Bowling ball rubber sheet analogy

[Naty1]

The typical rubber sheet bowling ball analogy to "explain" gravity visually in layman's terms always seems to be two space dimensions. Why don't we use one dimension of space and the other of time? Both are curved by mass and everybody takes Eucledean/Cartesian type flat graphs of, say, x and t as a matter of course. Is it too much to imagine such a traditional layout deformed/curved? Or is there a fundamental flaw in an x,t curved representation that is worse than the typical representation?

 

[Desh627]

The typical rubber sheet bowling ball analogy to "explain" gravity visually in layman's terms always seems to be two space dimensions. Why don't we use one dimension of space and the other of time? Both are curved by mass and everybody takes Eucledean/Cartesian type flat graphs of, say, x and t as a matter of course. Is it too much to imagine such a traditional layout deformed/curved? Or is there a fundamental flaw in an x,t curved representation that is worse than the typical representation?

Your key word there is "layman."

While your examples may very well work, the majority of laymen haven't taken any physics outside of high school physics, and many others barely squeaked by in high school with a C in algebra 2/trig. Those people won't remember/care what a Cartesian graph is.

We use the bowling ball/rubber sheet explanation to give these people a clear picture of what we're trying to explain. The easier it is for you to break something down to a fundamental level, the more likely you are to communicate what you're trying to say.

I gave a lecture on Tuesday on an Introductory Quantum Mechanics course I'm taking, and my audience was a bunch of high school freshmen and sophomores who were only there because their teacher was offering them extra credit for attending. Because of this I could only graze over a lot of the more intense linear algebra (e.g. infinite dimensional vector spaces, operators and commutators, etc.) in order to keep things on a level that they could understand. I learned after the first proof I gave (simple normalization of psi) that no one understood it, and that I had to keep things simple in order for them to kind of get the gist of what I was saying.

Moral of the story: keep it simple, or else your audience won't understand.

 

[MikeLizzi]

With all due respect to those trying to offer some simple analogy into a very complicated subject, I don’t think the rubber sheet analogy works.

The problem I have with the rubber sheet analogy is that it appears to be more appropriate for the Newtonian theory of gravity. I’ve used it that way. The depth that a single bowling ball sinks is proportional to its Newtonian gravitational force. The changing depth of the sheet around the ball demonstrates the force field gradient perfectly. The depth around multiple balls demonstrates force field superposition. The direction the balls move demonstrates Euclidian vector addition. Etc. Etc. Etc. As far as I can tell, it demonstrates nothing about the unique characteristics of general relativity.

Intelligent laymen, having pondered the rubber sheet analogy, conclude that general relativity is nothing more that a different way of describing Newton’s theory. That's not good.

 

[A.T.]

The typical rubber sheet bowling ball analogy to "explain" gravity visually in layman's terms always seems to be two space dimensions. Why don't we use one dimension of space and the other of time?

It has been done:
http://www.relativitet.se/spacetime1.html
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.adamtoons.de/physics/gravitation.swf

Or is there a fundamental flaw in an x,t curved representation that is worse than the typical representation?

Well, you have only one space dimension so you cannot visualize how circular orbits work. Just linear free fall, along the radial coordinate.

We use the bowling ball/rubber sheet explanation to give these people a clear picture of what we're trying to explain.

It is not a clear picture. It confuses people, who really try to understand how mass attraction is explained by GR. The space curvature represented by the bowling ball/rubber sheet has only marginal effects (greater light bending, orbit precession) most laymen don't even know about. What they know are apples falling from trees, and the bowling ball/rubber sheet analogy doesn't explain this.

Intelligent laymen, having pondered the rubber sheet analogy, conclude that general relativity is nothing more that a different way of describing Newton’s theory. That's not good.

I second that. Rubber sheets are good to represent Newtonian gravitational potential. Not to explain GR:
http://en.wikipedia.org/wiki/Gravity_well#Gravity_wells_and_general_relativity

 

[feynmann]

The typical rubber sheet bowling ball analogy to "explain" gravity visually in layman's terms always seems to be two space dimensions. Why don't we use one dimension of space and the other of time? Both are curved by mass

Actually, to "explain" gravity, curved time only suffice. The curvature of space is very small in the solar system. It's almost flat, about 10^-8. That's why it took 100-year observation to find out something is wrong with the Mercury orbit. Since the perihelion shift of Mercury is just too small.
In his book, Gravity from the Ground Up, Schutz says, "All of Newtonian gravitation is simply the curvature of time".

