The Universe - infinite or not ?

[Neandethal00]

... The set of positive integers is infinite.

No they are not infinite. They are finite but unbounded.

Added Later: Numbers are not physical entities, the universe is.

 

[Fuzzy Logic]

Whether one believes the universe is infinite or not, one must believe in infinity.

If one believes that the universe is finite, then what is beyond the universe (both in time and space)? And what was before the universe?

One cannot say that there was no before or beyond because there was no time or space. The mere notion of a singularity directly contradicts that concept. The existence of a singularity implies a void of some kind that the singularity itself resided in and expanded into.

If it is insisted that all of existence was within the singularity then how could space and time expand? What did it expand into? How does one conceive expansion of something into itself? Wouldn't it be more accurate to say that all of the matter in the universe got smaller?

If one now accepts that infinity must be possible, then why is it more plausible to have an infinite void instead of an infinite universe?

 

[revo74]

From my understanding we have indirect evidence of virtual particles. No one is debating whether they exist or not. What is speculative however is this notion that virtual particles could become Universes.

Assuming that Krauss is correct that our Universe was a virtual particle with the right conditions that underwent expansion and became a Universe, there is something I am confused about, which I'm hoping someone can address.

Krauss says that empty space or the vacuum of space at extremely small scales is not truly empty or "nothing". Instead there lies a brewing sea of energy where virtual particles pop in and out of existence in a fraction of a second. This suggests that this sea of energy is a feature of our Universe. It is not a separate entity. Now, it is my understanding that Krauss is claiming that our Universe spawned from this sea of energy, which suggests to me that one independent entity (our Universe) came from a separate entity (sea of energy). So does this mean that there are two entities? One which is a feature of our Universe and the other a realm of existence outside of our Universe where it came from.

 

[Primtall]

No they are not infinite. They are finite but unbounded.

Added Later: Numbers are not physical entities, the universe is.

Need to nail down some terminology : Finite to me , means that it can be measured using a Real number. Unbounded means that it has no "end". There is no real number that allows you to measure the set of positive integers thus it is infinite. The set of known prime numbers on the otherhand is Finite , as there is a definite amount of them. According to Euclid the number of prime numbers is infinite. What we have therefore is a finite set (the known primes) expanding into the infinite (the primes ). This is a good model for the expanding universe, expanding into the infinite

 

[Primtall]

"Added Later: Numbers are not physical entities, the universe is"
The post related to an assertion that 'only FINITE things can expand' . Logically this isn't so, and the example of an infinite set of numbers, expanding , supports (actually proves) this point, logically.
In the mathematical universe ,logic and physically realized logic, are one and the same thing. Without getting mystical, it can be said that the the universe is a symphonic expression of the logical - but that's a different thread.

 

[Fuzzy Logic]

No they are not infinite. They are finite but unbounded.

Added Later: Numbers are not physical entities, the universe is.

Why wouldn't real numbers be infinite? How can they be both finite and unbounded? At what value does real numbers end?

 

[Primtall]

Agree with you fuzzy logic. Finite things are supposed to be measurable by a real number and the set of real numbers can't be. I think the 'finite but unbounded' business relates to ants on spherical surfaces, or the way n-dimensional beings would experience n+1 dimensions ... from the perspective of a higher dimension , all of space-time might well be an ink blot on its fabric and finite in that sense.

 

[Neandethal00]

Assuming that Krauss is correct that our Universe was a virtual particle with the right conditions that underwent expansion and became a Universe, there is something I am confused about, which I'm hoping someone can address.

Krauss says that empty space or the vacuum of space at extremely small scales is not truly empty or "nothing". Instead there lies a brewing sea of energy where virtual particles pop in and out of existence in a fraction of a second. This suggests that this sea of energy is a feature of our Universe. It is not a separate entity. Now, it is my understanding that Krauss is claiming that our Universe spawned from this sea of energy, which suggests to me that one independent entity (our Universe) came from a separate entity (sea of energy). So does this mean that there are two entities? One which is a feature of our Universe and the other a realm of existence outside of our Universe where it came from.

