# Is the amount of matter in the universe infinite?

August 20, 2008 6:31 AM Subscribe

Is the amount of matter in the universe infinite, too? How does

So, okay, say our universe is infinite (current data supports this, right?). Since there are a finite number of ways that particles can be arranged, that must mean that if you go far enough you'll run into an identical earth with an identical history, identical population, an identical

I'd heard all that before, but I was listening to this Radiolab podcast (which is really very good!) and it doesn't mention the one thing I never understood - doesn't that mean that the amount of matter in the universe must

Honestly, in light of all this other nonsense, that tidbit wouldn't be that hard to swallow if it didn't directly contradict other weird stuff I've heard. For example, according to this episode of Astronomy Cast (maybe I shouldn't be getting all my information from podcasts), the Big Bang created slightly more matter than anti-matter, resulting in a mostly-matter universe. But how could it be

Now what? Is matter actually infinite? Is one of those wrong? Are they both supported, and there's something I'm missing?

*that*work?So, okay, say our universe is infinite (current data supports this, right?). Since there are a finite number of ways that particles can be arranged, that must mean that if you go far enough you'll run into an identical earth with an identical history, identical population, an identical

*you*. Even though that's hella weird and I could probably never explain it to my parents, I think I get it.

I'd heard all that before, but I was listening to this Radiolab podcast (which is really very good!) and it doesn't mention the one thing I never understood - doesn't that mean that the amount of matter in the universe must

*also*be infinite?

Honestly, in light of all this other nonsense, that tidbit wouldn't be that hard to swallow if it didn't directly contradict other weird stuff I've heard. For example, according to this episode of Astronomy Cast (maybe I shouldn't be getting all my information from podcasts), the Big Bang created slightly more matter than anti-matter, resulting in a mostly-matter universe. But how could it be

*more*if matter is infinite? They even give a number, I think it's something like ten billion particles of antimatter to ten billion and one of matter.

Now what? Is matter actually infinite? Is one of those wrong? Are they both supported, and there's something I'm missing?

Infinite is not a finite number, though. Which sounds odd (and a stupid thing to say in response!), but that is kind of the way you are treating it - that infinite is a point that you reach when it can't get any bigger, and that's not what it means. I don't think that saying that two thing are infinite necessarily precludes there being more of one than the other.

Perhaps 'infinite within our realms of measurement' is a better way of looking at it. One of the definitions is 'without bounds' or 'beyond measurement' or 'an incalculable number'. Just because we can't measure it, doesn't mean all infinite things are the same size, if you see what I mean. From that perspective, those statements don't contradict each other. Stop thinking of infinite as a size or number, and it may be easier to get your head around. It's more 'the point

posted by Brockles at 6:44 AM on August 20, 2008 [1 favorite]

Perhaps 'infinite within our realms of measurement' is a better way of looking at it. One of the definitions is 'without bounds' or 'beyond measurement' or 'an incalculable number'. Just because we can't measure it, doesn't mean all infinite things are the same size, if you see what I mean. From that perspective, those statements don't contradict each other. Stop thinking of infinite as a size or number, and it may be easier to get your head around. It's more 'the point

*beyond which*we are unable to attach a number to represent its size meaningfully'.posted by Brockles at 6:44 AM on August 20, 2008 [1 favorite]

The Universe may indeed be infinite. The "observable Universe" is not.

Everything, all matter in the finite "observable Universe" can be traced back to the Big Bang.

Make sense? Here's a diagram.

posted by vacapinta at 6:50 AM on August 20, 2008

Everything, all matter in the finite "observable Universe" can be traced back to the Big Bang.

Make sense? Here's a diagram.

posted by vacapinta at 6:50 AM on August 20, 2008

if the universe was infinite then yes, there would be an infinite amount of matter. infinite isn't a single number. two values can be infinite and one can be larger than the other. for example, take all the integers (1, 2, 3...) - there's obviously an infinite number of those. now consider the real numbers (ie with decimals). since you can keep on adding more detail after the decimal point there's an infinite number of those between each integer (eg. between 1 and 2 there's 1.1, 1.11, 1.111, 1.1111 etc). so there are more real numbers than there are integers. same kind of thing with anti-matter and dark matter.

posted by not sure this is a good idea at 6:52 AM on August 20, 2008 [1 favorite]

posted by not sure this is a good idea at 6:52 AM on August 20, 2008 [1 favorite]

not sure that was completely clear. there are an infinite number of integers. there are also an infinite number of real numbers. but i also showed that there are more real numbers than integers. so just because two things are infinite doesn't mean they are equal.

posted by not sure this is a good idea at 6:54 AM on August 20, 2008

posted by not sure this is a good idea at 6:54 AM on August 20, 2008

Grither: Universe is not used precisely in astronomy. Even the wikipedia article says that.

Brockles, nstiagi: Sorry, but the imbalance between matter and anti-matter is not an issue of Cantorian Cardinality. You guys are just guessing aren't you?

posted by vacapinta at 6:57 AM on August 20, 2008 [1 favorite]

Brockles, nstiagi: Sorry, but the imbalance between matter and anti-matter is not an issue of Cantorian Cardinality. You guys are just guessing aren't you?

posted by vacapinta at 6:57 AM on August 20, 2008 [1 favorite]

How can there be more matter than antimatter? Well there's more numbers not divisible by five than there are that are divisible by five.*

I wouldn't use 'not sure this is a good idea's point about reals versus integers. There's got to be a countable amount of matter as it comes in particles. Real numbers are not countable in this way.

With whether it is infinite or not, vacapinta's right. Basically it's currently consistent with being infinite, but this is not the same thing as actually being infinite.

*Well, ok, it's the same number if you look at it another way, but the point is about how you actually go about the process of pairing things up, as this is how the antimatter ends up getting eliminated. You can only pair an antimatter particle up with a nearby one of matter if you want it to annihilate. The point is that in any given region you have more matter, even if the total of both is infinite.

posted by edd at 6:58 AM on August 20, 2008

I wouldn't use 'not sure this is a good idea's point about reals versus integers. There's got to be a countable amount of matter as it comes in particles. Real numbers are not countable in this way.

With whether it is infinite or not, vacapinta's right. Basically it's currently consistent with being infinite, but this is not the same thing as actually being infinite.

