GTR & STR: Could 9 Dimensions Unify Theory?

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I try to understand if the GTR could work together with theories, where physical reality contains more than 4d
Let's play pretend a progressive alien civilisation contacts us and an irrelevant conversation begins. Later on, an alien-scientist says: "by the way, the physical reality contains 9 dimensions. I heard a famous human theorist announced, that it should be 4. You have to touch up."

Could the GTR (and STR) be imbedded in a higher grade manifold of grade 5 or even higher instantly or does the boundary condition, that "real spacetime" has 5+ dimensions mean, that GTR/STR are no more meaningful ?

Thanks in advance
Carlo
 
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eaglechief said:
Summary:: I try to understand if the GTR could work together with theories, where physical reality contains more than 4d

Let's play pretend a progressive alien civilisation contacts us and an irrelevant conversation begins. Later on, an alien-scientist says: "by the way, the physical reality contains 9 dimensions. I heard a famous human theorist announced, that it should be 4. You have to touch up."

Could the GTR (and STR) be imbedded in a higher grade manifold of grade 5 or even higher instantly or does the boundary condition, that "real spacetime" has 5+ dimensions mean, that GTR/STR are no more meaningful ?
At the "I" thread level: What difference could it possibly make? Embedded or not, the world we live in is what it is. GTR is an apt description.

At a higher level, a quick trip to Google says that yes, one can embed a 4 dimensional pseudo-Riemannian manifold in a higher dimensional manifold in a metric-preserving way.

https://mathoverflow.net/questions/127734/nash-embedding-theorems-for-pseudo-riemannian-manifolds.

[Though this stuff is well above my head].
 
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There are many embedding theorems which describe how lower dimensional curved spaces may be embedded into higher dimensional flat spaces. They make no physical predictions so they are usually not worth the effort, but they can be used if desired for aesthetic reasons.
 
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Thank you for your replies.

My question is heading in that direction: Given we accept as hypothetic boundary condition, that the physical reality contains of say 9 dimensions. Then my assupmtion would be, that STR and GTR are limited in describing the "entire" physical truth, due to it is written in 4d.

As far as i recall modern string-theories deal with 7d, 8d, 9d, ... strings.

So, could STR and GTR describe a 9d reality at all ?

Cheers
Carlo
 
I don’t think that 9 dimensions is sufficient. Are you really interested specifically in 9 dimensions or was that just a random number used as an example?

See: On the Global Isometric Embedding of Pseudo-Riemannian Manifolds
C. J. S. Clarke
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 314, No. 1518 (Jan. 13, 1970), pp. 417-428 (12 pages)
Published By: Royal Society
 
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After post #4 it isn't clear what the question is. Are you asking about imbedings in the mathematical sense? Or are you asking whether space-time is actually higher dimensional and we only see 4 of the dimensions and how GR handles this?
 
Thanks for your replies.
dave: 9d was just a random number.
martin: this >> Or are you asking whether space-time is actually higher dimensional and we only see 4 of the dimensions and how GR handles this?