On the infinity of the Universe

bapowell

That's just about the definition of a sticky problem. Of course, it's likely that there is no singularity to speak of, and that quantum gravitational effects smooth things out at a finite energy scale. Would this avert the conceptual difficulty that you see?

JamesOrland

Erm... not really. What quantum gravitational effects would do anything there? I'd thought quantum gravity was still in the limbo of unfinished theories...

Mark M

It seems counter-intuitive, but is very much possible.

Here's a video of Alan Guth explaining that a "bubble" universe arising from inflation can still appears to be infinite:

http://www.youtube.com/watch?v=rfeJhzPq3jQ

bapowell

Seriously? Are you familiar with the understanding that singularities signal a breakdown of the classical theory? Singularities correspong to unphysical infinities that indicate that the theory is ill-behaved in the corresonding energy regime. I'm guessing you know all that and you mean something else. But whether we have an accepted theory of quantum gravity yet or not, it is evident that a UV-complete theory of gravity is needed, and that resolving singularities -- i.e. giving sensible physical results at the Planck scale -- is a generic property of whatever that final theory is.

JamesOrland

Hm, I am in fact familiar with that, but I'd never thought of it quite that way. To be honest, now that you mention it and now that I analyse my previous thought processes, I'd up until right now always thought of an original singularity as sort of a property of the universe (as if spacetime really did break down in it) instead of a property of a theory (or the lack thereof). Mind Projection Fallacy all the way there.

Yes, I did know both that singularities are a breakdown in the description of a particular physical event, and that a final theory should explain that sort of thing, but I'd never really connected the two pieces of knowledge together.

That is... great. Thank you :)

bapowell

Cool. In fact, while admittedly not complete, loop quantum cosmology (based on -- you guessed it -- loop quantum gravity) predicts a bounce at the Planck scale. I'm not an expert (I'm hoping Marcus drops by at some point...he can shed much more light on this), but I think the bounce solution is quite generic in lqc.

Mark M

A similar thing occurs in string theory. If a particular curled up dimension collapsed to the Planck Length, unwound strings (that is, strings that are not wrapped around that dimension) become very heavy, and are too large to measure distance. So, instead, winding mode strings, strings that are wrapped around a dimension, must be used to measure distance. Since WM strings measure distance as the inverse of the unwound strings, this will create the perception that the universe is huge and expanding after hitting the Planck Length.

JamesOrland

Wait, what? Correct me if I'm wrong, but... I understood that at the Planck Scales the other spatial dimensions become relevant and it's actually our spatial dimensions that get curled up, is that it? Or something like that.

Mark M

James,

You are making a small mistake in confusing a dimension being "small" and a dimension being curled up. In string theory (or more precisely, now M-Theory) the other 7 spatial dimensions are curled up into tiny Calabi-Yau manifolds. When you talk about the length of a dimension, you are talking about how much distance must be covered to traverse the entire dimension. Saying that a dimension is curled up is essentially saying you can return to your starting position after traversing that dimension.

So you are correct that when the 3 large dimensions shrink down to a planck length, the other dimensions become noticeable. It is not known if our dimensions are curled up or not, but if the universe if unbounded it would suggest that they are curled up.

But if a dimension is curled up, it is curled up - period. Even if it changes size, it still retains it's shape. (Though the string theorist Brian Greene showed in the 90's that Calabi-Yau shapes can tear and recombine, changing dimensional arrangement. But that's getting off topic.)

JamesOrland

Um, I think I understand as well as I can right now given my current (lack of) understanding of M-Theory. But I think the WMAP had shown evidence that the Universe might after all be flat and (therefore?) unbounded.

I'm sorry, I have a... strong enough grasp of physics up until basic Quantum Mechanics, but once we get to the point of discussing M-Theory or other potential TOEs, I have no idea what I'm talking about.

Mark M

Oh, OK. If you are interested in a non-technical introduction to String Theory, I'd suggest The Elegant Universe by Brian Greene. It is probably the most well known book on the topic.

