The Universe - infinite or not ?

[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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