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B GR gravity path confusion

  1. Jun 14, 2016 #1
    Ok. I get that objects seem to fall because of curved spacetime, when they're actually just moving in straight paths. I get the example of ants walking in straight lines on the surface of a sphere, thinking that something attracts them to each other. What I don't get is how the "ants" are "attracted" to each other without walking. What that means is, how is a stationary object attracted to another stationary object? I don't get this.
     
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  3. Jun 14, 2016 #2

    Jonathan Scott

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    You're thinking of curved space only. In curved spacetime, stationary objects are effectively moving along the time axis at speed c, so the curvature of free fall paths as the object moves through time accelerates it even if it isn't moving in space.
     
  4. Jun 14, 2016 #3

    phinds

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    Start with the first scenario you posited. An object "seems to fall because of curved spacetime". Now expand it to encompass the "falling" object and the object towards which is it falling. Now you have exactly the scenario in your question. Two objects "attract" each other because of the space-time geometry between them. If they are stationary relative to each other, that means that there is a force involved that is keeping them apart. In your first part, you said they are moving towards each other with means no, or small, other force. In the part where you say they are stationary you have (without realizing it) posited another force. A good example of this is you standing on the surface of the Earth. the force keeping you from falling into the Earth towards the center is the electrostatic repulsion of your feet with the ground. If you jumped out of an airplane, there would be no such force so the space-time geometry would cause you to move towards the center of the Earth.
     
  5. Jun 14, 2016 #4
    Ah ok, I think I get it now. So it moves in time, but it doesn't in space.
     
  6. Jun 14, 2016 #5
    You don't have to be affected by a force in order not to be moving relative to another object... I think you misunderstood what I said.
     
  7. Jun 14, 2016 #6

    phinds

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    Oh? How do you figure that? Give me an example
     
  8. Jun 14, 2016 #7

    A.T.

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    Yes, initially. But due to the space-time geometry it deviates from the purely temporal direction, and starts moving in space.

     
  9. Jun 14, 2016 #8
    You are nearly there, you already have it in terms of space. Two ants at the equator will approach each other as they move towards the "North pole". Now think of the latitude as a time axis, and you have rudimentary "gravitation".
     
  10. Jun 16, 2016 #9
    Why would that be the case? Can't two bodies be stationary in space? Since when? I think you're using the conclusion from what I want explained to explain it to me. Anyway, my question was explained.
     
  11. Jun 16, 2016 #10
    Oh, I think I get it now, I can picture it now in 2 spatial dimensions, I obviously can't in 3 :)
     
  12. Jun 16, 2016 #11

    phinds

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    No, they cannot. Gravity will pull them together unless they are kept apart by some other force. Any other examples? (hint ... there aren't any).
     
  13. Jun 16, 2016 #12

    A.T.

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    You can visualize a curved 2D space-time, but one of the dimensions needs to be time, so you actually have just 1 spatial dimension (like the straight vertical fall in the video I posted above). Correctly visualizing it for 2 spatial dimestions + time (for example to show orbits as geodesics) is difficult,
     
  14. Jun 16, 2016 #13
    That's what I am saying. You are using the conclusion coming from what I want explained to explain it.
    -How can bodies be "pulled together" due to spacetime geometry by gravity in GR if they are stationary?
    -They can't be stationary.
    -
    Why can't they be stationary?
    -Because they are pulled together by gravity.

    You probably misunderstood my question.
     
  15. Jun 16, 2016 #14

    phinds

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    Must have.
     
  16. Jun 16, 2016 #15
    Ah, no, I only visualized the concept of 2 particles on a 2-d surface being attracted to each other, nothing more complicated than that! I imagined something like 2 balls inside a sphere. The height of the sphere is time. Ok, it's not accurate, it's just the concept that I wanted to visualize, thanks!
     
  17. Jun 16, 2016 #16

    A.T.

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    That's fine. For two bodies pulled together along a straight line one spatial dimension is enough (the one along that line). The 2nd dimension on your sphere is time.

    But what you are visualizing here is how particles of negligible mass are pulled together by the gravity gradient of a bigger mass (tidal gravity), not how masses attract each-other with their own mass.
     
  18. Jun 16, 2016 #17

    stevendaryl

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    I would say that the idea of gravity as curvature only works when you think that we reside in 4-dimensional spacetime, rather than 3-dimensional space. And furthermore, every object has a nonzero velocity in the time-direction (we are all moving into the future).

    If you think of time as a dimension like space, then how gravity works is perhaps easier to understand. When you say that an object is "stationary", that only means that the spatial components of its velocity are zero, but the time component of its velocity is nonzero: It is moving into the future. Now, add gravity, and that path becomes bent--it starts moving purely in the time direction, but bends to start moving in a spatial direction, as well.
     
  19. Jun 17, 2016 #18
    Because they age into the future; see post #17 for details.
     
  20. Jun 17, 2016 #19
    Sure. I just wanted to realize the concept.
     
  21. Jun 17, 2016 #20
    Yeah, that was explained by Jonathan Scott and A.T.
     
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