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phoenixthoth

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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

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- Thread starter phoenixthoth
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- #1

phoenixthoth

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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

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

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phoenixthoth

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cheers,

phoenix

- #4

phoenixthoth

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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

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

- #6

arivero

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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.

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marcus

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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)

- #8

arivero

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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.

- #9

marcus

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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

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