Bowling ball rubber sheet analogy

[A.T.]

GR is based on geometric concepts like geodesics and intrinsic curvature, which can be easily visualized and understood on 2D manifolds. The extension to 4D is not necessary for simple examples like movement along one space dimension, which are sufficient to explain how geodesics and intrinsic curvature imply what we perceive as mass attraction.

Is GR based on 4D objects or not?

In general yes, but for specific cases 2D is sufficient, which allows visualization.

 

[altonhare]

In general yes, but for specific cases 2D is sufficient, which allows visualization.

Is the universe, or anything that exists, 2D?

 

[A.T.]

Is the universe, or anything that exists, 2D?

Depends on the meaning of 'exists', but I'm not interested in philosophical discussions.

 

[DrGreg]

Is GR based on 4D objects or not?

Of course, GR is 4D, but there are some situations where all the relevant information is contained within a 2D cross-section -- in the same way that some aspects of Euclidean geometry can be understood in two dimensions only.

I have studied N-dimensional vector spaces, not only when N is finite and greater than 3, but even when N is infinite. And I used my geometrical intuition to help me. Concepts like orthogonality and "length" still make sense in higher dimensions -- as coordinate-independent concepts -- and a geometrical picture can help you cope with such concepts. (For example, to find the distance between a point and a hyperplane, drop a perpendicular.) Of course, you have to back up your intuition with rigorous calculation, but the geometrical picture is still a big help in getting to grips with the subject. The trick, which comes with experience, is to know which concepts generalise to higher dimensions and which don't.

Remember GR is a model of reality, it is not reality itself. In circumstances where a 2D model gives the same answer as a 4D model (because the other two dimensions are irrelevant), by all means use the simpler 2D model which is easier to visualise.

 

[altonhare]

Depends on the meaning of 'exists', but I'm not interested in philosophical discussions.

the scientific definition: shape and location

Done, as far as science is concerned. In philosophy they can go on and on all they want.

DrGreg just reiterated what I said, that visualizations are merely models we use to help guide our intuition. Sometimes they extend and sometimes they don't. But the fact is you can't visualize 'a' 4D "object" anymore than you can visualize 'a' 1D "object". DrGreg mentioned calculations, the argument here, in this thread, is about visual analogies. I'm saying you cannot understand GR through visualization or any visual analogy because you cannot visualize a single "object" of GR.

 

[A.T.]

DrGreg just reiterated what I said, that visualizations are merely models we use to help guide our intuition.

No, he said that GR itself is a model of reality, and not only the visualizations. And I fully agree with that. He also agrees that 2D models in GR are sufficient for some cases, which is exactly what I have been saying, and you have been disputing.

I'm saying you cannot understand GR through visualization or any visual analogy, because you cannot visualize a single "object" of GR.

Of course I can. The worldline of a point particle that is moving along a line in space has no extension in the other two space-dimensions. It can be easliy visualized in a 2D diagram.

 

[altonhare]

Of course I can. The worldline of a point particle that is moving along a line in space has no extension in the other two space-dimensions. It can be easliy visualized in a 2D diagram.

You fooled yourself. All objects of GR, whatever their "extent" in any direction, are embedded in a "4D space" without exception. Indeed, it is the "space" in which an object is embedded that distinguishes one geometric theory from another! Therefore, to dispose of the "4D space" in which the "object" moves is to dispose of whatever theory you were talking about in the first place.

 

[A.T.]

You fooled yourself. All objects of GR, whatever their "extent" in any direction, are embedded in a "4D space" without exception.

So everyone who uses 2D-space-time diagrams, even in classical mechanics, is fooling himself, by omitting the other two space-dimensions? Thanks for the enlightenment. .

Indeed, it is the "space" in which an object is embedded that distinguishes one geometric theory from another! Therefore, to dispose of the "4D space" in which the "object" moves is to dispose of whatever theory you were talking about in the first place.

