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Curvature of space

  1. Nov 17, 2004 #1

    DaveC426913

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    I have not been keeping up on current cosmology theory.

    Once was said that if you flew your "Spaceship of the Mind" X billion light years "thataway", and didn't stop or turn, you eventually would find yourself back where you started. The idea here is that 3-dimensional space is actually curved through a 4th dimension so that it wraps upon itself.

    Is this still the prevailing notion of modern physics?



    In an only loosely-related question: Is this the same curvature of 3D space upon which the eventual Big Crunch depends? i.e. if space is flat, the universe will expand forever. (I think these two questions are unrelated, despite their overlap of terms.)
     
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  3. Nov 17, 2004 #2

    turbo

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    That's not necessarily a bad thing! :rolleyes: Just joking, but cosmology is very much a flavor-of-the-month prospect in some regards.

    OK, you have two different concepts going here, and you realize that, so it'll be easy for you to sort them out. First off, if you can head out in one direction and come back on yourself from the opposite direction, you are in a universe that has a topology that is closed, like a sphere, a torus, or a moebius strip, etc.

    The question of curvature concerns the fate of the universe, as you have accurately determined. If we are in a Big Bang universe, and the universe has a positive curvature (like a ball), the expansion of the universe will eventually slow and collapse back upon itself (closed universe). If the universe is has no curvature, it will continue expanding forever, gradually slowing, but not collapsing (flat universe). If the universe has negative curvature, it will simply continue expanding forever (open universe).
     
  4. Nov 17, 2004 #3

    DaveC426913

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    "...you are in a universe that has a topology that is closed, like a sphere, a torus, or a moebius strip, etc. ..."

    Yup, this was the heart of my question (the other bit was a tangent).

    So, is the current prevailing theory that we live in a closed universe? That we would eventually come back to our starting point? Or is this even theory at all, as opposed to conjecture?
     
  5. Nov 17, 2004 #4

    turbo

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    Topology is an open question for most people, and the thought that you might come back upon yourself from the opposite direction is not that widely accepted.

    The "curvature" question, which can simply be equated to "is there enough mass in the universe to make it collapse back in onto itself" is more widely viewed as settled, in that most folks think the universe is either flat or open.

    There are folks like myself that think the Big Bang theory is not a proper model of the universe. We are in the minority at this point, but the revolution is coming. :surprised
     
  6. Nov 18, 2004 #5

    Chronos

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    In a flat universe, as current measures indicate, the universe is spatially infinite.
     
  7. Nov 18, 2004 #6

    hellfire

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    The current observations indicate that space is almost flat (zero curvature). There are lots of geometries which fit with the requirement of zero curvature of space. The most trivial one is an infinite space R^3, but a 3-cylinder or a 3-torus inside a four dimensional spacetime can have also a flat metric on it.

    This is indeed the curvature on which the fate of the universe depends, if you consider only a classical content (no dark energy). Otherwise (with dark energy), there is no direct relation between curvature and fate of the universe (a closed universe may expand forever, if it contains enough dark energy).
     
  8. Nov 18, 2004 #7
    In the Issue of May of Physical Review Letters of this year there was a study searching for paired circles in the CMB, that is, to see the same configuration in opposite sides. No such paired circles were found, this is a great support for the idea that space is flat
     
  9. Nov 21, 2004 #8

    Chronos

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