7. Anthony Crabbe, Different Geometries for Special Relativity

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Volume 17: Pages 166-176, 2004

Different Geometries for Special Relativity

Anthony Crabbe

Nottingham Trent University, Bonington 209, Burton Street, Nottingham NG1 4BU U.K.

This paper introduces a different timemeasuring convention for special relativity (SR), where a time interval t can be measured by dc, the distance traveled from an origin by the spherical wavefront 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 wavefront of a light pulse provides both a fourth set t of framedependent 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 ≈ ∞. Furthermore, the form of the new model excludes any notion of “travel” with respect to time.

Keywords: time, conventionalism, Minkowski geometry, circular function geometry, time travel, infinite energy

Received: October 16, 2003; Published online: December 15, 2008