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Using Rotations to Control Observable Relativistic Effects

Author

Listed:
  • Danail Brezov

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

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.

Suggested Citation

  • Danail Brezov, 2024. "Using Rotations to Control Observable Relativistic Effects," Mathematics, MDPI, vol. 12(11), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1676-:d:1403460
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