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Infinite universe and big bang singularity

  1. Jun 27, 2012 #1
    Hello. Cosmologists leave open the possibility that the universe as a whole may be infinitely big. My question is, does that mean that the entire infinite universe was compressed into the initial singularity? And how can a universe go from a singularity to being infinitely big in a finite time?
     
  2. jcsd
  3. Jun 27, 2012 #2
    "Singularity" doesn't mean "point in space", it refers to a mathematical phenomenon that signals that our models no longer work (or, at least, probably don't describe physical reality). A singularity is a quirk of the equations, not an actual, physical "thing".
     
  4. Jun 27, 2012 #3

    phinds

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    To add to what Number Nine said, the universe is known to have been MUCH smaller at one Plank Time after the singularity than it is now, but it MIGHT have been infinite then (which of course implies infinite now). If it was not infinite then, it is not infinite now.

    Our observable universe (currently some 90+ billion light years in diameter) at that time is stated in various reports as sizes ranging from a golf ball down to much smaller. Reports that put it as a point are patently ridiculous.
     
  5. Jun 27, 2012 #4

    marcus

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    Well said. Thanks, it's an important message to get across to new members. People get fooled by the word "singularity" because it sounds like it refers to a "single point". But instead it refers to a failure of some man-made mathematics. History shows that in the past physicists have gotten rid of singularities in various other theories by improving the equations so they don't blow up. Now they are working on curing the singularity that occurs in the conventional model of the cosmos, right at the start of expansion.

    An equation does not necessarily fail at a single isolated point. It can fail everywhere along a wide frontier--at infinitely many points. In which case the singularity is said to occur throughout the whole region where the model breaks down.

    As Phinds rightly indicated, it is logically possible that our universe began expanding with an infinite volume. It would necessarily have begun infinite if it is spatially infinite today. We do not yet know whether to consider space finite or infinite. The region we are now looking at is evidently not the whole thing.
     
    Last edited: Jun 27, 2012
  6. Jun 27, 2012 #5

    jcsd

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    Describing singularities in general in GR is a problem let alone trying to describe them physically (not that I think singualrities are physical). That said some singualrities do, for example, resemble points in space.

    An infinite universe is always infinite until the point of the singularity; however at the singularity all distances between objects, no matter how far apart they are later in time, goes to zero.
     
  7. Jun 27, 2012 #6

    marcus

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    At the classical model's singularity, distances between objects are not defined. What "objects"?
    The model blows, it no longer applies to nature and it is meaningless to talk about distances between objects being this that or the other thing. That's my take on it. If you want to imagine differently, fine.

    There are now rival models, waiting to be tested, which go back further in time to before the start of expansion, where the classic 1915 model blows up. I'd guess you know about them and currently which are getting the most research attention.
    In the new models it is NOT true that all distances are zero :biggrin: at the start of expansion.
    However with the new models at least you might be able to talk meaningfully about that kind of stuff. What the highest density is, that is reached at the moment the bounce happens, and so on...

    The idea of objects and distances between them is somewhat nebulous under the circumstances, but the energy density (how much crowded into a unit volume) is finite and well-defined and can sort of take the place of the "distance between objects" idea.
     
    Last edited: Jun 27, 2012
  8. Jun 27, 2012 #7

    jcsd

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    I said "go to zero" (well I actually made a gammatical error due to editing and said "goes", but that's neither here nor there).

    edit: just to make this clear I am saying that as t->0 where 0 is the big bang singualrity d->0 (where is d is the distance between any two objects).
     
    Last edited: Jun 28, 2012
  9. Jun 28, 2012 #8
    This is valid for finite distances but in an infinite universe there are also infinite distances.
     
  10. Jun 28, 2012 #9
    Eh...that's a touchy issue. Even on the plane (which is infinite), any two defined points have a finite distance between them. It's entirely possible that two points could never reach each other (say, due to FTL expansion), but the distance between any two points is finite.
     
  11. Jun 29, 2012 #10

    jcsd

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    No there are no infinite distances, even in an infinite Universe- in standard big bang theory anyway
     
  12. Jun 29, 2012 #11
    Assuming we have n+1 points in a row with equal distances dr. Than the distance between point 0 and point n is r=n·dr and the limes of r for n->oo (this is possible in an universe with infinite size) is infinite.
     
  13. Jun 29, 2012 #12
    Does the observable universe make up 80% of the universe? Or 20%? I have heard different numbers..
     
  14. Jun 29, 2012 #13
    Nobody can't tell you that, there are some lower bound estimates which tells that hole thing must have some considerably larger volume then OU (hate to dig for exact number right now), but then again it can be infinite, which means that it is infinitely larger then OU.
     
  15. Jun 29, 2012 #14

    jcsd

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    But assuming [itex]n \in \mathbb{N}[/itex] then n is never equal to ∞ and hence r is never equal to ∞ as well. Of course that doesn't conclusively show that there are non-existance of infinite proper distances in standard big bang cosmology, however it is the case.
     
  16. Jun 29, 2012 #15
    Of course not. ∞ is not a number. But if the limes of r is ∞ than you get r'=0·∞ when the scale factor goes to zero. This term is not necessarily zero. It could even be infinite.
     
  17. Jun 29, 2012 #16
    When I was reading roger penrose book the road to reality, he seemed to say that general relativity should be regarded higher that quantum mechanics and that general relativity should not have to compromise to fit with quantum physics but the other way around. I could be mistaken. Most of the book went over my head. But if Penrose is right about relativity being correct, then doesnt that mean that per the hawking penrose singularity theorems a primordial singularity before the hot big bang is inevitable?
     
  18. Jun 29, 2012 #17
    The problem is that you're now talking about something completely different. The distance between any two given points is finite; the fact that the distance tends towards infinity as you move the points further apart only means that distance is unbounded, which is something different entirely.
     
  19. Jun 29, 2012 #18
    I am still talking about infinite distances. Distances between given points are something completely different. The latter are finite and shrink to zero in the big bang singularity. The former do not need to be zero in the singularity which therefore do not need to be a point.
     
  20. Jun 29, 2012 #19
    kuartus:
    no, he did not say the GR is predomininant....In fact on page 713 he points out that for a black hole singularity
    and no the the second part as well:

    http://en.wikipedia.org/wiki/Singularity_theorem

    This again shows an emphasis in favor of quantum theory over relativity.
     
  21. Jun 30, 2012 #20

    jcsd

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    There no such thing as 'infinite distances', at least not in this scenario.

    What you are trying to say is that whilst all distances tend to zero, the length of say an infinitely-long curve in space will not tend to zero will remain infinite as t->0.

    This is somewhat moot as the singularity is not a point on the manifold.
     
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