*Well, ok, it's the same number if you look at it another way, but the point is about how you actually go about the process of pairing things up, as this is how the antimatter ends up getting eliminated. You can only pair an antimatter particle up with a nearby one of matter if you want it to annihilate. The point is that in any given region you have more matter, even if the total of both is infinite.

posted by edd at 6:58 AM on August 20, 2008

ni, i'm not just guessing - i thought it was an easy way to show two values can be infinite without being equal. i didn't even mention cardinality.

i'm curious if i'm wrong though - are you saying that the amount of matter and the amount of anti-matter must be equal?

posted by not sure this is a good idea at 6:59 AM on August 20, 2008

i'm curious if i'm wrong though - are you saying that the amount of matter and the amount of anti-matter must be equal?

posted by not sure this is a good idea at 6:59 AM on August 20, 2008

"i'm curious if i'm wrong though - are you saying that the amount of matter and the amount of anti-matter must be equal?"

Yes and no. You could take an 'equal' but infinite amount of matter and antimatter and if you had total freedom to arrange them as you wish you could end up with any amount of matter or antimatter left over you wanted, from none, to a kilogram, to a galaxy's worth to an infinite amount of either. The universe doesn't have such freedom in pairings however.

(caveat: I've not thought about this before, but it seems straightforward to me. However, finding yourself dealing with infinities to be straightforward might be taken as a worrying sign)

posted by edd at 7:06 AM on August 20, 2008

Yes and no. You could take an 'equal' but infinite amount of matter and antimatter and if you had total freedom to arrange them as you wish you could end up with any amount of matter or antimatter left over you wanted, from none, to a kilogram, to a galaxy's worth to an infinite amount of either. The universe doesn't have such freedom in pairings however.

(caveat: I've not thought about this before, but it seems straightforward to me. However, finding yourself dealing with infinities to be straightforward might be taken as a worrying sign)

posted by edd at 7:06 AM on August 20, 2008

right, but then you'd break the cosmological principle.

i looked at the question, tried to see what the original poster had a problem with, and it seemed to me that the one sticking point was that they thought "infinite" was a simple value. so i gave an example that showed that wasn't true.

i certainly wasn't suggesting that the amount of matter is of a different cardinality to the amount of anti-matter and i'm kind of pissed that vacapinta thinks that was my argument.

posted by not sure this is a good idea at 7:12 AM on August 20, 2008

i looked at the question, tried to see what the original poster had a problem with, and it seemed to me that the one sticking point was that they thought "infinite" was a simple value. so i gave an example that showed that wasn't true.

i certainly wasn't suggesting that the amount of matter is of a different cardinality to the amount of anti-matter and i'm kind of pissed that vacapinta thinks that was my argument.

posted by not sure this is a good idea at 7:12 AM on August 20, 2008

*"not sure that was completely clear. there are an infinite number of integers. there are also an infinite number of real numbers. but i also showed that there are more real numbers than integers."*

Actually, you didn't show that, either. Mathematicians do talk about orders of infintude and the cardinality of the reals, but the only effective way of talking about the cardinality of infinite sets is by mapping corresponding elements of them. The reals are larger than the rationals because every member of the rationals maps onto itself in the reals, and the reals also include irrational numbers like pi, the square root of 2, and lots of other things that can't be expressed as ratios (hence

*rational*) between natural numbers.

As I understand the physics of space-time (and IANAP), the universe is not thought to be infinite, properly speaking. It is thought to be finite but unbounded. That is, there is a finite amount of space, but no boundary to it. You cannot reach the edge of the universe, beyond which would lie some metaphysical no-man's land, I guess. Space-time bends back on itself in other spatial dimensions of the manifold. In other words, think of peeling off the surface of a globe and laying it flat on a table. It would be a finite amount of 2-dimensional space on the table before you. Now take it and wrap it around the globe again; it is still a finite amount of space, but it has no boundaries because it has been wrapped back upon itself in three dimensions. Likewise, if you think of the three dimensions of space-time we are accustomed to experiencing being wrapped back upon themselves in a fourth dimension of the manifold, you could have a finite amount of space with no boundaries. Not that you could reach any such boundary anyway; you'd have to have been traveling the speed of light since the Big Bang just to catch up with the expansion. And you're certainly going to fit only a finite amount of matter into a finite amount of space.

posted by el_lupino at 7:14 AM on August 20, 2008

jeez. tough crowd. yes, i didn't do diagonalisation. i was trying to be convincing, not rigorous. ok, i give up.

posted by not sure this is a good idea at 7:16 AM on August 20, 2008

posted by not sure this is a good idea at 7:16 AM on August 20, 2008

No actually, you were onto the right idea, I think. Show that one infinte set can be a subset of the other. Just need to emphasize the idea of mapping each of those things onto itself in the other set.

posted by el_lupino at 7:20 AM on August 20, 2008

posted by el_lupino at 7:20 AM on August 20, 2008

*Brockles, nstiagi: Sorry, but the imbalance between matter and anti-matter is not an issue of Cantorian Cardinality.*

Looks like you have misunderstood both arguments - matter and antimatter were irrelevant to my point. My perception of the question was that because two things are infinite, one cannot be larger than the other - therefore considering the various statements to be contradictory. I was attempting to show that something being 'infinite' is, by definition, not a 'solid point' so doesn't preclude two infinite things being of differing sizes necessarily. 'Immeasurable' and 'Immeasurable +1' are both immeasurable (to use schoolyard logic) the fact that I use 1, or a banana or scatological terms to try and show that is neither here nor there.

The core of the issue seemed to be one of misunderstanding the concept of infinite, to me, rather than any deeper understanding of the universe. Whether one or both of the two statements are

*wrong*is a matter for physics (and I don't claim to know anything about that in any depth). Whether they

*contradict*isn't necessarily anything more than English and Mathematical definitions.

posted by Brockles at 7:32 AM on August 20, 2008

Response by poster: Okay, stop dick-waving. I still don't get it.

According to the astrophysicist in that Radiolab podcast, the universe is infinite. It's not finite but unbounded (but I understand that, too), it's actually, really infinite. So, whether or not this is true (for the purposes of this question, I don't care), it's a possibly valid theory and some scientists who are not quacks support it.

So then,

posted by borkingchikapa at 7:39 AM on August 20, 2008

According to the astrophysicist in that Radiolab podcast, the universe is infinite. It's not finite but unbounded (but I understand that, too), it's actually, really infinite. So, whether or not this is true (for the purposes of this question, I don't care), it's a possibly valid theory and some scientists who are not quacks support it.

