alt_f13 Posted June 16, 2006 Share Posted June 16, 2006 Whenever somebody tries to explain curvature in spacetime, they always bring up the ol' "bowling ball on a trampoline" analogy. I'm wondering, isn't this a little like using a word in the sentence that is defining it? I saw a lecture where gravity was explained as not accellerating matter towards matter, but rather that matter "moving" in our 3 dimentions of common experience was actually at rest, and the act of resisting gravity was more like moving. I was wondering if there might be a scenario analogous to this way of thinking that doesn't involve gravity in the explanaiton. Perhaps with our medium expanding away or compressing towards our pieces of matter? Link to comment Share on other sites More sharing options...
swansont Posted June 16, 2006 Share Posted June 16, 2006 It's an analogy, not a definition. Just a way to visualize it. Link to comment Share on other sites More sharing options...
alt_f13 Posted June 17, 2006 Author Share Posted June 17, 2006 It's an analogy, not a definition. Just a way to visualize it. I find that intruducing a new dimension (the trampoline) is problematic: from the time that someone visualises cause of gravity using the effect of gravity as an example, they are stuck visualising gravity as being an effect of gravity, which is rather useless. There is a curve in spacetime - so what? What does that actually mean? All I'm saying is the analogy describes the effect of gravity, when it purports to describe the cause - it sounds a bit circular. Anyway, the other issue - I found the lecture/talk on the Perimeter Instutute site: http://streamer.perimeterinstitute.ca:81/mediasite/viewer/ in the Grand Opening Gala section, though I cannot remember which speaker it was. I'll post again when I find the video. Basically he described how gravity acting on an object is, in concept, less a force than a force used to escape gravity.(Sorry for the poor paraphrase. I'll post back when I find the video.) I'm looking for help coming up with an analogy to describe this. Link to comment Share on other sites More sharing options...
Sisyphus Posted June 17, 2006 Share Posted June 17, 2006 You're not introducing a new dimension, you're taking one away. (The curved 2D plane of the trampoline is standing in for the curved 3D space) And what's wrong with that? Human beings can't think in more than 3 dimensions, and so something like the curvature of space needs to be reduced in order to be able to be visualized. It's just like the "inflating beachball" model for explaining the expansion of space. I really don't see what the problem is. Link to comment Share on other sites More sharing options...
Janus Posted June 17, 2006 Share Posted June 17, 2006 I find that intruducing a new dimension (the trampoline) is problematic: from the time that someone visualises cause of gravity using the effect of gravity as an example' date=' they are stuck visualising gravity as being an effect of gravity, which is rather useless. There is a curve in spacetime - so what? What does that actually mean? [/quote'] Actually, you do not need to assume gravity for this analogy to work. You can assume that the trampoline is accelerating normal to its flat surface. Link to comment Share on other sites More sharing options...
alt_f13 Posted June 17, 2006 Author Share Posted June 17, 2006 You're not introducing a new dimension, you're taking one away. (The curved 2D plane of the trampoline is standing in for the curved 3D space) And what's wrong with that? Human beings can't think in more than 3 dimensions, and so something like the curvature of space needs to be reduced in order to be able to be visualized. It's just like the "inflating beachball" model for explaining the expansion of space. I really don't see what the problem is. The problem is how the example uses gravity (alowing the small ball to fall towards the big ball on the trampoline) to explain the curvature of spacetime, which causes gravity. A warped 3D grid would be a vastly superior substitute as it would show the effect in 3D, not 2D as with the trampoline, and gravity is not used as part of the demonstration of gravity (where on the trampoline, the balls are drawn together because of the force pulling down, towards the ground, rather than the force pulling the two together). As a visualization, a computer model of what I described would be far more helpful. I will admit, though, it's rather hard to explain vs telling people "spacetime curvature is like the warped surface of a trampoline," but pictures and movies are much more appropriate anyway. Actually, you do not need to assume gravity for this analogy to work. You can assume that the trampoline is accelerating normal to its flat surface. And how exactly would you explain that to someone who needs a visual to explain spacetime curvature? Besides, that doesn't eliminate the problem of the extra dimension, when in real life, that dimension is already in use. Link to comment Share on other sites More sharing options...
