How do dimensions in string theory interact?

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SUMMARY

The interaction of dimensions in string theory is primarily observed through the compactification of extra dimensions on 6-dimensional manifolds, specifically Calabi-Yau manifolds, which are complex 3-dimensional structures. This complexity arises from the combination of two real dimensions plus additional structural elements. String theory effectively integrates principles from general relativity, such as curvature, and quantum mechanics, particularly the concept of discreteness. Research indicates that geodesics may demonstrate finite, quantized uncertainty at the Planck scale, potentially resolving into piecewise sinusoidal strings through interdimensional Fourier transforms, a concept anticipated by John Archibald Wheeler in his notion of "pregeometry."

PREREQUISITES
  • Understanding of string theory fundamentals
  • Knowledge of complex manifolds, specifically Calabi-Yau manifolds
  • Familiarity with general relativity and quantum mechanics principles
  • Basic grasp of Fourier transforms in mathematical physics
NEXT STEPS
  • Research the properties and implications of Calabi-Yau manifolds in string theory
  • Explore the relationship between curvature in general relativity and string theory
  • Study the concept of quantized uncertainty at the Planck scale
  • Investigate John Archibald Wheeler's contributions to pregeometry and its relevance to modern physics
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The discussion is beneficial for theoretical physicists, string theorists, and advanced students of physics interested in the intersection of geometry and quantum mechanics within string theory.

Loren Booda
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How do dimensions in string theory interact?
 
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Well one thing you don't often see discussed is that the 6-dimensional manifolds (Calabi-Yau or whatever) that the extra dimensions are compacted on are actually complex 3-dimensional manifolds. A complex dimension is two real dimensions plus some structure. And there's plenty of string research on that structure.
 
String theory seems to have the best of general relativity (curvature) and quantum mechanics (discreteness). I guess that geodesics exhibit finite, quantized uncertainty at the Planck scale over dimensions of interval and dynamics, and there may resolve as piecewise sinusoidal strings under interdimensional Fourier transform. John Archibald Wheeler was prescient of such artifacts as strings in his "pregeometry."
 

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