Is Spacetime a Closed Volume or a Convoluted Surface?

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The discussion centers on whether spacetime is a closed volume or a convoluted surface, emphasizing that everything in the universe exists within spacetime. Understanding the universe requires a perspective outside of spacetime, which is deemed impossible. The "inside" of elementary particles allows for the derivation of properties like mass and charge, while the singularity of black holes is considered a closed object from which no information can be extracted. The nature of spacetime in the macrocosmos remains uncertain, as we cannot observe it from an external viewpoint. Ultimately, the openness or closeness of spacetime, particularly regarding its density and structure, remains an unresolved question in modern cosmology.
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Everything in the universe is inside of spacetime. But in order to fully understand the universe, the vantage point must be outside of spacetime. This point of view is impossible to reach. For the quantum universe of the elementary particles, an "inside" exists for all particles. This "inside" can give properties of mass, charge, spin, and magnetic dipole moment. But will we ever be able to see in? Will we be able to see the "inside" of the singularity?
 
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Can we say that the singularity has an \Omega > 1?
 
In Brane world cosmology there is no beginning and end, yet the ideas of critical density can still be spoken too?

Andrey Kravtsov model let's us understand that there is this basis to a cosmological reality and that if we were to consider the strings, how would we see such congregations? In the early universe supersymmetric points woud point to supergravity

So we look at the nature of such congregations and try and define this dynamical movement. Let's say that in the early universe supersymmetry was a reality, then what was first shown by Andrey, let's us know the basis of that reality as all pervasive? But, if the reality is to include gravity how would you retain time, but as a dimensional value in the strengths and weakness of that gravity field?

what has been revealed in mass considerations? http://online.itp.ucsb.edu/online/plecture/thorne/oh/03.html

The solidifcation of the model of Andrey's reveals time a dimensionally significant?

But I then, wanted to add this last statement for you as well.

http://www.superstringtheory.com/forum/topboard/messages3/39.html

So we needed a way in which to capture this cyclical nature. A black hole does not necessarily assume critical density, but instead ignites and turns to fission?
 
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sol2,

Thanks for these wealth of information.

The purpose of this thread is to discuss whether spacetime is closed like a volume or a convoluted surface.

I think the microcosmos (such as an electron or a quark) is not completely closed (closed surface) since we still can derived physical properties from it like mass, charge, spin, and magnetic moment. The big bang singularity (or black hole) is a closed object since we cannot derived any information from it.

The openness and closeness of the macrocosmos cannot be decided since we are living inside it instead of looking from a vantage point outside.

The spacetime of the microworld is not closed. The \Omega of spacetime of the macroworld cannot be positively decided by modern cosmological studies.
 
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