Nonsensical representation of gravity

[#Thomas#]

Greetings all,

I am the newest addition of the PF community and let me express my excitement of finally tracking down this intelectual family and hopefully making myself eventually an equal member of it. Now, I will not waste too much of your time let us get down to this PFbuisness=pleasure, shall we?

I may be just an enthusiast in the world of astrophysics in general but there is something that disturbs me:

Most educational literature I have come across persistantly visualises the force of gravity and similar phenomena in insuficient dimentions. A typical example would be a visual representation of the curvature of space-time, inflicted by the gravity of an interstellar body. They simply put down a 2D web, curved by the object that sits upon it. We all know that this is simply an insuficient representation, just as as saying "the sun comes up", which is simply inacurate.

So what I would like to ask is what is their motivation for disseminating such information in such an oversimplified manner?

It also may be a possibility that I have simply come across such items which were designed for a low level laiman, in that case I would apreiciate it if you could direct to some "higher-level" materials on the topic of astrophysics, preferably some video please or scientific columns with more accurate information...

Thank you all and have a nice day!

 

[Simon Bridge]

It also may be a possibility that I have simply come across such items which were designed for a low level laiman

This is, indeed, what has happened. You are referring to descriptions aimed at people without the math to handle the whole model.

I would apreiciate it if you could direct to some "higher-level" materials on the topic of astrophysics, preferably some video please or scientific columns with more accurate information.

Yu won't get it in video - those are aimed at the layman. The full theory is describable only in mathematics ... so you need text references.

Any senior or post-graduate work on general relativity would give you the theory you need. It is possible that you will need to upgrade your math first ... but you'll find out quite fast. For the real ultra-recent models for gravity, though, you want a work on quantum gravity ... which requires a different kind of math.
Enjoy.

 

[Jasongreat]

Greetings all,

I am the newest addition of the PF community and let me express my excitement of finally tracking down this intelectual family and hopefully making myself eventually an equal member of it. Now, I will not waste too much of your time let us get down to this PFbuisness=pleasure, shall we?

I may be just an enthusiast in the world of astrophysics in general but there is something that disturbs me:

Most educational literature I have come across persistantly visualises the force of gravity and similar phenomena in insuficient dimentions. A typical example would be a visual representation of the curvature of space-time, inflicted by the gravity of an interstellar body. They simply put down a 2D web, curved by the object that sits upon it. We all know that this is simply an insuficient representation, just as as saying "the sun comes up", which is simply inacurate.

So what I would like to ask is what is their motivation for disseminating such information in such an oversimplified manner?

It also may be a possibility that I have simply come across such items which were designed for a low level laiman, in that case I would apreiciate it if you could direct to some "higher-level" materials on the topic of astrophysics, preferably some video please or scientific columns with more accurate information...

Thank you all and have a nice day!

If your reason for discussing science, is to make yourself feel superior, then describing things in the most complicated manner possible would make sense. However if you would like for most people to learn the basics, you have to describe it in a way most can understand.

If you would like to discuss 'higher-level' stuff go here:https://www.physicsforums.com/forumdisplay.php?f=68, and there also is a learning materials section at the very top of the list of forums here at physicsforums.

 

[#Thomas#]

Ugh... I cursed the math at school and now I curse the day I snoozed my way through it.:zzz:

Everytime I did an exam my physics professor asked what's my math grade and i reply: #ehem# flung, #ehem ehem# summer school...! And he grinned everytime, fortunately he was a crackpot and was more interested in my understanding of the matter rather than my scribblings on that piece of paper.

I'll get it though. My own drooling over the subject will keep me going. I presume I can get everything I need from you fine gents?

If your reason for discussing science, is to make yourself feel superior, then describing things in the most complicated manner possible would make sense. However if you would like for most people to learn the basics, you have to describe it in a way most can understand.

If you would like to discuss 'higher-level' stuff go here:https://www.physicsforums.com/forumdisplay.php?f=68, and there also is a learning materials section at the very top of the list of forums here at physicsforums.

