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Does Infinity mean 'potential' Infinity?

  1. Jun 18, 2015 #1
    Potential for infinity?

    According to Inflation theory, (Big Bang type models)

    The observable Universe can be measured. We put a specific size on space/time of 13.8 billion years based on expansion from some Singularity.

    My question. When we speak of 'infinity' are we speaking about infinity being the size of space or is infinity the 'potential' size/age the Universe will become?

    Another approach. We draw a line and say it goes on to infinity. We then put a point on the line. Is the current size of the Universe at 'that' point on the line (13.8 billion years) or is it Infinity? In future, a hundred billion years or a trillion, we can move that point along the line but it is always 'finite'.

    We can say something goes on forever 'in theory' but can it only be as old/ big as whatever space/time is 'now'? We can say something 'will' expand forever (infinity) but this doesn't me it has 'already' expanded forever. Can something with a current finite size be infinite? Is Infinity always a 'potential' but not the reality at any current moment?
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  3. Jun 18, 2015 #2
    It isn't settled yet if the universe is infinite or finite in space at present time. (Note that we have to make strong assumptions about the universe to even meaningfully talk about a "present time" at far off parts of the universe.) If it is infinite now, then it was always infinite all the way back to the singularity, at which point all of our theories break down. Note that you can have expansion of an infinite universe. It just means everything gets farther apart. A galaxy a billion l-yr away becomes 2 billion l-yr away, and a galaxy 2 billion l-yr away becomes 4 billion, etc.

    The universe appears very close to spatially flat and somewhat close to isotropic and homogenous. If the universe is spatially flat or hyperbolic and globally isotropic (and homogeneous), then it has to be infinitely large. The problem is that there is no way to fully measure that the universe is globally isotropic; there could always be edges lying just outside our detection range.
  4. Jun 18, 2015 #3

    One of your points makes me rephrase my question. One can have expansion 'within' an infinite Universe but if the Universe itself is infinite, is it itself expanding? Does a spatially flat Universe expand?

    I know than infinity is a mathematical concept. I can get my brain around the theory. However, outside of theory within mathematics is there such a thing as Infinity? We can say a line goes on forever, but there is no actual line. There is a symbol for an infinite line...a symbol for an infinite number.

    Anyways, seems that Infinity is always a potential state rather than an actual state of existence. Perhaps like added dimensions in String theory, our human brains aren't capable of getting around the concept of infinity, other than in math.
  5. Jun 18, 2015 #4


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    All we have are tantalizing hints and that may be all we ever have. Observation strongly suggests the universe is of finite age - around 14 billion years. A universe of finite age is spatially constrained to a size called the 'observable universe' due to the finite speed of light. It could be larger than that but, due to cosmic exansion, there is no way to ever know with any certainty. Light from sufficiently remote regions of the universe will never reach us, not even in theory. So its not like we can just wait around for a terayear for light from regions currently beyond our view to cross the gulf and reveal hitherto unseen vast expanses of the universe.
    Last edited: Jun 18, 2015
  6. Jun 19, 2015 #5


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    Yes, it does. Infinite isn't just a large number. 3 x 1 billion = 3 billion, however 3 x infinite = infinite. So if the universe is infinite and the distances between the Galaxies grow by factor 3 it is still infinite. You can't distinguish a larger infinite universe from a smaller one. You can do that if you look at a finite part of the infinite universe, like the observable universe.
    No, the universe is either finite or infinite. To my impression most cosmologists think of an infinite universe. In this case it was infinite from the very beginning with the observable universe as a tiny part of it at all times. However the universe must not necessarily be infinite. That question depends on it's topology. Theoretically and even if spatially flat the universe could be e.g. a torus ( like a donut) and would be spatially finite then in finite time.
    Last edited: Jun 19, 2015
  7. Jun 19, 2015 #6
    A spatially flat universe can be expanding.
    Simply, we don't know if anything in the universe is truly infinite because all of our experiments are finite. But just because we can't measure infinite doesn't mean that it doesn't exist. Some people have some philosophical issues with infinity, but some people have philosophical issues with motion or with quantum mechanics, so I don't think pure philosophy can be relied on to tell us what we want to know about the universe. Science works by inductive reasoning. We haven't found an edge (or repeat zone) of the universe yet, so we assume one doesn't exist. It's not mathematically rigorous, but that's all we have.
  8. Jun 19, 2015 #7

    True. However, my issues with infinity are not philosophical. I would say that infinity itself is usually a philosophical 'filler' for what we don't know. It's a mathematical construct to rationalize our very limited ability to isolate and measure variables of existence. Is the observable Universe all that there is? Perhaps it is finite but a quintillion times larger. Not infinite. A sextillion is not a large number mathematically...easy to add a few powers of 10....then some more. Anything less than infinity is small on an infinite scale but overwhelming on a human perceptional scale.

    Anyways, there seems to be some point at which physics is less about observation and more about mathematics. Some assumption (philosophical assumption) that the Universe conforms to the math. Of course, math may be all we have to study it those levels beyond observation. Infinities fit math models and we assume they might apply to explaining matter and energy.
  9. Jun 23, 2015 #8
    No. It's mean very very large value.
    Always there is a potential greater than which we are considering.
    Potential is a function of space. Since space is never ending then potential is also never ending.
    Therefore we're talking about an infinite potential.:wink:
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