# Are infinite universes possible?

June 8, 2010 4:18 PM Subscribe

TheoreticalPhysicsFilter: A mathematical question (from a non-math person) about the viability of the parallel universe theory. In short, wouldn't there be infinite parallel universes, making the whole concept impossible for humans to understand?

I know that the multiverse theory is not a theory in the scientific sense, but more in the hypothetical, thought exercise sense.

If, as "they" say, there's another universe in which I took that one job, or dated that one person, or didn't do [whatever], and right now, there's an entire universe with only that small difference present, otherwise completely identical.

But it's obvious that that scenario, if true for one instance, must be true for an uncountably large number of instances. For example, there's another universe in which the pencil on my desk is 0.02 cm to the left, another one in which it's 0.01 cm to the left, another one in which it's 0.001 cm to the right, etc. etc.

Even with my limited imagination, I can think up infinite examples of differences that would distinguish separate universes. (Or can I?)

I suppose my question is: is an infinite number of universes impossible? If so, then the multiverse theory is impossible. Please feel free to lay on the math.

I know that the multiverse theory is not a theory in the scientific sense, but more in the hypothetical, thought exercise sense.

If, as "they" say, there's another universe in which I took that one job, or dated that one person, or didn't do [whatever], and right now, there's an entire universe with only that small difference present, otherwise completely identical.

But it's obvious that that scenario, if true for one instance, must be true for an uncountably large number of instances. For example, there's another universe in which the pencil on my desk is 0.02 cm to the left, another one in which it's 0.01 cm to the left, another one in which it's 0.001 cm to the right, etc. etc.

Even with my limited imagination, I can think up infinite examples of differences that would distinguish separate universes. (Or can I?)

I suppose my question is: is an infinite number of universes impossible? If so, then the multiverse theory is impossible. Please feel free to lay on the math.

I don't have much to say about the multiverse approach but, in general, a theory having consequences that are "impossible for humans to understand" isn't necessarily the problem it once was. I mean that both sarcastically wrt. some very opaque theoretical physics, but also formally. There's a lot of work premised on the idea that a true description of the universe cannot be grasped by the mind or expressed in mathematics.

posted by caek at 4:25 PM on June 8, 2010

posted by caek at 4:25 PM on June 8, 2010

Best answer: You may be interested in the responses to a similar question I asked a couple of years ago.

posted by Rhaomi at 4:30 PM on June 8, 2010

posted by Rhaomi at 4:30 PM on June 8, 2010

There is a difference between a "concept" being incomprehensible and the actual physical universe described by that concept being impossible for us to fully grasp. That's actually a riddle that's always true of infinity.

Forget multiple universes for a moment: I explain to you that the real numbers are infinite. (You can pick some different example if you care about the differences between countable and uncountable infinities, which I'm going to assume you don't). You respond that even with "limited imagination," you can think up infinite examples of numbers. True enough. But that doesn't mean that you can't comprehend the "concept" of infinity. On the contrary, you just confirmed that you do understand the concept!

Same thing with multiple universes. Yes, under most versions of parallel universe, there are an infinite number of such universes. But that doesn't mean that theory is incomprehensible. It DOES mean that you can't actually count, list, enumerate, or imagine all of the parallel universes. That is why we have the concept of infinity-- as a method of talking about and trying to understand numbers that are too big to count.

posted by willbaude at 4:33 PM on June 8, 2010 [5 favorites]

Forget multiple universes for a moment: I explain to you that the real numbers are infinite. (You can pick some different example if you care about the differences between countable and uncountable infinities, which I'm going to assume you don't). You respond that even with "limited imagination," you can think up infinite examples of numbers. True enough. But that doesn't mean that you can't comprehend the "concept" of infinity. On the contrary, you just confirmed that you do understand the concept!

Same thing with multiple universes. Yes, under most versions of parallel universe, there are an infinite number of such universes. But that doesn't mean that theory is incomprehensible. It DOES mean that you can't actually count, list, enumerate, or imagine all of the parallel universes. That is why we have the concept of infinity-- as a method of talking about and trying to understand numbers that are too big to count.

posted by willbaude at 4:33 PM on June 8, 2010 [5 favorites]

Why would an infinite number of universes be impossible? There are an infinite number of natural numbers.

