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Thread: Help with general relativity?

  1. #1 Help with general relativity? 
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    Im having trouble understanding curved spacetimes in general relativity. What I do understand is that mass and energy warps the spacetime and makes it curved. What I dont get is how this curved spacetime can explain gravity or why objects would go towards the distortions in the spacetime? Any explanation would be great


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    Forum Isotope Zelos's Avatar
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    just imagen that you got a rubber area, like those ballons are made of just stretched out

    then place a heavy ball in it, you´ll see the ball sink down and the rubber area around it bend. this is spacetime curvation in a 2D world.

    now take another ball and roll it forward so it gets close to the other ball. as you see the path of the second ball gets curved. and if we were to have 0 friction you can easly imagen that it will, if low enough speed, go around and around like a normal orbital body.

    bodies allways go in a straightline in 4D but since space is bent it appear to go around and around in 3D

    hope that helped, i usually hate analogies but this time i think it was neccisery


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  4. #3 Re: Help with general relativity? 
    Forum Ph.D. Steve Miller's Avatar
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    Quote Originally Posted by Trogdor
    Im having trouble understanding curved spacetimes in general relativity. What I do understand is that mass and energy warps the spacetime and makes it curved. What I dont get is how this curved spacetime can explain gravity or why objects would go towards the distortions in the spacetime? Any explanation would be great
    Hey, congratulations!

    I already stopped at 'spacetime' and did never figure what that would mean.

    Steve
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    Forum Radioactive Isotope mitchellmckain's Avatar
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    The difficult part of GR is the higher dimensional mathematics required to make the essential ideas explained by Zelos work in a three dimensional space (actually a four-dimensional space-time to be more accurate). The key concept is that of the metric, which measures distances. You are probably used to the cartesian metric used in Euclidean space:

    ds = square root of (dx^2 + dy^2 +dz^2)

    (if you are not familiar with this, then perhaps you are familiar with the pythagorean theorem which this is kind of a generalization of)

    Well in general relativity this is NOT the metric and the space is NOT Euclidean. The metric in GR is affected by presence of energy (including mass).

    Part of the problem is that it is all based completely different formulation of physics based on Lagrange actions rather than forces. This Newtonian physics with forces is first year physics and GR is more like eighth year physics. So it is a little hard to understand GR without all the other physics in between. And that is impossible to cover in a post in this forum.
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    Forum Ph.D. Steve Miller's Avatar
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    Yes, truly!

    When I got on with mathematics and calculated 0 as result regardless of which
    algebraic sign, ok, that's funny, but to me was not a clue either.

    Steve
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    here is where i get confused. In 4 dimensional space earth moves in a straight line but because we see things on in 3 dimensions it looks like it has an elliptical motion? Im not sure if thats right but even if it is I dont understand it. Also how does this relate to spacetime being curved?
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  8. #7  
    Forum Ph.D. Steve Miller's Avatar
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    Hello Trogdor!

    The elliptical motion was certainly no false perception. The seasons are made by it imaginably.

    Earth closer to sun --> hotter weather, summer;earth in a remote distance --> colder weather,
    winter. That's pretty much possible.

    Steve
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  9. #8  
    Forum Isotope Zelos's Avatar
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    Quote Originally Posted by Trogdor
    here is where i get confused. In 4 dimensional space earth moves in a straight line but because we see things on in 3 dimensions it looks like it has an elliptical motion? Im not sure if thats right but even if it is I dont understand it. Also how does this relate to spacetime being curved?
    thats pretty much it, time is also bent with it but i excluded it to not cause to much confusion.
    spacetime = space and time, since its bent space is bent and time aswell, time goes slower in gravitational fields
    I am zelos. Destroyer of planets, exterminator of life, conquerer of worlds. I have come to rule this uiniverse. And there is nothing u pathetic biengs can do to stop me

    On the eighth day Zelos said: 'Let there be darkness,' and the light was never again seen.

    The king of posting
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  10. #9  
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    Trogdor: the rubber sheet and bowling ball analogy isn't very good, because you need gravity to explain gravity. But make few small changes, and there is a useful analogy to be had.

    Instead of a bowling ball causing a depression, imagine a knot somehow tied in the rubber sheet. Around this knot there's an area where the rubber sheet is under higher tension. This tension increases nearer the knot, and affects light propagation. Light moves more slowly where the tension is higher. Electron orbits and all other atomic processes are similarly affected.

    Now imagine you're a one-electron atom skirting the area of tension - you are part of the rubber sheet, but free to move within it. As you approach, the side of you that is closer to the knot is slowed down fractionally more than the other side. So you veer towards the knot, akin to refraction. Scale this up a dimension and you should get the picture.

    Note that curved spacetime is just the path you follow, and one has to take the time-derivative to get a handle on the underlying tension gradient. The variable c is something you can never measure directly, because it affects all your electrons and atoms, and your clocks and rulers.
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  11. #10  
    Forum Ph.D. Steve Miller's Avatar
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    Hello!

    You see, there gravity comes in. We had not been talking about gravity. Although, the curvature of spacetime
    could cause other forces than gravity dragging.? It was not spoken about gravity in space.

    Steve
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  12. #11  
    Forum Isotope Zelos's Avatar
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    Trogdor: the rubber sheet and bowling ball analogy isn't very good, because you need gravity to explain gravity. But make few small changes, and there is a useful analogy to be had.
    it is good enough to explain why the curvation do effect motion. but you dont really need gravity just acceleration

    Instead of a bowling ball causing a depression, imagine a knot somehow tied in the rubber sheet. Around this knot there's an area where the rubber sheet is under higher tension. This tension increases nearer the knot, and affects light propagation. Light moves more slowly where the tension is higher. Electron orbits and all other atomic processes are similarly affected.
    light dont move slower
    it allways move C
    I am zelos. Destroyer of planets, exterminator of life, conquerer of worlds. I have come to rule this uiniverse. And there is nothing u pathetic biengs can do to stop me

    On the eighth day Zelos said: 'Let there be darkness,' and the light was never again seen.

    The king of posting
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  13. #12  
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    on a side note does anyone know of any site with good diagrams to use on a essay about both special relativity and general relativity
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