B What is the nature of dimensionality in 11 dimension M-theory?

Paige_Turner
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What are the signatures and distance metrics for the compactified dimensions?
They're dimensions, so they DO have a metric equation, right? Does energy flow cyclically between pairs of dimensions? To me, that's what rotation is.
 
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Paige_Turner said:
Summary:: What are the signatures and distance metrics for the compactified dimensions?

They're dimensions, so they DO have a metric equation, right?
Are you trying to learn here? There's a pretty decent explanation in "Gravity" by James Hartle (the only undergraduate-level general relativity textbook I known of) including an example of a metric tensor for a manifold with a compactified dimension.
Does energy flow cyclically between pairs of dimensions? To me, that's what rotation is.
Or are you trying to see how many times we'll let you violate the forum rule about personal speculation?
 
If you want to discuss M-theory, @Paige_Turner, then it is best to do it in the "Beyond the Standard Model" forum. However, it is an extremely technical subject, that cannot be dealt with on a "B" level thread. You will need to learn QFT and string theories first, and there is no shortcut.

It is something else to ask about the topology of compactifications. For questions about them, I recommend choosing some easier examples like the Riemann sphere.

The question as stated is unanswerable, so I close this thread.
 
We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.

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