So then,

*within this conjecture*, is matter also infinite? Was an infinite amount of matter created at the Big Bang? Or, in light of Brockles' answer, is the amount of matter in the universe roughly as infinite as space in the universe?**I guess what I'm actually asking**is for someone to clarify the issue the quantity of matter in the universe (again, pertaining to this theory that the universe is infinite). Every discussion of it I've heard focuses on the craziness of the idea that*space*goes on forever. That's wacky, yeah, but is there enough stuff to fill it? If I go past that identical Earth with the identical me typing this identical question, will I eventually get to a point where there is no more matter and only space?posted by borkingchikapa at 7:39 AM on August 20, 2008

borkingchikapa: I've answered your question. I have a physics degree. edd agrees with me and he's an astrophysicist.

Yes, in an infinite universe, matter is also infinite. No, a finite amount of matter was created at the Big Bang because, despite what you've been told, the Big Bang did not give rise to the infinite Universe only the finite one.

posted by vacapinta at 7:43 AM on August 20, 2008

*So then, within this conjecture, is matter also infinite? Was an infinite amount of matter created at the Big Bang? Or, in light of Brockles' answer, is the amount of matter in the universe roughly as infinite as space in the universe?*Yes, in an infinite universe, matter is also infinite. No, a finite amount of matter was created at the Big Bang because, despite what you've been told, the Big Bang did not give rise to the infinite Universe only the finite one.

posted by vacapinta at 7:43 AM on August 20, 2008

Response by poster:

Whoa, what? Where did the rest of it come from?

posted by borkingchikapa at 7:45 AM on August 20, 2008

*No, a finite amount of matter was created at the Big Bang because, despite what you've been told, the Big Bang did not give rise to the infinite Universe only the finite one.*Whoa, what? Where did the rest of it come from?

posted by borkingchikapa at 7:45 AM on August 20, 2008

There is, by definition, a finite amount of matter and energy in the universe. Infinity works for mathematics and geometry, but not for the world of matter and energy.

The truth is, we have no idea what is beyond the observable universe, including whether there is any there there. So there.

posted by megatherium at 7:45 AM on August 20, 2008 [1 favorite]

The truth is, we have no idea what is beyond the observable universe, including whether there is any there there. So there.

posted by megatherium at 7:45 AM on August 20, 2008 [1 favorite]

Let's try a different tack for a moment:

Assume that the universe is infinite, just space beyond space, and no matter how far out you go, there's more space. However, that space is empty. There's nothing in there, not air, single molecules, not even atoms, quarks, or photons. Nothing at all.

As our

Regardless, the amount of matter does not have to be infinite in an infinite universe, because most of the universe is empty (truly empty, hard vacuum) space.

posted by explosion at 8:08 AM on August 20, 2008

Assume that the universe is infinite, just space beyond space, and no matter how far out you go, there's more space. However, that space is empty. There's nothing in there, not air, single molecules, not even atoms, quarks, or photons. Nothing at all.

As our

*observable*universe expands into this infinite universe, the already thin intergalactic (and interstellar) medium expands, along with the background radiation, etc. that defines the observable universe.Regardless, the amount of matter does not have to be infinite in an infinite universe, because most of the universe is empty (truly empty, hard vacuum) space.

posted by explosion at 8:08 AM on August 20, 2008

The universe is very very big. That's all we know for sure. It's consistent with being infinite, it's also consistent with being finite but unbounded. Anyone that says it is proven either way is, to the best of my knowledge, wrong. I don't even know how you

For the same reasons as you can't show it's infinite, if it goes on forever we can't know what the universe is really like all the way through it. There's just no time for the light to get from there to here - it'd obviously take an infinite amount of time (it's exactly the same argument as why the observable universe is finite of course) The most reasonable assumption is that every bit of the universe has stuff to fill it - because every bit of the universe we can see looks largely like every other bit, so you might assume that every bit of the universe you can't see looks largely like every other bit.

But we don't know, and, as I said, perhaps we can't know.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#RB

posted by edd at 8:19 AM on August 20, 2008 [2 favorites]

*could*prove that it's infinite - only show that it's finite.For the same reasons as you can't show it's infinite, if it goes on forever we can't know what the universe is really like all the way through it. There's just no time for the light to get from there to here - it'd obviously take an infinite amount of time (it's exactly the same argument as why the observable universe is finite of course) The most reasonable assumption is that every bit of the universe has stuff to fill it - because every bit of the universe we can see looks largely like every other bit, so you might assume that every bit of the universe you can't see looks largely like every other bit.

But we don't know, and, as I said, perhaps we can't know.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#RB

posted by edd at 8:19 AM on August 20, 2008 [2 favorites]

There is so much confusion in this thread, I had to walk away for a second to take a breath. Let me just say:

1) Brockles is completely wrong with regard to the infinity thing, physics aside. Two things which are of the same Cardinality are equal by any mathematical measure. It makes no sense to say that there is 10 times as much matter as anti-matter but they are both infinite. This is Mathematics. Unless, they are of different Cardinalities. Which they are not.

2) Our current observable Universe has a finite amount of matter/energy in a finite amount of space. All indications are that all of this stuff was compressed into a small, finite, ball of matter/energy. The Big Bang.

There are two senses in which it is correct to say "The Universe is infinite":

A) The observable Universe could be expanding into something else. Probably isotropic. The geometry of our observable Universe (that it seems Euclidean) suggests that we are likely a small part of a larger Universe. This doesn't contradict any current theories nor support them.

B) Our Universe is infinite in space-time. Since it is known that the Universe is expanding and perhaps even accelerating it seems likely that it will keep expanding forever. That is, its size, not in space, but in

In the case of A) there is probably infinite matter as well based on nothing more than Universality principles. In the case of B) the amount of matter is finite but becomes less dense as the Universe expands into infinity.

posted by vacapinta at 8:21 AM on August 20, 2008 [1 favorite]

1) Brockles is completely wrong with regard to the infinity thing, physics aside. Two things which are of the same Cardinality are equal by any mathematical measure. It makes no sense to say that there is 10 times as much matter as anti-matter but they are both infinite. This is Mathematics. Unless, they are of different Cardinalities. Which they are not.