This isn't about me feeling superior in any way, or feeling anything at all, its about my own personal pursuits and expanding the horizons of my understanding, but not in a limited form that standard materielle has to offer.

I don't intend to use this as a subject of bragging in my conversations, this is for me and me alone and i came here asking for some guidance from you experienced people, there really is no cause to insult me.

 

[Simon Bridge]

Mathematics is the language of physics.
You cannot go past the lay descriptions without it.

You will get everything you need from your efforts and resources, we can only help you as you get confused or stuck and only briefly - unless, of course, you want to pay for the tuition?

 

[Jimmy Snyder]

there really is no cause to insult me.

I think Jasongreat was talking about the author of the book, not you. I don't understand exactly what you are proposing though. Do you want a 4 dimensional picture, and if not, then no picture at all.

 

[#Thomas#]

Yes, well, I drifted away from it a little... i roughly understand how a mapping of the distorsion of spacetime around a black hole should look like, but my question is why do the TV series such as "the universe" and "nova" oversimplify such phenomena when they have actual access to physicists who can help them construct a more accurate model?

They do it the same with Alcubierre's warp drive, gravity in general and all other similar things.

 

[f95toli]

Mainly because there is no way to visualize an accurate model, there is no way to "properly" represent 4 dimensions. You can of course do it using maths, but that would be completely incomprehensible to almost everyone (including most physicists).

There is nothing wrong with simplified models as long as you keep their limitations in mind.

 

[Pengwuino]

Mainly because there is no way to visualize an accurate model, there is no way to "properly" represent 4 dimensions. You can of course do it using maths, but that would be completely incomprehensible to almost everyone (including most physicists).

There is nothing wrong with simplified models as long as you keep their limitations in mind.

Beat me to it.

@Thomas: It's sometimes hard enough to model even 3-dimensional phenomenon using 3 dimensions, let alone 4-dimensional phenomenon. If you can figure out a better way to represent it, we would be happy to hear it. I mean, think about it. You need that third dimension in your typical picture to given an idea of the magnitude of the curvature of the 2 other dimensions. If you were to use the third dimension as an actual space-time dimension, how do you show the magnitude of the curvature?

 

[#Thomas#]

Yes, but they already did it so nicely, such as this image:
http://www.world-mysteries.com/newgw/gravity5.jpg

Its a lot more suitable to the matter at hand, all you would have needed to add would be some twist in direction of the Earth's rotation and the image would be perfect!

Instead, what they do is this, which is folly and insuficient:

 

[Jimmy Snyder]

I have seen that second image many times on TV and in books. I always thought it was overly simplistic, but I didn't realize until now that it is wrong. If you compare it to the first image you see that the curvature goes the wrong way. The Earth is pushing the lines away rather than pulling them in.

 

[Vanadium 50]

Its a lot more suitable to the matter at hand, all you would have needed to add would be some twist in direction of the Earth's rotation and the image would be perfect!

No, because it would still neglect curvature in the 0-direction, which for some circumstances is the most important direction.

It's an analogy. It is not reasonable to expect an analogy to work in all situations. I recognize the problem that when people come to the limits of the analogy, they cling to it, sometimes even to the point of refusing to believe the correct answer when it conflicts with it. But that's a general problem, not one with a specific analogy.

 

[#Thomas#]

I have seen that second image many times on TV and in books. I always thought it was overly simplistic, but I didn't realize until now that it is wrong. If you compare it to the first image you see that the curvature goes the wrong way. The Earth is pushing the lines away rather than pulling them in.

I presume that now you see the problem of attempting to represent this in limited dimentions?

May I ask - why would the Earth push the lines out if gravity pulls stuff towards the gravitating body? Doesn't it contract space?
(I'll doublecheck... now where's that ebook...)

