# My problem with the relativity representation on gravity.

1. Mar 11, 2013

### 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, lets 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?

2. Mar 11, 2013

### 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.

3. Mar 11, 2013

### 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.

4. Mar 12, 2013

### MikeGomez

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.

Last edited by a moderator: Sep 25, 2014
5. Mar 12, 2013

### ZapperZ

Staff Emeritus
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.

6. Mar 12, 2013

### ModusPwnd

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

7. Mar 12, 2013

### sophiecentaur

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

And where does the "pushing' come from?

8. Mar 12, 2013

### Staff: Mentor

So do most people here.

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

9. Mar 12, 2013

### ModusPwnd

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...

10. Mar 12, 2013

### Staff: Mentor

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.

Last edited: Mar 12, 2013
11. Mar 12, 2013

### 1977ub

12. Mar 12, 2013

### Staff: Mentor

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.

13. Mar 12, 2013

### A.T.

Here the animated version:

14. Mar 12, 2013

### jaydnul

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

15. Mar 12, 2013

### A.T.

16. Mar 12, 2013

### 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

17. Mar 12, 2013

### Staff: Mentor

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.

18. Mar 12, 2013

### Thinker007

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.

19. Mar 12, 2013

### pervect

Staff Emeritus
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 cant 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.

20. Mar 12, 2013

### ikjyotsingh

A clarification

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.

21. Mar 12, 2013

### Staff: Mentor

But they are, almost without exception.

22. Mar 12, 2013

### pervect

Staff Emeritus
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.

23. Mar 12, 2013

### ikjyotsingh

Corrections and Clarifications

24. Mar 12, 2013