# If the universe is infinite, does it mean that everything exists?

Besides things that are obviously impossible like four-sided triangles.

Logically no. The natural numbers are an infinite set but they don't include other kinds of numbers, such as negative integers.

In the physical sense how you do define "everything"? Given infinite time one might say that any event that can occur will occur. That is, if an event has a non zero probability of occurring, it must occur, given infinite time. In fact it must occur an infinite number of times because any fraction of an infinite set is infinite. (I'm not considering 0/x, x>0; or 0/0 to be true fractions.) However, the way probabilities are defined, the probability of drawing a particular number 'a' from the infinite set of positive integers is zero, although it's intuitive you must draw some number. Strange but true.

To see this another way, take any natural number that ends in 3. The number of natural numbers that end in 3 is infinite but such numbers are only 1/10 of all natural numbers.

Have I thoroughly confused you? Infinity is strange.

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Besides things that are obviously impossible like four-sided triangles.
A triangle has 3 sides by definition. We name a thing with 3 sides, triangle. We could have named it square, but we didn't. The fact that something with only 3 sides doesn't have 4 sides is purely a matter of being consistent with a definition.

Triangles don't actually exist in nature. A triangle is a useful generalization, because the world we observe is very consistent with regards to dimensions.

Infinite is merely the negation of 'finite'. Finite is a generalization that describes the limits of objects. Nothing is another example; a useful negation, the lack of a defined thing or things.

These can be very useful in mathematics and logic, but since they don't describe actual things, but rather abstract extensions of things, they can create all sorts of problems if you try and treat them as actual things, instead of just as useful abstractions.

Infinite is merely the negation of 'finite'. Finite is a generalization that describes the limits of objects. Nothing is another example; a useful negation, the lack of a defined thing or things.

These can be very useful in mathematics and logic, but since they don't describe actual things, but rather abstract extensions of things, they can create all sorts of problems if you try and treat them as actual things, instead of just as useful abstractions.
I generally agree, but some cosmologists still entertain the idea that the universe is infinite.The apparent flatness of spacetime certainly suggests this could be true.

So suppose, for the sake of argument, there were an infinite number of discrete objects (everything) scattered uniformly in an infinite space. In principle we could assign a unique natural number to every such object given an infinite supply of natural numbers. This is one way make the rather vague idea of "everything" mathematically tractable..

Now cosmologists don't believe the universe is like this. There are strong reasons for believing the amount of matter in the universe is finite. But this leads to a mathematical conundrum. If spacetime is infinite and matter is finite than the probability of matter is zero. Say 'a' is the finite number of particles in the universe and x is the volume of the universe. It's clear that as x as goes to infinity then a/x goes to zero at the limit..

If a finite "island" of matter is expandiing into infinite space, then there is a non-zero density of matter within the island but the island itself occupies zero volume in infinite space.

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Q_Goest
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Besides things that are obviously impossible like four-sided triangles.
Scientific American had an article on the same idea, if not a very similar idea a few years ago. Author is Max Tegmark.

Is there a copy of you reading this article? A person who is not you but who lives on a planet called Earth, with misty mountains, fertile fields and sprawling cities, in a solar system with eight other planets? The life of this person has been identical to yours in every respect. But perhaps he or she now decides to put down this article without finishing it, while you read on.

The idea of such an alter ego seems strange and implausible, but it looks as if we will just have to live with it, because it is supported by astronomical observations. The simplest and most popular cosmological model today predicts that you have a twin in a galaxy about 10 to the 1028 meters from here. This distance is so large that it is beyond astronomical, but that does not make your doppelganger any less real. The estimate is derived from elementary probability and does not even assume speculative modern physics, merely that space is infinite (or at least sufficiently large) in size and almost uniformly filled with matter, as observations indicate. In infinite space, even the most unlikely events must take place somewhere. There are infinitely many other inhabited planets, including not just one but infinitely many that have people with the same appearance, name and memories as you, who play out every possible permutation of your life choices.
Ref: http://www.scientificamerican.com/article.cfm?id=parallel-universes

"The simplest and most popular cosmological model today predicts that you have a twin in a galaxy about 10 to the 10^28 meters from here."

so every '10 to the 10^28 meters from here, in every direction, we have a twin; and, if the universe is infinite, we have a infinite number of 'twins'-----

wow, infinite deja vu 's!

