1. 3D Bubble universe..jpg

Is it possible that our universe is a 3D (spacial) bubble in an infinite 3D universe, without resorting to a fourth spacial dimension ? Do the maths work?

The picture is a 1D representation of what I mean: B is the infinite universe, A is our bubble universe and C is the intersection, the origin where our Big Bang presumably would have happened. If the 1D representation is mathematically valid, what characteristics would one expect from a 3D version? Would it resemble our universe from within the bubble? Would the point of the big bang still be everywhere, or would there be a point of origin somewhere?

I might need a new thread for this.  2.

3. Originally Posted by KALSTER [Is it possible that our universe is a 3D (spacial) bubble in an infinite 3D universe, without resorting to a fourth spacial dimension ? Do the maths work?
Yes. You can, mathematically, describe a 3 dimensional "surface" which is curved, without embedding it in a four dimensional space. This is hard to visualise because it can only be done for three dimensions or more. GR describes the universe as made up of 4-dimensions (3 space plus 1 time) which are curved but not in a fifth dimension; it is "intrinsic" curvature.

(Didn't really "get" your diagram or the second part so I won't comment on it)  4. Originally Posted by Strange  Originally Posted by KALSTER [Is it possible that our universe is a 3D (spacial) bubble in an infinite 3D universe, without resorting to a fourth spacial dimension ? Do the maths work?
Yes. You can, mathematically, describe a 3 dimensional "surface" which is curved, without embedding it in a four dimensional space. This is hard to visualise because it can only be done for three dimensions or more. GR describes the universe as made up of 4-dimensions (3 space plus 1 time) which are curved but not in a fifth dimension; it is "intrinsic" curvature.

(Didn't really "get" your diagram or the second part so I won't comment on it)
Yes, that is what I understand too, as explained by the balloon analogy. To cover the second part, one can extend the balloon analogy to the 2D surface of a balloon connected to an infinite 2D plane by a single point, I think, if it is mathematically valid (I recall faintly that the point would mean that the balloon and surface can not be described as the same manifold, or some such..). The question is, what would that look like in 3D; would that resemble what we have observed about our own universe thus far?  5. Originally Posted by KALSTER Yes, that is what I understand too, as explained by the balloon analogy. To cover the second part, one can extend the balloon analogy to the 2D surface of a balloon connected to an infinite 2D plane by a single point, I think, if it is mathematically valid (I recall faintly that the point would mean that the balloon and surface can not be described as the same manifold, or some such..). The question is, what would that look like in 3D; would that resemble what we have observed about our own universe thus far?
Does this mean you are proposing to eliminate the time coordinate altogether, thus creating a static universe ?  6. Originally Posted by Markus Hanke  Originally Posted by KALSTER Yes, that is what I understand too, as explained by the balloon analogy. To cover the second part, one can extend the balloon analogy to the 2D surface of a balloon connected to an infinite 2D plane by a single point, I think, if it is mathematically valid (I recall faintly that the point would mean that the balloon and surface can not be described as the same manifold, or some such..). The question is, what would that look like in 3D; would that resemble what we have observed about our own universe thus far?
Does this mean you are proposing to eliminate the time coordinate altogether, thus creating a static universe ?
No. I am discussing the space-like geometry of our universe only (I think the term is comoving coordinates). "A" (circle/sphere) in the diagram is still the same working analogy as before. I am just adding the "B" (line/plane) and "C" intersection as possible solutions to both an idea of an infinite universe and as the cause behind the big bang. But for now, I am just wondering if the 3D space-like version of the sphere-on-plane analogy is possible with intrinsic curvature and if mathematically so, how would an observer in the bubble section experience it?

I think I'll move the discussion to New Hypothesis.  7. So what you mean is if the universe ( the spatial part ) can exist as a 3-D closed subset of a flat higher dimensional manifold ?  8. Not higher dimensional though. The diagram is in 1D, a ball on an infinite plane in 2D. If those two are mathematically possible, what of a 3D version of that setup? How would such a universe look like for an observer on the sphere?  9. Originally Posted by KALSTER Not higher dimensional though. The diagram is in 1D, a ball on an infinite plane in 2D. If those two are mathematically possible, what of a 3D version of that setup? How would such a universe look like for an observer on the sphere?
Just to make sure I really get you - you mean a 4-sphere on an infinite, flat 3-manifold, right ?  10. A 3-sphere connected to a flat 3-manifold by a point. Sorry if I am being unclear.

My thinking is that as long as they are connected, that they don't need a 4th spacial dimension to exist in? I am wondering if a point is sufficient connection to classify the flat/sphere combo as one complex 3-manifold.

Does this make sense?  11. Originally Posted by KALSTER A 3-sphere connected to a flat 3-manifold by a point. Sorry if I am being unclear.

My thinking is that as long as they are connected, that they don't need a 4th spacial dimension to exist in? I am wondering if a point is sufficient connection to classify the flat/sphere combo as one complex 3-manifold.

Does this make sense?
I know what you mean now, but I don't know the answer to be perfectly honest. This would require either a mathematician ( Guitarist ?? ) or some serious pondering over a topology textbook...
I'll have a think about it anyway I think we would be dealing with a topological defect/discontinuity at the connection point.  12. Thanks!

I found this: Tangent space - Wikipedia, the free encyclopedia. Does that help?

The question is if the combo can be thought of as a single manifold?

Edit: Also http://en.wikipedia.org/wiki/Submanifold. Could our bubble be an embedded submanifold of a flat 3-manifold? OR rather Immersed.....  13. Why not have a flat 3-manifold, with an additional 3 dimensions curled up into some radius R at each point ? So in essence you would have a 6-dimensional manifold, with 3 flat macroscopic dimensions and 3 curled-up microscopic ones...  14. That's quite a bit more complicated though, no? I am aiming for simplicity as much as possible, to determine the most simple set of attributes needed where after letting it go would produce our universe. This is just a part of it. But that's for later...

The spherical part need not be spherical either. I just chose it because it would offer the most simple 1D diagram to represent our finite bit "big banging" out of an infinite expanse.

The questions are how the flat infinity would interact with the finite bit and how the universe would look like from inside the finite bit. I can't picture the step up from the 2D scenario of a sphere resting on a plane to the 3D version of it.  15. Originally Posted by KALSTER The questions are how the flat infinity would interact with the finite bit and how the universe would look like from inside the finite bit. I can't picture the step up from the 2D scenario of a sphere resting on a plane to the 3D version of it.
I think it would not be visible at all for someone inside the "bubble". They are connected only at a single point, at which the curvature of the manifold suddenly "jumps" from zero to some non-zero value. The curvature function at that point would be continuous, but not differentiable; I have absolutely no idea how such a topological defect would manifest itself for an observer in the universe - my feeling is it would look quite spectacular !

As for the maths, I doubt that this would be compatible with the Einstein equations, because they as being differential equations would not allow any solutions which contain non-differentiable terms in the metric tensor. That's just a thought though, I haven't actually done any maths...  Bookmarks
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