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.
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.

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