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Calabi-Yau spaces are important in string theory, where one model posits the geometry of the universe to consist of a ten-dimensional space of the form , where is a four dimensional manifold (space-time) and is a six dimensional compact Calabi-Yau space. They are related to Kummer surfaces. Although the main application of Calabi-Yau spaces is in theoretical physics, they are also interesting from a purely mathematical standpoint. Consequently, they go by slightly different names, depending mostly on context, such as Calabi-Yau manifolds or Calabi-Yau varieties.
Although the definition can be generalized to any dimension, they are usually considered to have three complex dimensions. Since their complex structure may vary, it is convenient to think of them as having six real dimensions and a fixed smooth structure.
Originally posted by jkrog08
reply to post by liquidself
Either way, timelines are a causality of individual space, and not hyperdimensional. They are likely dictated by the quantum laws of each separate physical universe.
Originally posted by jkrog08
reply to post by liquidself
As I said, the "Many Worlds" interpretation corresponds more to wave function principles than it does hyperdimensions. Spatially there is nothing different within each probability, they are only separated by phases, or string vibrations.
Originally posted by jkrog08
reply to post by constantwonder
While you are correct in your definition of the Calibi-Yau manifold and it's description of the microscale structure of strings, you have omitted branes, and of course the Ads/CFT Correspondence, as well the hyperdimensional brane physics. As it does appear there is a fractal "contraction-expansion" effect due to clashing P-Branes of hyperspace.
So, hyperspatial dimensions exist likely not only within strings, but outside of our world volume brane.
Hopefully, Jkrog, the fellows at cern will crack the extra spatial dimensions soon.
I have a feeling that the boards are going to explode with info about this stuff in the next several months and next couple years. Should be an interesting ride