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What proof?

  1. Jul 25, 2012 #1
    Anytime I ask this question it is met with people who angrily argue that there is nothing outside our universe.

    What proof is there that time started at the moment of the big bang and that there is nothing that our universe is expanding into..

    The universe expanding faster and faster everyday does not prove that it is not expanding into another (space time), the fact that everything breaks down at a singularity also does not explain. So how come it is so widely accepted that nothing lies beyond our universe? Especially since we cannot see outside our observable universe?
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  3. Jul 25, 2012 #2
    None, but so what? There's nothing to suggest that such a thing is the case, so the only reasonable thing to do is proceed as if it's not true. Science doesn't deal in this "proof" of yours.
  4. Jul 25, 2012 #3


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    As I understand it "outside our universe" makes as much sense in our cosmological models as "the corner of a circle". Just do a search on this forum for threads that ask about the edge or middle of the universe and perhaps read this.
    Just FYI proof only exists in mathematics. The rest of science deals in terms of evidence for and against, we can never be absolutely sure of anything so when a scientist says anything factual it comes with the unspoken caveat "to the best of our current knowledge".
    We don't know this to be true but we can only explain the universe from after the initial moment of the big bang.
    See above.
  5. Jul 25, 2012 #4
    I don't know where you got the idea that this is an accepted fact. It gets thrown around a lot, and it's a possibility, but I don't know if very many people believe it. Non-singular cosmologies have become preferable, such as the bounce model of Loop Quantum Cosmology.

    Correct. The universe isn't expanding into anything. The FRW metric requires both homogeneity and isotropy, so boundaries are not allowed. Because general relativity governs the universe over large scales, the universe needs to have a structure of a smooth manifold. It may be infinite, but if it's finite, it's either simply or non-simply connected. For example, a 3-sphere.

    Not sure what this means. We know there is no outside space-time because of our observations of homogeneity and isotropy.

    Singularities are a relic of trying to apply classical general relativity to the big bang. Quantum gravity resolves any singularity.
  6. Jul 25, 2012 #5
    Ryan, the balloon analogy doesn't tell me how anyone knows what lies beyond our boundaries.

    What i'm really saying, is there an experiment, or a math problem that you can say, here look at this, this is why there is nothing outside of the universe.
  7. Jul 25, 2012 #6
    It does. If our universe has spatial curvature, then it would have the topology of a 3-sphere, a higher dimensional analogue of a balloon. Hence, no boundary.

    Yes, basic topology. Smooth manifolds don't have boundaries. If the universe has no curvature, then it's infinite or has the topology of a 3-torus. If it has spatial curvature, then it must, by definition, be simply or non-simply connected.
  8. Jul 25, 2012 #7


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    My impression of how science has been going for the past several hundred years is that the general custom is not to worry about things there is no evidence for, or a logical necessity for.

    It's kind of a custom or tradition that helps characterize empirical science.

    When you say "lies beyond our boundaries", my reaction is to ask "What boundaries?". Does talking about boundaries necessarily mean anything? Do you know of any evidence that our universe HAS boundaries? Or do you know of any logical necessity for it to have? I can't think of any, but maybe you can point to some.

    One point of the 2D balloon example (all existence concentrated on the infinitely thin surface, no inside or outside of the balloon, only the 2D spherical world) is its boundarylessness. It's meant to help people (whose everyday experience leads them to think that everything has a boundary) understand that there is no logical necessity for space to have a boundary or anything outside of it.

    As for wanting evidence that there is no boundary. The tradition is not to bother about that unless there is some reason to suppose that there is a boundary. You seem to be like someone asking us to PROVE THERE ARE NO PINK UNICORNS ORBITING PLUTO!
    We don't have to give proof or evidence of that, I think. It's just not an interesting question to resolve. Unnecessary complication. There is no need to waste time proving the non-existence of stuff there's no evidence or need for.
    Last edited: Jul 25, 2012
  9. Jul 25, 2012 #8


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    Imagine you are on the surface of a balloon and you travelled in one direction. How long until you reach a boundary? Never because there are none.
  10. Jul 25, 2012 #9


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    DeepSpace9, the mathematical term for the hypothesis that our spacetime is expanding into something is that spacetime is embedded in a manifold of higher dimension (ie five or more dimensions), in the same way that the 3D hypersurface of the balloon in the analogy (two spatial and one time dimensions) is embedded in our 4D spacetime.
    This is possible. John Nash (of 'A beautiful mind' fame) proved with his embedding theorem that every Riemannian manifold can be embedded in a higher dimensional manifold of sufficient dimensions*. But it is not necessary to assume that is the case in order to be able to do any of the practical science. There is no evidence that such embedding occurs so it would simply introduce a whole bunch of superfluous and complicating baggage to start making assumptions that our spacetime is embedded in something else.

    So you are correct that there is nothing to prove that our spacetime is not embedded, and if you wish to imagine that it is so embedded it is not irrational for you to do so. That idea won't be able to be any more than a speculative hypothesis though, because we currently have no way of looking for evidence of such an embedding.

