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Dealing with Infinity

  1. Dec 16, 2012 #1
    How do we deal with the concept on infinity? It seems to linger about the limits of everything.

    For me, this is the biggest problem in some sense. I wanted to ask the question in the context of the the multiverse. This is a big trend now in physics and cosmology and usually gets lots of people excited

    Since we have now started saying that our Universe might not be the only one, haven't we simply pushed up the problem into a higher category. Let's just imagine that the Universe is a finite soap bubble and so as in common analogy, there are many bubbles/universes in the multiverse but if I ask whether all these bubbles are in finite bath tub? then the answer is equivalent to saying that our single Universe is infinite.

    Suppose we did start saying that someday that our Multiverse is also a finite one, a really big bubble with lots of bubbles in it which share some common properties (superset, subset), then there would suddenly be the multi-multi verse! So really at this point, aren't we just pushing infinity higher and higher to avoid dealing with it?

    Now suppose we take the brane theory and there are all these parallel branes stacked and they touch every once in a while creating big bangs, well these branes are supposed to stretch infinitely so where would they touch? Not to mention, there is an infinite stack of these membranes.

    Then there is the black hole-white hole theory. Ok, some our Universe might be in a black hole opening into another realm the opposite side of which is a white hole and we see it as the big bang. So its like branching since we know lots of black holes are there in our Universe. Where then does the first black hole com from?

    Of course, there are many theories but this infinity thing runs as a common thread. For me, dealing with infinity is the same as studying a black hole. The gravitational singularity comes into play right at the start of our Universe and we encounter the same thing at the center of black holes.

    Why aren't we all just working on figuring out what happens at singularities. At this point we're pretty sure that black holes DO exist but how is infinite density possible/zero volume possible? What is its nature? Can it be described definitely rather than in infinite terms?

    if something falls towards a singularity, what happens to it? does it emerge elsewhere in another form? We we could know, wouldn't we automatically know how things can come out of singularities like out Universe?

    Is there a conceivable limit to what we can know and answer quantitatively and qualitatively?

    Also, just a side question about our Universe itself? Isn't it supposed to have finite matter/energy? and there is a definite rate of expansion so it must be finite in the sense that it has only stretched so much? also, it has a definite age so it seems like that itself must impose a limit/boundary. I'm not hinting towards the sort of thing where I then ask what exists outside this boundary? I've seen posts before that asked this question and it was frowned upon but is there a distance from our point of view in every direction where the Universe has still not expanded to?

    The CMBR should not exist at a certain point or rather, there should be a point where there is no temperature.
  2. jcsd
  3. Dec 17, 2012 #2
    There could be. We can try, and if after a million or so years there is no progress then I would be tempted to give up. But those in search of a PhD will still find something to write about, I suppose.

    If the Universe is finite then it has finite matter and energy.
    If the Universe is infinite and homogeneous then it has infinite matter and energy.
    It could have been infinite at creation in which case it is still infinite.
    It could have been finite at creation in which case it is still finite and will very likely always be so.

    The future exists outside of the boundary of the Universe's age. There is also a limit as to how far we can see with telescopes, that's called the visible universe. Beyond the visible universe is the transvisible universe, I guess.

    It could be that the universe is finite in which case it has a radius. Traveling in a straight line one would very roughly return to the point at which one started. It seems that the Universe would look pretty much the same at every point in the journey.

    The wavelength could eventually be close to infinity.
  4. Dec 17, 2012 #3
    See but that's just it, we are answering infinity with infinity.

    For example, when you say that the wavelength could tend to infinity, how can that possibly be true other than in theory? I mean assume that the wavelength keeps getting longer and longer, the frequency will decrease (more distance between peaks), then at some point (infinity), there is no trough or wave because you could not define when the next peak will occur? but what does this say about the amplitude? is it even a wave? the curvy sine wave would just keep going in 1 direction or the other and never turn at any maximum or minimum which doesn't exist? how can this be possible?

    Also, I don't think the Universe has infinite matter even if it extends to infinity. This would be because the Universe had a definite temperature at creation (this is a lie, it had a definite temperature, the Planck temperature at Planck Time) and therefore an equivalent definite mass.

    Another way of looking at this is knowing that infinite matter and antimatter could not interact. They had to be finite.

    I guess I might have phrased it wrong. i should really have asked what the nature of vacuum is.

    I guess I would simply ask what happens if a spacecraft (voyager) just keep going out there, does it hit a brick wall (not literally)? I know we have had these questions many times in the past but seriously, some people have suggested that this depends on the geometry of the Universe and that it might be possible to come back where you start. My question then would be is there an energy or certain velocity that would eject you outside the Universe? like imagine if you were moving on the balloon analogy of our Universe? could you ever leave the surface?

    These questions seem amateurish but I think I really want to hit at the concept of infinity!

