- #1

- 1,569

- 2

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

- Thread starter phoenixthoth
- Start date

- #1

- 1,569

- 2

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

- #2

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

The theorem says that any Riemann manifold can be (isometrically) embedded in

- #3

- 1,569

- 2

cheers,

phoenix

- #4

- 1,569

- 2

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?

- #5

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

I repeat, no. An n-dimensional manifold cannot be embedded in an m-dimensional manifold for m < n.

- #6

arivero

Gold Member

- 3,311

- 64

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.

- #7

marcus

Science Advisor

Gold Member

Dearly Missed

- 24,738

- 785

glad you are back, long time no seeOriginally 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.

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)

- #8

arivero

Gold Member

- 3,311

- 64

Hi!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)

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.

- #9

marcus

Science Advisor

Gold Member

Dearly Missed

- 24,738

- 785

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

- Last Post

- Replies
- 0

- Views
- 2K

- Last Post

- Replies
- 10

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 0

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 3K

- Last Post

- Replies
- 0

- Views
- 2K

- Last Post

- Replies
- 23

- Views
- 5K

- Replies
- 9

- Views
- 3K

- Replies
- 43

- Views
- 7K

- Last Post

- Replies
- 3

- Views
- 985