    *Our spacetime is pseudo-Riemannian, not Riemannian, so the original Nash Embedding Theorem is not applicable, but I'm guessing that the theorem can be extended to cover pseudo-Riemannian manifolds.
  11. Jul 25, 2012 #10
    It means a lot, if one was to prove the universe has boundaries, i'm sure it would be the biggest discovery in the physics/cosmology world.

    Logical necessity for having a boundary , I believe is human nature, I don't think anyone on this forum (despite what they say) can 100% feel comfortable with not knowing what lies beyond our universe, or to at least wonder about it in their life.

    They hole balloon analogy theory always breaks down to me at the point of, obviously the balloon has boundaries, that is how we are able to view the balloon in the first place, the balloon is indeed expanding into something bigger.

    Are you serious?
    My question is equivalent to asking, is there pink unicorns orbiting pluto?
    Highly disagree, just because we have not found any evidence yet of the boundaries, does not mean that it is irrelevant, after all this could tell us what caused the big bang, could it not? That sounds like a big deal to me.

    If you held a balloon in your hand, are you not grasping all of its boundaries?

    So besides our 3d? and time, you are suggesting that there must have to be another dimension?
  12. Jul 25, 2012 #11
    I already provided you an explanation of why the universe can't have boundaries. This is a known fact, not just an idea. Saying the universe has boundaries makes about as much sense as saying the universe has a center.
  13. Jul 25, 2012 #12
    The balloon you're holding is embedded in a higher dimensional space; the Universe is not. A point on the surface of a balloon has only two dimensions in which to move.

    That's not logical necessity, it's a driving emotion need that originates from a lack of imagination ("no boundary" doesn't make sense to me/feels weird, therefore a boundary must exist).

    A sphere (or anything "sphere-like") does not have a boundary. You can embed a sphere in some higher dimensional space, at which point it becomes possible to move outside of the sphere, but there is no evidence and no reason to believe that such an embedding has taken place with regards to the Universe.
  14. Jul 25, 2012 #13
    SO if our universe was embedded in a higher dimension, like the balloon, would it than have boundaries?

    This is hypothetical.
  15. Jul 25, 2012 #14


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    Not quite. I am suggesting that if our 4d spacetime is embedded in something else (which is what is necessary in order for statements about 'boundaries' and 'expanding into' things to have any meaning) then that something else must have at least one extra dimension, probably more.

    But none of our scientific theories require or suggest that our spacetime is embedded in anything else, and theoretically there is no need for it to be embedded in anything, in order for it to have the properties we observe. Hence only those who wish to imagine spacetime expanding into something else need to postulate extra dimensions. I have no such wish, although I can see no in-principle objection to the hypothesis.
  16. Jul 25, 2012 #15
    With all the research going on surrounding higher dimensions, and the possibility of 11 dimensions existing. A lot of physicists do believe that there are more than 3 Dimensions, and if a lot of scientists do believe in higher dimensions.

    Wouldn't that conclude that, there is a strong chance that they also believe our universe could have boundaries, after all they believe in more dimensions, so it would only be right for our universe to also have boundaries..?

    Is it possible for our universe to be embedded in a higher dimension, but STILL not have boundaries?
  17. Jul 25, 2012 #16
    The discovery of cold fusion would be an enormous discovery. That doesn't mean it's true.
    Well, it's wrong.
    I wondered about it before I learned about cosmology and general relativity and the mathematics behind them. I can be 100% comfortable with it, and so is everyone here who is knowledgable about cosmology.
    That's because the balloon is a ball. The surface of the balloon is a sphere. We can talk about an expanding sphere with a metric using intristic geometry without an embedded space.
    Pretty much.
    It isn't about evidence. It's a matter of the mathematics that underlie cosmology and GR.
    Which demonstrates the limits of an analogy.
    He certainly didn't imply that. He said it is perfectly consistent for a Reimannian manifold to be embedded in a higher dimensional space. That doesn't mean our universe is.
  18. Jul 25, 2012 #17
    In higher dimensional theories (such as M-theory) the extra dimensions are compactified into sub-manifolds of our space, such as 6-manifolds called Calabi-Yau manifolds.
  19. Jul 25, 2012 #18


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    Topologically speaking, every point of our spacetime (I won't call it a universe because 'universe' to me means 'everything there is', which would include whatever our spacetime is embedded in) would be a boundary point under the subspace topology if it were embedded in a higher-dimensional space, in the same way that every point of the line y=0 is a boundary of that line considered as a subset of the two-dimensional number plane.

    If our spacetime were embedded in a 7-dimensional space (5 dimensions may not be enough to host an embedding of our spacetime) and we could somehow propel ourselves in a direction that is perpendicular to all three of our spatial directions and to our time direction (think of an ant jumping up off the balloon in the analogy) we would immediately be 'out of' our spacetime as soon as we had travelled the tiniest distance in that direction.

    You must bear in mind though that these are all just mathematical possibilities. There is no scientific evidence for or against them and they bear no relation to our current scientific theories and observations. (hence this thread would fit better under mathematics or philosophy than here in cosmology).
  20. Jul 25, 2012 #19
    Okay thanks guys, I think all my questions have been answered.
  21. Jul 25, 2012 #20
    Not in the sense your thinking about. It could be spatially separated (via the extra dimensions) from other regions of the universe. But it isn't as if there is some kind of boundary separating them.
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