Link from the book "Gravity from the Ground Up" by Schutz
http://www.gravityfromthegroundup.org/pdf/timecurves.pdf

 

[Naty1]

AT: thanks in particular for the three "IT HAS BEEN DONE"...I have seen #3, but forgot about it...

 

[Naty1]

As far as I can tell, it demonstrates nothing about the unique characteristics of general relativity.

well of course it does: it gives "first look" for many at what curved spacetime means...if that's as far as it goes, it's a useful little tool...all one has to do is to think that the sheet deforms in the presence of the ball rather than due to it's direct contact weight to get a slight feel for curved space. And of course it's use like any analogy or simplified explanation requires constraints.

In any case, I was not trying to advocate anything here one way or another, just wondering.

 

[A.T.]

to get a slight feel for curved space. And of course it's use like any analogy or simplified explanation requires constraints.

The main problem is that curved space alone doesn't explain gravity in sense of mass attraction. The layman wants to know, why apples are falling from trees (time curvature). And instead he gets served effects like orbit precession (space curvature), which he cannot observe himself.

 

[Naty1]

The main problem is that curved space alone doesn't explain gravity in sense of mass attraction.

I don't think that's necessarily so: for example if one pictures a bowling ball already depressing a rubber sheet and then a marble being introduced with some velocity at the edge of the depression, it's possible to visualize how "curved/depressed space" causes the marble to orbit the bowling ball...yes it's imperfect, the question is whether it's better than no visualization at all.

 

[A.T.]

I don't think that's necessarily so: for example if one pictures a bowling ball already depressing a rubber sheet and then a marble being introduced with some velocity at the edge of the depression, it's possible to visualize how "curved/depressed space" causes the marble to orbit the bowling ball.

That's all very nice, but not a visualization of general relativity, but rather Newtonian gravitation with the rubber sheet representing the field potential. The Newtonian force is the negative gradient of this potential and points to the steepest descent, where the marble is also accelerated towards.

Where is GR here? Where are geodesics? People already familiar with Newton will ask "What's new about this? Where is the difference?"

yes it's imperfect, the question is whether it's better than no visualization at all.

I'm very in favor of visualizations, but the right ones, that make sense to the thinking laymen too. I posted links to examples above.

 

[MikeLizzi]

I would like to make a partial concession to Naty1 and admit that the rubber sheet analogy does have some use. It was the first example I ever saw that suggested that the consequences of gravity could come from some kind of distortion in the space between masses.

But I still think of it as a good visual aid for Newton's gravity. For general relativity, I only "got it" last year, when I saw the the example posted by A.T.

 

[feynmann]

I would like to make a partial concession to Naty1 and admit that the rubber sheet analogy does have some use. It was the first example I ever saw that suggested that the consequences of gravity could come from some kind of distortion in the space between masses.

But I still think of it as a good visual aid for Newton's gravity. For general relativity, I only "got it" last year, when I saw the the example posted by A.T.

It's incorrect to say "the consequences of gravity could come from some kind of distortion in the space between masses". It comes from the "curvature of time".

All of Newtonian gravitation is simply the curvature of time.
http://www.gravityfromthegroundup.org/pdf/timecurves.pdf

 

[MikeLizzi]

It's incorrect to say "the consequences of gravity could come from some kind of distortion in the space between masses". It comes from the "curvature of time".

All of Newtonian gravitation is simply the curvature of time.
http://www.gravityfromthegroundup.org/pdf/timecurves.pdf

Thanks feynmann. So I guess I got the wrong idea from the rubber sheet analogy. At this point, someone could tell me gravity is like an ice cream cone and all I could say is "Wow".

 

[A.T.]

At this point, someone could tell me gravity is like an ice cream cone and all I could say is "Wow".

http://www.relativitet.se/spacetime1.html" .

 

[altonhare]

I think, with regards to the "rubber sheet" analogy, we're all missing the elephant in the room. This analogy is meaningless because it uses gravity to explain gravity. The ball pushes "downward" (whatever that actually means) on the rubber sheet only because there is something else under the sheet pulling on the ball.

This analogy is so flawed it is rendered meaningless, it's not only circular but also acausal.

 

[A.T.]

I think, with regards to the "rubber sheet" analogy, we're all missing the elephant in the room. This analogy is meaningless because it uses gravity to explain gravity.

