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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!"

25 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.

    --
    The world's burning. Moped Jesus spotted on I50. Details at 11.
    1. Re:Um... by bloodhawk · · Score: 4, 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.

      ^this, many analogies in science are made to give a layperson a general/basic understanding of the concepts at work. They were never meant to be or expected to be working mathematical models.

    2. Re:Um... by nashv · · Score: 3, Interesting

      In the analogy of the rubber sheet, the earth's gravitational acceleration is the passage of time.

      --
      Entia non sunt multiplicanda praeter necessitatem.
    3. Re:Um... by joe_frisch · · Score: 4, Interesting

      The dented rubber sheet (done in earth's gravity) is a not too bad analogy for Newtonian gravity.

      Let me try the "ant" analogy in a bit more detail:

      The "orange" is curved space time. here we have 1 space like dimension and one time like dimension, curved into 3d.
      The "ants" walk forward. This walking is the analogy to moving forward in time.

      On a big flat surface, two ants that started near each other walking on parallel paths (both moving forward in time and at rest relative to each other) would stay the same distance apart.

      On the curved orange though as the ants walk forward, they wind up getting closer: Imagine they start at the equator and both head due north. The start out parallel, and both walk in as straight a line as is possible on the surface. After a while they find themselves closer together - as if some mysterious force (gravity) is attracting them. (this is as they get to the north pole.

      The orange analogy isn't all that great either because the curvature isn't shaped right for GR. Unfortunately humans aren't good at imagining curved 4-dimensional space.

      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.

       

    4. 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.

    5. 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.

    6. Re:Um... by Twinbee · · Score: 3, Insightful

      Here's my problem. What does the rubber sheet model do to explain relativity any more than explain Newtonian gravity? It seems perfect to demonstrate the latter.

      --
      Why OpalCalc is the best Windows calc
    7. Re:Um... by girlintraining · · Score: 3, Insightful

      ^this, many analogies in science are made to give a layperson a general/basic understanding of the concepts at work. They were never meant to be or expected to be working mathematical models.

      But how can we claim to be more smarter than the next person if we can't take a useful analogy and utterly destroy it by being overly pedantic?

      The main way in which we acquire new knowledge is by relating it to old knowledge. We introduce concepts progressively, building on primitives and emerging with complex models. Geometry can be reduced to a finite set of axioms (with an optional postulate) yet results in a near-infinite number of complex interactions. When we describe how computers work, we discuss in terms of layers of abstraction, from transistors and resistors, to APIs and data flows.

      Yet at every level and skill level, I can find people who scoff at those who continue to conceptualize things based on a earlier or lower level of abstraction. These people are what I call petty intellectuals: They aren't actually smart or gifted, they just read a lot of books and memorized a bunch of shit, and think this makes them "better" than others. The truly gifted will make you feel like you, too, can be gifted. This is the real lesson out of this article -- people who pick apart analogies for being "wrong" are usually simple-minded folk of average to below-average intelligence who desperately want to be "better" than you.

      The rubber sheet analogy works because it gives us a way to visualize a natural phenomenon; Not everyone has an aptitude for complex math, or the patience for it. The essentials of the theory of relativity can be relayed without resorting to complex math -- ie, describing space time as a "rubber sheet". It may not be as accurate, but accuracy is not the goal: Understanding is. It is also why we talk about "strings" in string theory, despite them having not much to do with a ball of yarn. It's why Heisenburg's black cat is forever dying in internet memes. It's why quarks have some rather strange names ... owing to leading a decidely charmed existance. Communicating concepts and relationships is what analogies are good for: They build a foundation for later learning to be given context and meaning.

      This is not a small problem in the scientific community either: Richard Feynman was laughed at for years for Feynman diagrams. He was told in no uncertain terms that visualizing these complex interactions couldn't be done, shouldn't be done, and was an abomination and a sin against those who practiced "proper" science. It wasn't supposed to be simple, dammit.

      Today, the Feyman diagram is one of the most recognizable images in quantum physics. The pedantics lost... but it was a bitter fight.

