Gravity Visualized
December 3, 2013 1:06 AM Subscribe
I hate the rubber sheet analogy with a passion. It encourages the (fairly obviously circular) reasoning that things move through the curved space because they're somehow rolling downhill.
I suspect it came out of the entirely legitimate idea of an embedding diagram, where you show the curvature of a 2D space by embedding it in 3D.
This analogy encourages the point of view that a flat spacetime that's tilted looks like a gravitational force that is uniform in one direction, which it isn't (it's flat, no curvature, no gravity). It encourages the point of view that if I curved the sheet by pulling up instead of pushing down it would look like an antigravity field, which it isn't (it's the same curvature just embedded differently, so the gravitational field is the same).
The gravitational field you get from the curvature is because of how the straight line paths are no longer straight because they're on a curved surface, not because things are trying to settle to the bottom of the potential formed by a depression - which obviously only happens because the demonstration is done in a gravitational field, which is the thing it's trying to explain.
It's a perfectly legitimate example of classical motion in a potential well, but it's certainly not a useful example of motion in curved space, as in general relativity.
posted by edd at 3:26 AM on December 3, 2013 [14 favorites]
I suspect it came out of the entirely legitimate idea of an embedding diagram, where you show the curvature of a 2D space by embedding it in 3D.
This analogy encourages the point of view that a flat spacetime that's tilted looks like a gravitational force that is uniform in one direction, which it isn't (it's flat, no curvature, no gravity). It encourages the point of view that if I curved the sheet by pulling up instead of pushing down it would look like an antigravity field, which it isn't (it's the same curvature just embedded differently, so the gravitational field is the same).
The gravitational field you get from the curvature is because of how the straight line paths are no longer straight because they're on a curved surface, not because things are trying to settle to the bottom of the potential formed by a depression - which obviously only happens because the demonstration is done in a gravitational field, which is the thing it's trying to explain.
It's a perfectly legitimate example of classical motion in a potential well, but it's certainly not a useful example of motion in curved space, as in general relativity.
posted by edd at 3:26 AM on December 3, 2013 [14 favorites]
I don't think the rubber sheet analogy is designed for you, with respect. It's designed for the man and woman in the street with little or no physics education. It's just intended to show the principle that a huge mass can capture a smaller mass into orbit.
posted by GallonOfAlan at 3:30 AM on December 3, 2013 [4 favorites]
posted by GallonOfAlan at 3:30 AM on December 3, 2013 [4 favorites]
I hate the rubber sheet analogy with a passion.
Favorited so hard I'm going to need to replace my desk.
posted by a snickering nuthatch at 3:35 AM on December 3, 2013 [2 favorites]
Favorited so hard I'm going to need to replace my desk.
posted by a snickering nuthatch at 3:35 AM on December 3, 2013 [2 favorites]
I don't think the rubber sheet analogy is designed for you, with respect. It's designed for the man and woman in the street with little or no physics education. It's just intended to show the principle that a huge mass can capture a smaller mass into orbit.
As I said - "It's a perfectly legitimate example of classical motion in a potential well". If you want to demonstrate how in Newtonian gravity masses can move in an orbit it is entirely legitimate. The Newtonian idea of a potential and the force being proportional to the gradient of the potential is replicated well by the rubber sheet, and how the energy is related to the position in the potential, but it shouldn't be conflated with the space time distortion of Einstein and how that leads to gravity.
posted by edd at 3:41 AM on December 3, 2013 [1 favorite]
As I said - "It's a perfectly legitimate example of classical motion in a potential well". If you want to demonstrate how in Newtonian gravity masses can move in an orbit it is entirely legitimate. The Newtonian idea of a potential and the force being proportional to the gradient of the potential is replicated well by the rubber sheet, and how the energy is related to the position in the potential, but it shouldn't be conflated with the space time distortion of Einstein and how that leads to gravity.
posted by edd at 3:41 AM on December 3, 2013 [1 favorite]
If you think our analogies for physics are flawed, wait till you learn about ecosystems.