2) Our current observable Universe has a finite amount of matter/energy in a finite amount of space. All indications are that all of this stuff was compressed into a small, finite, ball of matter/energy. The Big Bang.

There are two senses in which it is correct to say "The Universe is infinite":

A) The observable Universe could be expanding into something else. Probably isotropic. The geometry of our observable Universe (that it seems Euclidean) suggests that we are likely a small part of a larger Universe. This doesn't contradict any current theories nor support them.

B) Our Universe is infinite in space-time. Since it is known that the Universe is expanding and perhaps even accelerating it seems likely that it will keep expanding forever. That is, its size, not in space, but in

*space-time*is probably infinite. Most current theories favor this.In the case of A) there is probably infinite matter as well based on nothing more than Universality principles. In the case of B) the amount of matter is finite but becomes less dense as the Universe expands into infinity.

posted by vacapinta at 8:21 AM on August 20, 2008 [1 favorite]

*1) Brockles is completely wrong with regard to the infinity thing, physics aside. Two things which are of the same Cardinality are equal by any mathematical measure. It makes no sense to say that there is 10 times as much matter as anti-matter but they are both infinite. This is Mathematics. Unless, they are of different Cardinalities. Which they are not.*

Therefore all things that are infinite are of exactly the same size. That doesn't make any sense. If that is not your conclusion, then you have misunderstood my post, or I didn't make myself clear.

Part of the definition of infinite is that it is impossible to measure. Surely you would be unable to determine it's Cardinality to establish if it matches something else. For your conclusion to work, an infinite 'thing' would have to be a tangible thing that you can measure or work with. Kind of the point of infinite is that it is immeasurable.

Nothing in the definition of infinite that I have been taught, or can find, suggests that infinity dictates a known and equal amount. Therefore nor does it dictate that all infinite things are the same size - it's a 'level' that a large number of 'things' goes beyond, not a point that it reaches. Consequently, infinite objects are not

*necessarily*equal, which prevents the earlier comments from being contradictory.

I'm talking about concepts (perhaps a little to much on the philosophical side for you to drop the physics knowledge a bit and see what I mean), and you are talking specifics of matter. Unless astrophysics uses a different concept for infinite to English and Mathematics (which I am not aware that it does) then this logic holds true.

posted by Brockles at 8:33 AM on August 20, 2008

Brockles: "

Schoolyard logic isn't applicable here. Though I am sure I yelled it as a child myself, "infinity plus one" doesn't have any particular meaning and it certainly doesn't denote anything larger than plain old infinity. Yes, there are different cardinalities, but that isn't really germane here.

posted by ssg at 8:34 AM on August 20, 2008

*I was attempting to show that something being 'infinite' is, by definition, not a 'solid point' so doesn't preclude two infinite things being of differing sizes necessarily. 'Immeasurable' and 'Immeasurable +1' are both immeasurable (to use schoolyard logic) the fact that I use 1, or a banana or scatological terms to try and show that is neither here nor there.*"Schoolyard logic isn't applicable here. Though I am sure I yelled it as a child myself, "infinity plus one" doesn't have any particular meaning and it certainly doesn't denote anything larger than plain old infinity. Yes, there are different cardinalities, but that isn't really germane here.

posted by ssg at 8:34 AM on August 20, 2008

*It makes no sense to say that there is 10 times as much matter as anti-matter but they are both infinite.*

Absolutely. Because you would have to be able to measure each item to compare their relative sizes. Because both are infinite (if that is true, I have no opinion, nor have I voiced one) it is impossible to measure them to work out which is bigger. This does not, however, imply that therefore they must be equal. Trying to apply Cardinality to infinite amounts is fundamentally flawed anyway - one precludes the other as one is a unit of distinct measurement (of sorts) and the other is the definition of 'immeasurable'.

posted by Brockles at 8:36 AM on August 20, 2008

Brockles, you might find some of these useful. A quick google will surely show you more if you aren't convinced.

posted by ssg at 8:46 AM on August 20, 2008

posted by ssg at 8:46 AM on August 20, 2008

Given matter and antimatter come in the form of particles, I struggle to see how you can possibly think that if there's an infinite number of particles how that infinite cardinal number can be anything other than aleph-null.

posted by edd at 8:46 AM on August 20, 2008 [1 favorite]

posted by edd at 8:46 AM on August 20, 2008 [1 favorite]

The observable universe is finite in spacial extent, and the mass the observable universe contains is also finite. It seems to me to be very hard to form an actual scientific theory about this possible region of space outside the observable universe--what is the testable hypothesis that arises from Greene's thought experiment?

posted by jepler at 9:04 AM on August 20, 2008

posted by jepler at 9:04 AM on August 20, 2008

ssg: From a quick read, that seems to support my position, though (or at least, nothing precludes it from being true). Maybe I'm just not explaining it well.

My base point was that two things being infinite doesn't stop one being bigger than the other. If I represented that wrongly, then that is possibly my issue, but my impression was that the OP was assuming that There are an infinite number of a, and there are an infinite number of b" means "There is more a than b can't be true".

If I misunderstood the confusion, then fine. But, as I say, none of those links suggests that my statement (however badly put) is false, unless I am missing something glaring. Infinite a does not necessarily equal infinite b, because as the first link says "Infinity is a

concept, not a number, so we can't do arithmetic with it."

Maybe I'm having a bad day, but that was actually my point. You can't do sums with infinity, as it is not a number, but a concept to represent not having a number to quantify something with.

posted by Brockles at 9:11 AM on August 20, 2008

My base point was that two things being infinite doesn't stop one being bigger than the other. If I represented that wrongly, then that is possibly my issue, but my impression was that the OP was assuming that There are an infinite number of a, and there are an infinite number of b" means "There is more a than b can't be true".

If I misunderstood the confusion, then fine. But, as I say, none of those links suggests that my statement (however badly put) is false, unless I am missing something glaring. Infinite a does not necessarily equal infinite b, because as the first link says "Infinity is a

concept, not a number, so we can't do arithmetic with it."

*Schoolyard logic isn't applicable here.*Maybe I'm having a bad day, but that was actually my point. You can't do sums with infinity, as it is not a number, but a concept to represent not having a number to quantify something with.

posted by Brockles at 9:11 AM on August 20, 2008

(I'm aware I'm derailing, so I'll stop now. I am off at a tangent that doesn't work with the question. Sorry for the derail.)

posted by Brockles at 9:28 AM on August 20, 2008

posted by Brockles at 9:28 AM on August 20, 2008

Perhaps I'm misunderstanding what you're going for here, but:No actually, you were onto the right idea, I think. Show that one infinte set can be a subset of the other.