As JoeDawg said, a four sided triangle is a contradiction by definition. It's like saying 3=4. I don't see this as relevant to a Many Worlds interpretation which is what you're more or less referring to. Afaik, infinite matter is not compatible with the physics of the universe we observe. If you're talking about MWI, those 'other' universes are fundamentally inaccessible. Therefore its metaphysical speculation which is OK in a philosophy forum if there is some discipline/logic involved. I don't think there is here. In MWI, all those 'other' universes are a possible version our own and we would observe the same physics in each world because it is just another possible line of evolution of our universe. And I would like to know how anyone could determine how far way these other universes are or how the idea of "distance" is even relevant to MWI.

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As Joe Dawg said, a four sided triangle is a contradiction by definition. It's like saying 3=4. I don't see this as relevant to a Many Worlds interpretation which is what you're more or less referring to. Afaik, infinite matter is not compatible with the physics of the universe we observe. If you're talking about MWI, those 'other' universes are fundamentally inaccessible. Therefore its metaphysical speculation which is OK in a philosophy forum if there is some discipline/logic involved. I don't think there is here.
no, MWI in my finite world of logic is not realistic or logical

However, if the universe is infinite, it would infer that there is infinite mass/matter in the universe.

no, MWI in my finite world of logic is not realistic or logical

However, if the universe is infinite, it would infer that there is infinite mass/matter in the universe.
Then how do you explain the behavior of water in a rotating bucket?

Then how do you explain the behavior of water in a rotating bucket?
friction and the 'centrifugal' force*

*some definitions by some scientists, to me, sound like they put 'centrifugal' force in the same thoughts as unicorns

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friction and the 'centrifugal' force*
What is centrifugal 'force'? It's inertia, not a true force. When you rotate the bucket, you change the inertial frame. What is happening when you change the inertial frame? Acceleration. What is the cause of inertia and acceleration. Why does applying a force produce the effect we observe or feel? Actually, no one knows for sure, but the prevailing view is called Mach's Principle. Look it up.

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friction and the 'centrifugal' force*

What is centrifugal 'force'? It's inertia, not a true force. When you rotate the bucket, you change the inertial frame. What is happening when you change the inertial frame? Acceleration. What is the cause of inertia and acceleration. Why does applying a force produce the effect we observe or feel? Actually, no one knows for sure, but the prevailing view is called Mach's principle. Look it up.

well, I guess my opinion is different than yours. That's one reason I added the footnote with the "*".

I don't think all of relativity is correct either. It may come up with close, very close answers to some of the problems, but the initial concepts in relativity are not quite right. I believe that centrifugal 'force' is the solution for the water bucket.

well, I guess my opinion is different than yours. That's one reason I added the footnote with the "*".

I don't think all of relativity is correct either. It may come up with close, very close answers to some of the problems, but the initial concepts in relativity are not quite right. I believe that centrifugal 'force' is the solution for the water bucket.
I could accept that infinite matter is possible although it would seem to contradict both General Relativity and Big Bang cosmology, but "centrifugal force" is not a true force. It's inertia. To say otherwise is flat out nonsense.

[I could accept that infinite matter is possible although it would seem to contradict both General Relativity and Big Bang cosmology, but "centrifugal force" is not a true force. It's inertia. To say otherwise is flat out nonsense.
well, you yourself said:

... Actually, no one knows for sure, but the prevailing view is called Mach's Principle. Look it up.
so, how can you call it (flat out) nonsense?

well, you yourself said:

so, how can you call it (flat out) nonsense?
You don't have the most basic understanding of physics.

You don't have the most basic understanding of physics.
hmmmm.....

I don't believe everything that I was taught in physics, if that's what you mean, and that includes not everything that I've read.

A lot of people are TRUE BELIEVERS in MWI, string, and the latest varieties; I don't find them very possible at all.

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I generally agree, but some cosmologists still entertain the idea that the universe is infinite.The apparent flatness of spacetime certainly suggests this could be true.
Then the question is, what does infinite universe mean? Infinite spacetime? An infinite number of quantum fluctuations within spacetime? You can have a universe the size of a popcan and still have infinities inside. The important part is how you apply the generalization.

