Is there any graphical model that accurately portrays the nature of the universe? Specifically, the fact that if you go in one direction, you eventually end up where you started is the property I’m trying to model.
A sphere doesn’t quite fit the bill, because you are actually changing direction as you circle the surface.
Such an environment could be simulated with computer animation, but is there any tangible mockup that one could build?
Side note: does anyone know of a universe simulator for PC? Something that has the general 3D layout of the various galaxies and such would be good for hours of geeky fun!
For starters, we’re nowhere near being certian that if you go far enough in any one direction you get back to your starting point. In fact, most cosmologists now think that that’s not, in fact, true.
There’s at least two different possiblilities for the Universe where that is true, though. The possibility most often considered is that the Universe is positively curved. In this case, the surface of a sphere is a pefect model, aside from the minor detail that it’s only two dimensional, not three. I’m not sure what you mean about constantly changing direction.
The second possibility is that the Universe is not simply connected. One possible model for this would be an Asteroids screen, or the equivalent: When you fly off one edge of the screen, you come back on the other. The unit cell might not necessarily be a square (or cube), but since we don’t even know if this is true, we also don’t know what the shape would be.
If you walk along the surface of a sphere–say–the earth, you are changing direction as you go. You are always curving along the surface, never in a straight line.
the two-dimensional aspect is exactly what I meant by it not fitting, is there any geometrical demonstration of this type of situation (even if the universe isn’t really shaped like that)?
What I’m essentially looking for is a model of this theoretical repeating universe–but viewed from the outside.
Please let me know if I’m not making any sense.
You can’t go in a straight line and stay on the surface. The best you can do is a geodesic or an arc of a great circle. If the universe is curved, so are we. And so are our lines. They may not be straight, but they are the closest we can get.
For a two dimensional universe, the surface of a sphere or a torus is a model. If you want a model of a three dimensional universe, you would have to have a four dimensional model.