We are not missing it. It has been https://www.physicsforums.com/showpost.php?p=2042081&postcount=7".

The ball pushes "downward" (whatever that actually means) on the rubber sheet only because there is something else under the sheet pulling on the ball.

For explaining space curvature via embedding the "bump" should be shown going up, to prevent people getting the wrong idea.

This analogy is so flawed it is rendered meaningless, it's not only circular but also acausal.

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

 

[nickyrtr]

Maybe the rubber sheet cartoon is not completely hopeless at representing GR.

First, it can manifest the propagation of gravity waves, if the rubber is floppy enough. Wobble the bowling ball around somewhat briskly, and the disturbance propagates outward in finite time, unlike the instantaneous reaction that Newtonian gravity would predict.

It might also demonstrate the precession of apsides for Mercury. The shape formed by the stretched rubber funnel around the bowling ball is not exactly a cone; the heavier the bowling ball, the less conical it will be. Therefore orbits of a marble rolling around the funnel will not quite be conic sections, i.e. the extrema of a nearly-elliptical orbit in the funnel will precess.

 

[altonhare]

We are not missing it. It has been https://www.physicsforums.com/showpost.php?p=2042081&postcount=7".

Nobody mentioned it in this particular thread, and it's the most obvious reason why the "rubber sheet" interpretation is wrong.

For explaining space curvature via embedding the "bump" should be shown going up, to prevent people getting the wrong idea.

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

Yes s/he should. The "bump" going up doesn't fix anything. Now why does the marble "fall" toward the bowling ball?

 

[A.T.]

For explaining space curvature via embedding the "bump" should be shown going up, to prevent people getting the wrong idea.

The "bump" going up doesn't fix anything. Now why does the marble "fall" toward the bowling ball?

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_spacetime.html" can be used to visualize the curvature of space, not spacetime. There is no bowling ball or marbles involved. It explains minor effects, but not mass attraction.

 

[A.T.]

It might also demonstrate the precession of apsides for Mercury. The shape formed by the stretched rubber funnel around the bowling ball is not exactly a cone;

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_space2.gif"

 

[altonhare]

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_spacetime.html" can be used to visualize the curvature of space, not spacetime. There is no bowling ball or marbles involved. It explains minor effects, but not mass attraction.

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_spacetime.html" can be used to visualize the curvature of space, not spacetime. There is no bowling ball or marbles involved. It explains minor effects, but not mass attraction.

So we are visualizing some curved "thing" around an object. Now, why does the other object move toward it?

In the rubber sheet analogy the object falls down the curved surface of this "space object". But the effect we're trying to explain is what we observe as "falling down". So we observe that objects "fall down" to Earth and the rubber sheet analogy says that yes, objects do indeed "fall down" toward each other. See? What the ball "fall down".

The analogy is just plain worthless. The reason GR correctly correlates Mercury's orbit is because "time dilation" contributes +4BF, "space contraction" contributes -2BF, and momentum increase (with increasing speed) contributes +1BF giving the observed amount, 3BF. BF is the "basic form" for describing elliptical motion: n*u/(c²*a*(1-e²)) where n=2*pi/P is the orbital mean motion of the planet, P is its orbital period, u is the product of the gravitational constant and the mass of the Sun (in the case of Mercury), a is the semi-major axis (mean distance) of the orbit, e is orbital eccentricity, and c = speed of light. Of course Einstein was aware that Mercury's orbit is 3 integer multiples of this formula (within experimental error) and adjusted the metrics accordingly.

Of course this is not very good for the layman, but the rubber sheet analogy is either patronizing or disinformative. Worst of all it may be deceptive, making the layman believe GR has a physical interpretation when it is just an excellent quantitative description.

Don't use the rubber sheet analogy, let it die, it's awful. If you want to understand GR start with Newton and move forward, reading as much of the original work as you can get your hands on. These cartoons inhibit understanding and sometimes move it backwards, don't do yourself the disservice. To understand GR you need math, because GR is a mathematical theory. You can't understand GR by visualization, no matter how hard popularizers of the theory try to do so. Every visual analogy suffers fatal flaws that render it meaningless.

 

[A.T.]

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_spacetime.html" can be used to visualize the curvature of space, not spacetime. There is no bowling ball or marbles involved. It explains minor effects, but not mass attraction.

So we are visualizing some curved "thing" around an object

Not some curved thing but the spatial curvature and its effects like orbit precession.

