How Can an Infinite Universe Have Finite Energy?

[JamesOrland]

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.

1. Yes, I understood the part that the Conservation Laws apply locally :)
2. Also yes, as I said in my last post, I realized 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/2009/090415/full/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 doesn't 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:[/URL]

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

 

[JamesOrland]

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/2009/090415/full/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 doesn't 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:[/URL]

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

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 [I]still[/I] 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]

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

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.)

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/2009/090415/full/458820a.html

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)

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

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.

 

[JamesOrland]

And to be clearer, I'd thought the Chaotic Model was the only Eternal Inflation Model, I didn't know there were other Eternal Inflation theories. But I didn't really do enough research on the field as of yet so I'm just going with the flow for now until I obtain more knowledge on that and can actually participate more actively in such discussions.

 

[skydivephil]

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.

Thats fascinating, i didnt realize that matter bounce in Horava gravity prodcued B mode polarisation. To be fair that's a pretty new paper. I do note that the author concluded we can still assess the different models via their tilt, so I think its still true that if we can produce the spectrum from the B mode it could be the decider on inflation, but I guess not in the same way that the Nature article implied.

As far as disputing the initial singualrity in eternal inflaiton, this is a an exmaple within the eternal inflation community:

http://arxiv.org/abs/0712.0571
Of course the loop guys wouold dispute from a very different angle ie a bouncing comsology

 

[bapowell]

I do note that the author concluded we can still assess the different models via their tilt...

Yes, I noted that as well and decided to write a paper about it: http://arxiv.org/abs/1106.5059
Shameless self-promotion aside, what you find is that the tensor spectrum must have a rather significant tilt in order decisively differentiate between the models.

Also, Baumann and Zaldarriaga wrote a cool paper about how to tell primordial B-modes apart from those produced later via things like topological defects: http://arxiv.org/abs/0901.0958

 

[Mark M]

Noted. And if I want a technical one?

See the String wiki, it has a list of books for a wide variety of string-related topics:

http://www.stringwiki.org/w/index.php?title=String_Theory_Wiki

But like I said, it also recommends The Elegant Universe for newcomers to the theory.

 

[bapowell]

But like I said, it also recommends The Elegant Universe for newcomers to the theory.

I don't know; pop science treatments are not necessarily useful for developing an initial understanding of the technical aspects of a field. I would say instead invest your time in learning some quantum field theory and general relativity, then pick up an introductory string theory text like Zwiebach.

 

[Mark M]

I don't know; pop science treatments are not necessarily useful for developing an initial understanding of the technical aspects of a field. I would say instead invest your time in learning some quantum field theory and general relativity, then pick up an introductory string theory text like Zwiebach.

True. But I had recommended that he read it for non-technical purposes, because he had said he didn't have any idea about string theory, or any quantum gravity theories. Obviously, any standard string theory introduction is far better for seriously grasping string theory.

And by Zweibach, you are referring to A First Course in String Theory, correct? In which case, I can also say it is an excellent introduction. It's just that it seemed a little "over the top" to recommend a textbook to someone just to read about string theory. That's why I linked him to the wiki for a list of technical books if he was interested in them.

 

[JamesOrland]

I don't know; pop science treatments are not necessarily useful for developing an initial understanding of the technical aspects of a field. I would say instead invest your time in learning some quantum field theory and general relativity, then pick up an introductory string theory text like Zwiebach.

I do have a pretty firm understanding of general relativity, while I admit that my knowledge of quantum field theory is somewhat lacking.

True. But I had recommended that he read it for non-technical purposes, because he had said he didn't have any idea about string theory, or any quantum gravity theories. Obviously, any standard string theory introduction is far better for seriously grasping string theory.

And by Zweibach, you are referring to A First Course in String Theory, correct? In which case, I can also say it is an excellent introduction. It's just that it seemed a little "over the top" to recommend a textbook to someone just to read about string theory. That's why I linked him to the wiki for a list of technical books if he was interested in them.

Oh, I don't mind technical. I don't want to have superficial knowledge of the theory, since my current goal in life is eventually taking college at least twice again, one of those being to major in physics, and doing research. I don't want to 'just read' about string theory, I want to understand everything about it, mathematics and all. That would be lovely :)

 

[Mark M]

I do have a pretty firm understanding of general relativity, while I admit that my knowledge of quantum field theory is somewhat lacking.



Oh, I don't mind technical. I don't want to have superficial knowledge of the theory, since my current goal in life is eventually taking college at least twice again, one of those being to major in physics, and doing research. I don't want to 'just read' about string theory, I want to understand everything about it, mathematics and all. That would be lovely :)

Great! then definitely pick up A First Course in String Theory by Barton Zweibach. It's well known as a great technical introduction to string theory. Here's a link for Amazon:

https://www.amazon.com/dp/0521831431/?tag=pfamazon01-20

 

[JamesOrland]

Great! then definitely pick up A First Course in String Theory by Barton Zweibach. It's well known as a great technical introduction to string theory. Here's a link for Amazon:

https://www.amazon.com/dp/0521831431/?tag=pfamazon01-20

Will do, thanks :)

 

[DennisN]

Hi James! I just want to mention something about what you wrote on page 1:

If ∞ + 1 = ∞, what's to prevent energy from being created out of nowhere?

Are you aware that ∞ + 1 = ∞ is not mathematically correct for real numbers? If not, let me know if you want me to show you, it's easy.

 

[JamesOrland]

Are you aware that ∞ + 1 = ∞ is not mathematically correct for real numbers? If not, let me know if you want me to show you, it's easy.

Um... why is it not mathematically correct?
lim(x -> +∞) x + 1 = +∞ isn't it? It's what I was thinking about when I wrote that.

I mean, of course writing ∞ + 1 doesn't even make any mathematical sense in R because ∞ is not a real number, but the idea was what I wrote with the limit.

Unless you're talking about hyperreal numbers?

 

[DennisN]

Hi James, all good and understood. I thought you might be aware of it but I was not certain. I remember being drilled by my math teacher to be careful with infinities, so I try to keep that spirit . All the best, and good luck with your continued studies!