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Special Relativity using Perplex Numbers

Shyamkant Anwane

Imaginary numbers are not merely a part of mathematical jugglery they are of relevance in the real world too. Mathematical models involving real-time and imaginary space are efficient in predicting observable effects and beyond. This research paper aims to reformulate the special relativity using perplex numbers or split complex numbers also known as hyperbolic complex numbers which mankind has been familiar with even before we knew about relativity. Hypotheses that time is real and space is imaginary offers a new look at the space-time fabric. The invariant quantities in special relativity are of hyperbolic formats. This eventually leads to hyperbolic geometry that supports the basic structure of equations. Therefore, the use of hyperbolic complex numbers or perplex numbers handles all perspectives of special relativity with elegance and offers a great degree of simplicity so that even with a meager knowledge of mathematics allows the reader to handle special relativity. The findings support the hypothesis that time is real and space is imaginary in perplexes number representation. A few applications of special relativity in the realm of Quantum Mechanics and Nuclear Physics viz Berkley Collider, Compton’s Effect, Quantum Doppler Effect have been successfully explored.