Extending special relativity via the perplex numbers
Abstract
In analogy to the complex numbers z=x+iy, where the ``imaginary'' i is such that i2=-1, a system of perplex numbers z=x+hy is introduced, where the ``hallucinatory'' h is such that ‖h‖=-1. This system, invented by four freshmen at St. Olaf College, appears to have relevance in physics. In particular, it provides a natural way to extend the usual formalism of special relativity to the case ‖v‖>c. This is done by means of a velocity parameter φ, such that v=c tanh φ, where tanh is an extension of the ordinary hyperbolic tangent function. The fact that this extension has two different angles φ for each velocity v accounts for the different approaches in the literature to superluminal phenomena.
- Publication:
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American Journal of Physics
- Pub Date:
- May 1986
- DOI:
- Bibcode:
- 1986AmJPh..54..416F
- Keywords:
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- 02.10.Lh;
- 03.30.+p;
- Special relativity