What if I have an infinite stack of popcans? I have an infinite number, but only in one nominal dimension. I could also have infinite popcans if I filled the infinite universe with them, in every direction. (No room left for me, but we'll pretend I'm god, for the sake of argument)
But I don't even need an infinite universe to have an infinite number of popcans, I can have the universe the size one popcan, and then just say that every instant of time represents a new popcan. Then I just need infinite time. Or I could accelerate my one popcan to the speed of light and taking into account different reference frames....
So suppose, for the sake of argument, there were an infinite number of discrete objects (everything) scattered uniformly in an infinite space. In principle we could assign a unique natural number to every such object given an infinite supply of natural numbers. This is one way make the rather vague idea of "everything" mathematically tractable..
Problem with objects is you have to distingish between them. In this case you have an infinite number of popcans, but also an infinite amount of nothing in-between. Can you count the empty spaces too? And if so what does the resulting number even mean? Which infinity is bigger? Does that even make sense? Not a mathematician.

Which reminds me of this:

http://en.wikipedia.org/wiki/Hole_theory
Now cosmologists don't believe the universe is like this. There are strong reasons for believing the amount of matter in the universe is finite. But this leads to a mathematical conundrum. If spacetime is infinite and matter is finite than the probability of matter is zero. Say 'a' is the finite number of particles in the universe and x is the volume of the universe. It's clear that as x as goes to infinity then a/x goes to zero at the limit..
You can get around that if you include the big bang as a trully random event. But it was my undertanding that the bigbang implies spacetime has a beginning, so its only infinite in one time direction....again whatever that means.
If a finite "island" of matter is expandiing into infinite space, then there is a non-zero density of matter within the island but the island itself occupies zero volume in infinite space.
It is spacetime that is expanding, matter is just along for the ride.

Then the question is, what does infinite universe mean?
It means it has infinite volume and time has no end.

What If I have an infinite stack of popcans? I have an infinite number, but only in one nominal dimension.
That's not our universe. Current cosmology is that universe has 3+1 extended dimensions.

But I don't even need an infinite universe to have an infinite number of popcans, I can have the universe the size one popcans.
That would be a bounded universe with finite volume.

, and then just say that every instant of time represents a new popcan. Then I just need infinite time.
Yes, That would be infinite time either with or without a beginning.

Or I could accelerate my one popcan to the speed of light and taking into account different reference frames....
I don't understand. Do your popcans have mass?

Problem with objects is you have to distingish between them. In this case you have an infinite number of popcans, but also an infinite amount of nothing in-between. Can you count the empty spaces too? And if so what does the resulting number even mean? Which infinity is bigger? Does that even make sense? Not a mathematician.
This was a mathematical argument that with a finite number of particles in an infinite volume either the particle density is zero at the limit if the particles are asymptotically uniformly distributed in space, or the particle cloud has zero volume at the limit if distributed in a finite region of an infinite volume. The volume of the finite particles doesn't matter. In infinite space they become pointlike at the limit.

But it was my undertanding that the bigbang implies spacetime has a beginning, so its only infinite in one time direction....again whatever that means.
It means what you said. I don't see a logical problem. I'll leave the science to the cosmologist.

It is spacetime that is expanding, matter is just along for the ride.
That's the prevailing model as I understand it, and it implies spacetime is finite at any point in time ATB. As for the future, I believe one possibility is an ultimate reversal of expansion leading to collapse and the end of time. The other possibility is expansion forever. I understand the latter is favored today,

