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Bowling ball rubber sheet analogy

  1. Jan 23, 2009 #1
    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?
     
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  3. Jan 23, 2009 #2
    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.
     
  4. Jan 23, 2009 #3
    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.
     
  5. Jan 23, 2009 #4

    A.T.

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    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
    Well, you have only one space dimension so you cannot visualize how circular orbits work. Just linear free fall, along the radial coordinate.
    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.
    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
     
    Last edited: Jan 23, 2009
  6. Jan 23, 2009 #5
    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
     
    Last edited: Jan 24, 2009
  7. Jan 24, 2009 #6
    AT: thanks in particular for the three "IT HAS BEEN DONE"...I have seen #3, but forgot about it....
     
  8. Jan 24, 2009 #7
    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.
     
  9. Jan 24, 2009 #8

    A.T.

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    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.
     
  10. Jan 25, 2009 #9
    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.
     
  11. Jan 25, 2009 #10

    A.T.

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    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?"
    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.
     
  12. Jan 25, 2009 #11
    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.
     
  13. Feb 7, 2009 #12
    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
     
  14. Feb 9, 2009 #13
    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".
     
  15. Feb 9, 2009 #14

    A.T.

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  16. Feb 10, 2009 #15
    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.
     
  17. Feb 10, 2009 #16

    A.T.

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    We are not missing it. It has been pointed out quit often.
    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.
     
  18. Feb 10, 2009 #17
    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.
     
  19. Feb 10, 2009 #18
    Nobody mentioned it in this particular thread, and it's the most obvious reason why the "rubber sheet" interpretation is wrong.

    Yes s/he should. The "bump" going up doesn't fix anything. Now why does the marble "fall" toward the bowling ball?
     
  20. Feb 11, 2009 #19

    A.T.

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    The sheet with the bump 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.
     
  21. Feb 11, 2009 #20

    A.T.

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