Just because one infinite set is a subset of another does

*not*mean that it's of smaller cardinality.

For example, the set of even integers is an infinite set. It is a subset of the set of integers, which is also an infinite set.

They are of exactly the same cardinality.

posted by Flunkie at 9:36 AM on August 20, 2008

You might wan to check out Infinity and the Mind for just about everything you ever wanted to know about infinity.

posted by zengargoyle at 11:29 AM on August 20, 2008

posted by zengargoyle at 11:29 AM on August 20, 2008

Did anyone actually listen to the podcast to which he referred? I had exactly the same question as borkingchikapa when I listened to it last week.

By way of introduction, they describe a situation in which a person wants to be able to wear a different combination of shoes and dresses every day, and never repeat themselves. But because she has a finite number of shoes and dresses, and an effectively infinite number of days on which to wear them, eventually she'll have to start repeating combinations. Thus what she wants is impossible.

So to apply this idea to the Universe, most people have this idea that if we keep exploring the far reaches of space, we'll find new things, unique arrangements of particles. But based on the data available there seems to be a finite variety of particles (quarks, protons, neutrons, electrons, etc), and infinite space-time in which to arrange those particles. Thus, at some point in the infiniteness of space-time the Universe will be forced to repeat itself, and come up with another galaxy, another solar system, another planet that is exactly like the one we're in, with every particle arranged in exactly the same way.

Though that sounds a little like Donald Sutherland explaining how we're a just spec under a giant's thumbnail, I feel like I get it on a logical/conceptual level. But it implies that in addition to space-time being infinite and ever-expanding, there also are infinite particles with which to arrange in infinite space-time (though a finite variety of those particles). And that's where I get lost.

In the podcast they gloss over this like it's no big deal, and maybe it isn't. What am I missing?

I guess my confusion comes from my understanding of The Big Bang and the nature of infinite space-time, which seems to imply that space is created over time as the universe expands and particles move away from each other. So if space is expanding because particles are moving away from each other, I'm having trouble grasping how those particles can be infinite in number.

And yes, I got a D in high school physics and an Art degree in college, thanks for noticing.

posted by sportbucket at 2:53 PM on August 20, 2008

By way of introduction, they describe a situation in which a person wants to be able to wear a different combination of shoes and dresses every day, and never repeat themselves. But because she has a finite number of shoes and dresses, and an effectively infinite number of days on which to wear them, eventually she'll have to start repeating combinations. Thus what she wants is impossible.

So to apply this idea to the Universe, most people have this idea that if we keep exploring the far reaches of space, we'll find new things, unique arrangements of particles. But based on the data available there seems to be a finite variety of particles (quarks, protons, neutrons, electrons, etc), and infinite space-time in which to arrange those particles. Thus, at some point in the infiniteness of space-time the Universe will be forced to repeat itself, and come up with another galaxy, another solar system, another planet that is exactly like the one we're in, with every particle arranged in exactly the same way.

Though that sounds a little like Donald Sutherland explaining how we're a just spec under a giant's thumbnail, I feel like I get it on a logical/conceptual level. But it implies that in addition to space-time being infinite and ever-expanding, there also are infinite particles with which to arrange in infinite space-time (though a finite variety of those particles). And that's where I get lost.

In the podcast they gloss over this like it's no big deal, and maybe it isn't. What am I missing?

I guess my confusion comes from my understanding of The Big Bang and the nature of infinite space-time, which seems to imply that space is created over time as the universe expands and particles move away from each other. So if space is expanding because particles are moving away from each other, I'm having trouble grasping how those particles can be infinite in number.

And yes, I got a D in high school physics and an Art degree in college, thanks for noticing.

posted by sportbucket at 2:53 PM on August 20, 2008

Okay, unless I've totally misunderstood the OP's question, here's the same question put another way:

posted by sportbucket at 3:51 PM on August 20, 2008

I’ve got three kinds of yarn, and infinite time and space in which to knit scarves.Matter=yarn, for those of you playing along at home.(I'd also need eternal life and an insatiable desire to knit scarves, so let's take that as a given.)At some point I will run out of unique patterns to knit so I'll have to repeat myself. But won’t I also run out of yarn?

posted by sportbucket at 3:51 PM on August 20, 2008

*Well there's more numbers not divisible by five than there are that are divisible by five*

I realize that your asterisk qualifies this comment, but nevertheless it is incorrect. Both sets are countable and can be placed in one-to-one correspondence. They have the same cardinality of infinity.

posted by Neiltupper at 5:57 PM on August 20, 2008

sportbucket, I haven't listened to it, but I think the key word is "eventually." Let's take a more traditional "infinite ... eventually" problem: if I had an infinite number of monkeys with typewriters, they'd eventually reproduce Shakespeare's plays. When is "eventually"?

I happen to be sitting at a computer that listens to environmental noise --- keyboard taps, mouse motion, network packet arrivals, whatever --- and uses those to make real random numbers. If all I want is the 52 upper- and lower-case letters, a dozen kinds of spaces and punctuation, I can make those pretty fast: about sixteen million per second. How long will it take my random number generator to write the title of a play, "Hamlet, Prince of Denmark"? Well, on average, every 64th letter is "H." Every 64th "H" is followed by an "a." Every 64th "Ha" is followed by an "m," and so on. After making 64

Of course, I'm just one monkey with one (fast) typewriter. If everybody on earth did this, we'd go seven billion times faster, right? So somebody, somewhere in the world would get "Hamlet, Princ" every couple of years. In thirty years we might have a "Hamlet, Prince"; in 2000 someone would have "Hamlet, Prince " with a trailing space; in 120,000 years someone would have "Hamlet, Prince o". In that same 120,000 years you'd probably also find a "Romeo and Juli" and a "King Lear. Act" and a few dozen "the comedy of" and so on. Even if everyone on earth banged out random characters at this rate, it would take millions of years just to get an unsorted list of all the