 

[Jimmy Snyder]

Actually, I've changed my mind about both images. If the lines are meant to be geodesics, then they should be pushed out away from the earth. You can see this in the following correct image:

http://en.wikipedia.org/wiki/File:Gravitational_lens-full.jpg
Graviational lens

Therefore, if the lines are meant to represent geodesics, then the 3D image is completely wrong. The 2D image is slightly better, but it is only correct in 1 dimension, north to south. The other 2 dimensions still show the Earth pulling the geodesic lines in. What's more, if a literally 2 dimensional image were created, it could show the effect perfectly well because of the spherical symmetry.

 

[KrisOhn]

That 3D image is just like they put a box around the Earth and pushed in the sides, which is still not an accurate representation of gravity in the 3 spatial dimensions. As was said before me: If you keep the limitations in mind with the 2 dimensional image it serves as a perfectly well representation of gravity and is something that is very simple for everyone to conceptually grasp.

 

[zoobyshoe]

Actually, I've changed my mind about both images. If the lines are meant to be geodesics, then they should be pushed out away from the earth. You can see this in the following correct image:

The light isn't being pushed away from that massive body, the way I read that image. The rays approaching that body are divergent, in straight lines, as they come from the distant galaxy pictured, then they are redirected into convergence by the massive body's gravity and focused onto the earth, creating the illusion of a different source location, as depicted by the larger orange arrows. The light rays are definitely being deflected toward the massive body. Extend the original lines as they emerge from the distant galaxy, and you'll see that, if they didn't encounter the gravity lens, they wouldn't hit the Earth at all.

 

[zoobyshoe]

That 3D image is just like they put a box around the Earth and pushed in the sides, which is still not an accurate representation of gravity in the 3 spatial dimensions. As was said before me: If you keep the limitations in mind with the 2 dimensional image it serves as a perfectly well representation of gravity and is something that is very simple for everyone to conceptually grasp.

I don't see how you're characterizing one as 3d and the other not. They both look 3d to me. The 'traditional' second one has always looked completely non-sensical to me: a globe sitting on a rubber sheet distorting it by its 'weight'.

 

[Jimmy Snyder]

The light isn't being pushed away from that massive body, the way I read that image. The rays approaching that body are divergent, in straight lines, as they come from the distant galaxy pictured, then they are redirected into convergence by the massive body's gravity and focused onto the earth, creating the illusion of a different source location, as depicted by the larger orange arrows. The light rays are definitely being deflected toward the massive body. Extend the original lines as they emerge from the distant galaxy, and you'll see that, if they didn't encounter the gravity lens, they wouldn't hit the Earth at all.

Simply compare the curved lines in my link to the curved lines in the 3d image. In my link, the gravitating body is at a focal point of the hyperbola. That is to say, inside the curve. Just think about the path of a comet as it nears the sun. It doesn't pass in front of the sun, it goes behind it. Thus, the sun is inside the curve, not outside of it.

 

[Simon Bridge]

The "2D" image is the "rubber sheet" model and only intended to work on a single plane through the planet - the pic of the planet is supposed to show where it is, not how space-time bends around it. This is why the 2D one looks sort-of OK as a representation of the geodesic. Remove the cute pic of the planet and put x-y-x axes on it instead.

Of course - the representation could be anything - none of the pics have labelled what the grids are supposed to be: we are just guessing. Perhaps it's a spatial representation of the chance of finding intelligent life at the coordinates?

The point of this sort of picture is to give an idea of how geometry can lead to something like the behavior a layman would expect ... but it's way off and can lead to the idea that there is a sort-of meta-gravity "outside space-time" pulling objects into the 3D hollows pressed into it by planets.

But let's face it - the primary purpose of a TV show is not to provide accurate information and imagery, the primary purpose of a TV show is to [strike]make money[/strike] be entertaining enough so people will watch it ... creating an audience, with somewhat predictable demographics, to advertise to. The purpose of the show is to sell advertising. The station's profit is the difference between the cost of bringing you the show and what they can sell the advert slots for.

