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Experiments Reveal That Deformed Rubber Sheet Is Not Like Spacetime

Posted by Unknown on from the deformed-example dept.

KentuckyFC writes "General relativity is mathematically challenging and yet widely appreciated by the public. This state of affairs is almost entirely the result of one the most famous analogies in science: that the warping of spacetime to produce gravity is like the deformation of a rubber sheet by a central mass. Now physicists have tested this idea theoretically and experimentally and say it doesn't hold water. It turns out that a marble rolling on deformed rubber sheet does not follow the same trajectory as a planet orbiting a star and that the marble's equations of motion lead to a strangely twisted version of Kepler's third law of planetary motion. And experiments with a real marble rolling on a spandex sheet show that the mass of the sheet itself creates a distortion that further complicates matters. Indeed, the physicists say that a rubber sheet deformed by a central mass can never produce the same motion of planet orbiting a star in spacetime. So the analogy is fundamentally flawed. Shame!"

9 of 264 comments (clear)

  1. Um... by MightyMartian · · Score: 5, Insightful

    I'm not sure the analogy was ever meant to be a rigorous and exact model, but more of a kind of way of visualizing space-time. All analogies break down if you try to map them exactly to the phenomenon you're trying to explain. After all, it's an analogy, not a model.

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    1. Re:Um... by Anonymous Coward · · Score: 5, Informative

      If the rubber-sheet demo is done without earth's gravity it isn't a terrible analogy, but I don't think I've ever seen it show that way. It seems to always be shown as this curved surface where the EARTH's gravity causes the marbles to roll to the center.

      If it's done without the Earth's gravity then nothing happens, the ball just fucking sits there, and nothing makes a "dent" in the rubber because... there's no gravity.

      It's an analogy, not a physical model. You're supposed to ignore the presence of Earth's gravity when you look at it, and understand that the way the balls deform the surface is in some respects similar to how an object deforms space-time.

      I can't say this enough: An ANALOGY is not the same thing as a MODEL. It's not supposed to be a physically accurate representation, you should NOT expect to roll a ball across the surface and get results that match actual real-world physics. That's why we call it an ANALOGY.

    2. Re:Um... by tlhIngan · · Score: 5, Interesting

      I agree, the marble will still follow a curve if it sticks to the rubber in zero-g - so the curvature does change its trajectory. Usually when this is shown though ,it is done in earth gravity and that is the largest effect on the marble. Even in zero-g, the analogy with GR is very thin because the curvature of the rubber sheet doesn't involve the time coordinate, so the effect on the marble's path doesn't really look like gravity in GR.

      Done right the rubber sheet can be a barely OK analogy, as it is usually done though it is just confusing.

      The problem is the rubber sheet is a 2D surface. It can represent two dimensions. It can be two of space (as is normal), one space and one time, etc.

      Real spacetime is a 4D entity - 3 (elongated) space, 1 time. The reason we use the rubber sheet analogy is because visualizing the distortions in spacetime (a 4D entity) is quite... difficult. Even visualizing a 3D representation is quite hard (pick your mix of space and time dimensions you want to show).

      However, a 2D representation is quite easy to demonstrate and show to a class so they can visualize that happens. Sure, gravity is the biggest reason why the rubber sheet curves and what causes the marble to follow the curves, but it's a remarkably intuitive image of the warping of spacetime. (Then again, gravity is what causes the warping to begin with, and while we're using the earth to warp a rubber sheet because it's convenient...).

      To be honest, it isn't a rigorous mathematical model, but it was never supposed to be. It's a practical demonstration on the weirdness of spacetime and gravity, illustrated on a 2D plane because we, despite being 4D entities have a hard time imagining it.

      No one's going to derive equations for general relativity based on the rubber sheet analogy (or model - our physics class had a real model and we all had a chance to play with it). But it's certainly a great "a ha!" style of demonstration to solidify what is happening from dozens of equations and dry text.

      And face it - modern physics is really damn hard to show people what is happening - either things are too big (relativity) or too small (quantum physics) that most people do not have any sort of grasp of it. At best, you have a model or an analogy. And never mind gravity is an extremely weak force to deal with.

      So no, you aren't going to be mathematically correct. You are, however, going to get a lot of "I get it now!" reactions. Because in normal everyday life, gravity is not like what the theory says it is. We experience gravity like what Newton said it is. We don't see gravitational lensing or other such things

      I say the rubber sheet model is more adept at getting the public to understand relativity than anything else.

  2. This is old news by Anonymous Coward · · Score: 5, Informative

    This was figured out more than 100 years ago. A rubber sheet can be mapped to a scalar theory of gravity. If you made it past the first two lectures of a class on General Relativity, you would know that Relativity is a tensor theory. That is why it is so horrendously complicated.

  3. I don't think .... by therealkevinkretz · · Score: 5, Insightful

    ... that anyone who had a grasp of high school phsyics, and who understood the analogy - of 3D matter flattened to represent a 2D metaphor for our real 3D world, which lives in 4D spacetime - or who understood that gravity attracted mass towards mass and not towards the "down" direction perpendicular to the sheet - would think for a second that such a demonstration would create the same exact trajectory as actual interaction between 3D objects in 4D spacetime.

  4. All analogies are fundamentally flawed by Koen+Lefever · · Score: 5, Interesting

    Analogies help to understand something... up to a certain point.

    It only illustrates the basic concepts. After that, one has to go beyond the analogy and do the math.

    I remember a poster on a door at the math department of my university (parafrazing from memory): "Do not try to visualize a space with more than 3 dimensions. Nobody can do that, trying will just twist your mind. Just use the formulas with the correct number of variables and leave it at that."

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  5. For Pete's Sake! by Tablizer · · Score: 5, Funny

    Next they are gonna to tell me my Fisher Price bath boats are not sufficient for planning naval invasions.

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    Table-ized A.I.
  6. Rubber sheet analogy explained by Anonymous Coward · · Score: 5, Funny

    Suppose that you had a big rubber sheet stretched out, and onto that sheet you place a ball. Now suppose that there's a force that pulls the ball down, creating a depression in the sheet. Well, gravity is a lot like that force. Really a lot like it.

  7. Obligatory XKCD by Anonymous Coward · · Score: 5, Informative

    Obligatory XKCD

    http://xkcd.com/895/