Omitting elements of a model, which don't affect the result in a particular case is not equal to "disposing the theory".

 

[altonhare]

Of course I can. The worldline of a point particle that is moving along a line in space has no extension in the other two space-dimensions. It can be easliy visualized in a 2D diagram.

I should also question whether you can visualize this "point particle". I believe they are defined as having "0 extent" i.e. they are 0D. This alone renders this supposed "visualization" meaningless.

So everyone who uses 2D-space-time diagrams, even in classical mechanics, is fooling himself, by omitting the other two space-dimensions? Thanks for the enlightenment. .



Omitting elements of a model, which don't affect the result in a particular case is not equal to "disposing the theory".

If they are visualizing a 2D image but think they are visualizing a 3D image, then yes they are fooling themselves.

Omitting elements of a model may not affect the results quantitatively but we're not talking about that! We're talking about if we can visualize the physical components of the theory itself.

So far we have.

Point particles which look like this:

4D space-time that looks like this:

 

[A.T.]

I should also question whether you can visualize this "point particle".

I was talking about the worldline of a point particle.

I believe they are defined as having "0 extent" i.e. they are 0D. This alone renders this supposed "visualization" meaningless.

Please, go explain to the mathematicians not to visualize points as dots anymore, because it makes their diagrams meaningless and they "are fooling themselves".

Omitting elements of a model may not affect the results quantitatively but we're not talking about that!

Well I don't know what you are talking about. But I am talking about visualizing those parts of the model that affect the results in a particular case. Why should I visualize irrelevant stuff?

 

[altonhare]

I was talking about the worldline of a point particle.Please, go explain to the mathematicians not to visualize points as dots anymore, because it makes their diagrams meaningless and they "are fooling themselves". Well I don't know what you are talking about. But I am talking about visualizing those parts of the model that affect the results in a particular case. Why should I visualize irrelevant stuff?

The 4D space in which events occur in a theory is irrelevant to visualizing what is happening in the theory!?

 

[A.T.]

Well I don't know what you are talking about. But I am talking about visualizing those parts of the model that affect the results in a particular case. Why should I visualize irrelevant stuff?

The 4D space in which events occur in a theory is irrelevant to visualizing what is happening in the theory!?

Some dimensions of the 4D spacetime are irrelevant in some cases. What is so hard to grasp about this for you? 2D diagrams in classical mechanics are also omitting one irrelevant space dimension:

 

[altonhare]

And are you visualizing an explanation involving 2 dimensions or 3?

 

[A.T.]

And are you visualizing an explanation involving 2 dimensions or 3?

Where?

 

[Naty1]

Is the universe, or anything that exists, 2D?

How about a holographic universe. Or a black hole event horizon.

 

[altonhare]

Where?

The diagram in your post. Is this an illustration in 2D or 3D?

How about a holographic universe. Or a black hole event horizon.

How about a unicorn or a gargoyle?

 

[A.T.]

The diagram in your post. Is this an illustration in 2D or 3D?

It is obviously a 2D diagram, that omits one space dimension. Is it therefore "meaningless" and using it is "fooling yourself"?

 

[altonhare]

It is obviously a 2D diagram, that omits one space dimension. Is it therefore "meaningless" and using it is "fooling yourself"?

If you think you are visualizing a 3D image then, yes, you are fooling yourself. GR, first and foremost, takes place in 'a' 4D space-time. This is the central hypothesis. You cannot visualize the fundamental hypothesis of the theory and so only visualize the theory through analogy and metaphor.

 

[Mentz114]

If you think you are visualizing a 3D image then, yes, you are fooling yourself. GR, first and foremost, takes place in 'a' 4D space-time. This is the central hypothesis. You cannot visualize the fundamental hypothesis of the theory and so only visualize the theory through analogy and metaphor.

