Using Rotations to Control Observable Relativistic Effects

Danail Brezov ()
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Danail Brezov: Deptartment of Mathematics, University of Architecture, Civil Engineering and Geodesy, 1 Hristo Smirnenski Blvd., 1164 Sofia, Bulgaria

Mathematics, 2024, vol. 12, issue 11, 1-13

Abstract: This paper examines the possibility of controlling the outcome of measured (flat space-time) relativistic effects, such as time dilation or length contractions, using pure rotations and their nontrivial interactions with Lorentz boosts in the isometry group SO + ( 3 , 1 ) . In particular, boost contributions may annihilate leaving only a geometric phase (Wigner rotation), which we see in the complex solutions of the generalized Euler decomposition problem in R 3 . We consider numerical examples involving specific matrix factorizations, along with possible applications in special relativity, electrodynamics and quantum scattering. For clearer interpretation and simplified calculations we use a convenient projective biquaternion parametrization which emphasizes the geometric phases and for a large class of problems allows for closed-form solutions in terms of only rational functions.

Keywords: special relativity; kinematics; matrix decomposition; Thomas precession; geometric phases (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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