The other late night I was listening to a talk radio (guess!) where one physicist for an hour kept babbling "the universe came from nothing, things can come from nothing", etc.
Sometimes I wonder why some simple things do not come to some brilliant minds. If something comes from a place, that place is NOT nothing. Just because we do not see or do not know yet, does not mean that place is nothing.

Krauss is right, Space is a medium. Empty space is not empty. We do not yet know the true nature and structure of this medium. Sometimes, I'm afraid we may never know. That's why to us it appears things come from nothing. Energy explanation of Krauss is a possibility.

 

[Neandethal00]

Why wouldn't real numbers be infinite? How can they be both finite and unbounded? At what value does real numbers end?

A few posters including me are insisting the universe is finite. It does not matter how many ways, in how many words we write this, many of you will not be able to figure out exactly where this argument comes from until you start visualizing any physical object and taking it (or its properties) to infinity. Where ever you stop, it is finite.

The post related to an assertion that 'only FINITE things can expand'

Primtall.

No, the assertion is all physical things are finite.

 

[Primtall]

A few posters including me are insisting the universe is finite. It does not matter how many ways, in how many words we write this, many of you will not be able to figure out exactly where this argument comes from until you start visualizing any physical object and taking it (or its properties) to infinity. Where ever you stop, it is finite.

Primtall.

No, the assertion is all physical things are finite.

Again, not true.
My fingernail is Infinite. It is composed out of the infinite by the imposition of an arbitrary boundary condition, in the same way that the perfect circle bounds infinity
(pi being 3.14159 ... ad infinitum). What we call the Finite is just some demarkation or
Limit imposed on the infinity of the infinitesimally small (to us). This applies equally whether you are talking about the size of the universe or the size of the coastline of Ireland (scale and Zoom being just arbitrary parameters). In the case of the expanding universe,the discussion is really about expanding Limits. Infinity is already there (your container) , and the limit of the universe as t goes to infinity , is infinity. The model of the 'set of known primes' expanding into the 'set of primes' captures the relationship quite well.

 

[Primtall]

Further, there's been a lot of nonsense posted about 'something' co-existing alongside 'nothing'. It's not like light and pockets of darkness. Nothing means 'nothing at all, ie. no potential , no quantum flux, no entropic chaos, no fuzz on the tv screen before the coherent signal is received, Nothing AT ALL. It really is one or the other - as apart from 'something' there is nothing. Prof. Hawking was surely wandering when he said that m-theory solved the mystery of 'why there is something instead of nothing'. If you define 'nothing' as any of the above then yes , but you may as well go mystical and say that the material world emerges spontaneously from the non-material etheric realm. "Why is there m-theory instead of nothing ? " professor ?

 

[minio]

I doubt that it could not be determined. I personally agree with theories that our universe in 3D has currently some 80 billions ly across. However if time is considered as another dimension then we cannot say if universe is finite because we have just one limit (big bang 14 bilion years ago), but not other and thus is IMHO not possible to make conclusions unless we hit the end of time. However I am not physicist nor matematician, so I might be wrong :)

 

[Primtall]

just logically, if 3D can be measured by a real number (80 bil in this case) then it would be finite. Can it be though, when the thing being measured is expanding ? i would have thought not but maybe there is some convoluted definition somewhere, that makes it, according to that definition, Finite.

 

[Neandethal00]

Again, not true.
My fingernail is Infinite. It is composed out of the infinite by the imposition of an arbitrary boundary condition, in the same way that the perfect circle bounds infinity
(pi being 3.14159 ... ad infinitum). What we call the Finite is just some demarkation or
Limit imposed on the infinity of the infinitesimally small (to us). This applies equally whether you are talking about the size of the universe or the size of the coastline of Ireland (scale and Zoom being just arbitrary parameters). In the case of the expanding universe,the discussion is really about expanding Limits. Infinity is already there (your container) , and the limit of the universe as t goes to infinity , is infinity. The model of the 'set of known primes' expanding into the 'set of primes' captures the relationship quite well.

Whatever...

Numbers have no meaning until you use (physical) them.
This arguments will go no where.. Let's not waste our mental energy.