Maybe that is why we ve destroyed so many.
posted by eustatic at 4:51 AM on December 3, 2013 [2 favorites]
Maybe that is why we ve destroyed so many.
posted by eustatic at 4:51 AM on December 3, 2013 [2 favorites]
I hate the rubber sheet analogy with a passion. It encourages the (fairly obviously circular) reasoning that things move through the curved space because they're somehow rolling downhill.
I don't think the rubber sheet analogy is designed for you, with respect.
The linked xkcd, on the other hand, is totally for you.
posted by AdamCSnider at 5:07 AM on December 3, 2013 [3 favorites]
I don't think the rubber sheet analogy is designed for you, with respect.
The linked xkcd, on the other hand, is totally for you.
posted by AdamCSnider at 5:07 AM on December 3, 2013 [3 favorites]
Evaluating an analogy is to evaluate the concordance between the analogy and its subject matter. That's why by default every flawed or limping analogy for anything is potentially valuable, because pointing out the flaws means clarify the subject matter. Imagine the teacher in xkcd 895 embracing the question instead of sighing. Or edd could learn to love the analogy, because he get's to set things straight every time it is mentioned.
posted by quoquo at 5:46 AM on December 3, 2013 [3 favorites]
posted by quoquo at 5:46 AM on December 3, 2013 [3 favorites]
Your favorite gravity analogy sucks.
posted by ReeMonster at 5:57 AM on December 3, 2013 [7 favorites]
posted by ReeMonster at 5:57 AM on December 3, 2013 [7 favorites]
An interesting moment comes at the end of the video when Mr. Burns concedes that the topic isn't part of the state standards and if teachers want to teach this unit to their students they have to "fit it in after the STAR test."
posted by kjh at 6:07 AM on December 3, 2013
posted by kjh at 6:07 AM on December 3, 2013
I hate the rubber sheet analogy with a passion. It encourages the (fairly obviously circular) reasoning that things move through the curved space because they're somehow rolling downhill.
to be fair, the analogy only really fails if the paths of the marbles don't follow along geodesics of the surface you have created. it's not immediately obvious that this occurs for any random catenary-like surface created with spandex, but I believe it is true with the hard exponential horns people roll coins down. either way, it's really a demonstration of how kinematic changes can be the result of curvature rather than some impelled force... which is perhaps an issue with accepting einstein's theory of gravity.
personally, i think experimental physics is the devil and encourages magical thinking but that's just me. IMHO it's way harder to get insight from the world, rather than deducing logical conclusions from what must be true. sometimes it's necessary but i think these demonstrations tend to paper over the difficult points. it all kind of goes back to Saint Faraday, and his miraculous invention of field theory (Maxwell just wrote it out in equations) using table-top experiments. at the end of his career he was trying to unify gravity with the electro-magnetic field. the point being that Faraday was certainly not being guided by nature, he was using the tools at this disposal to investigate his own philosophy (including the method of analogies itself)... which is quite a different thing from the way experimental physics is usually introduced.
posted by ennui.bz at 6:54 AM on December 3, 2013 [1 favorite]
to be fair, the analogy only really fails if the paths of the marbles don't follow along geodesics of the surface you have created. it's not immediately obvious that this occurs for any random catenary-like surface created with spandex, but I believe it is true with the hard exponential horns people roll coins down. either way, it's really a demonstration of how kinematic changes can be the result of curvature rather than some impelled force... which is perhaps an issue with accepting einstein's theory of gravity.
personally, i think experimental physics is the devil and encourages magical thinking but that's just me. IMHO it's way harder to get insight from the world, rather than deducing logical conclusions from what must be true. sometimes it's necessary but i think these demonstrations tend to paper over the difficult points. it all kind of goes back to Saint Faraday, and his miraculous invention of field theory (Maxwell just wrote it out in equations) using table-top experiments. at the end of his career he was trying to unify gravity with the electro-magnetic field. the point being that Faraday was certainly not being guided by nature, he was using the tools at this disposal to investigate his own philosophy (including the method of analogies itself)... which is quite a different thing from the way experimental physics is usually introduced.
