Space is curved, so how do I model it?

Discussion in 'General Discussion' started by K.I.L.E.R, Jul 8, 2006.

  1. K.I.L.E.R

    K.I.L.E.R Retarded moron
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    It's almost impossible to think about this.
    Is the universe a giant torus?

    I'm actually trying to model this in my program however I will NOT be using stupid models of space that every other program in this world ever made has used.
    I want to create the universe's curvature EXACTLY as it is in real life, complete from the universe to how we see things in space.

    I will not be modelling the contents inside the universe but I do want to model the universe itself. Ony rough approximations will be used for planets and stars.

    Can someone in this area please tell me what I'm really trying to do(Lack of understanding in this area does hurt)?
    I've read about this stuff before and seen documentaries but it doesn't really help when someone tells you that you can bend space.
    Is it like bending a mathematical plane?
     
  2. Dersaidin

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    I think you may have to wait a long time for humans to figure that out before you can model it correctly :/
     
  3. kimg

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    Imagine it simplified:

    X and Y axis is the galaxy's plane, the flat disc. Z is the height.

    Then, add a new effect, a "bending", define the model for bending after physics, store it as a x,y based map, with info for reach(this will be a little inacurate outside the zone in the middle, but is useable), define the direction bending, produce running "bent" coordinates for the used of coordinates(players, ships, simulated ships, etc), x2 y2 z2, who is used.

    of couse this would need to rethinking "line of sight" , to allow sight to be bent, and other effects.
     
  4. K.I.L.E.R

    K.I.L.E.R Retarded moron
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    That's incorrect unless you are taking into account:
    Density of energy vs density of matter.

    If matter is more dense than energy then the universe is ecliptic.
    If the reverse is true then the universe is hyperbolic.
    If they are equal then the universe is a plane.

    Euclidean geometry is only correct on our planet and even then with a margin of error.
    I want to model the universe as it is modelled in real life.

    I can simulate the above conditions however I really wan to know how much more is there to model the universe correctly and whether or not I know what I'm really asking.
     
  5. digitalwanderer

    digitalwanderer Dangerously Mirthful
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    Try e-mailing Stephan Hawkings about it. [​IMG]
     
  6. _xxx_

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    Use a nice Pam Anderson pic as your desktop background, that might give you a better Idea of curves ;)
     
  7. Blazkowicz

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    I know a good simulation of an universe with torus topology :

    Asteroids :)
     
  8. KimB

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    Learning how to properly deal with curvature can be very difficult. But fortunately, if you just want to look at the Universe, you don't need to worry about it much. The Universe is very, very flat. We don't yet know what the overall topology of the Universe is (i.e. if you go far enough in one direction, will you end up at the other end of the Universe?), but given the current accelerated expansion, the overall topology probably doesn't matter, and will likely never be found.

    The only place where curvature really starts to matter is near massive objects. For this, there are a number of visualization websites. Here's a list of a few of them:
    http://math.ucr.edu/home/baez/RelWWW/visual.html

    I wouldn't even try to properly-model spacetime curvature until you get a lot more math under your belt. Differential geometry is not to be taken lightly (it requires a rather strong base of multivariable calculus).
     
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  9. Fred

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    In other words you have to solve Einsteins field equations. Which as Chalnoth said, requires differential geometry, and being familiar with physicists tensor or differential form notation which I suspect you don't have yet.
     
  10. KimB

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    Well, you don't necessarily have to solve Einstein's field equations (lots of people have done this already), but you do have to know how to calculate geodesics, which can be very challenging.
     
  11. K.I.L.E.R

    K.I.L.E.R Retarded moron
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    Differentiable goemetry.
    Sounds like the stuff I've been doing in computer graphics class.

    Partial ODEs used in geometry?
    If so then, easy!
     
  12. Arun

    Arun Unknown.
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    Just think about varying density and you'll have the right idea tbh.
    Curvature is an ugly term that refers to little more than the implicit apparent refraction you get from varying spacetime density.


    Uttar
    P.S.: Chalnoth, if you think that's downright stupid, please feel free to explain why ;)
     
  13. KimB

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    Not differentiable, differential. Here's a link that gives you an idea of what's involved:
    http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/tc.html
     
  14. K.I.L.E.R

    K.I.L.E.R Retarded moron
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    I've looked through the maths and I recognise a fair bit of it.
    The maths isn't hard by a longshot.
    The hardest part would be deriving the stuff by yourself.

     
  15. KimB

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    There's a reason that General Relativity is typically a graduate course, KILER. Your statement that it's not that hard just shows that you don't understand what's involved in doing GR calculations. Until you've got some variational calculus under your belt, I wouldn't even bother trying to start with GR.
     
  16. fellix

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    By some recent studies (inspired by the string theory) postulating that there was a pre-Universe before the Big Bang and the "bang" itself was just a flip-flop, the actual number of dimensions in the real Universe is in fact a matter of...choise, and I'm not talking just for the dimensions in the XYZ-ordinate system.
    The point of all this is that our rational 3D Universe is a kind of "hologram" if we look from sub/quantum-mechanic level of perspective. Take any one of the tree geometrical dimensions, ignore it and imediately the Holly Grail of the Phisycs - the quantum gravity could be explained and eventually evaluated in mathematical manner (not yet done AFAIK). Actually this way we can ignore the gravity effects at all in the "simplified" 2D projection of our "holographic" Universe and thus greatly reduce the complexity of evaluation for all the known phisycs.
    Of cource, any sort of singularity in the above description is prohibited - there is no place for infinitie small point particles here, eg. there is no singularity at all.
     
  17. K.I.L.E.R

    K.I.L.E.R Retarded moron
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    I'm going to take a swing at it anyway.
    If I have to learn new things in the process then I'm better for it.

     
  18. Frank

    Frank Certified not a majority
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    It's actually really simple to do. Instead of storing the distance as coordinates, you store the matter/energy density. You need a correction step in either case, but it doesn't matter one bit for the model you use if your geometry consists of distance or density.
     
  19. K.I.L.E.R

    K.I.L.E.R Retarded moron
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    Chalnoth, you have experience in this area? I know you do, you probably taken the course before I was born.
    If I were to pay you real money, would you consider running a private class for me?
    Obviously not now, but if I were to pick this up at a later time out of interest and after I've become more experienced in my mathematics would you consider such a proposal?

    Is it possible for me to learn this stuff going only by books?
     
  20. KimB

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    If you want to learn GR, the only realistic way would be to take graduate courses in mathematics or physics (which require either an undergraduate degree in mathematics or physics to understand, or just being very good at math and/or having an excellent professor).

    Having learned it in the above way, I don't know whether or not it would be possible to learn from just books. You could, of course, attempt to learn from one of the GR texts that is out there (Sean Carroll has a good one), but those will set you back quite a bit of cash, and would probably be very hard to understand without a strong physics background.

    One reason why GR math is so challenging is just due to the large number of equations and parameters. We write these equations in tensor form, so that they are relatively simple to write down, but actually doing calculations with 3rd-rank tensors is very cumbersome and requires you to be very precise about your mathematics (I remember taking an entire weekend to derive the Friedmann equations for the first time from the FRW metric with constant spatial curvature, and that's one of the simplest problems you can do).

    Granted, I've never done numerical GR solving, so in principle that might be easier, as you don't have to deal with the cumbersome algebra, but you still have to deal with cumbersome algebraic manipulations regardless.
     
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