JamesOrland

Noted. And if I want a technical one?

ImaLooser

Easy. The conservation laws apply in every finite subvolume. Extend to infinity by having an infinity of such finite subvolumes.


Since essentially nothing is known of the nature of the singularity it is hard to say. Nothing is known about why it expanded at all. Why wasn't it content to remain as it was? No one knows. We are left with guessing.

I think that perhaps you are assuming the singularity was finite. It could have been infinite. If the Universe is infinite now then I would think the singularity was infinite as well. But now I too am guilty of guessing.


Both. The visible universe is a subset of the universe as a whole.

JamesOrland

1. Yes, I understood the part that the Conservation Laws apply locally :)
2. Also yes, as I said in my last post, I realised I was committing the Mind Projection Fallacy with singularities, assuming they were a property of the world instead of a property of the theory. My mindset is adjusted now, so that problem was also dissolved.
3. And yeah, when I said that I meant 'The Universe or only the Observable Universe', that is, I was asking whether it was the origin of our whole bubble or exclusively the part we can see of it.

skydivephil

A few things I thinks its worth mentioning.
1) Eternal inflation and chaotic inflation are not the same.
read here:
http://arxiv.org/pdf/gr-qc/0409055.pdf
2) Inflation has good evidence for it but its not a done deal yet, we still need to see the B mode polarisation for it to passs its final hurdle. Well nothing is ever final, but this is a key test, see here:
http://www.nature.com/news/2009/0904...l/458820a.html
3)Borde , Guth and Vilenkin have argued that eternal inflaiton has an initial singualrity, but that has been disputed by Aguirre and Gratton. see here:
http://arxiv.org/abs/0712.0571
If anyone knows of any way to observationally resolve this dispute, I'd love to hear it but I suspsect there is not.
4) Guth claims most inflationary models are eternal , but I note he doesnt say all.So if ifnaltion is shown beyond reaosnable doubt, there is stil a chance its not eternal. see here http://arxiv.org/abs/hep-th/0702178:

5 LQC resolves singualrities inlcuding the one proposed at the beginning of eternal inflation by Borde Guth and Vilkenkin , see here:
http://arxiv.org/abs/0812.4703

JamesOrland

1) Is that so? Wikipedia does redirect to Eternal Inflation when you type in Chaotic Inflation :P
2) I didn't think it was a done deal, but I kinda like the idea. Plus it kind of appeals to my physical sense.
3 & 5) I'm pretty sure bapowell addressed this with a pretty good point: singularities state the breakdown of a theory, not the breakdown of physics. If a theoretical model possesses a singularity, that's evidence for its incompleteness, so saying that 'Eternal Inflation has an initial singularity' is pretty much the same as saying 'Eternal Inflation is still not a good enough theory.' So even if LQC doesn't turn out to be true, the final theory should have as a property the ability to dissolve singularities.
4) Yes, I understand that, too, although I really like the idea of an Eternal Inflation. Of course, me liking it and it being true are not correspondent, and I haven't studied science for long enough to know whether my scientific hunches are anywhere on spot. I'm just going to follow them where science doesn't know what it's doing.

bapowell

Yes, indeed. To be clear, above James and I were discussing chaotic inflation, which is necessarily eternal (hence my phrasing "chaotic eternal inflation"). There are models of eternal inflation that are not technically chaotic (which refers to the distribution of the initial field values.)
Yes, but if B-modes are not detected that doesn't falsify inflation (nor does it necessarily confirm it, see the quick note by Brandenberger on some other B-mode sources: http://arxiv.org/abs/1104.3581)
Interesting. I was not aware that it was under dispute. For completeness, here's a reference to the original paper by Borde and Vilenkin: http://arxiv.org/abs/gr-qc/9312022. The later paper with Guth was an extension.

And James, for a good technical introduction to string theory try Zwiebach. I've not read it myself but it seems highly praised by many in the field. More advanced standards are the texts by Polchinski and Green, Schwarz, and Witten. The latter is a now out-dated by has its unique strengths.