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Is universe finite or infinite?

  1. Mar 31, 2012 #1
    If the universe is finite then what is beyond? If infinite then how can humanity conceive the 'big picture'?
     
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  3. Mar 31, 2012 #2

    cepheid

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  4. Mar 31, 2012 #3
    cite: "Standard cosmological models come in three flavors, open, flat, and closed,[Carroll] whose spatial curvatures are negative, zero, and positive. The open and flat types have infinite spatial volume. The closed one has finite spatial volume; spatially, it is the three-dimensional analog of the surface of a sphere. Since all three are solutions to the Einstein field equations, the finiteness or infiniteness of the universe is something that cannot be determined solely by logic but only by observation.

    Current observations of the cosmic microwave background's anisotropy show that our universe is very nearly flat.[Komatsu] If it is exactly flat, then it is a special case lying on the boundary between the more general open and closed cases. However, the range of uncertainty in the curvature is wide enough to be consistent with either positive or negative curvature, so right now the finiteness or infiniteness of the universe is an open question.

    Sometimes people use the word "universe" when they really mean "observable universe." The observable universe is finite in volume because light has only had a finite time to travel since the Big Bang."

    May we presume the cosmological model is using the first definition and not the second?
     
  5. Mar 31, 2012 #4

    cepheid

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    Yes, the theoretical models are for all of spacetime, not just the portion of it that we can see.

    To elaborate on the OPs question about boundaries and what exists beyond them. The answer is that nothing exists beyond the boundaries, because there are no boundaries. In the standard models, if the universe is finite, then it is unbounded, meaning that it has no edges. This is made possible by spatial curvature. An analogy is a two-dimensional being living on the surface of a sphere. This surface has a finite area, and yet it has no edges for the being to reach. If the being travels far enough in any direction, it will end up back where it started.
     
    Last edited: Mar 31, 2012
  6. Mar 31, 2012 #5
    I see. Then does there exist some point in the "whole of the universe" at which some object within a finite distance that was moving away from me is now moving toward me or does the rate of expansion preclude that from happening? And if that is the case, then wouldn't the rate of expansion have to exceed 'C' in order to preclude neutrinos from doubling back - thus invalidating Einstein (if neutrinos haven't already done that)?
     
  7. Mar 31, 2012 #6
    When talking about the expansion of the universe, you must specify two points, so a sufficiently far object will be receding much faster than light. But remember, general relativity puts no limit the expansion of the universe, just the observers within it. Also, neutrinos do NOT move faster than light. That is impossible, though they move very close.
     
  8. Mar 31, 2012 #7
    Yet, a two-dimensional theory does not directly address the question. Pinning 'no beginning and no ending' on "Spatial curvature" does not solve the three dimensionality dilemma of the infinite universe
     
  9. Mar 31, 2012 #8
    Hmmmmm. So there is no limit to the expansion. Could it therefore be or have been infinite (no limit)? Certainly if the cosmos is only 13+billion light years in size, there must be some calclation as to the rate of expansion from t=1....or is it possible we can only detect 13+B light years of data...which would render the age approximation of the cosmos moot?

    Also in some speculative models, Neutrinos have a tachyonic nature and travel faster than 'C'. Those Lorentz violating variants of quantum gravity are part of the Standard-Model Extension.

    Also mass is just a condition - readily exchangeable with energy. Only those things with the property of mass are subject to the speed limit.
     
  10. Mar 31, 2012 #9

    cepheid

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    The theory itself is not two-dimensional. It is a full description of the four dimensions of spacetime that employs the idea of curvature and non-Euclidean geometry. In other words, saying that you live in a closed universe is saying that, in this universe, geometry doesn't behave like the way you learned in school. In a closed universe, parallel lines eventually meet. The sum of the three angles of a triangle is greater than 180 degrees. If you travel far enough in any given direction, you'll end up back where you started. So the geometry in this curved 3D space is analogous to the geometry on a curved 2D surface. I was using a direct lower-dimensional analogy to give you a way to visualize the implications of this curvature in the higher-dimensional case.
     
  11. Mar 31, 2012 #10
    Two excellent points. I presume the calculated age reflects 'detectable' data.
     
  12. Mar 31, 2012 #11
    Can you detail a bit more about three-dimensional universe curvature as it relates to infinitely? Many thanks.
     
  13. Mar 31, 2012 #12

    cepheid

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    It is unclear here what you mean by "no limit." If you mean that the expansion will continue forever, then that is the view that is currently supported by the best observational data.

    In the simplified picture that was described in the FAQ page I linked to above, there is a direct relationship between the geometry of the universe (which is determined by its mass-energy content) and the ultimate fate of the universe. For the closed model, the universe is closed because there is enough mass to provide enough positive spatial curvature. It turns out that this critical amount of mass also determines whether the universe's expansion will continue forever, or if it will eventually slow down, and then reverse, leading to the universe recollapsing in a so-called "Big Crunch."