Now, why does the other object move toward it?

If you mean Newtonian mass attraction: Purely spatial curvature doesn't explain it. You need the time dimension like http://www.relativitet.se/spacetime1.html" .

To understand GR you need math, because GR is a mathematical theory.

Every physical theory uses math. But GR is also a geometrical theory.

You can't understand GR by visualization, no matter how hard popularizers of the theory try to do so. Every visual analogy suffers fatal flaws that render it meaningless.

I disagree. Visualization is very useful to understand geometrical theories. Einstein wouldn't have come up with GR, if Minkowski had not visualized SR.

 

[nickyrtr]

...Worst of all it may be deceptive, making the layman believe GR has a physical interpretation when it is just an excellent quantitative description. [...] To understand GR you need math, because GR is a mathematical theory. You can't understand GR by visualization, no matter how hard popularizers of the theory try to do so. Every visual analogy suffers fatal flaws that render it meaningless.

That seems a rather bold assertion, that GR shall never be explained on physical grounds that can be visualized. Maybe not bowling balls and a rubber sheet, but perhaps some visual model not yet known to us will one day let high school students learn mathematically correct GR in their honors Physics courses.

 

[altonhare]

"Not some curved thing" -AT

Okay so space is not a thing. The "space" in GR is just a useful parameter in the equations, not a physical thing. Things are visualizable, non-things are not visualizable.

"Every physical theory uses math" -AT

Only at the conclusion step of the sci meth, if at all. Mathematical correlations are just additional evidence at the end to convince everyone else of your theory. The first step we do in physics is visualize the physical entity(ies) involved. If we cannot visualize them, the theory is not a physical explanation, it's a mathematical model.

"But GR is also a geometric theory" -AT

Geometry is the study of shape. But GR's "space" and "time" are not things with shape, they are just concepts. Einstein may have guided his intuition by visualization, but his theory has nothing to do with geometry if space and/or time are not things.

nick,

GR is based on 4D "objects". I am saying that nobody will ever visualize a 4D "object". This alone renders GR only physically comprehensible by analogy, and we call it an "analogy" for a reason, it never quite matches "the real thing".

 

[A.T.]

The "space" in GR is just a useful parameter in the equations, not a physical thing. Things are visualizable, non-things are not visualizable.

Everyone got that memo? We are not allowed to use diagrams to visualize space-time anymore!

GR is based on 4D "objects". I am saying that nobody will ever visualize a 4D "object". This alone renders GR only physically comprehensible by analogy, and we call it an "analogy" for a reason, it never quite matches "the real thing".

If something moves along a line in space, you can omit 2-space dimensions, and visualize a 2D-spacetime. Works fine for me, and you don't have to use it, if you don't like it.

 

[altonhare]

Everyone got that memo? We are not allowed to use diagrams to visualize space-time anymore!

If something moves along a line in space, you can omit 2-space dimensions, and visualize a 2D-spacetime. Works fine for me, and you don't have to use it, if you don't like it.

Are you reading your own posts? You just said it was NOT some curved "thing". Things people can visualize, non-things people cannot visualize.

Are you reading carefully? Omitting 2 space dimensions reduces the problem to an analogy. Just like putting a stick figure on a sphere. It's just an analogy. If it were the "real thing" it wouldn't be an analogy and we'd be able to visualize "the real thing".

Go ahead, show us 'a' 4D space-time?

 

[A.T.]

Are you reading carefully? Omitting 2 space dimensions reduces the problem to an analogy. Just like putting a stick figure on a sphere. It's just an analogy. If it were the "real thing" it wouldn't be an analogy and we'd be able to visualize "the real thing".

I guess you just disagree with my usage of the term "visualization", and would like me to use "analogy" or "geometric interpretation" instead?

 

[altonhare]

I guess you just disagree with my usage of the term "visualization", and would like me to use "analogy" or "geometric interpretation" instead?

The only time a visualization equals understanding is if you can visualize what you are trying to understand. If you are trying to understand GR, and GR is based on 4D entities, then you cannot visualize nor by extension understand GR through visualization. When we visualize a stick figure on a rubber sheet with depressions in it and stick figures "living" on/in it we are not understanding GR. We are understanding a theory about Flatland at *best*.

 

[A.T.]

If you are trying to understand GR, and GR is based on 4D entities, then you cannot visualize nor by extension understand GR through visualization.

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.

 

[altonhare]

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?

 

[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.