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.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?
Or are you trying to see how many times we'll let you violate the forum rule about personal speculation?Does energy flow cyclically between pairs of dimensions? To me, that's what rotation is.
Dimensionality in 11 dimension M-theory refers to the number of spatial dimensions required to describe the universe. In this theory, there are 11 dimensions, with 3 of them being the familiar dimensions of length, width, and height, and the remaining 8 being compactified or curled up dimensions that are too small for us to observe directly.
11 dimension M-theory is a unifying theory that attempts to reconcile the differences between the five different versions of string theory. It proposes that the universe is made up of tiny strings and that these strings vibrate in different ways to give rise to the different particles and forces in our universe. Unlike other theories, 11 dimension M-theory includes gravity and also allows for the possibility of multiple universes or a multiverse.
Scientists use mathematical models and experiments to study and test the concept of 11 dimensions in M-theory. They use supercomputers to simulate the behavior of strings in different dimensions and also conduct experiments at high-energy particle colliders, such as the Large Hadron Collider, to search for evidence of extra dimensions.
11 dimension M-theory has the potential to revolutionize our understanding of the universe and the fundamental laws of physics. It may provide a unified framework for all known forces and particles and also offer insights into the nature of space and time. Additionally, the concept of a multiverse in M-theory raises questions about the existence of other universes and the possibility of parallel dimensions.
While 11 dimension M-theory is still a theoretical concept, it has already had some real-world applications. For example, the mathematical techniques used in M-theory have been applied to other fields, such as condensed matter physics and black hole thermodynamics. Additionally, the study of extra dimensions in M-theory has led to advancements in the development of new materials and technologies, such as high-temperature superconductors and quantum computers.