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I've never really understood this visualization. It's a cheat in so many ways (wrong dimensionality, reliance on actual gravity to work, etc.). While such "gee-

by mhartl 12y ago

I've never really understood this visualization. It's a cheat in so many ways (wrong dimensionality, reliance on actual gravity to work, etc.). While such "gee-whiz" demonstrations are great at getting people excited about science, I worry that they create false expectations. They often produce the feeling of understanding without conveying actual understanding (and the limitations thereof). The unfortunate truth is that many subjects in physics, including general relativity, are impossible to visualize in the conventional sense. I learned GR from Kip Thorne at Caltech and wrote my Ph.D. dissertation on the dynamics of rotating (Kerr) black holes, and my intuition for the subject is still fuzzy and inchoate. The best you can do is have a cobbled-together half-picture that kind-of, sort-of works, some of the time. Human brains simply are not designed to understand, at a deep intuitive level, things like the geometry of four-dimensional pseudo-Riemannian manifolds.

ksk 12y ago
Wow, you sound very confused to me. Your "false expectations" bit is nonsense. Using your logic, kids shouldn't be told to wash their hands before they eat because it creates the "false expectation" that by washing their hands they're getting rid of all harmful germs. (re: They often produce the feeling of understanding without conveying actual understanding (and the limitations thereof) Reality is complicated and kids already know that. Its just that they're way better than adults at being comfortable with not knowing everything. > Human brains simply are not designed to understand, at a deep intuitive level, things like the geometry of four-dimensional pseudo-Riemannian manifolds. "Hey kids ! Lets get real.. you won't understand this stuff at a "deep intuitive level" but please choose physics as a career." - Doesn't sound motivational to me.
- mturmon 12y ago
  You're not giving the above comment the respect it deserves. Whenever you offer up an analogy, you want to choose it carefully, and be sure to convey its limitations. The video didn't discuss its limitations (which is OK, it's just a video showing off a rig). So we're left to do it here. And trust me, learning GR with Kip Thorne (http://en.wikipedia.org/wiki/Kip_Thorne http://en.wikipedia.org/wiki/Kip_Thorne) makes the above commenter qualified to offer an opinion.
  - ksk 12y ago
    >Whenever you offer up an analogy, you want to choose it carefully, and be sure to convey its limitations. Yes, maybe if you're presenting at a conference or a lecture or something like that. Not if you want to get a bunch of kids motivated/interested in a topic. In the case of this video, the limitations can only be understood by people in that field. Sure, You can hand-wave a general clarification like "this isn't actually how it is, because <insert boring text that nobody will remember>" - which would be pointless (IMO) and convey no real information. Because the "real" information takes several years of academic training to understand and comprehend. >And trust me, learning GR with Kip Thorne (http://en.wikipedia.org/wiki/Kip_Thorne http://en.wikipedia.org/wiki/Kip_Thorne) makes the above commenter qualified to offer an opinion. Sorry but it changes nothing in my mind. If the OP had said "Hey I would have said it this way and guess what I've successfully used it to motivate X, Y and Z into taking up science" - I'd have been way more impressed and given the "above comment the respect it deserves".
leephillips 12y ago
The height as a function of position of the elastic sheet is a solution to Poisson's equation, which is the same equation that gives you the (classical) gravitational potential. So the demonstration is an analogue computation that solves the analogous problem in gravity.
gcanyon 12y ago
Thanks! This visualization has frustrated me for many years, for many of the same reasons you list above, but I don't have the Ph.D. to back up my skepticism, so it's good to know that my bad understanding of gravity wasn't taken in by this.
mturmon 12y ago
I agree that the demo is mixing concepts (esp.: relies on actual gravity to work) and tempting confusion. As a teacher, you'd have to be careful to clarify this so you don't confuse students. I note that he says the demo is about GR, but then uses his rig and two handfuls of marbles to explain how almost all solar system orbits go in the same direction. (He doesn't need GR for that.) In this context, the rubber-sheet model is a very nice testbed for what is in effect a demonstration of stochastic initialization with positive or negative net angular momentum determining how it plays out. I liked that a lot. It also hooks up with various strands of current research: use of numerical gravitational simulations, solar system dynamics at long time scales, and the surprising discovery of many exoplanets with retrograde motion relative to their host star. If you'll grant that that is OK, you might have really lost it when he stuck the plastic strut underneath the sheet and said that was like dark energy! So that makes me want to re-think his rig in a more granular way. It seems like one key question is: does the curvature you get with a mass in the 2d sheet have the same local properties as the curvature you get via GR in Minkowski space? Is this what is really driving the paths of objects in the simulation to be ellipses, hyperbolas, etc.? What is a notable example of some GR prediction that is NOT accounted for by his rig?