posted by ennui.bz at 6:54 AM on December 3, 2013 [1 favorite]
Los Gatos is Spanish for "The Cats."
posted by RhymesWithToaster at 7:42 AM on December 3, 2013
posted by RhymesWithToaster at 7:42 AM on December 3, 2013
Experimental physics is what corrects you when you start "reasoning" that heavier objects must fall faster, vacuum or not. People have used logic, throughout history, to convince themselves of things which simply are not true when you look at the real world. Without experiments, you're basically doing the Glass Bead Game.
posted by adipocere at 7:42 AM on December 3, 2013 [2 favorites]
posted by adipocere at 7:42 AM on December 3, 2013 [2 favorites]
Of course the argument about whether heavier objects fall faster than lighter ones is one of the classic examples of where a thought experiment sufficed.
posted by edd at 7:47 AM on December 3, 2013
posted by edd at 7:47 AM on December 3, 2013
He uses a pole sticking up underneath the sheet to analogize dark energy. Would a better analogy be stretching out the sheet equally from all directions? (Not that there's any practical way to do that with this setup). But I don't think dark energy bunches up like that.
posted by Jacob Knitig at 8:39 AM on December 3, 2013
posted by Jacob Knitig at 8:39 AM on December 3, 2013
No. Dark energy is uniform and actually helps make the universe spatially flat (flat space not being the same as flat spacetime - another difficulty with explaining this stuff). Why it has the effect of accelerating expansion is maybe best explained in this and this recent blog post.
posted by edd at 8:50 AM on December 3, 2013
posted by edd at 8:50 AM on December 3, 2013
I'm curious if the pedants also hate movies cause they're 2-d so how can someone be in the background? It's a flat screen! Geez! Morons!
Come up with something better that everyone can understand, then. The rubber sheet analogy gave me an insight to something unreproducable to human senses. So I went and learned more about it. It gave me an inkling of how things work. Isn't that the idea?
posted by umberto at 9:07 AM on December 3, 2013 [3 favorites]
Come up with something better that everyone can understand, then. The rubber sheet analogy gave me an insight to something unreproducable to human senses. So I went and learned more about it. It gave me an inkling of how things work. Isn't that the idea?
posted by umberto at 9:07 AM on December 3, 2013 [3 favorites]
It encourages the (fairly obviously circular) reasoning that things move through the curved space because they're somehow rolling downhill
I always thought you were meant to assume that those things would always be "rolling downhill" from whatever angle you looked at it. Hence Newton's famous catchphrase, "It's all downhill from here!"
posted by Panjandrum at 9:10 AM on December 3, 2013
I always thought you were meant to assume that those things would always be "rolling downhill" from whatever angle you looked at it. Hence Newton's famous catchphrase, "It's all downhill from here!"
posted by Panjandrum at 9:10 AM on December 3, 2013
ReeMonster: "Your favorite gravity analogy sucks."
I was into rubber sheets before they were cool.
posted by IAmBroom at 9:58 AM on December 3, 2013 [2 favorites]
I was into rubber sheets before they were cool.
posted by IAmBroom at 9:58 AM on December 3, 2013 [2 favorites]
Come up with something better that everyone can understand, then. The rubber sheet analogy gave me an insight to something unreproducable to human senses. So I went and learned more about it. It gave me an inkling of how things work. Isn't that the idea?
The 'something better that everyone can understand' is calculus and Newton's laws. The even better explanation that hardly anyone understands is general relativity.
posted by empath at 10:34 AM on December 3, 2013
The 'something better that everyone can understand' is calculus and Newton's laws. The even better explanation that hardly anyone understands is general relativity.
posted by empath at 10:34 AM on December 3, 2013
"Come up with something better that everyone can understand, then. The rubber sheet analogy gave me an insight to something unreproducable to human senses. So I went and learned more about it. It gave me an inkling of how things work. Isn't that the idea?"
