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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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    http://www.relativitet.se/spacetime1.html" [Broken].
     
    Last edited by a moderator: May 4, 2017
  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 https://www.physicsforums.com/showpost.php?p=2042081&postcount=7".
    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.
     
    Last edited by a moderator: Apr 24, 2017
  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?
     
    Last edited by a moderator: Apr 24, 2017
  20. Feb 11, 2009 #19

    A.T.

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    http://www.physics.ucla.edu/demoweb...and_general_relativity/curved_spacetime.html" 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.
     
    Last edited by a moderator: Apr 24, 2017
  21. Feb 11, 2009 #20

    A.T.

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    Last edited by a moderator: Apr 24, 2017
  22. Feb 11, 2009 #21
    So we are visualizing some curved "thing" around an object. Now, why does the other object move toward it?

    In the rubber sheet analogy the object falls down the curved surface of this "space object". But the effect we're trying to explain is what we observe as "falling down". So we observe that objects "fall down" to earth and the rubber sheet analogy says that yes, objects do indeed "fall down" toward each other. See? What the ball "fall down".

    The analogy is just plain worthless. The reason GR correctly correlates Mercury's orbit is because "time dilation" contributes +4BF, "space contraction" contributes -2BF, and momentum increase (with increasing speed) contributes +1BF giving the observed amount, 3BF. BF is the "basic form" for describing elliptical motion: n*u/(c2*a*(1-e2)) where n=2*pi/P is the orbital mean motion of the planet, P is its orbital period, u is the product of the gravitational constant and the mass of the Sun (in the case of Mercury), a is the semi-major axis (mean distance) of the orbit, e is orbital eccentricity, and c = speed of light. Of course Einstein was aware that Mercury's orbit is 3 integer multiples of this formula (within experimental error) and adjusted the metrics accordingly.

    Of course this is not very good for the layman, but the rubber sheet analogy is either patronizing or disinformative. Worst of all it may be deceptive, making the layman believe GR has a physical interpretation when it is just an excellent quantitative description.

    Don't use the rubber sheet analogy, let it die, it's awful. If you want to understand GR start with Newton and move forward, reading as much of the original work as you can get your hands on. These cartoons inhibit understanding and sometimes move it backwards, don't do yourself the disservice. To understand GR you need math, because GR is a mathematical theory. You can't understand GR by visualization, no matter how hard popularizers of the theory try to do so. Every visual analogy suffers fatal flaws that render it meaningless.
     
    Last edited by a moderator: Apr 24, 2017
  23. Feb 11, 2009 #22

    A.T.

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    Not some curved thing but the spacial curvature and its effects like orbit precession.
    If you mean Newtonian mass attraction: Purely spacial curvature doesn't explain it. You need the time dimension like http://www.relativitet.se/spacetime1.html" [Broken].

    Every physical theory uses math. But GR is also a geometrical theory.
    I disagree. Visualization is very useful to understand geometrical theories. Einstein wouldn't have come up with GR, if Minkowski had not visualized SR.
     
    Last edited by a moderator: May 4, 2017
  24. Feb 11, 2009 #23
    That seems a rather bold assertion, that GR shall never be explained on physical grounds that can be visualized. Maybe not bowling balls and a rubber sheet, but perhaps some visual model not yet known to us will one day let high school students learn mathematically correct GR in their honors Physics courses.
     
  25. Feb 13, 2009 #24
    "Not some curved thing" -AT

    Okay so space is not a thing. The "space" in GR is just a useful parameter in the equations, not a physical thing. Things are visualizable, non-things are not visualizable.

    "Every physical theory uses math" -AT

    Only at the conclusion step of the sci meth, if at all. Mathematical correlations are just additional evidence at the end to convince everyone else of your theory. The first step we do in physics is visualize the physical entity(ies) involved. If we cannot visualize them, the theory is not a physical explanation, it's a mathematical model.

    "But GR is also a geometric theory" -AT

    Geometry is the study of shape. But GR's "space" and "time" are not things with shape, they are just concepts. Einstein may have guided his intuition by visualization, but his theory has nothing to do with geometry if space and/or time are not things.

    nick,

    GR is based on 4D "objects". I am saying that nobody will ever visualize a 4D "object". This alone renders GR only physically comprehensible by analogy, and we call it an "analogy" for a reason, it never quite matches "the real thing".
     
  26. Feb 13, 2009 #25

    A.T.

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    Everyone got that memo? We are not allowed to use diagrams to visualize space-time anymore! :rolleyes:
    If something moves along a line in space, you can omit 2-space dimensions, and visualize a 2D-spacetime. Works fine for me, and you don't have to use it, if you don't like it.
     
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