Different Geometries for Special Relativity

摘要

This paper introduces a different time-measuring convention for special relativity (SR), where a time interval t can be measured by dc, the distance traveled from an origin by the spherical wave-front of a light pulse c. Adoption of this convention leads to a Euclidean geometry for SR, different from the Euclidean geometry already proposed by Montanus. The present geometry is governed by the functions of the circle, rather than the hyperbola, and the spherical wave-front of a light pulse provides both a fourth set t of frame-dependent coordinate points and a parameter w for measuring intervals that are invariant between reference frames. Since sine values under the circle range from 1 to 0, rather than 1 to , the new model does not allow, for a reference frame velocity & c, any interval to have length & oo. Furthermore, the form of the new model excludes any notion of "travel" with respect to time.