An aside though, having a infinite amount of something doesn't mean that you can't count or list them. You can list the natural numbers, but you'll just never stop. However, you can't list the real numbers.

posted by demiurge at 4:46 PM on June 8, 2010 [1 favorite]

An aside though, having a infinite amount of something doesn't mean that you can't count or list them. You can list the natural numbers, but you'll just never stop. However, you can't list the real numbers.

posted by demiurge at 4:46 PM on June 8, 2010 [1 favorite]

*wouldn't there be infinite parallel universes, making the whole concept*

Yes.

posted by flabdablet at 5:18 PM on June 8, 2010 [2 favorites]

If it makes you feel better, the you can argue that the Schroedinger's Cat thought experiment suggests that the universe(s) stop keeping track if it doesn't matter.

posted by Kid Charlemagne at 5:36 PM on June 8, 2010

posted by Kid Charlemagne at 5:36 PM on June 8, 2010

I agree with the handwavy thing, but as far as the size of infinity goes, it's really big. It's so big that size sort of stops making sense. For example: there are as many different points inside a square as there are along one of its sides. That little side of the square has uncountably many points, and the inside of the square has uncountably many point, and the whole Cartesian plain (or R

So if you're asking if human mathematicians can make up infinities "big" enough to contain every single possible universe imaginable, the answer is yes.

posted by Aizkolari at 5:47 PM on June 8, 2010

^{2}, if you will) has an uncountably infinite number of points, and they all have THE SAME NUMBER of these points.So if you're asking if human mathematicians can make up infinities "big" enough to contain every single possible universe imaginable, the answer is yes.

posted by Aizkolari at 5:47 PM on June 8, 2010

*In short, wouldn't there be infinite parallel universes, making the whole concept impossible for humans to understand?*

I take no stand on the larger metaphysical question, but infinity does not make something insurmountable to comprehension. On the contrary, our understanding of infinity is very well developed.

posted by advil at 5:48 PM on June 8, 2010 [1 favorite]

*So if you're asking if human mathematicians can make up infinities "big" enough to contain every single possible universe imaginable, the answer is yes.*

Just want to point out quickly that 'infinite' doesn't necessarily mean 'every imaginable possibility'. There are an infinite number of even numbers, but you can imagine a lot of odd numbers that aren't part of that set. Even if there is, hypothetically, an infinite number of universes, it doesn't mean that every possible universe is included in that number of universes.

posted by Jairus at 6:26 PM on June 8, 2010

Best answer: Caveat lector: I'm an astronomer, and don't deal with the more involved points of quantum theory very often or in very much detail. However, I have studied it much more than the average Joe.

I've always come to terms with the many worlds interpretation of quantum mechanics thus:

In the many worlds interpretation, a "universe" is equivalent to a possibility. We only observe one, but we are aware of many more. In fact, we are aware of infinitely more.

Take Philadelphia as an example. All streets basically run on a grid. Let's say I want to figure out how I want to get from my office on 33rd and Walnut to my favourite pub on 2nd and Market. I could take the subway. I could walk up to Market and then to 2nd. I could walk on Walnut to 2nd and then up to Market. I could walk on Walnut to 17th street, and then up to Market and then over to 2nd. I could be stupid and walk west (opposite direction of the pub), and turn around and then walk back to 2nd and Market.

In effect, there are a countable infinite number of ways for me to walk to the pub on Friday night. If I had the time or the effort, I could sit down and count them one by one.

This is the idea of "countable infinity" -- the number is endless, but if I had time, I could try to sit down and count them all.

How does this pertain to quantum theory?

Quantum mechanics is in fact quantized. This means, that everything that exists in the world of quantum mechanics can be explained in terms of some counting numbers (1,2,3,4,...). Hence, quantum mechanics, in a sense, is countably infinite. (This is incomplete, but good for pedagogical purposes.)

So, in a sense, each one of these quantum numbers is its own universe. If I describe an electron via the numbers 5,3,2; this is a totally separate universe in which that electron is described by 4,3,2. However, each of these possibilities (universes) has a certain, non-zero probability of being measured, so in a sense, they both exist. When I measure one, I am only choosing which universe in which to live.

To answer your question about the usefulness of many worlds theory, think about a tool called the 'Feynman Propagator." Basically, the Feynman Propagator says I want to take into account each and every one of these possibilities/universes, and find the most likely value for some measurement in all of them.

For instance, if I wanted to find the average distance to my pub, I would take into account the walking distance of each of the infinite routes, but I would also take into account the probability that I would take that route. For instance, I would count the routes which I am more likely to take (the ones for which I walk past the bank or the ones with the shortest distance), and not count as much the ones which I am very unlikely to take (the ones that take me to Chicago and back). I integrate over all of these possibilities, and get some finite number. 2 miles, let's say.

I apply something like a Feynman propagator to the distance to the pub, take into account each of the many universes in which I take a different route to the pub, weigh each by it's probability, and get some result. Average of 2 miles to the pub. (but then I take the subway anyways because I'm lazy.)

I think the big 'what the fuck is going on here' moment really is the concept that you can add an infinite number of finite values and still get a finite number, but that's just me.

I hope this helps.

posted by chicago2penn at 7:04 PM on June 8, 2010 [4 favorites]

I've always come to terms with the many worlds interpretation of quantum mechanics thus:

In the many worlds interpretation, a "universe" is equivalent to a possibility. We only observe one, but we are aware of many more. In fact, we are aware of infinitely more.