Infinity is fucking

So now let's live dangerously and mix this with cosmology. Suppose you travel to some remote corner of the universe and find an alter-Earth, where an alter-sportbucket is reading an alter-Metafilter about reproducing the works of an alter-Shakespeare. What are the odds that the alter-me picked the same play for illustration? Well, we've just seen that there's (roughly) one alter-world in 64

So, do we have evidence that the universe is infinite? No. We have evidence that stars tend to aggregate in groups of a few billion, a few dozen light-years across; these are "galaxies." (The Milky Way, with 100 billion stars in a diameter of 100,000 light years, is biggish as galaxies go.) Galaxies also aggregate into clusters: from here to Andromeda, the other big galaxy in our local group, "only" 95% of the distance is intergalactic emptiness. As you look farther away, the news gets older. We can see far enough back that it was too hot for stars --- that's where this "hundred billion light-years across" figure comes from. The evidence is that the entire volume is just about uniformly filled with galaxies (though they clump up, too). There is room for 10

What we know --- from the fact that the clumpiness of galaxies doesn't change over the visible universe --- is that if the universe

posted by fantabulous timewaster at 6:02 PM on August 20, 2008 [2 favorites]

I happen to be sitting at a computer that listens to environmental noise --- keyboard taps, mouse motion, network packet arrivals, whatever --- and uses those to make real random numbers. If all I want is the 52 upper- and lower-case letters, a dozen kinds of spaces and punctuation, I can make those pretty fast: about sixteen million per second. How long will it take my random number generator to write the title of a play, "Hamlet, Prince of Denmark"? Well, on average, every 64th letter is "H." Every 64th "H" is followed by an "a." Every 64th "Ha" is followed by an "m," and so on. After making 64

^{6}random numbers --- about an hour's work, assuming my computer has enough noise to feed on --- I'll probably have a "Hamlet" somewhere. To get "Hamlet," with the comma would take about three days. To get "Hamlet, Princ" my poor computer would (on average, if that's still meaningful) have to make random numbers for fifteen billion years. During that time the sun will swell up and become a red giant, engulfing the earth and probably ending my program.Of course, I'm just one monkey with one (fast) typewriter. If everybody on earth did this, we'd go seven billion times faster, right? So somebody, somewhere in the world would get "Hamlet, Princ" every couple of years. In thirty years we might have a "Hamlet, Prince"; in 2000 someone would have "Hamlet, Prince " with a trailing space; in 120,000 years someone would have "Hamlet, Prince o". In that same 120,000 years you'd probably also find a "Romeo and Juli" and a "King Lear. Act" and a few dozen "the comedy of" and so on. Even if everyone on earth banged out random characters at this rate, it would take millions of years just to get an unsorted list of all the

*titles*of Shakespeare's plays.Infinity is fucking

*big*. Even with all the monkeys.So now let's live dangerously and mix this with cosmology. Suppose you travel to some remote corner of the universe and find an alter-Earth, where an alter-sportbucket is reading an alter-Metafilter about reproducing the works of an alter-Shakespeare. What are the odds that the alter-me picked the same play for illustration? Well, we've just seen that there's (roughly) one alter-world in 64

^{6}where that play's title starts with "Hamlet." And that assumes you can discount all the alter-worlds where I went to mow the lawn instead of answering this post, or the alter-worlds where you're alive and I'm not, or alter-worlds where vertebrates didn't come out ahead in the Cambrian explosion. That's an awful lot of near-misses, if you want to find your alter-you.So, do we have evidence that the universe is infinite? No. We have evidence that stars tend to aggregate in groups of a few billion, a few dozen light-years across; these are "galaxies." (The Milky Way, with 100 billion stars in a diameter of 100,000 light years, is biggish as galaxies go.) Galaxies also aggregate into clusters: from here to Andromeda, the other big galaxy in our local group, "only" 95% of the distance is intergalactic emptiness. As you look farther away, the news gets older. We can see far enough back that it was too hot for stars --- that's where this "hundred billion light-years across" figure comes from. The evidence is that the entire volume is just about uniformly filled with galaxies (though they clump up, too). There is room for 10

^{15}pairs like the Milky Way and Andromeda. That's about 10^{26}stars --- about as many stars in the visible universe as there are molecules in a jug of water. Enormous. Not infinite.What we know --- from the fact that the clumpiness of galaxies doesn't change over the visible universe --- is that if the universe

*does*have some edge, it's far away compared to the hundred billion light-year visible limit. Maybe the edge is two hundred billion light years off, and there are 10^{27}stars. Maybe the edge is a trillion light years off and there are 10^{30}stars. Ours is still the only one where anyone has written Hamlet.posted by fantabulous timewaster at 6:02 PM on August 20, 2008 [2 favorites]

Olbers' paradox shows that the universe can't be both infinitely large and infinitely old. We know how long ago the universe was too hot for stars, which is as far back as we can see. Setting limits on what's behind that veil takes more subtlety.

posted by fantabulous timewaster at 11:19 PM on August 20, 2008

posted by fantabulous timewaster at 11:19 PM on August 20, 2008

*I realize that your asterisk qualifies this comment, but nevertheless it is incorrect. Both sets are countable and can be placed in one-to-one correspondence. They have the same cardinality of infinity.*

Absolutely, I've no argument with that. I was basically being deliberately incorrect, but doing so to highlight how in any sufficiently long section of consecutive integers the indivisible ones dominate. This is analogous to any sufficiently large region of space having matter dominate.

posted by edd at 2:41 AM on August 21, 2008

fantabulous timewaster: That was interesting, I've never heard the monkeys/Shakespeare thing played out with numbers before. I think you misunderstood the question, though.

The question is not "when is eventually?", or anything to do with how likely or how remote any particular outcome is. Given infinite space-time in which to arrange themselves, particles will

The part I don't get is how matter, the stuff being arranged, relates to the infiniteness of space-time. Is it all the same matter, being re-used over and over again as stars are born and die? (Like Imelda Marcos re-using dresses and shoes to get different combinations; or someone flipping the same coin over and over in sets of 10) Or, as the universe expands, does the amount of matter somehow stay constant relative to the expanse of space-time? If so, doesn't that mean that matter is either infinite, or is being continually created?

Of course, all of this is taking for granted Brian Greene's (the scientist on that podcast) assertion that the best current data suggests that space-time is, indeed, infinite.

Of course, towards the end of the podcast he starts talking about bubble universes with differing laws of physics and the possibility that we're living in a simulated reality ala The Matrix, which Greene says is not only possible, but "quite likely." So, you know, it's all kind of out there.

