# To infinity and beyond

November 30, 2011 1:18 PM Subscribe

If the expanse of the universe is infinite, does it necessarily follow that the number of stars and planets is also infinite?

IANAAP

I'm not sure any of that is really established.

Infinite matter, and space would also seem to imply infinite energy (and perhaps dark matter and dark energy) but those things exist in proportion to one another.

String theory allows for vast number of multiple universes (for example), as one explanation as to why dark energy is precisely the level needed to allow for our current livable condition.

There is also the idea of the eventual heat death of the universe where matter becomes so spread out and entropy basically runs down all the energy to a base level which doesn't seem possible in an infinite matter/energy system.

posted by edgeways at 1:32 PM on November 30, 2011

I'm not sure any of that is really established.

Infinite matter, and space would also seem to imply infinite energy (and perhaps dark matter and dark energy) but those things exist in proportion to one another.

String theory allows for vast number of multiple universes (for example), as one explanation as to why dark energy is precisely the level needed to allow for our current livable condition.

There is also the idea of the eventual heat death of the universe where matter becomes so spread out and entropy basically runs down all the energy to a base level which doesn't seem possible in an infinite matter/energy system.

posted by edgeways at 1:32 PM on November 30, 2011

Current theory is that the universe is not infinite in size. (Nor in mass, nor in energy.)

If the universe was infinite in size, that wouldn't require infinite mass or infinite energy. It would theoretically be possible for there to be one area where a finite clump of mass existed, surrounded by unending completely-empty space.

posted by Chocolate Pickle at 1:35 PM on November 30, 2011 [3 favorites]

If the universe was infinite in size, that wouldn't require infinite mass or infinite energy. It would theoretically be possible for there to be one area where a finite clump of mass existed, surrounded by unending completely-empty space.

posted by Chocolate Pickle at 1:35 PM on November 30, 2011 [3 favorites]

Depends on your theory.

There are people who believe that the "space" in the universe is infinite, but the amount of matter in it came from a finite source and so there is a finite amount that keeps rattling around no matter how big the space gets. Also, some matter can transform into other matter, which means that even if there is a finite amount of

Reminds me of my favorite science/religion paradox: If god made everything, and space goes on forever, wouldn't god still be creating space, and if so, wouldn't that necessarily mean that it wouldn't go on forever?

posted by juniperesque at 2:24 PM on November 30, 2011 [1 favorite]

There are people who believe that the "space" in the universe is infinite, but the amount of matter in it came from a finite source and so there is a finite amount that keeps rattling around no matter how big the space gets. Also, some matter can transform into other matter, which means that even if there is a finite amount of

*matter*in the universe, there is a constantly fluctuating amount of*mass*in the universe.Reminds me of my favorite science/religion paradox: If god made everything, and space goes on forever, wouldn't god still be creating space, and if so, wouldn't that necessarily mean that it wouldn't go on forever?

posted by juniperesque at 2:24 PM on November 30, 2011 [1 favorite]

Here's the problem with "infinity": what do you mean by it?

Let's drop down a dimension. Consider a famous example: the Koch Snowflake. It is "infinite", because the length of the perimeter at iteration n is (4/3)^n, and as n -> infinity, this blows up ("increases without bound"). But the area is clearly finite---the snowflake is bounded by a finite circle.

My point here is that "infinity" is weird, and saying something like "the expanse of the universe is infinite" is ill-defined.

(Some more weirdnesses:

--there are a infinite number of positive even numbers. True.

--There are an infinite number of positive integers. True.

--There are exactly twice as many integers as even integers. Well, true...you can construct a 2-to-one correspondence between the positive integers and the evens.

--There are exactly as many integers as even integers. Also true!

And in fact this collision is precisely why we say that both the evens and the integers are infinite sets.)

posted by leahwrenn at 2:28 PM on November 30, 2011 [1 favorite]

Let's drop down a dimension. Consider a famous example: the Koch Snowflake. It is "infinite", because the length of the perimeter at iteration n is (4/3)^n, and as n -> infinity, this blows up ("increases without bound"). But the area is clearly finite---the snowflake is bounded by a finite circle.

My point here is that "infinity" is weird, and saying something like "the expanse of the universe is infinite" is ill-defined.

(Some more weirdnesses:

--there are a infinite number of positive even numbers. True.

--There are an infinite number of positive integers. True.

--There are exactly twice as many integers as even integers. Well, true...you can construct a 2-to-one correspondence between the positive integers and the evens.

--There are exactly as many integers as even integers. Also true!