 

[Primtall]

all right

 

[minio]

My fingernail is Infinite. It is composed out of the infinite by the imposition of an arbitrary boundary condition, in the same way that the perfect circle bounds infinity
(pi being 3.14159 ... ad infinitum).

I am to sure if I get you completely right, but your argument stands only if the spacetime is continuous. If it is discrete, once you have boundaries you have finite size, in the sense that you have finite number of elements contained within boundaries.

Can it be though, when the thing being measured is expanding?

In case the expansion has limit where it stops than yes.

 

[Primtall]

The discrete is really just a normalisation of the continuos (something to make equations and digital circuitry work - like normalising Planck density). Even the samples of digital signal processing are normalisations of continuos signals. But yes, if ST was discrete and the expansion stopped, then in theory you could tot up all the blobs and all would be finite - except for within the blobs themselves where infinity would still rage ( infinitesimally small = infinitely divisible) . Whats Between the blobs though ? if the answer is 'nothing' then ST is continuos. There could well be some higher dimensional fabric between them though. Several programs running in the memory of my pc are separated by ... the operating system i suppose ...
I don't know Minio, i think we'd have to be higher dimensional beings to know this one. The existence of a boundary satisfies the definition of 'Finite', and the fingernail or the circle are finite in that sense, but because they are infinitely divisible, in another sense , from some other level of reality, they are each an infinite universe. And 'our' level of reality is really just an arbitrary scaling parameter.

 

[Primtall]

by the way, it is thought that the rate of expansion is actually increasing, so a rate of
0.007% per million years might become .008% at some time in the future :-)
This doesn't suggest convergence onto a limit as t goes to infinity, If it did then i would call it finite.

 

[minio]

The question is, if time is infinite. However I agree that we would need to be "Gods" to get definite answer for infinity of our universe :)

 

[Primtall]

Yes. My own belief is that the standard model of reality is backwards. We get taught that consiousness exists within Space Time , but i believe that Space Time exist within consiousness and hence the exasperating perplexity with the concept of infinity (as the free and the infinite are attributes of consiousness)

 

[Drakkith]

Yes. My own belief is that the standard model of reality is backwards. We get taught that consiousness exists within Space Time , but i believe that Space Time exist within consiousness and hence the exasperating perplexity with the concept of infinity (as the free and the infinite are attributes of consiousness)

Please, leave the philosophy to it's own forum.

 

[Drakkith]

just logically, if 3D can be measured by a real number (80 bil in this case) then it would be finite. Can it be though, when the thing being measured is expanding ? i would have thought not but maybe there is some convoluted definition somewhere, that makes it, according to that definition, Finite.

Sure it can be measured while expanding. The key is knowing where to start and stop your measurements and accounting for the finite speed of light and the expansion over time.

 

[Primtall]

Sure it can be measured while expanding. The key is knowing where to start and stop your measurements and accounting for the finite speed of light and the expansion over time.

please go on ... so you start at the BB and where do you stop ?
ca. 14 bil yrs old but radius of ca. 80 bil ly , so expansion rate > c , expansion rate actually increasing we are told. What does c have to do with it ? Do you factor in the relativity of time ? Is it finite in the sense that it converges on a limit ? Not being confrontational here, just genuinely curious.

 

[Fuzzy Logic]

This whole topic is philosophy.

For all practical purposes, infinity is of no real value to us. In any given frame of reference you can say that something is finite, but without considering the whole picture you are just being ignorant and pedantic.

 

[Primtall]

its all philosophy actually, even physics (hence the title phd). If you think its productive to lobotomize away infinity then knock yourself out - see how that goes for you.

 

[minio]

please go on ... so you start at the BB and where do you stop ?
ca. 14 bil yrs old but radius of ca. 80 bil ly , so expansion rate > c , expansion rate actually increasing we are told. What does c have to do with it ? Do you factor in the relativity of time ? Is it finite in the sense that it converges on a limit ? Not being confrontational here, just genuinely curious.

Actually, if you consider universe a hypersphere with diameter of ca 14. bil years, then the circumference would be 80 bil ly. So to get this no expansion > c would be needed just expansion = c.