The common graphics are used because they are popular with the target audiences.

 

[#Thomas#]

The point of this sort of picture is to give an idea of how geometry can lead to something like the behavior a layman would expect ... but it's way off and can lead to the idea that there is a sort-of meta-gravity "outside space-time" pulling objects into the 3D hollows pressed into it by planets.

But let's face it - the primary purpose of a TV show is not to provide accurate information and imagery, the primary purpose of a TV show is to be entertaining enough so people will watch it ... creating an audience, with somewhat predictable demographics, to advertise to. The purpose of the show is to sell advertising. The station's profit is the difference between the cost of bringing you the show and what they can sell the advert slots for.

Yes, excelent, now we're getting somewhere!

However, I would like to stress that the lines posted previously in my upper image are supposed to represent the spacetime web distorting on the gravitation of a single body, in this case: the earth!

 

[zoobyshoe]

The "2D" image is the "rubber sheet" model and only intended to work on a single plane through the planet - the pic of the planet is supposed to show where it is, not how space-time bends around it. This is why the 2D one looks sort-of OK as a representation of the geodesic. Remove the cute pic of the planet and put x-y-x axes on it instead.

The point of this sort of picture is to give an idea of how geometry can lead to something like the behavior a layman would expect ... but it's way off and can lead to the idea that there is a sort-of meta-gravity "outside space-time" pulling objects into the 3D hollows pressed into it by planets.

But let's face it - the primary purpose of a TV show is not to provide accurate information and imagery, the primary purpose of a TV show is to be entertaining enough so people will watch it ... creating an audience, with somewhat predictable demographics, to advertise to. The purpose of the show is to sell advertising. The station's profit is the difference between the cost of bringing you the show and what they can sell the advert slots for.

The common graphics are used because they are popular with the target audiences.

#Thomas#'s contention, though, and I agree with him, is that this illustration actually confuses the target audience. It's used over and over without actually being popular or enlightening.

 

[Simon Bridge]

What does "space-time web" mean? Do they tell you?
I agree it confuses the target audience.
The question was "why is it used when experts are available" (paraphrase)
We know why:
It is not cost effective to get it right - for the kinds of reasons referred to by others.
Anyway - TV stations are not in the business of making hard ideas clear to people.

Now if that was in college textbook...

 

[zoobyshoe]

Now if that was in college textbook...

It is. I just walked three blocks down to the public library and found it in Halliday/Resnick/Walker, which is a well respected, widely used text. I also found it in a 'self teaching guide' called "Advanced Physics Demystified, sort of a "for dummies", but intended to be rigorous rather than to entertain.

It's also been discussed here, at PF, as a proper depiction (if you understand it properly):

https://www.physicsforums.com/showthread.php?t=5737

 

[Simon Bridge]

Then that wasn't the question I was responding to and you'd have to look very carefully at what is being claimed, exactly. And I stand by my reply in post #2 ... it is a simplification for people starting out to get an idea without getting the idea.

The challenge is to improve on that description at the level that text is speaking to.

I'll bet the same text does a bit of SR but no GR and reinforces the planetary model of the atom and other simplifications? Would you have more accurate versions of these also added to the same text?

There are constraints on college texts too.

(Personally I'd be disappointed if anything more than a 101 course is taught from that book. Yeah it causes confusions but what can you do? The trick is to try for a better description at the level, and remember to apply the same standard to the other sections as well.)

The link you post explicitly spells out that the rubber-sheet picture is an analogy.
To be useful it has to be understood properly - like any analogy.
(Or any idea at all really.)
What's wrong with that?

 

[Tosh5457]

Ugh... I cursed the math at school and now I curse the day I snoozed my way through it.:zzz:

Everytime I did an exam my physics professor asked what's my math grade and i reply: #ehem# flung, #ehem ehem# summer school...! And he grinned everytime, fortunately he was a crackpot and was more interested in my understanding of the matter rather than my scribblings on that piece of paper.