    Since the condition for the universe being closed is that it has greater than the critical amount (or actually density) of matter, the conclusion is that closed universes will recollapse, whereas flat and open universe, which have (respectively) just equal to, and less than the critical density of matter, will continue to expand forever (albeit at an ever decreasing rate).

    What muddles up this simplified picture is the presence of dark energy. In particular, dark energy breaks this simple relationship between the geometry of the universe, and its ultimate fate. It is possible for even a spatially-closed universe with dark energy to continue to expand forever, due to the repulsive effect that that dark energy tends to have.

    In any case, the observational data currently support a universe with dark energy whose expansion rate is increasing and that will therefore continue to expand forever. Observations show that the geometry of the universe is very close to spatially flat (i.e. Euclidean).

    The universe is not merely 13 billion ly in size, not even the observable portion of it. See here: https://www.physicsforums.com/showthread.php?t=506987 [Broken] for an explanation why.

    Highly speculative models. I had thought that tachyons were the name for a new theorized particle that was capable of travelling faster than light. (As as opposed to an adjective used to described faster than light neutrinos). I had also thought that the theory that proposed the existence of tachyons had mostly been ruled out. Furthermore, there is no ONE single extension to the Standard Model of particle physics. This is an area of active research, and many different theories are attempting to achieve such an extension.


    I don't know if I'd call it a "condition", but rather a property of matter. I do agree that it is interchangeable with energy. I also agree that only massive particles are restricted to speed less than c by Special Relativity. I'm just not sure what your point is.
     
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  14. Mar 31, 2012 #13

    cepheid

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    The age of the universe is NOT estimated based on the size of the observable portion of it. It is determined independently through other observational means.
     
  15. Mar 31, 2012 #14
    Thank you.

    I must; however, admit I am somewhat skeptical about the validity of expansion related red shift. Would it not seem reasonable to assume if a body is moving away at high velocity that its signature - width of its apparent diameter and strength of signal or luminocity - should also evidence a correspoding dimunition? I know of no such corroborating data or evidence.

    Any links you might provide would be appreciated.
     
  16. Mar 31, 2012 #15

    cepheid

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  17. Mar 31, 2012 #16

    cepheid

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    It's unclear what you're asking. But as described in the first FAQ page that I linked to, only the models with a closed spherical geometry are spatially finite. These are the models with positive curvature. The 2D analogy for them is the surface of a sphere.

    Models with a flat geometry would be spatially infinite. The 2D analogy for them would be a flat infinite plane.

    Models with open geometry (also called hyperbolic geometry) would also be spatially infinite. The 2D analogy for them would be an infinite 2D surface shaped somewhat like a "saddle."

    See the first figure in this article:

    http://en.wikipedia.org/wiki/Shape_of_the_Universe
     
  18. Mar 31, 2012 #17

    cepheid

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    *Sigh*

    I have no idea what you mean by the part in bold, so I cannot address your specific objection. However, we have an FAQ page for this as well. This is the third cosmology FAQ article that I have linked to this thread:

    https://www.physicsforums.com/showthread.php?t=506994 [Broken]

    Maybe you just check out all of them first, and then come back with questions:

    https://www.physicsforums.com/forumdisplay.php?f=206 [Broken]
     
    Last edited by a moderator: May 5, 2017
  19. Mar 31, 2012 #18
    Yes CMB not light. 13+B light years of it may be calculable, but that is the limit of our ability to detect, not necessarily the limit of the phenomenon. Any observations we might make are limited by our technology, not the nature of the cosmos.
     
  20. Mar 31, 2012 #19
    The estimate of the age of the universe at 13.7 billion years is correct, we know this. But, it is non-relativistic. If an observer was around at the time of the big bang he would most certainly measure the universe as having a different age on his watch. This is why in eternal inflation, there can be many infinitely large bubble universes.

    When an observer falls into a black hole, (we'll call him 'A') another observer in flat space ('B') sees him slowing down due to gravitational time dilation, until he reaches the event horizon, when B will say A is moving infinitely slow. So while A says a finite amount of time passed during his fall, B would say it is infinite. Similarly an observer inside an inflating region of spacetime will say that time is flowing infinitely slow - allowing his region to become infinite in spatial extent.

    Alan Guth actually did the calculation, and showed it is possible.(though I can't find his paper!)

    But in regard to your original question, 13 billion years is the completely objective age of the universe, and is correct.
     
  21. Mar 31, 2012 #20

    cepheid

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    No. If you think that the determination of the age of the universe using the CMB is based on the measurement of the redshift/distance out to the CMB (which is the farthest out we can see), then you are mistaken.

    How it's actually done is that the distribution (i.e. power spectrum) of the angular sizes of the statistical temperature fluctuations of the CMB is used to measure the values of the cosmological model parameters including H0, Ω0, ΩΛ. The age of the universe is a parameter that can be derived from these fundamental ones.

    Just to be clear: the different models all stem from the same underlying theory. How they differ is in the values of the model parameters, which lead to different spatial geometry and expansion history. What the observations enable us to do is to measure the values of these quantities in nature, thereby determining which of the specific models best describes the universe.
     
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