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Garrett Lisi: Retired Off Apple Stock Then Revolutionized Physics Living in Hawaii

Theories of Everything with Curt Jaimungal

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Embrace the Geometry of Rotations

Quaternions can be represented in a 4x4 real format, particularly useful for rotations of vectors via the spin group, which is derived from Clifford algebra. For effective spin group representation, it’s essential to utilize gamma matrices, fundamental to capturing the preferred chiral or Weyl representations in quantum mechanics. In this framework, gamma matrices correspond to spacetime dimensions, creating a pseudoscalar that acts as a geometric volume element. Notably, Clifford algebra excels in performing both rotations and reflections. Simply put, any rotation can be conceptualized as a product of two reflections, demonstrating the expansive capability of this mathematical structure in modeling the geometry of spacetime transformations.

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