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Vast
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Suppose the universe is bounded and not infinite, would it require more dimensions for the universe to curve back upon itself? Like most, I find it impossible to picture 3 dimensional space having a boundary.
So does everybody else; that is why applying the Cosmological Principle to a closed universe (Friedmann model with [itex]\Omega[/itex] > 1) gives you a finite unbounded hyper-surface. Analogous to the 2D surface of the Earth.Vast said:Suppose the universe is bounded and not infinite, would it require more dimensions for the universe to curve back upon itself? Like most, I find it impossible to picture 3 dimensional space having a boundary.
Garth said:So does everybody else; that is why applying the Cosmological Principle to a closed universe (Friedmann model with [itex]\Omega[/itex] > 1) gives you a finite unbounded hyper-surface. Analogous to the 2D surface of the Earth.
Chronos said:The universe is not 3 dimensional, it is 4 dimensional. Try to imagine that having an edge!
I use the term "hypersurface" as it is used in differential geometry and topology, to mean a surface of one-dimension less than the manifold being considered. So as Chronos said as space-time is four dimensional the hypersurface I was referring to is three dimensional space. This means we have to foliate, or 'slice' 4D space-time in a particular way to obtain this hypersurface.Vast said:Well yes, omega greater than 1 gives a positively curved spherical geometry, but wouldn’t that also be a closed bounded universe? not unbounded? This may depend on what you mean by an unbounded hypersurface, I’m not exactly clear on what a hypersurface is, whether it’s a 4 manifold, or some other geometry?
Chronos said:In a 4 dimensional universe, time [the 4th dimension] defines the 'edge' of the universe. So the only way to reach the edge, from any point in space, is to travel in excess of the 'speed of time'. This is impossible by our current understanding of physics - and logic.
Vast said:Is it correct to say the edge of the observable universe is the edge of the universe?
APPLAUSE!Vast said:Suppose the universe is bounded and not infinite, would it require more dimensions for the universe to curve back upon itself? Like most, I find it impossible to picture 3 dimensional space having a boundary.
Thor said:If space was not infinite then for any point in the universe there must exist another point within a finite distance at which motion in any direction would not increase the distance between the two.
At whatever moment of time you consider and regardless of the speed of the expansion the "next" increment of distance would not exist until the FOLLOWING moment.Vast said:I don’t see how that follows: Isn’t an expanding surface of a sphere finite and yet the points are moving away from each other?
Incorrect. In the understanding of GR it is space itself that expands, the galaxies etc. are carried along with it. It doesn't have to expand into anything.Thor said:And what is the universe "expanding" into except space which already exists?
Incorrect. In the Friedmann models an infinite flat or hyperbolic universe also expands from a singularity. However, you cannot say anything about the volume of that initial singularity.If the universe was 'created' from a point of singularity then unless it expanded at an infinite rate or for an infinite amount of time, it must be finite in nature.
Garth said:Incorrect. In the understanding of GR it is space itself that expands, the galaxies etc. are carried along with it. It doesn't have to expand into anything. Incorrect. In the Friedmann models an infinite flat or hyperbolic universe also expands from a singularity. However, you cannot say anything about the volume of that initial singularity.
Garth
No, it does not need an extra dimension. Curvature, and the spatial expansion of a universe with curvature, can all be completely described intrinsically by the behaviour of 'marker' points within it relative to each other. The angles and distances between such 'marker' points are described by the metric and the Riemannian and Ricci tensors derived from the metric.Nacho said:Did the original question ever get answered? I take it to be: For a 3 spatical dimension Universe that is finite and unbounded to expand, does that require a 4th spatial dimension within which to expand?
However to visualise what is going on you may find it more convenient to embed such a hyper-surface in a flat static higher dimensional manifold.
Mathematically you can embed the 3D space in a higher dimensional manifold, the question is whether these higher dimensions have any physical significance.Nacho said:The GR expressions you use describing a 3 spatial dimension Universe, are they equivalent to what would be used in 4 spatial dimension math to describe a 3 spatial dimension "bubble" within it?
A bounded universe is a theoretical concept in which the universe has a finite size and is enclosed within a boundary or edge. This is in contrast to an unbounded universe, which has no boundaries and is infinite in size.
Currently, we do not have definitive evidence or proof that the universe is either bounded or unbounded. Scientists continue to study and gather data in order to better understand the nature of our universe.
In order for a universe to be bounded, it would need to have a finite size and be enclosed within a boundary. This would require an additional dimension to contain the boundaries, as our current understanding of the universe includes only three spatial dimensions (length, width, and height).
Some theories, such as string theory, propose the existence of additional dimensions beyond the three spatial dimensions we are familiar with. These theories suggest that the universe may be bounded in order to accommodate these extra dimensions.
If the universe is indeed bounded, it would have significant implications for our understanding of the universe and its origins. It could also potentially impact our understanding of space and time, as well as the laws of physics that govern our universe.