Take Philadelphia as an example. All streets basically run on a grid. Let's say I want to figure out how I want to get from my office on 33rd and Walnut to my favourite pub on 2nd and Market. I could take the subway. I could walk up to Market and then to 2nd. I could walk on Walnut to 2nd and then up to Market. I could walk on Walnut to 17th street, and then up to Market and then over to 2nd. I could be stupid and walk west (opposite direction of the pub), and turn around and then walk back to 2nd and Market.

In effect, there are a countable infinite number of ways for me to walk to the pub on Friday night. If I had the time or the effort, I could sit down and count them one by one.

This is the idea of "countable infinity" -- the number is endless, but if I had time, I could try to sit down and count them all.

How does this pertain to quantum theory?

Quantum mechanics is in fact quantized. This means, that everything that exists in the world of quantum mechanics can be explained in terms of some counting numbers (1,2,3,4,...). Hence, quantum mechanics, in a sense, is countably infinite. (This is incomplete, but good for pedagogical purposes.)

So, in a sense, each one of these quantum numbers is its own universe. If I describe an electron via the numbers 5,3,2; this is a totally separate universe in which that electron is described by 4,3,2. However, each of these possibilities (universes) has a certain, non-zero probability of being measured, so in a sense, they both exist. When I measure one, I am only choosing which universe in which to live.

To answer your question about the usefulness of many worlds theory, think about a tool called the 'Feynman Propagator." Basically, the Feynman Propagator says I want to take into account each and every one of these possibilities/universes, and find the most likely value for some measurement in all of them.

For instance, if I wanted to find the average distance to my pub, I would take into account the walking distance of each of the infinite routes, but I would also take into account the probability that I would take that route. For instance, I would count the routes which I am more likely to take (the ones for which I walk past the bank or the ones with the shortest distance), and not count as much the ones which I am very unlikely to take (the ones that take me to Chicago and back). I integrate over all of these possibilities, and get some finite number. 2 miles, let's say.

I apply something like a Feynman propagator to the distance to the pub, take into account each of the many universes in which I take a different route to the pub, weigh each by it's probability, and get some result. Average of 2 miles to the pub. (but then I take the subway anyways because I'm lazy.)

I think the big 'what the fuck is going on here' moment really is the concept that you can add an infinite number of finite values and still get a finite number, but that's just me.

I hope this helps.

posted by chicago2penn at 7:04 PM on June 8, 2010 [4 favorites]

Oh, and the mathematical definition of infinity is this:

M is infinite if and only if for any n, M>n.

Basically, infinity is just higher than you care to count.

By the way...

posted by chicago2penn at 7:06 PM on June 8, 2010

M is infinite if and only if for any n, M>n.

Basically, infinity is just higher than you care to count.

By the way...

posted by chicago2penn at 7:06 PM on June 8, 2010

"M is infinite if and only if for any n, M>n."

What if n=M+1? Is "infinity plus one" not a defined concept?

posted by mikeand1 at 8:11 PM on June 8, 2010

What if n=M+1? Is "infinity plus one" not a defined concept?

posted by mikeand1 at 8:11 PM on June 8, 2010

If n = M + 1, then M < n; therefore M is not infinite.

posted by flabdablet at 8:25 PM on June 8, 2010

posted by flabdablet at 8:25 PM on June 8, 2010

*I think the big 'what the fuck is going on here' moment really is the concept that you can add an infinite number of finite values and still get a finite number*

You and Zeno both.

posted by flabdablet at 10:40 PM on June 8, 2010

*M is infinite if and only if for any n, M>n*

IANAmathematician, but I think infinity is not a number! A set is infinite if it can be placed in one-to-one correspondence with a proper subset of itsself. For example, you can map the set of all natural numbers to the set of even numbers by mapping n to 2n, therefore the natural numbers are infinite.

The infinity symbol used, say, when doing calculus is just shorthand for "as big as you want", you are not supposed to use it in calculations.

posted by Dr Dracator at 10:54 PM on June 8, 2010 [1 favorite]

The only time I apply the concept of infinite universes is when I am sitting in traffic. I realize that in some parallel universe my parallel self is sitting in the same traffic, but he is in a Mad Max style vehicle. Suddenly he snaps and plows his way through traffic, flipping the van in front of him over and careening to his destination. My parallel self rules.

posted by msbutah at 2:04 PM on June 9, 2010

posted by msbutah at 2:04 PM on June 9, 2010

*Basically, infinity is just higher than you care to count.*

I'm a mathematical imbecile, basically, but this seems like a bad way to conceptualize infinity -- it seems more important to keep in mind that the highest number you can count to is still closer to zero than it is to infinity by an almost infinite margin.

posted by newmoistness at 8:28 AM on June 11, 2010

Actually it isn't, because infinity isn't something you can be close to

posted by flabdablet at 2:08 AM on June 12, 2010

*at all*, let alone allowing for different*degrees*of closeness. No finite number (and they're*all*finite) is closer to infinity than any other. Infinity is not a reference mark. "Closer to infinity," strictly speaking, is meaningless.posted by flabdablet at 2:08 AM on June 12, 2010

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