euclidean embedding of the Schwarzschild vacuum metric only applies in this metric. You cannot have the rubber sheet analogy in any other context in G.R. It only applies for a static, spherically symmetric, vacuum, and asymptotically flat metric. Embed the S-metric into Euclidean space and you get the rubber sheet, there is simply no other context in G.R. which can produce the rubber sheet analogy.

The Schwarzschild solution, perhaps due to the prediction of black holes is the most popular solution in G.R. (other than FLRW), that's why these rubber sheet diagrams have taken on so much momentum, but they only apply in the S-metric case.

The idea then, is not flawed at all, and the embedding diagram is where the analogy comes from!

A rubber sheet supporting a weight doesn't deform into Flamm's paraboloid. It deforms approximately into a gravity well. The rubber sheet analogy is simply not an embedding diagram of any spacetime, even the Schwarzschild spacetime.

 

[ikjyotsingh]

Rubber shet

A rubber sheet supporting a weight doesn't deform into Flamm's paraboloid. It deforms approximately into a gravity well. The rubber sheet analogy is simply not an embedding diagram of any spacetime, even the Schwarzschild spacetime.

Anything supporting a mass in G.R. necessarily deforms into Flamms' paraboloid. I have a challenge for you then, in this regard. Find a solution of the Einstein Field equations that supports a mass other than the S-metric!

 

[Dale]

Anything supporting a mass in G.R. necessarily deforms into Flamms' paraboloid.

No, that is not true. A spring supporting a mass certainly doesn't even remotely deform into a Flamms paraboloid. On the surface of the Earth where the weak field limit is appropriate a rubber sheet deforms to first order into a Newtonian potential well, not a Flamm's paraboloid. Here is an explanation:

http://en.wikipedia.org/wiki/Gravity_well#The_rubber-sheet_model

I have a challenge for you then, in this regard. Find a solution of the Einstein Field equations that supports a mass other than the S-metric!

The point is that the deformation in a rubber sheet is not a solution to the EFE.

 

[ikjyotsingh]

Rubber Sheet model

No, that is not true. A spring supporting a mass certainly doesn't even remotely deform into a Flamms paraboloid. On the surface of the Earth where the weak field limit is appropriate a rubber sheet deforms to first order into a Newtonian potential well, not a Flamm's paraboloid. Here is an explanation:

http://en.wikipedia.org/wiki/Gravity_well#The_rubber-sheet_model

The point is that the deformation in a rubber sheet is not a solution to the EFE.

How would you even model a spring supporting a mass in T_{ab}? I don't know what that has to do with anything.

So, according to your wikipedia article, spacetime is being modeled by a physical rubber sheet, of course that's nonsense. In all my years of studying G.R., I have never considered "rubber sheet" to mean an actual rubber sheet. This won't work in general, but not for the reasons listed in this forum thus far. The deformations in the rubber sheet are given by the Poisson's equation which is a second-order ELLIPTIC partial differential equation. Such PDEs are acausual and thus would not exist in a pseudo-Riemannian manifold. This is actually why the rubber sheet analogy considering an actual, physical rubber sheet would fail.

 

[Dale]

So, according to your wikipedia article, spacetime is being modeled by a physical rubber sheet, of course that's nonsense. In all my years of studying G.R., I have never considered "rubber sheet" to mean an actual rubber sheet.

Many people get fooled by that nonsense. I am glad that you weren't, but that is why we get so many questions here on this topic.

 

[EskWIRED]

Here is a youtube video from someone who took the effort to do a more reasonable job. We could poke holes in this one also, but at least he saw the problems with the standard explanations and tried to do a better job. I think he succeeded.

I like what he did.

I've been wanting to see an interactive program that would allow you to draw such an array. Ideally, it would allow you to alter the "mass" and the size of the center attractor, and to see the effect on the gridlines due to the changes.

Even better would be the ability to add another, small mass, and see it go into orbit (or not) depending on its velocity and direction. I'd love to model black holes using software like that.

 

[1977ub]

Isn't it a bit misleading for all [not all but most] of the video's captions to refer to "space" as being curved by gravity? After all, it is not objects which are distorted or bent by the presence of the planet, but space-TIME which is curved, inclining freely *moving* objects to veer toward the Earth unless held aloft.


"...space all around an object is bent...space is bent toward the objects..."

 

[A.T.]

I am confused. The rubber sheet model is frequently used in conjunction with discussions about GR, in which it's used to show the concept of "space/time" being distorted in the presence of mass.

The rubber sheet with dents in conjunction with GR shows just the spatial distortion described by the Schwarzshild metric. It looks similar to potential wells:

http://en.wikipedia.org/wiki/Gravity_well#Gravity_wells_and_general_relativity

But it has nothing to do with them. The spatial curvature is irrelevant to objects at rest in space, like an apple that starts to fall.

 

[stevendaryl]

I agree with you 100% They are doing exactly what you say. They are explaining gravity in term of gravity. It’s stupid, annoying, and does not explain anything.

I don't think it's that bad. The trampoline model works like this: You have a bowling ball sitting on a trampoline, causing the trampoline's surface to become warped, so it's no longer flat. Then you roll a marble across the surface of the trampoline. Its path isn't straight, but is curved.

General Relativity can be thought of as describing two different effects: (1) How does matter and energy affect spacetime curvature, and (2) How does spacetime curvature affect the motion of particles (and more generally, other non-gravitational physical phenomena)? The trampoline model helps to understand effect number (2), but not effect number (1). As far as I know, there is no help for understanding effect number (1).

The part that too me is the hardest to understand from the trampoline model is that in GR, the warping is to spacetime, not space alone.