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I Infinite versus finite space

  1. Sep 1, 2017 #1
    I have read some of the other posts about this topic but am still left unsatisfied. Could just be me. :cool:

    Did the universe, one minute after the big bang, consist of a finite volume of spacetime?

    If so, then is it not logically inconsistent that the universe can possibly be infinite now? If we say that spacetime is expanding into nothing, and that nothing is what is infinite, does not language itself make that a nonsensical statement? Isn't that like saying I have an infinite amount of 0 dollars in my bank account? I have not really said anything at all.

    Thanks for the replies.
     
  2. jcsd
  3. Sep 1, 2017 #2

    PeterDonis

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    Not according to our best current model, no. According to our best current model, the universe is and always has been spatially infinite.

    Our observable universe had a very small, finite volume one minute after the Big Bang; but it has a (much, much larger) finite volume now.

    Our cosmological model does not say that.
     
  4. Sep 1, 2017 #3
    Thanks PeterDonis, I appreciate the reply.

    What are you saying is the best current model? I am not up to date on all this stuff. How much consensus does this view have?

    If the current consensus model states that the universe is eternally spatially infinite, then why do so many take the theory of inflation to be an explanation of flat geometry? It would seem to me to render that cause and effect relationship of inflation to geometry unnecessary?

    Thanks
     
  5. Sep 1, 2017 #4

    PeterDonis

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    The Lambda-CDM model:

    https://en.wikipedia.org/wiki/Lambda-CDM_model

    The full details of the model are always being refined, but the part about the universe being spatially infinite is pretty solid.

    Because "spatially infinite" and "spatially flat" are not the same thing.
     
  6. Sep 1, 2017 #5
    Stephen Hawking's book A brief history of time explains the following.
    According to Netwon, every body of certain mass attracts another body of certain mass, and this force of attraction is propotional to square of their masses. So, shouldn't asteroids and meteorites and all other space stuff be colliding onto the earth or vice-versa?
    That's where infinite universe comes into play. Masses don't collide onto each other because if the universe is infinite, there would not be a center for all the masses to collide onto! And observation shows that the universe is expanding, providing for the big bang theory of "infinitely small" particle. (Expanding universe in the sense it must have been all together at some point, that's why "infinitely small" particle!)
    Hope that suffices :D
     
  7. Sep 2, 2017 #6

    PeterDonis

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    Unfortunately, pop science books even by very deservedly famous scientists aren't good sources from which to learn actual science.

    This argument is not correct, because it ignores the fact that even if the universe were spatially finite, it would have no center. The spatial topology of a spatially finite universe is that of a 3-sphere; there is no point within a 3-sphere that is its "center", just as there is no point on the surface of the Earth--an example of a 2-sphere--that is the "center" of that surface.
     
  8. Sep 2, 2017 #7
    True, I get it
    Gracias!
     
  9. Sep 2, 2017 #8
    https://en.wikipedia.org/wiki/Lambda-CDM_model

    Thanks, I read the wiki article to refresh my memory. I am assuming that the information therein is correct. I can't do the math, so everything we discuss using equations will need to be translated into English for me. :smile: I am not totally math inept, but my calculus and such is long out of shape due to disuse.



    What are the properties of what you are calling the universe? What does it mean that it is spatial? I realize that we are not talking about the observable universe with it's radiation, matter, and four dimensions of spacetime.



    What other geometry besides a Euclidean flat geometry could be infinite? I'm not talking unbounded, but in what other geometry do two parallel lines not intersect at some point? How could we detect a geometry other than flat if it was infinite?
     
  10. Sep 2, 2017 #9

    Bandersnatch

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    Hyperbolic geometry:
    600px-Hyperbolic_triangle.svg.png
    Detection method is the same as for spherical geometry - measurement of internal angles of large triangles.
     
  11. Sep 2, 2017 #10
    How would you know if you can only measure angles within the observable universe? Does not the geometry appear flat in the observable universe where you can actually use objects to construct a triangle? Do not the angles sum to 180 degrees using objects at the "edge" of the observable universe?
     
  12. Sep 2, 2017 #11

    Bandersnatch

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    They do in our universe (within error bars), and that's an indication it's flat or with sufficiently small curvature that we can't detect it. They wouldn't add up to 180 if it the universe weren't flat.
    The curvature is intrinsic - it's detectable from inside the space.
     
  13. Sep 2, 2017 #12
    When you say that the curvature is intrinsic, are you talking about the localized curvature due to gravitational fields from energy and matter?
     
  14. Sep 2, 2017 #13

    jbriggs444

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    "Intrinsic" curvature is curvature which is detectable using instruments purely within the space being measured. For example, by laying out three points connected by shortest paths (i.e. a triangle) and seeing that the sum of the internal angles is not 180 degrees.

    By contrast, "extrinsic" curvature involves representing the space you are interested in by "embedding" it in a higher dimensional space. For instance, a plane that is embedded in a three dimensional volume and rolled into a tube. That plane is an example of a two-dimensional space with non-zero extrinsic curvature but zero intrinsic curvature.

    We can measure and talk about curvature without needing to ask what is causing it.
     
  15. Sep 2, 2017 #14

    PeterDonis

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    The four dimensions of spacetime in the Lambda CDM model describe the entire universe, not just the part of it that we can observe. When we say the universe is "spatially flat", what we mean is that spacelike hypersurfaces of constant time for comoving observers (observers that see the universe as homogeneous and isotropic) are flat--i.e., they are Euclidean 3-spaces.
     
  16. Sep 2, 2017 #15
    I'll have to think on that example for a while. Is this bringing in ideas from higher dimensional theories like string theory or is this dimensional idea encapsulated within LCDM?

    Well, you know how to stifle a curious mind. :smile:
     
  17. Sep 2, 2017 #16
    I do appreciate all the responses. I'll have to think on this one for a while. Would the language then be inaccurate to say that spacetime from the big bang was expanding into eternal spacetime with the same four dimensions. In other words, if this view was correct, does not space have something to expand into? Thanks.
     
  18. Sep 2, 2017 #17

    PeterDonis

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    Yes. Spacetime doesn't "expand". The spacetime model that describes the universe is a single 4-dimensional geometry that includes the Big Bang and our current universe. When we say the universe is "expanding", we just mean that this 4-dimensional geometry has a particular shape.

    No. Spacetime is a 4-dimensional geometry that doesn't expand at all--see above. So it's meaningless to even ask whether it has something to expand into.
     
  19. Sep 2, 2017 #18

    jbriggs444

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    Nothing so fancy. This is as simple as rolling up a piece of graph paper into a tube and noticing that the geometry of lines on paper is unaffected. That's "extrinsic" curvature.
    Physics is not just about the amazing flashing lights. It also about understanding the simple stuff so that you can appreciate the amazing flashing lights. Curved space or curved space-time is more meaningful if you know what "curved" means first.
     
  20. Sep 2, 2017 #19
    It makes me wonder which is more difficult; to understand the concepts intuitively or to solve the equations and program the computer models to simulate them? Brain needs rest......
     
  21. Sep 2, 2017 #20
    Do either of these ideas depend on the existence of the multiverse, as opposed to our universe being the only one?
     
    Last edited: Sep 2, 2017
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