Perturbation Posted June 18, 2006 Share Posted June 18, 2006 It's only an analogy. I don't know any better way of explaining it without going into the mathematics. Space-time is some abstract thing that has non-zero curvature around bodies with mass-energy. If you really hate using the trampoline with gravity just say it's a naturally positively curved trampoline. Maybe some grossly obese person has fallen asleep on it and left an indentation. Link to comment Share on other sites More sharing options...
gcol Posted June 18, 2006 Share Posted June 18, 2006 It's an analogy, not a definition. Just a way to visualize it. Can I quote you on that? It might make a good signature by-line! For example "All science and religion is an analogy. Just a way to help visualise the unknowable". I shall have to work on it....... Link to comment Share on other sites More sharing options...
Zanket Posted June 19, 2006 Share Posted June 19, 2006 Whenever somebody tries to explain curvature in spacetime, they always bring up the ol' "bowling ball on a trampoline" analogy. I'm wondering, isn't this a little like using a word in the sentence that is defining it? Yes it is. The excellent book Relativity Visualized (by Lewis Carroll Epstein), says: "A lot of popular books on this subject show the warp as a down bump, caused by the Earth's weight, and illustrate gravity as objects rolling down into the hole, as if there were an up and down in empty space! This is a powerfully misleading notion, so strike it from your mind." I was wondering if there might be a scenario analogous to this way of thinking that doesn't involve gravity in the explanaiton. A lot of those "popular books" don't take the time to mention that the "bowling ball on a trampoline" analogy is a chart showing how spacetime curvature (which, BTW, is nothing more or less than the tidal force) changes in a plane that bisects the Earth (or whatever central object). The 3rd dimension shows the degree of spacetime curvature in the plane. Instead this could be shown by, say, a color gradient, with a legend to match the color gradient to a curve that shows the degree of spacetime curvature. The "bowling ball on a trampoline" analogy is okay as long as the book carefully explains it, like the book Black Holes & Time Warps (by Kip Thorne) does. Link to comment Share on other sites More sharing options...
alt_f13 Posted June 19, 2006 Author Share Posted June 19, 2006 The 3rd dimension shows the degree of spacetime curvature in the plane. Instead this could be shown by, say, a color gradient, with a legend to match the color gradient to a curve that shows the degree of spacetime curvature. I was going to suggest the color gradient, but I like the idea of a 3D representation, so I went with the warped grid. Perhaps a series of points with either varying densities in distribution, or same distribution but varying size would be more appropriate. I just don't like the idea of the concept being used to describe the concept. Like I said though, there's hardly an analogy that you can express verbally that can match the bowling ball analogy as far as how easy it is to visualize. I just wish there was. Link to comment Share on other sites More sharing options...
Zanket Posted June 19, 2006 Share Posted June 19, 2006 Human beings can't think in more than 3 dimensions, and so something like the curvature of space needs to be reduced in order to be able to be visualized. I don't buy that, assuming there are only 3 spatial dimensions to visualize. For example, this popular image shows 3 spatial dimensions and uses color to show the various layers of the Earth, a 4th dimension of information. It's just like the "inflating beachball" model for explaining the expansion of space. A good artist could no doubt redo this model as an animated graphic, to show all 4 dimensions. Were the image above changing with time, it would be a 5-dimensional graphic. Check out this six-dimensional (six-variable) chart: "Probably the best statistical graphic ever drawn, this map by Charles Joseph Minard portrays the losses suffered by Napoleon's army in the Russian campaign of 1812." Link to comment Share on other sites More sharing options...
JustStuit Posted June 19, 2006 Share Posted June 19, 2006 I think you are refering to a different definition of dimension. Link to comment Share on other sites More sharing options...
Zanket Posted June 19, 2006 Share Posted June 19, 2006 I don't see how. The "bowling ball on a trampoline" analogy is a 2D grid (a plane that bisects the bowling ball) along with the degree of spacetime curvature for every x,y point shown as a 3rd dimension. This 3rd dimension is shown as a spatial dimension, but is really just additional info about each x,y point. This info could just as well be shown by, say, a color gradient. Then the type of this 3rd dimension is no different than the type of the 4th dimension--the colors--of the Earth image above. Link to comment Share on other sites More sharing options...
alt_f13 Posted June 19, 2006 Author Share Posted June 19, 2006 This was the definition I was going by/referring to. Link to comment Share on other sites More sharing options...
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