But infinite matter? Again, how would that work?

posted by sportbucket at 9:07 AM on August 21, 2008

The question is not "when is eventually?", or anything to do with how likely or how remote any particular outcome is. Given infinite space-time in which to arrange themselves, particles will

*eventually*exhaust all possible configurations. I'm more or less comfortable with that idea.The part I don't get is how matter, the stuff being arranged, relates to the infiniteness of space-time. Is it all the same matter, being re-used over and over again as stars are born and die? (Like Imelda Marcos re-using dresses and shoes to get different combinations; or someone flipping the same coin over and over in sets of 10) Or, as the universe expands, does the amount of matter somehow stay constant relative to the expanse of space-time? If so, doesn't that mean that matter is either infinite, or is being continually created?

Of course, all of this is taking for granted Brian Greene's (the scientist on that podcast) assertion that the best current data suggests that space-time is, indeed, infinite.

Of course, towards the end of the podcast he starts talking about bubble universes with differing laws of physics and the possibility that we're living in a simulated reality ala The Matrix, which Greene says is not only possible, but "quite likely." So, you know, it's all kind of out there.

But infinite matter? Again, how would that work?

posted by sportbucket at 9:07 AM on August 21, 2008

It's not "when is eventually?" but "where is eventually?". Matter does not get continually created, thermodynamics tells you things wind down, stars process matter from one form to another and it doesn't get recycled back (for the overwhelmingly most part). It's not stuff being arranged into all possible configurations as the universe goes on, but any one current configuration of matter having to be replicated somewhere else

You can argue there must be other copies of me writing this comment elsewhere in the universe but they must all be broadly at the same stage of cosmological evolution. They couldn't exist in the early universe, and they probably won't be able to exist much later in the universe.

Infinite monkeys can write the Complete Works, but one monkey given infinite time cannot - it'll drop dead and just rot for an infinite time.

The universe has to be broadly the same across all space for the (aforementioned) cosmological principle to hold true, but it certainly does not have to be broadly the same across all time.

posted by edd at 10:07 AM on August 21, 2008

*at that time*if the universe is infinite.You can argue there must be other copies of me writing this comment elsewhere in the universe but they must all be broadly at the same stage of cosmological evolution. They couldn't exist in the early universe, and they probably won't be able to exist much later in the universe.

Infinite monkeys can write the Complete Works, but one monkey given infinite time cannot - it'll drop dead and just rot for an infinite time.

The universe has to be broadly the same across all space for the (aforementioned) cosmological principle to hold true, but it certainly does not have to be broadly the same across all time.

posted by edd at 10:07 AM on August 21, 2008

*It's not stuff being arranged into all possible configurations as the universe goes on, but any one current configuration of matter having to be replicated somewhere else at that time if the universe is infinite.*

But I thought the "infinite" part about the universe applied to space-time, not simply space. It seems like you're saying that given infinite space, any one configuration of particles would have to be replicated somewhere in the universe at any given point in time. If so, wouldn't you need matter to be infinite in order to fill infinite space?

posted by sportbucket at 1:25 PM on August 21, 2008

sportbucket, I disagree with Greene's interpretation of the evidence. I agree that the universe seems to be uniformly full of stuff for 100 billion light years in every direction. Unless we are "exactly in the middle," which is unlikely, that suggests the universe is uniformly filled with stuff for a few times that distance, at least. This rules out a few different types of finite universe.

For instance, Einstein suggested the universe might be the three-dimensional surface of a four-dimensional sphere, like the surface of the earth is the two-dimensional surface of a three-dimensional sphere. But, much like you can climb a mountain and measure the curvature of the earth, you can tell from the distribution of galaxy clusters what's the curvature of the universe.

There are other reasons to suspect that the hypersphere idea isn't right, which I won't go into. But without that model, the data only tell you about the visible universe. Greene is right that that there's no evidence the universe

edd: yes, good points.

posted by fantabulous timewaster at 2:15 PM on August 21, 2008 [1 favorite]

For instance, Einstein suggested the universe might be the three-dimensional surface of a four-dimensional sphere, like the surface of the earth is the two-dimensional surface of a three-dimensional sphere. But, much like you can climb a mountain and measure the curvature of the earth, you can tell from the distribution of galaxy clusters what's the curvature of the universe.

*If*the universe*is*the surface of a hypersphere, the radius of that sphere is too large for us to determine from the fraction of the universe that's visible. So if we lived in such a universe, it would contain no fewer than some large number of stars. Maybe the visible universe is like an atom of the multiverse, and there are 10^{26}universes that we can't see, evolving just like the one we can see. That gives us 10^{50}suns! Still not enough to get an alter-Hamlet. (If there were 10^{1050}suns, there wouldn't be enough entropy to coincidentally get an alter-you.)There are other reasons to suspect that the hypersphere idea isn't right, which I won't go into. But without that model, the data only tell you about the visible universe. Greene is right that that there's no evidence the universe

*isn't*infinite. But there's no evidence that it*is*, either. If you want to interpret the available evidence as "the universe is at least big enough to contain an alter-me," you have to assume you can correctly extrapolate to 1 starting from the twenty-fifth or fiftieth or five hundredth decimal place, with no surprises. That's silly. That was my point in plugging in numbers.edd: yes, good points.

posted by fantabulous timewaster at 2:15 PM on August 21, 2008 [1 favorite]

It still seems like you're not answering the question I'm asking, at least not within the context of Greene's multi-verse idea. But I guess that's understandable, since you seem to be looking at the data differently than Greene, so you can't speak to or defend the same conclusions. (Perhaps you have different data? Is this podcast old?)

I, on the other hand, have no idea what that data is, what it looks like, nor would I have any idea what to do with it if someone were to hand it to me, so I have to ask fairly simplified conceptual questions.

In my experience, when I ask vague conceptual questions and repeatedly get answers that don't seem to address the question I thought I asked, it usually means my question is flawed, or there's some fundamental assumption about which I'm either ignorant or flat-out wrong.

Um, paging Doctor Greene?

posted by sportbucket at 3:25 PM on August 21, 2008

I, on the other hand, have no idea what that data is, what it looks like, nor would I have any idea what to do with it if someone were to hand it to me, so I have to ask fairly simplified conceptual questions.

