Manifold embedding

1,570
1
nash proved that any manifold can be embedded in R^3 in which the higher dimensional manifold gets crumpled and smoothness is lost.

is it possible that 11 dimensional space has already crumpled into our three dimensional universe and that wormholes exist precisely as a direct result of the crumpling?

cheers,
phoenix
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,845
17
1,570
1
there was a big embedding theorem by nash, which is the one you're talking about, and a small embedding theorem, which is the one i'm talking about. it was mentioned in the "a beautiful mind," but i can't find the paper on the web.

cheers,
phoenix
 
1,570
1
i did a little more research and found this quote from nash's autobiographical essay for winning the nobel:

So as it happened, as soon as I heard in conversation at M.I.T. about the question of the embeddability being open I began to study it. The first break led to a curious result about the embeddability being realizable in surprisingly low-dimensional ambient spaces provided that one would accept that the embedding would have only limited smoothness. And later, with "heavy analysis", the problem was solved in terms of embeddings with a more proper degree of smoothness.

so again i ask this: is it possible that the higher dimensional space has either fully or partially collapsed in the three dimensional space and that the nonsmoothness has resulted in wormholes?
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
14,845
17
I repeat, no. An n-dimensional manifold cannot be embedded in an m-dimensional manifold for m < n.
 

arivero

Gold Member
3,284
51
a lot more

actually if you want a lorentzian metric in both manifold, the embedding rises, it needs a lot more of dimensions. About ninety or so, perhaps.
 

marcus

Science Advisor
Gold Member
Dearly Missed
24,713
783
Re: a lot more

Originally posted by arivero
actually if you want a lorentzian metric in both manifold, the embedding rises, it needs a lot more of dimensions. About ninety or so, perhaps.
glad you are back, long time no see
I need to know the Cartan subgroup of SL(2,C)
(I am told there is just one and I suspect it is
the diagonal matrices but am not sure)
 

arivero

Gold Member
3,284
51
Re: Re: a lot more

Originally posted by marcus
glad you are back, long time no see
I need to know the Cartan subgroup of SL(2,C)
(I am told there is just one and I suspect it is
the diagonal matrices but am not sure)
Hi!

I am back just on a errand for nuclear data. I am afraid I can not confirm your guess -it seems a good one- without browsing across manuals :-( Two years teaching computer science and you see, one loses the training.
 

marcus

Science Advisor
Gold Member
Dearly Missed
24,713
783
In the Archive section of this forum I just posted what I think is the Weyl group of SL(2,C). These are new ideas for me, they seem nice

I think the normalizer of the (main) diagonal matrices in SL(2,C) consists of the union of the major and minor diagonal matrices

and then N(H)/H the Weyl group comes down to Z_2

which just flips the diagonal matrix to the other direction--major to minor and viceversa, but there is a minus sign in there too

you cant fool me, you have not gotten all that rusty by teaching computer science. it could even give you ideas
 

Related Threads for: Manifold embedding

  • Posted
Replies
0
Views
2K
  • Posted
Replies
10
Views
3K
  • Posted
Replies
2
Views
2K
  • Posted
Replies
0
Views
2K
  • Posted
Replies
6
Views
3K
  • Posted
Replies
0
Views
2K
  • Posted
Replies
23
Views
5K
Replies
43
Views
7K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top