How Can an Infinite Universe Have Finite Energy?

[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!