by mhartl 12y ago

ksk 12y ago

Wow, you sound very confused to me. Your "false expectations" bit is nonsense. Using your logic, kids shouldn't be told to wash their hands before they eat because it creates the "false expectation" that by washing their hands they're getting rid of all harmful germs. (re: They often produce the feeling of understanding without conveying actual understanding (and the limitations thereof) Reality is complicated and kids already know that. Its just that they're way better than adults at being comfortable with not knowing everything. > Human brains simply are not designed to understand, at a deep intuitive level, things like the geometry of four-dimensional pseudo-Riemannian manifolds. "Hey kids ! Lets get real.. you won't understand this stuff at a "deep intuitive level" but please choose physics as a career." - Doesn't sound motivational to me.

mturmon 12y ago
You're not giving the above comment the respect it deserves. Whenever you offer up an analogy, you want to choose it carefully, and be sure to convey its limitations. The video didn't discuss its limitations (which is OK, it's just a video showing off a rig). So we're left to do it here. And trust me, learning GR with Kip Thorne (http://en.wikipedia.org/wiki/Kip_Thorne http://en.wikipedia.org/wiki/Kip_Thorne) makes the above commenter qualified to offer an opinion.
- ksk 12y ago
  >Whenever you offer up an analogy, you want to choose it carefully, and be sure to convey its limitations. Yes, maybe if you're presenting at a conference or a lecture or something like that. Not if you want to get a bunch of kids motivated/interested in a topic. In the case of this video, the limitations can only be understood by people in that field. Sure, You can hand-wave a general clarification like "this isn't actually how it is, because <insert boring text that nobody will remember>" - which would be pointless (IMO) and convey no real information. Because the "real" information takes several years of academic training to understand and comprehend. >And trust me, learning GR with Kip Thorne (http://en.wikipedia.org/wiki/Kip_Thorne http://en.wikipedia.org/wiki/Kip_Thorne) makes the above commenter qualified to offer an opinion. Sorry but it changes nothing in my mind. If the OP had said "Hey I would have said it this way and guess what I've successfully used it to motivate X, Y and Z into taking up science" - I'd have been way more impressed and given the "above comment the respect it deserves".

leephillips 12y ago

The height as a function of position of the elastic sheet is a solution to Poisson's equation, which is the same equation that gives you the (classical) gravitational potential. So the demonstration is an analogue computation that solves the analogous problem in gravity.

gcanyon 12y ago

Thanks! This visualization has frustrated me for many years, for many of the same reasons you list above, but I don't have the Ph.D. to back up my skepticism, so it's good to know that my bad understanding of gravity wasn't taken in by this.

mturmon 12y ago

I agree that the demo is mixing concepts (esp.: relies on actual gravity to work) and tempting confusion. As a teacher, you'd have to be careful to clarify this so you don't confuse students. I note that he says the demo is about GR, but then uses his rig and two handfuls of marbles to explain how almost all solar system orbits go in the same direction. (He doesn't need GR for that.) In this context, the rubber-sheet model is a very nice testbed for what is in effect a demonstration of stochastic initialization with positive or negative net angular momentum determining how it plays out. I liked that a lot. It also hooks up with various strands of current research: use of numerical gravitational simulations, solar system dynamics at long time scales, and the surprising discovery of many exoplanets with retrograde motion relative to their host star. If you'll grant that that is OK, you might have really lost it when he stuck the plastic strut underneath the sheet and said that was like dark energy! So that makes me want to re-think his rig in a more granular way. It seems like one key question is: does the curvature you get with a mass in the 2d sheet have the same local properties as the curvature you get via GR in Minkowski space? Is this what is really driving the paths of objects in the simulation to be ellipses, hyperbolas, etc.? What is a notable example of some GR prediction that is NOT accounted for by his rig?