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Do infinities exist in nature?

#1
C C Offline
http://plus.maths.org/content/do-infinit...t-nature-0

EXCERPT: What would you see if you came to the edge of the Universe? It's hard to imagine so it's tempting to conclude that the Universe doesn't have an edge and therefore that it must be infinite. That's not a necessary conclusion however. There are things that are finite in extent but still don't have an edge, the prime example being the surface of a sphere. It's got a finite area but when you walk around on it you'll never fall over an edge. The question of whether the Universe is finite or infinite is one that still hasn't been answered, and there are mathematical models that allow for both possibilities. More generally, the question of whether any infinite quantities can arise in the Universe is a deep one.

[...] "What people understood early on was that the inflationary theory gives a whole bunch of suggestive predictions, many of which have come true and many of which will be tested in upcoming experiments. That gives us a lot of confidence in inflation, but it also has very interesting side effects." [...] One of these side effects is that inflation might have gone on at different rates in different regions of the Universe. In some region, the rapid doubling in size will have stopped after a while, resulting in a region of observable Universe like ours. In other regions though, because of spatial variations in the make up of the universe, inflation might go on forever. "You have an infinite spacetime not because you've postulated spacetime is infinite, but because you thought of a process that naturally leads to an infinite spacetime," says Aguirre. "I think that's a very interesting difference, because you can test that process in other ways." If your tests make you believe that this is what actually happened, then the infinity of spacetime pops out as a result of a consistent theory.

Intriguingly, theory also suggests that the extent of space and time depend on your view point. With his general theory of relativity Einstein told us that time and space are inextricably linked, hence the term spacetime. If you want to say something about space or time separately, you need to chop that spacetime up mathematically. "It turns out that even questions like 'Is space finite or infinite?' can depend on how you define space and time separately," explains Aguirre. "There is spacetime, that's what Einstein teaches us; we can choose to cut it into space and time separately in many different ways. They're all fundamentally valid, they'll all give the same results to any particular experiment we think of, but they have different intellectual implications and some are much more convenient for certain purposes than others."

"If you've got an infinite spacetime, there will often be certain ways that you can cut it up so that it looks like the Universe is, say, finite and expanding. [It may be expanding] forever and getting infinitely big, but at any time it's finite. At the same time, the very same spacetime can be chopped up in such a way that at any time it's spatially infinite, so it's an infinite, expanding Universe." In an inflationary Universe it turns out that once the inflation stops there is a most natural way of chopping it up; a way in which the Universe is close to homogeneous. And this gives a Universe that is spatially infinite. "Inflation very naturally gives rise to homogeneous infinite universes that would evolve into something like what we see. I think it's really neat that we can get suggestive evidence for such a rich, and multifaceted, and interesting picture [in which] the Universe is infinite." [...]
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#2
Magical Realist Offline
Quote:At the same time, the very same spacetime can be chopped up in such a way that at any time it's spatially infinite, so it's an infinite, expanding Universe." In an inflationary Universe it turns out that once the inflation stops there is a most natural way of chopping it up; a way in which the Universe is close to homogeneous. And this gives a Universe that is spatially infinite. "Inflation very naturally gives rise to homogeneous infinite universes that would evolve into something like what we see. I think it's really neat that we can get suggestive evidence for such a rich, and multifaceted, and interesting picture [in which] the Universe is infinite." [...]
That is mindblogglingly profound. All sorts of possibilities arise in a universe that is infinite, especially if the quantum vacuum is infinite as well. The only issue now is why 3 headed purple monkeys or giant ectoplasmic octopi don't poof into being every few seconds instead of the same old virtual photons, Maybe the universe evolves laws that constrain the chaotic probablistic ingression of all possibilities into its spacetime. Actuality more like a filter to screen out all the equal and practically inevitable realizations of every conceivable thing, property, or state. Who was it Hawking? that said that time was invented to keep everything from happening at once.
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