Learn some maths. I can calculate the radial geodesics in a spherical spacetime in 2D - completely ignoring the angular dimensions and get correct results ( agreeing with experiment). Reducing the dimensions in a physically meaningful way is not 'visualising' or 'fooling' anyone.

 

[A.T.]

It is obviously a 2D diagram, that omits one space dimension. Is it therefore "meaningless" and using it is "fooling yourself"?

If you think you are visualizing a 3D image then, yes, you are fooling yourself.

What I think is, that the 2D diagram visualizes the relevant space dimensions of the trajectories.

GR, first and foremost, takes place in 'a' 4D space-time. This is the central hypothesis.

4D space-time was already introduced Minkowski to visualize SR. And guess what, he used 2D diagrams too. The central hypothesis of GR is that the 4D space-time is curved and that free fallers have geodesic world lines. This are mathematical concepts which can be explained in lower dimensional spaces easily.

You cannot visualize the fundamental hypothesis of the theory and so only visualize the theory through analogy and metaphor.

But I don't want to visualize the hypothesis, just particular applications of it. People want to understand why apples are falling from trees. And in such particular cases irrelevant dimensions can be often omitted allowing visualization.

 

[Pete62]

altonhare,

I don't understand why you are being so obstinate. As a layman trying to grasp GR I have found the 2D and 3D visualizations to be not just valuable but required to understanding the subject. I simply could not get it until I tossed out 2 space dimensions and focused on a 2D Time-space coordinate system. Emphasis on time.

BTW, the rubber sheet analogy was worse than useless, it set me back years. I kept imagining space as having an intrinsic pressure created by mass curvature and that is what created the force of gravity.

 

[jefswat]

If they are visualizing a 2D image but think they are visualizing a 3D image, then yes they are fooling themselves.

So if I see something in 2D like, for example, the eraser in my hand and see only height and width from a certain angle, your reasoning leads me to conclude that because I see it in 2D I am fooling myself by thinking it is really 3D

Your argument is clearly flawed, direct substituion with my eraser:

If they are visualizing a [2D eraser] (from the side view as per example) but think they are visualizing a [3D eraser], then yes they are fooling themselves

I believe that is what A.T is trying to get at. because I do not see the length of my eraser it doesn't mean it isn't there. And not seeing the length certainly won't affect my answer,for example, of the area calculation for the side with width and height. As for the bowliverse I have no contribution to make to that argument ... .............. Preserve the bowliverse!

 

[Edwin McCravy]

The guy who first used it to explain GR should be stoned with bowling balls.

The problem is with words. The person who should have been stoned with bowling balls was the first guy to have ever used the word "curve" to describe gravitational behavior. All it did was confuse the lay public. Other language would have expressed it much better. For instance, "distort" would have been a better word.

 

[Pieroz]

OK, I am completely new here and have millions of questions lodged in my head and have had trouble finding an appropriate place to discuss them and am hoping that I finally have, LoL... but today I just have a quick question in relation to the GP-B Probe apparently having proven parts of Einsteins theory...

I think I have grasped the whole idea - but when looking at the diagrams and animations etc I find myself wondering why it is not shown to be surrounding the entire Earth in the same manner? as in 360 degrees? Surely this "dimple" would be surrounding the space around the Earth itself and not just around the south pole?

I suppose I am arguing that a flat rubber sheet certainly does not represent open space as the planets etc are not actually sitting on anything... From what I understand the space time is a dimple around the Earth not just beneath it - and that the Earth does not actually rest upon or within the dimple but simply creates it around the Earth...

Also do you think they will manage to measure the actual size of the Earth space-time vortex and hence be able to calculate similar for the rest of our solar system?

 

[Naty1]

I would point out this thread is over two years old now...funny, because I barely expected any reply when I posted it Feb 2009!

 

[Edwin McCravy]

I've responded to older posts than yours. Sooner or later somebody is bound to Google most any topic you post and respond to it, even if it takes two years.

 

[nitsuj]

agreed physics moves much slower lol