In my experience, when I ask vague conceptual questions and repeatedly get answers that don't seem to address the question I thought I asked, it usually means my question is flawed, or there's some fundamental assumption about which I'm either ignorant or flat-out wrong.

Um, paging Doctor Greene?

posted by sportbucket at 3:25 PM on August 21, 2008

sportbucket, for data check out the WMAP mission. This big news is a couple years old. There is a lot of nontechnical summary around on the web, of varying quality.

My answer to the original question is that its premise is a little flawed. There's evidence that the universe is very big, but there's no

You seem to have another subtle question about the relationship between matter and spacetime. If you can put that succinctly (perhaps after browsing some books) that might make for another interesting discussion.

posted by fantabulous timewaster at 5:11 PM on August 21, 2008

My answer to the original question is that its premise is a little flawed. There's evidence that the universe is very big, but there's no

*compelling*evidence that the universe is big*enough*that there's another copy of you somewhere you could fly to. There's no evidence that the universe*isn't*infinite, which prompted the question. But science can't distinguish between "infinite" and "larger than X, the limit of my method." Big difference. I was trying to set a scale for X.You seem to have another subtle question about the relationship between matter and spacetime. If you can put that succinctly (perhaps after browsing some books) that might make for another interesting discussion.

posted by fantabulous timewaster at 5:11 PM on August 21, 2008

"But I thought the "infinite" part about the universe applied to space-time, not simply space. It seems like you're saying that given infinite space, any one configuration of particles would have to be replicated somewhere in the universe at any given point in time. If so, wouldn't you need matter to be infinite in order to fill infinite space?"

Yes. If there's infinite space, I'd assume there's infinite matter unless given a very good reason to think otherwise.

Infinite time is a very different kettle of fish from infinite space. We know the universe changes over time (you only have to know there was a big bang to realise this). We have very good reason to believe the universe does not change over space, at least on the scale of the observable universe.

posted by edd at 5:15 PM on August 21, 2008

Yes. If there's infinite space, I'd assume there's infinite matter unless given a very good reason to think otherwise.

Infinite time is a very different kettle of fish from infinite space. We know the universe changes over time (you only have to know there was a big bang to realise this). We have very good reason to believe the universe does not change over space, at least on the scale of the observable universe.

posted by edd at 5:15 PM on August 21, 2008

*You seem to have another subtle question about the relationship between matter and spacetime. If you can put that succinctly (perhaps after browsing some books) that might make for another interesting discussion.*

Yeah, I don't think my understanding of this stuff is sophisticated enough to articulate such a question. I was kind of hoping someone could recognize the fundamental error I'm making and clarify it for me. Time to hit the books, I guess.

*Yes. If there's infinite space, I'd assume there's infinite matter unless given a very good reason to think otherwise.*

Okay, so that's a "yes," at least within the parameters of this question. But conceptually, I just don't get that. If all matter is moving out from the point of the Big Bang (is that even accurate?), and both matter and spacetime are infinite, wouldn't that mean that matter is just continually springing out from that point of origin, like a fountain? What's feeding the fountain? An infinitely dense pool of particles compressed into a single point in space?

My brain hurts.

posted by sportbucket at 10:26 AM on August 22, 2008

sportbucket, the usenet physics FAQ addresses the Big Bang's (lack of a) point of origin.

posted by fantabulous timewaster at 1:11 PM on August 22, 2008

posted by fantabulous timewaster at 1:11 PM on August 22, 2008

I imagine that would change my perception of things, if I could just wrap my mind around it. Excuse me, my brain is full.

posted by sportbucket at 1:38 PM on August 22, 2008

posted by sportbucket at 1:38 PM on August 22, 2008

"If all matter is moving out from the point of the Big Bang (is that even accurate?)"

All matter is remaining stationary as far as it is concerned (ignoring 'peculiar' motions, that is motion not counted as part of the general cosmological trend). Only the distance between things is getting bigger.

If this does not make sense, that's fine. It doesn't according to common sense. Confusion and bogglement is a natural state when confronted with this.

posted by edd at 2:22 PM on August 22, 2008

All matter is remaining stationary as far as it is concerned (ignoring 'peculiar' motions, that is motion not counted as part of the general cosmological trend). Only the distance between things is getting bigger.

If this does not make sense, that's fine. It doesn't according to common sense. Confusion and bogglement is a natural state when confronted with this.

posted by edd at 2:22 PM on August 22, 2008

*All matter is remaining stationary as far as it is concerned (ignoring 'peculiar' motions, that is motion not counted as part of the general cosmological trend). Only the distance between things is getting bigger.*

I think I kind of get that, actually. In that podcast (which none of you have listened to, right?) Greene described something like inverted swiss cheese, in which the holes are "stuff" (bubble universes, in this case) and the cheese parts are space. And that cheese/space is growing/expanding faster than the speed of light, so that the various bubbles cannot communicate with each other.

Apparently you have to speak in awkward metaphors, not numbers or theorems, to let a humanities guy like me get things.

posted by sportbucket at 5:30 PM on August 22, 2008

Wow, this thread certainly got derailed!

The answer to your question is: No-one knows. The consensus is, however, that if "space is infinite" (we can skip the mathematics), then so is the total mass of the matter. This is because the density is generally assumed to be roughly the same everywhere.

I will also remark that current consensus theories have nothing to say about your question one way or the other. While a flat, open LambdaCDM universe is probably the consensus right now, it says nothing about the

There

posted by hAndrew at 11:39 PM on September 1, 2008

The answer to your question is: No-one knows. The consensus is, however, that if "space is infinite" (we can skip the mathematics), then so is the total mass of the matter. This is because the density is generally assumed to be roughly the same everywhere.

I will also remark that current consensus theories have nothing to say about your question one way or the other. While a flat, open LambdaCDM universe is probably the consensus right now, it says nothing about the

*global*geometry. A flat universe may be finite (think surface of cylinder) or infinite (think infinite sheet of paper).There

*are*, of course, existing theories about global geometry, but they are untested and could not be considered consensus.posted by hAndrew at 11:39 PM on September 1, 2008

« Older Re-setting a mac for a new user. | Shouldn't there be some signs of sun damage by now... Newer »

This thread is closed to new comments.

From the wiki. I am pretty sure your first assumption that the universe is infinite is wrong.

posted by Grither at 6:43 AM on August 20, 2008