 

[Primtall]

Actually, if you consider universe a hypersphere with diameter of ca 14. bil years, then the circumference would be 80 bil ly. So to get this no expansion > c would be needed just expansion = c.

so you're saying the circumference is 80 bil ly ? Do u mean the circumference or the diameter ? It seems the lower limit is a diameter of 80 bil and the expansion of ST is not bound by Einsteinian GR ?

 

[minio]

Circumference. Hyphershere has 3D surface and if what we call universe would be this surface, then, if this hypersphere has diameter ca 14. bilion years, it would have circumference about 86 bilions ly which would be length of this "surface universe" across.

 

[Primtall]

ok, a hypersphere ( with t as radius ? ). I've heard one theorist speculate that its more like a double doughnut with the expansion pouring out into one and the contraction being sucked into the other. Think i like this one better as it conforms with Newton (action/reaction). But with the rate of expansion increasing I'm still perflexed about the infinite/finite question. but thks for the explanation , b rgds

 

[minio]

It was just about > c expansion. It cannot answer finite/infinite question. If time is infinite it would infinitly expand at accelerating speed. If time is finite it will stop one day.

 

[Primtall]

Yeah, i guess we get into philosophy if we go near that question (whether t is finite or not). thks again, b rgds

 

[marcus]

ok, a hypersphere ( with t as radius ? ). I've heard one theorist speculate that its more like a double doughnut with the expansion pouring out into one and the contraction being sucked into the other. Think i like this one better as it conforms with Newton (action/reaction). But with the rate of expansion increasing I'm still perflexed about the infinite/finite question. but thks for the explanation , b rgds

The hypersphere is a common model for the case of finite spatial volume assuming overall positive curvature. A lower bound for the radius* has been estimated in one of the NASA reports ( WMAP 5th year data, Komatsu et al).

There is no simple relation between the radius and the age of the universe. It's probably not a good idea to think of the radius as a time coordinate.

Of course the U could be infinite spatial volume---this hasn't been ruled out. the way to get a numerical grip on the question is to estimate the curvature. But more refined measurement of curvature is needed. So far one can say that IF the curvature is positive and we are in the hypersphere case then with 95% certainty the curvature is LESS than a certain amount.

this corresponds to the radius of curvature being AT LEAST a certain length (with 95% certainty). And that lower bound turned out, according to Komatsu et al WMAP5 report, to be around 100 billion light years.

So by getting a quantitative handle on the curvature you get a quantitative handle on the current spatial volume of the universe in that case. IF it is finite at all, and if we are in the positive curve situation, then the radius is AT LEAST a certain amount.

It is still very iffy and preliminary. Better measurement is in progress but it could be a few years, or even many years, before we have a good grip on this curvature number, and thus on the radius in the hypersphere case. I'm clueless as to what to expect.

I like thinking about the hypersphere case but its still just a speculative exercise. I'll get a link to Komatsu et al in case you want to check it out.
Wow, I simply googled "Komatsu WMAP 5" and it came up first hit!
http://arxiv.org/abs/0803.0547
If interested, look at Table 2 on page 4 where it says "curvature radius". If the notation conventions are unfamiliar, ask.

The column to pick is WMAP+BAO+SN because that uses all the available data, not only WMAP but also galaxy counts at various distances and also supernovae. The number h can be taken to be h = 0.7. It is a way of letting people adjust according to their latest figure for the Hubble parameter. If you think the right figure is 71 km/s per Mpc then use h = 0.71. So then you see that in the positive curvature case R > 22 h-1 Gpc. That is roughly 100 billion ly. Just a lower bound, could be much larger.

 

[Primtall]

ok, thks

 

[voxilla]

Of course the U could be infinite spatial volume---this hasn't been ruled out. the way to get a numerical grip on the question is to estimate the curvature. But more refined measurement of curvature is needed. So far one can say that IF the curvature is positive and we are in the hypersphere case then with 95% certainty the curvature is LESS than a certain amount.

What about getting a grip on gradients ?

 

[Redbelly98]

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