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Trampoline analogy for gravity

  1. Mar 9, 2015 #1
    The trampoline analogy tries to explain gravity in terms of space time curvature
    the orbit of objects around a massive object can be understood, but what about centre of gravity of the massive object, the images of trampoline is generally shown as seen from top where the massive object is making a curvature downwards when looking from the top, if that is the case how to explain the gravitational attraction of the objects on the surface of the massive object at the bottom side of the curvature
     
  2. jcsd
  3. Mar 9, 2015 #2

    A.T.

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    Actually it just shows space curvature. There is no time dimension on that sheet.

    There is no down or top in space. The 4D space-time geometry is spherically symmetrical, but the trampoline just shows a selected 2D spatial slice of it.

    It doesn't explain attraction at all, because it doesn’t include the time dimension. These are better visualizations of the attraction:



     
  4. Mar 9, 2015 #3

    wabbit

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    That second video is just the simplest, most concise, and accurate illustration I've seen of spacetime curvature in GR - much better then any rubber sheet analogy. Very nice.
     
  5. Mar 9, 2015 #4

    DrGreg

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    To be pedantic, that video doesn't quite cover spacetime curvature. It covers steps A, B1 and B2 below, but step C is needed to cover spacetime curvature.

     
  6. Mar 9, 2015 #5

    wabbit

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    True, but it still illustrates it : ) and it's very easy to grasp. I guess the second series you show would be "part II" to that first illustration's "part I".
    Are these all from one website ?

    Edit : and as to something equivalent with true Lorentzian metric, I don't recall seeing one, is that even possible ? If we look at a picture of a surface we are always going to interpret it as euclidian it would seem ?


    Edit : removed incorrect mention of 1D/2D
    "Part I" refers to video # 2 in post # 2
    "Part II" refers to pictures A B C in post # 4
     
    Last edited: Mar 9, 2015
  7. Mar 9, 2015 #6

    A.T.

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    The two videos don't show intrinsic curvature, which is related to tidal effects, because they are negligible on small scale. Here is an applet that shows the global picture:

    http://www.adamtoons.de/physics/gravitation.swf

    For visualization purposes you can work with space-propertime diagrams, which are Euclidean.
     
  8. Mar 9, 2015 #7

    DrGreg

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    Sorry, I'm not clear exactly what you mean by "I" and "II" in this context.
     
  9. Mar 9, 2015 #8

    wabbit

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    Thanks - for some reason I can't open that video, (tablet now) will try on computer later.
    But C above (post 4) does show tidal effect/geodesic divergence, as far as i could tell that's how it differs from B2.
    Also I don't understand
    the issue is that the metric has null cones / negative intervals, which means any euclidean representation is wrong in the same way, as "visual distance" cannot match "lorentzian distance" ? - not at all to say the euclidean diagrams aren't useful, more that they're the best we can hope for but they cannot be exactly correct.
     
    Last edited: Mar 9, 2015
  10. Mar 9, 2015 #9

    A.T.

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  11. Mar 9, 2015 #10

    wabbit

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    Oh Thanks, looks like some good reading to do now.
     
  12. Mar 9, 2015 #11

    DrGreg

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    Sorry, I'm not clear what you mean by that, either, or what you mean by "series" in this context.
     
  13. Mar 9, 2015 #12

    wabbit

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    Corrected that post # 5 above, thanks DrGreg for pointing this out.
     
    Last edited: Mar 9, 2015
  14. Mar 10, 2015 #13
    Thanks AT, Wabbit and DrGreg
     
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