I'll get it though. My own drooling over the subject will keep me going. I presume I can get everything I need from you fine gents?




This isn't about me feeling superior in any way, or feeling anything at all, its about my own personal pursuits and expanding the horizons of my understanding, but not in a limited form that standard materielle has to offer.

I don't intend to use this as a subject of bragging in my conversations, this is for me and me alone and i came here asking for some guidance from you experienced people, there really is no cause to insult me.

Study linear algebra, differential and integral multivariable calculus and differential geometry and then you're ok to understand how the model really works Do you see now why these theories appear simplified?

 

[#Thomas#]

Im not talking about the theories, I am talking about the visual models!

Im also talking about the people who are supposed to explain everything to us, but as we have determined, they folly it up!

 

[Simon Bridge]

So come up with a better visual model.

I think it is silly to demand a visual model and then complain that it is misleading - show me one that isn't?

 

[zoobyshoe]

So come up with a better visual model.

I think it is silly to demand a visual model and then complain that it is misleading - show me one that isn't?

He didn't demand a visual model. It's offered voluntarily by the explainers.

 

[Simon Bridge]

Didn't say he did - check my other posts: the visual model is demanded by the marketplace.

Perhaps I was unclear? Perhaps I should say that it is unsurprising that the visual models offered have serious flaws in them, considering the limitations (already mentioned) of this means of expression?

However he does seem to be claiming that a good visual model is possible against the general skepticism of the responses, so let him demonstrate this.
Lets stop apologizing for it and let OP defend his position.

eg. Would it be better not to offer any visual representation at all?

 

[zoobyshoe]

Didn't say he did - check my other posts: the visual model is demanded by the marketplace.

The "marketplace" complained the model it demanded was misleading?

 

[#Thomas#]

I described it as an insuficient, you are the ones who dismissed it, i am following the discussion.

I already presented an image that could be better, if you weren't so busy attacking my position, you would notice it on the first page.

 

[Jimmy Snyder]

I already presented an image that could be better, if you weren't so busy attacking my position, you would notice it on the first page.

Are you referring to this image?
http://www.world-mysteries.com/newgw/gravity5.jpg
This image is wrong. The geodesic lines all curve in the wrong direction. If the lines were as the ones in that image, then during the eclipse, the sun would have hidden the grazing stars. The Earth should be at the focal point of the geodesic curves, and it is not.

 

[Simon Bridge]

The "marketplace" complained the model it demanded was misleading?

I've already owned that my statement could have been clearer and reworded it. Thanks for pointing this out.

 

[Simon Bridge]

I described it as an insuficient, you are the ones who dismissed it, i am following the discussion.

I already presented an image that could be better, if you weren't so busy attacking my position, you would notice it on the first page.

Well that's possible.
I only saw the one Jimmy references ... if there was another, I certainly missed it.
I have been unable to produce a graphical/visual representation that does a better job than the bendy-plane one (except maybe to leave the planet-picture off) but that may be a failure of imagination on my part.

Is it just that you'd prefer a 3D representation in the place of the cross-section normally shown?
What features do you think a decent visualization needs to show?
You seem to favor a grid of some kind - should the grid represent the geodesic? Something else?

 

[ThomasT]

Hi #Thomas#, I felt compelled to reply since apparently we have the same first name, and the visualizations of gravity don't do it for me either. My solution: I don't try to visualize gravity.
You got some good answers, especially from Simon Bridge and f95toli, wrt your question(s), imo.

The problem, imo, is that nobody really knows what gravity is. The visualizations of gravity are based on a geometrical interpretation of GR which might be an oversimplification of what's actually happening wrt the deep reality of gravitational behavior.

 

[Simon Bridge]

This would be fairly standard:

... to improve on it, for educational purposes, I'd want to remove the graphics of the Earth, the spacecraft , and the stars; add axis and label them.