Not everything that is worth understanding is easy to understand. An understanding of the problems with the rubber sheet analogy is absolutely essential for its intuitiveness not to steer you wrong, which it really easily can. I struggled for a bit to come up with a way to explain them in the FPP and only really came up with the xkcd link I included, but I'm really glad edd came in to do it better than I ever could.
There is that old saying the biologists are just physicists that can't do math.
posted by Blasdelb at 11:15 AM on December 3, 2013
Not everything that is worth understanding is easy to understand. An understanding of the problems with the rubber sheet analogy is absolutely essential for its intuitiveness not to steer you wrong, which it really easily can. I struggled for a bit to come up with a way to explain them in the FPP and only really came up with the xkcd link I included, but I'm really glad edd came in to do it better than I ever could.
There is that old saying the biologists are just physicists that can't do math.
posted by Blasdelb at 11:15 AM on December 3, 2013
The 'something better that everyone can understand' is calculus and Newton's laws.
Respectfully, I think this is wrong. Not everyone who is curious about gravity is equipped to learn calculus. Anecdata from a former Level I - III Calc TA. I put it on you smart guys to find better analogies.
Not everything that is worth understanding is easy to understand.
I concur. OTOH Gamow, Feynman and others found useful language to articulate things that are only properly understood via mathematics.
posted by j_curiouser at 11:43 AM on December 3, 2013 [3 favorites]
Respectfully, I think this is wrong. Not everyone who is curious about gravity is equipped to learn calculus. Anecdata from a former Level I - III Calc TA. I put it on you smart guys to find better analogies.
Not everything that is worth understanding is easy to understand.
I concur. OTOH Gamow, Feynman and others found useful language to articulate things that are only properly understood via mathematics.
posted by j_curiouser at 11:43 AM on December 3, 2013 [3 favorites]
I think I would simply use the surface of the Earth as an analogy. Walking lines of longitude, two people will get closer together or further apart as they go, while thinking they are going straight. That's down to the geometry and the curvature, just as things work in GR. It also doesn't require those walking the lines to go up or downhill.
Once you demonstrate that on a sphere, you can look at how it works on other shapes (using rubber sheets if you wish there).
The problem isn't the shape of the rubber sheet being misleading, but that the dynamics of a ball rolling along it is dominated by gravitational and normal forces and not the geometry directly.
posted by edd at 12:48 PM on December 3, 2013
Once you demonstrate that on a sphere, you can look at how it works on other shapes (using rubber sheets if you wish there).
The problem isn't the shape of the rubber sheet being misleading, but that the dynamics of a ball rolling along it is dominated by gravitational and normal forces and not the geometry directly.
posted by edd at 12:48 PM on December 3, 2013
An interactive Flash tool for visualizing warped space time--not falling prey to the flaws of the rubber-sheet analogy.
I dug it up via Physics StackExchange
posted by polecat at 1:43 PM on December 3, 2013 [3 favorites]
I dug it up via Physics StackExchange
posted by polecat at 1:43 PM on December 3, 2013 [3 favorites]
Also, I appreciate that the rubber mat is a nice way to introduce the idea that space-time is curved. However, it is frustrating to hear the analogy brought up again and again while (to my recollection) nobody who presents it ever says, "BTW, if you think about it a little harder you will realize this is an imperfect analogy." In this video, for example.
I thought examples of the moon shot, the moon orbiting the earth, and the planets revolving the same direction were pretty interesting in this video.
posted by polecat at 2:19 PM on December 3, 2013
I thought examples of the moon shot, the moon orbiting the earth, and the planets revolving the same direction were pretty interesting in this video.
posted by polecat at 2:19 PM on December 3, 2013
I should probably stop thinking about this so much, but it also occurs to me that for everyday gravity the fact that space is curved is quite irrelevant. If you think about it in terms of your four-velocity, you're almost entirely going along the time direction and barely moving in space, so you don't feel the spatial parts of the metric. Light does feel them, and that's why it is deflected by gravity twice as much as slow moving particles are. How you get across the idea of curved spacetime and not just curved space - well, that I have no good answer for.
posted by edd at 3:07 AM on December 4, 2013
posted by edd at 3:07 AM on December 4, 2013
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