And in fact this collision is precisely why we say that both the evens and the integers are infinite sets.)

posted by leahwrenn at 2:28 PM on November 30, 2011 [1 favorite]

“In astrophysics and physical cosmology, Olbers' paradox is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe … The paradox is that a static, infinitely old universe with an infinite number of stars distributed in an infinitely large space would be bright rather than dark.”

posted by caek at 3:18 PM on November 30, 2011 [1 favorite]

posted by caek at 3:18 PM on November 30, 2011 [1 favorite]

Also, IAAAP. The consensus is that the universe is not infinite.

posted by caek at 3:19 PM on November 30, 2011

posted by caek at 3:19 PM on November 30, 2011

Yeah, to add to the I Am A Physicist crowd, the "visible Universe" is not infinite. It's 13.7 billion years old, and somewhat larger than 90 billion light years across. It contains several hundred billion galaxies each with several hundred billion stars. Those galaxies comprise about 0.4% of the energy budget of the visible Universe, the remainder is made up of intergalactic gas (3.6%), dark matter (23%), and dark energy (73%). Over time, the percentage of the energy which is in dark energy will go up, and the rest will go down (though the AMOUNT of energy in matter will remain the same - barring proton decay).

There are something like 10^80 atoms in the Universe (mostly in hydrogen and helium). One gram of helium is about 10^24 atoms, so to first order, the Universe has about 10^53 kilograms of hydrogen. A star like our sun is about 10^30 kg (many stars are smaller than this), so if we wanted to build a Universe of just Sols, we'd have about 10^23 of them; which is 10^12 (or a trillion) galaxies of 100 billion stars each, which is not far off from the assumption in the first paragraph.

So while the number of stars (and planets) in the visible Universe is mind-boggling big, it is not infinite.

Now, the visible Universe is defined as "places that are close enough for the light to have reached us since the Big Bang/end of the inflationary phase of the the Universe's life." (the reason why more than 2 * 13.7 billion light years across is a bit complicated, basically, the expansion history of the Universe is not straightforward). There is no reason to believe that their isn't something further away than the visible Universe. Those places might have exactly the same conditions as here, and might go on forever. In which case, there are an infinite number of anything in the "Big U" Universe, including an infinite number of people who call themselves physicsmatt on an infinite number of metafilters.

This is one definition of the Multiverse - since most of the Universe is so far away, it can never be in casual contact with us, and we might as well call our visible Universe "The Universe," the bits that are so far away they can't contact us "other universes" and the whole shebang "the Multiverse." The issue is that, since I can't casually contact those other universes, I have no idea what their laws of physics are (or even if they exist). So you will never - even in principle - know whether they exist, and whether they contain laws of physics amenable to stars and planets. There's some theoretical evidence for this, from string theory and inflationary theory, but as I said, it's hard to see how we'd ever know this is really the way things are.

Alternatively, our little patch of reality might be all that there is, and there's not much past the edge (not that there'd be an edge really). In which case, the Universe is all there is, and the Multiverse is a pipedream.

Short answer, when physicists speak of the "the Universe," we usually mean the bit that we can see. In which case, the Universe is not infinite, and there's a finite number of stars and planets. Past that, I have no idea.

posted by physicsmatt at 3:42 PM on November 30, 2011 [12 favorites]

There are something like 10^80 atoms in the Universe (mostly in hydrogen and helium). One gram of helium is about 10^24 atoms, so to first order, the Universe has about 10^53 kilograms of hydrogen. A star like our sun is about 10^30 kg (many stars are smaller than this), so if we wanted to build a Universe of just Sols, we'd have about 10^23 of them; which is 10^12 (or a trillion) galaxies of 100 billion stars each, which is not far off from the assumption in the first paragraph.

So while the number of stars (and planets) in the visible Universe is mind-boggling big, it is not infinite.

Now, the visible Universe is defined as "places that are close enough for the light to have reached us since the Big Bang/end of the inflationary phase of the the Universe's life." (the reason why more than 2 * 13.7 billion light years across is a bit complicated, basically, the expansion history of the Universe is not straightforward). There is no reason to believe that their isn't something further away than the visible Universe. Those places might have exactly the same conditions as here, and might go on forever. In which case, there are an infinite number of anything in the "Big U" Universe, including an infinite number of people who call themselves physicsmatt on an infinite number of metafilters.

This is one definition of the Multiverse - since most of the Universe is so far away, it can never be in casual contact with us, and we might as well call our visible Universe "The Universe," the bits that are so far away they can't contact us "other universes" and the whole shebang "the Multiverse." The issue is that, since I can't casually contact those other universes, I have no idea what their laws of physics are (or even if they exist). So you will never - even in principle - know whether they exist, and whether they contain laws of physics amenable to stars and planets. There's some theoretical evidence for this, from string theory and inflationary theory, but as I said, it's hard to see how we'd ever know this is really the way things are.

Alternatively, our little patch of reality might be all that there is, and there's not much past the edge (not that there'd be an edge really). In which case, the Universe is all there is, and the Multiverse is a pipedream.