      --
      #fuckbeta #iamslashdot #dicemustdie
  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. Thought experiments by cold+fjord · · Score: 3, Insightful

    Thought experiments using analogues like the rubber sheet are often useful for visualization, organizing your thoughts, or providing a template to work on, but that doesn't mean that they necessarily provide a picture that is correct in all respects. The fact that they aren't accurate in all respects doesn't mean that they aren't useful representations.

    --
    much of left-wing thought is a kind of playing with fire by people who don't even know that fire is hot - George Orwell
  4. Works for the public by BringsApples · · Score: 3, Insightful

    Maybe it's just a general analogy for general relativity that's easy to understand, and not to be taken so so literally. Did they bother to come up with another analogy? Didn't think so. What dicks.

    --
    Politics; n. : A religion whereby man is god.
  5. 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.

    1. Re:I don't think .... by avandesande · · Score: 4, Insightful

      I don't think the scientists did either- I think this was more of a 'fun' experiment to see what happens when you actualize the analogy.

      --
      love is just extroverted narcissism
    2. Re:I don't think .... by ScentCone · · Score: 4, Funny

      actualize

      Stop that.

      --
      Don't disappoint your bird dog. Go to the range.
  6. Stupid by Anonymous Coward · · Score: 3, Insightful

    No analogy is perfect. However relativity is sufficiently complex that I don't know if any analogy would be perfect at all. This analogy at least provides a general sense of the way it works, it may not be 100% accurate but's relatively (see what I did there) close enough to provide a general understanding.

  7. Why did they bother? by AbsoluteXyro · · Score: 3, Interesting

    Who seriously expected the physics of a marble rolling on a rubber sheet to exactly match the physics of a planetary body in orbit? Who thought the analogy was ever meant to make that statement? It's still a pretty good analogy for giving a layperson the gist of how gravity works, and I seriously doubt it was ever meant to do any more than just that.

  8. Flawed, but not useful? by steelfood · · Score: 3

    All analogies are flawed in some way. They're analogies. They're not the actual thing. If the rubber sheet's characteristics match that of spacetime exactly, it probably is spacetime.

    But even if it's not exact, I think it's still a useful way to illustrate to the general relativity-illiterate (yours truly being among them) what the theory is all about, and why it's significant. General relativistic effects are not something that can be demonstrated (easily) in the classroom. Putting a marble on a rubber sheet is.

    --
    "If a nation expects to be ignorant and free in a state of civilization, it expects what never was and never will be."
    1. Re:Flawed, but not useful? by Darinbob · · Score: 4, Funny

      Analogies are like rubber sheets in that they have to be deformed to match their models.

  9. Analogy vs Model by EdmundSS · · Score: 4, Informative

    No. A rubber sheet is a flawed *model* for the shape of spacetime; as an *analogy*, it's still reasonable...

  10. 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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    /. refugees on Usenet: news:comp.misc
  11. 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.

    --
    Table-ized A.I.
  12. 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.

  13. The experts have spoken by steveha · · Score: 3, Interesting

    In other news, experts pointed out that rubber sheets provide a two-dimensional surface, while the real spacetime continuum provides three spatial dimensions and one of time. Experts also pointed out that rubber sheets have nonzero friction with rolling marbles, while empty space has zero friction; and that the rubber sheets do not provide the time dilation effects that gravity provides.

    Experts also pointed out that the whole rubber sheet thing is what is known as an "analogy" and pretty much by definition is inexact.

    Personally, I found the article interesting, but the tongue-in-cheek "Shame!" of the summary a bit over the top.

    P.S. From TFA:

    But the truth is that this work cannot diminish the extraordinary utility of this analogy. And so the public love affair with general relativity is safe. Long may it continue!

    --
    lf(1): it's like ls(1) but sorts filenames by extension, tersely
  14. Obligatory XKCD by Anonymous Coward · · Score: 5, Informative

    Obligatory XKCD

    http://xkcd.com/895/

  15. Monty Python by jeff13 · · Score: 3, Funny

    King; "Look! General Relativity!"

    Knights; "General Relativity!"

    Minion; "It's only a model."

    King; "Shh!"