I'd want to make explicit what the lines represent.
Perhaps the height of the sheet depicted represents the curvature of space-time at different 2D space coordinates on a cartesian plane passing close to the position of the Earth? Or a single sheet of the geodesic near the Earth (whatever that means?

The article in question is not clear what it means but is clear that it is entirely a fanciful illustration.

If we want to turn a 2D picture like this into a 3D one, we'd layer many of these sheets - stack them. The picture would look like the a planet making a bulge in a grid.

Would this be better?
It creates the impression of gravity as a pushing rather than a pulling effect though doesn't it? See... you can't win.

 

[Jimmy Snyder]

I doubt that Simon's image is one that #Thomas# would prefer. However, I find it has a very nice feature. You can see the curvature change polarity at the equator. This is correct.

 

[zoobyshoe]

I doubt that Simon's image is one that #Thomas# would prefer. However, I find it has a very nice feature. You can see the curvature change polarity at the equator. This is correct.

Are you talking about the bulge 'upward' right before the plunge 'downward'?

 

[Jimmy Snyder]

Are you talking about the bulge 'upward' right before the plunge 'downward'?

Actually, I've changed my mind about this too. The image is actually quite misleading. It seems to take two geodesic lines, one headed north of the earth, the other south, and cuts them in half at their intersection point to create the impression that they are a single geodesic.

The curvature of spacetime is a 4-dimensional affair. That is why geodesics are ellipses or hyperbolae depending on the speed of the smaller object. The grid lines in Simon Bridge's image consist of circles, which would be suitable for planets, and radial lines which would be suitable for light. This mixture of different types of geodesics in a single image is probably not helpful. What's worse is that the center of the Earth should be at the focal point (center) of the circles, and it is not.

 

[Simon Bridge]

... assuming it's intended to represent the geodesic.

I was quite curious about the bulge before the plunge - if that was just for dramatic effect. Most of the others look like they are just representations of gravitational potential samples across the surface of a plane that does not cross the surface of the Earth. The potential does come from the curvature so they are not lying exactly, but it is not the same as the geodesic either. The lines, therefore, are just a mesh-plot in polar coordinates.

 

[Jimmy Snyder]

In my opinion, the best image would be a set of two dimensional images. Each image would have vertical and horizontal geodesic lines bulged out at the center where the Earth is. Geodesic lines always are planar and the plane intersects the center of the earth, so no information would be imparted by a third dimension. Spherical symmetry would take care of that anyway. There should be several such images with greater and lesser degrees of curvature indicating the effect at different speeds of the smaller object.

 

[Containment]

I actually agree with this I remember the first time I saw an image of what the gravitational field of the Earth would look like and thought to myself "wow as a race are we really this bad at physics?" That was before I realized that the people that make most of the physics models probably have little to no understanding of what's actually happening or they just don't want to spend the time to make the models look good. Like in the case of school books where you might first run into these the company's most likely came up with the artwork. Also I happened to get my hands on a 9th graders science textbook a few years back when I was "babysitting" and the pictures in it are many times better the ones I had back in the good old days.

 

[Darkduke]

I think they use that representation becaue try as they might no one can come up with a better one.
I would like to undersand gravity better to but if the top theoretical physicists can't rap there heads round it what chance do i have lol
They say its a 2D representation of a 3D image if that's the case the 3D image would just be a ball with everything moving to the center but then why would a object circle the mass in the middle surley it would just head directly to the center. Unless it had another force that initiated the circular motion before hand.
If I am making no sense please feel free to tell me.

 

[Simon Bridge]

That's why the mass-geodesics are ellipses.

The problem is not so much modelling it so the top guys can understand it - but coming up with a picture that let's everyone else grasp some of the fundamentals ... to do that you have to sacrifice something.

The mass on a sheet metaphor is supposed to exploit peoples intuitive ideas about gravity to help them understand how something "curving" can lead to attraction and curved paths and so on.

So it is an analogy.
Two weights close together will roll together for example - not the same way that it happens with gravity but they come together. Scoot a small pellet across the sheet and it gets deflected by the bigger masses - line it up right and you can get it to go right around the bigger mass. And so on - it can be quite seductive.