Short answer, when physicists speak of the "the Universe," we usually mean the bit that we can see. In which case, the Universe is not infinite, and there's a finite number of stars and planets. Past that, I have no idea.

posted by physicsmatt at 3:42 PM on November 30, 2011 [12 favorites]

Short answer: yes

Medium length answer: Yes, if it's spatially infinite, and also if you assume that it is globally homogeneous (composed of the same stuff, and subject to the same physical laws) or at least that it includes regions similar to the observable universe with finite probability. On large scales, the parts of the universe we see appear to be uniformly good at making stars, and as far as we can tell stars often form planets. So, if the universe is infinite and not terribly different elsewhere from the way it is here, then the answer must be yes.

Longer answer: Yes, given the caveats about the universe being spatially infinite and homogeneous; however, if the question you care about is "are there any infinite number of planets in the actual universe that we live in," you need to worry about how likely it is those caveats are true. Observationally, the universe appears to be homogeneous for as far as we can see. It also appears to be spatially flat to within a small uncertainty, which is consistent with an infinite homogeneous universe.

Thus, observational cosmology is entirely consistent with an infinite universe full of infinite planets. But, it certainly isn't

But, the good news (assuming one likes the idea of there being lots of planets), is that we've got somewhere in the range of 10^23 stars to think about even if we restrict our attention to just the observable universe.

posted by eotvos at 4:06 PM on November 30, 2011

Medium length answer: Yes, if it's spatially infinite, and also if you assume that it is globally homogeneous (composed of the same stuff, and subject to the same physical laws) or at least that it includes regions similar to the observable universe with finite probability. On large scales, the parts of the universe we see appear to be uniformly good at making stars, and as far as we can tell stars often form planets. So, if the universe is infinite and not terribly different elsewhere from the way it is here, then the answer must be yes.

Longer answer: Yes, given the caveats about the universe being spatially infinite and homogeneous; however, if the question you care about is "are there any infinite number of planets in the actual universe that we live in," you need to worry about how likely it is those caveats are true. Observationally, the universe appears to be homogeneous for as far as we can see. It also appears to be spatially flat to within a small uncertainty, which is consistent with an infinite homogeneous universe.

Thus, observational cosmology is entirely consistent with an infinite universe full of infinite planets. But, it certainly isn't

*required*. A universe which is uniform and slightly curved and therefore finite in extent is also allowed, as are more exotic possibilities. (There's plenty of room for a long, lively, and rather unproductive argument about how to estimate the actual likelihood of the universe being exactly flat vs. nearly flat. If you ask me, it's not a terribly well-posed problem, but that doesn't mean there haven't been attempts to address it.) If you allow for significant variation in the properties of the universe on super-horizon scales - ie, if the bits that are so far away light hasn't had time to get to us from them yet are different from the bits we can see - then all bets are off. And, if inflation really did happen early in the history of the universe, it wouldn't be too surprising if that were the case.But, the good news (assuming one likes the idea of there being lots of planets), is that we've got somewhere in the range of 10^23 stars to think about even if we restrict our attention to just the observable universe.

posted by eotvos at 4:06 PM on November 30, 2011

*Now, the visible Universe is defined as "places that are close enough for the light to have reached us since the Big Bang/end of the inflationary phase of the the Universe's life."*

Worth thinking about is the fact that as far as we know,

*no*causal influence can propagate faster than light; so if there

*is*stuff further away than we will ever in principle see, then in principle it cannot possibly have any effect on us whatsoever, which means that there is no way even in principle to test its properties (even the most basic property of all, i.e. existence), which means that any belief you choose to form about it is of no consequence at all except for possible use as a tribal marker.

In other words, questions about what does or does not lie beyond the observable universe are essentially religious rather than scientific.

posted by flabdablet at 7:44 PM on November 30, 2011 [1 favorite]

Well, maybe. I'm not convinced that what we doctors call "making shit up" really counts as philosophy (whether or not it does so, though, probably counts as epistemology).

posted by flabdablet at 11:57 PM on November 30, 2011

posted by flabdablet at 11:57 PM on November 30, 2011

One of my high school teachers would say (to the best of my recollection), "The universe is finite and unbounded." I took that to mean it's not infinite, which avoids the absurdity of infinite stars, but you couldn't bump into a barrier at the end of it, which is a whole other absurdity.

But as said above, it's still mostly speculation, and I'm not sure current theory even supports an unbounded universe.

posted by mad bomber what bombs at midnight at 8:09 AM on December 1, 2011

But as said above, it's still mostly speculation, and I'm not sure current theory even supports an unbounded universe.

posted by mad bomber what bombs at midnight at 8:09 AM on December 1, 2011

This thread is closed to new comments.

posted by qxntpqbbbqxl at 1:21 PM on November 30, 2011