    What sort of definite mechanism can create infinity? perhaps a loop like system but what enables it?

    Also, want to jump into math theory for a second. Take Pi, we don't know its exact value other than in fraction. Does this mean we never accurately know what the radius, area or volume of a sphere is? (other than in fraction?) I suppose we would know it if the radius was 7 or a multiple in that it would cancel the 7 on the bottom but other than that? I'm trying to get tot he larger picture of what it means that we are unable to get exact definite values for the constants we have like G and h. Would there be any significance to those digits we are dropping in terms of exactly understanding out Universe?

    (on a side note, does a photon experience time?)

    Lastly, if the Universe was infinite, shouldn't CMBR have radiated to infinity already to give 0 K?

    I mean if you have a glass of hot water in an infinite ocean of cold water....or is the CMB itself infinite then? which means infinite photons?
  5. Dec 17, 2012 #4


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    You should review Cantor's theory on infinities.
  6. Dec 18, 2012 #5
    Most problems with infinity arise from the fact that it's frequently confused with 'very big' rather than what it really is.
    Infinity simply cannot exist in the same domain as dimensionality - and since we live in a universe with dimensions and dimensionality, infinity cannot exist within it.
    So within the universe, it's just a construct of the human mind - and cannot be used for calculations of realworld problems ... only in whole-universe theorisation.
    Understanding the origins of the universe will necessarily mean an understanding of the manner in which finity (dimensionality) and infinity sit 'relative' (for want of a better term) to one another.
    Last edited: Dec 18, 2012
  7. Dec 18, 2012 #6


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    Are there not an infinite number of real numbers in the interval [0,1]?
  8. Dec 18, 2012 #7
    Not in the real world, where there is a limit to the divisibility of matter ... assuming the existence of fundamental particles.
    If something conceptual cannot be applied to the physical world, then it's virtual ... a construct of the human mind - it is not of the realm of reality.
  9. Dec 18, 2012 #8


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    Why can't there be an infinite number of particles in an infinite universe?
  10. Dec 18, 2012 #9
    No reason at all.
    But there can't be an infinite number in a finite universe.
  11. Dec 18, 2012 #10


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    Sure. Who would dispute this?
  12. Dec 18, 2012 #11
    Why not, our visible universe is finite, limited in time, but may be infinite at both extremes.
  13. Dec 18, 2012 #12
    ... ehem.
  14. Dec 18, 2012 #13
    For the same reason you can't get a quart into a pint pot.
  15. Dec 18, 2012 #14
    Since we dont know if the universe is finite or infinite your argument seems mute.
  16. Dec 18, 2012 #15
    My argument was that infinity is not a valid operand in calculations applied to the real world.
    (And it's 'moot')
    Last edited: Dec 18, 2012
  17. Dec 18, 2012 #16


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    Unless the universe is infinite in spatial extent.

    And I'm curiuos for you to elaborate on your "ehem"...by all means explain how a finite volume can accomodate an infinite number of particles of finite volume.
  18. Dec 19, 2012 #17
    It's an emergent result of numeric processes on specific models and theories (Cosmology: Flat and Euclidean Universe) .Invalid, unreal and hard to get by but 'useful and applicable' (fractals, infinite series, imaginary number and so on).

    One way of dealing with infinite is to build counter model and hope our observation agrees 'more' with it.
  19. Dec 19, 2012 #18
    My teacher told me that parallel lines meet at infinity, however I am pretty sure that they dont, and even if they did it is so far away that it doesnt matter much to me all the way back here. Im not sure if that helps :)
  20. Dec 19, 2012 #19


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    They don't. (In Euclidean space, that is.)
  21. Dec 19, 2012 #20
    The wavelength TENDS to infinity, but it never gets there.

    If the universe is infinitely large and homogenous, then it has infinite mass and energy. It can still have a definite temperature. Temperature is (very roughly) heat energy divided
    by volume. If they are both infinite then one may not divide to get the ratio. But a physicist may measure the temperature and get the ratio that way, so this isn't a problem.
  22. Dec 20, 2012 #21
    Parallel lines, by definition, never meet. Parallel lines meeting at infinity is correct in one sense, in that, for instance, for a right triangle, as a leg and the hypotenuse approach being parallel, the point of intersection approaches being infinitely far off. This, however, doesn't mean they meet at infinity, saying so would be as correct as saying 1/0=∞.

    Absolutely correct. And I'd like to clarify this to everyone by saying that this doesn't mean that there's a point we can go out to which is an infinite distance away from our starting point, but it means that we can get however far away we want from our starting point.
  23. Dec 20, 2012 #22


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    Division by zero yields illogical results.
  24. Dec 20, 2012 #23
    Precisely, saying parallel lines meet at infinity also yields illogical results.
  25. Dec 20, 2012 #24


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  26. Dec 20, 2012 #25


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