However - you put a grid on the relaxed sheet and then put masses on it - the grid-lines bend towards the mass... no so helpful. However, what works better at the higher level risks losing the regular folk.

Like I said before, I don't think the pics we regularly see are supposed to be geodesics.
More something like this:

This is like those QM energy-level diagrams that also show the wavefunction using the level as an axis. The vertical dimension of each sheet is the gravitational potential at the horizontal coordinate on a plane that passes near a mass. The spheroid in the center represents the mass, not to scale, and I have sampled 4 parallel planes.

Flipping the direction of +V for the upper two sheets is for artistic license :), stops the top plots from obscuring the "planet", and reinforces the impression of the mass bending the space around itself.

I could probably do better by making the sheets slightly transparent.
It's a nasty fudge anyway but I think you can see what I mean.

 

[#Thomas#]

Now I see what's been bothering you people. You want the field lines to represent the field of gravity but not the path that an imaginary object would take while passing through the field...

So if i assume correctly, if an object would follow the red plain in the image posted above, it would be attracted by gravity towards the planet as it hits the "lump"?

I can see the difference now!
http://www.usefulbusiness.co.uk/storage/post-images/BigIdea.jpg?__SQUARESPACE_CACHEVERSION=1303031431987

 

[Jimmy Snyder]

Now I see what's been bothering you people. You want the field lines to represent the field of gravity but not the path that an imaginary object would take while passing through the field...

That is the exact opposite of what I have been saying. The path that an imaginary object would take while passing through the field is called a geodesic. I want the lines to represent geodesics.

 

[Simon Bridge]

#Thomas#: sort of - Jimmy would prefer the representation to show the geodesics, I'm saying that whatever any of us would prefer or expect from these pictures, they are not supposed to represent geodesics: not directly anyhow.

The red sheet represents the gravitational potential sampled at discrete x-y positions on a plane parallel to the x-y plane (through the center of the mass at z=+2.5 units. The magnitude of the potential is proportional to the displayed displacement of the sheet from z=2.5. The sign of the potential is always negative: so it doesn't matter which way up I draw the sheets.

Aside: the spheroid representing the mass is not drawn to scale.

I am hoping to illustrate that this is the sort of thing that is commonly depicted artistically - if not exactly what the artist has in mind.

The purpose is to illustrate a very narrow set of core ideas about gravity.

And you are right - an imaginary object hitting the bump will experience an attractive force towards the mass. Just not what Jimmy's going on about.

I'm trying to figure out how to graph the geodesics. For a mass, the exact paths would depend on the speed so this kind of 3-space sampling wouldn't be useful. Plotting the light-paths may be illustrative ... or maybe graphing the overall curvature at different points? Jimmy - help?

I've also been unsuccessful at getting octave to draw semi-transparent mesh or surface plots like MATLAB can. Anyone know how (or if) you use surface properties in octave?
In fact, I don't even know how to plot a set of ordered triples in octave.

 

[zoobyshoe]

That is the exact opposite of what I have been saying. The path that an imaginary object would take while passing through the field is called a geodesic. I want the lines to represent geodesics.

Wouldn't this just be the trajectory of a body in motion?

http://www.sciencephoto.com/media/363714/enlarge

 

[Simon Bridge]

Those would be the Newtonian trajectories.
Now do it for GR in a way that illustrates to the layman the way masses curve space-time :)

 

[zoobyshoe]

Those would be the Newtonian trajectories.

That's what I'm saying/asking: I've read it asserted that objects take the Newtonian trajectories because they are following the geodesic created by "curved" space-time. I'm thinking/asking if the representation of a specific geodesic (or a sampling of many geodesics) would be informative since it would be nothing but a Newtonian trajectory.

Now do it for GR in a way that illustrates to the layman the way masses curve space-time :)

Yes, this is the challenge.