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It means it has infinite volume and time has no end.
But if the universe is expanding, it does not have an infinite volume, it just has the ability to expand infinitely.
That's not our universe. Current cosmology is that universe has 3+1 extended dimensions.
Yes, I know, that's why I said 'nominal', what I meant was, you could have stacked, one on top of another.... infinitely in both directions, and therefore have an infinite amount of cans, but in a 3+1 universe, you could also have an infinite amount, by filling the universe in all 3+1 directions. Those are two different types of infinity, both in the same universe.
I don't understand. Do your popcans have mass?
I was making a joke.
This was a mathematical argument that with a finite number of particles in an infinite volume either the particle density is zero at the limit if the particles are asymptotically uniformly distributed in space, or the particle cloud has zero volume at the limit if distributed in a finite region of an infinite volume. The volume of the finite particles doesn't matter. In infinite space they become pointlike at the limit.
With a big bang, the universe is only infinite with time, not initially in terms of volume. So the universe becomes infinite in size, but is not currently.
That's the prevailing model as I understand it, and it implies spacetime is finite at any point in time ATB. As for the future, I believe one possibility is an ultimate reversal of expansion leading to collapse and the end of time. The other possibility is expansion forever. I understand the latter is favored today,
Heat death due to dark energy.

But if the universe is expanding, it does not have an infinite volume, it just has the ability to expand infinitely.

Actually it can have infinite volume and still expand, at least in a mathematical sense. Take the infinite string of natural numbers. Now systematically add rational fractions between the natural numbers: 1,2,3,... ; 1, 1.5, 2, 2.5, 3.... . There is more space between the natural numbers. The string is "expanding" even though it was infinite to begin with.

With a big bang, the universe is only infinite with time, not initially in terms of volume. So the universe becomes infinite in size, but is not currently.
Yes, that's the Big Bang cosmology. I was being provocative by suggesting an alternative. However the universe seems asymptotically flat by observation, For it to be closed, it must have positive curvature.

I'm not sure that a finite universe can ever be infinite. Mathematically you could make a case it could. The tangent of an angle is a finite number until it "suddenly" goes infinite at 90 degrees. I'm not sure where cosmologists stand on this, but think the answer they usually give is if finite, always finite, if infinite always infinite. (I actually asked this question the Cosmology Forum. This was the answer I got.)

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Actually it can have infinite volume and still expand, at least in a mathematical sense. Take the infinite string of natural numbers. Now systematically add rational fractions between the natural numbers: 1,2,3,... ; 1, 1.5, 2, 2.5, 3.... . There is more space between the natural numbers. The string is "expanding" even though it was infinite to begin with.
That seems to me more of a semantic difference, rather than useful distinction.
Although one could divide along the lines of visible universe vs what is beyond the visible universe. If that is the distinction you are making then I feel it could be instructive.
Yes, that's the Big Bang cosmology. I was being provocative by suggesting an alternative. However the universe seems asymptotically flat by observation, For it to be closed, it must have positive curvature.

I'm not sure that a finite universe can ever be infinite. Mathematically you could make a case it could. The tangent of an angle is a finite number until it "suddenly" goes infinite at 90 degrees. I'm not sure where cosmologists stand on this, but think the answer they usually give is if finite, always finite, if infinite always infinite. (I actually asked this question the Cosmology Forum. This was the answer I got.)
That just brings us back to the problem of defining infinity as it relates to the physical universe. What is the difference between a really really big universe and an infinite one. It might have mathematical significance... but the realities of cosmology might just make it a moot point.

wouldnt an infinite amount of copies of each of us exist in an infinite universe?

wouldnt an infinite amount of copies of each of us exist in an infinite universe?
yeah, that's what I thought (post #6)

That seems to me more of a semantic difference, rather than useful distinction.

Although one could divide along the lines of visible universe vs what is beyond the visible universe. If that is the distinction you are making then I feel it could be instructive.

That just brings us back to the problem of defining infinity as it relates to the physical universe. What is the difference between a really really big universe and an infinite one. It might have mathematical significance... but the realities of cosmology might just make it a moot point.
It is a purely mathematical statement that an infinite volume can indeed expand. However the observed value of the cosmological constant is a real problem for the current cosmological model which depends on the universe having positive curvature. There are real qualitative differences between a huge finite universe and an infinite one both scientifically and philosophically.

It's also a problem for those trying to find a fundamental theory linking General Relativity with Quantum Mechanics.

EDIT: In fact the OP introduced the concept of "everything" . (He/she still hasn't defined what is meant by "everything"). If everything means everything with no coherent rules for what's possible, than the answer I gave to the question is 'no'.

If the OP meant everything that's possible under some coherent set of rules or laws, than the answer is "yes".

Both are consistent with infinity.

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