On the Definition of Velocity and the Geometry of Special Relativity

This article uses the Symmetrical Reflected Radar Model (SRRM) that was described in viXra 2504.0064 to analyse special relativity. The SRRM was developed without making any assumptions about the definition of velocity so that the fundamental relationship between distance and time could be clearly identified. In the SRRM, the algebra of special relativity is reliably represented in a symmetrical spacetime diagram. The transformation equations and geometry of the SRRM describe two symmetrical orthogonal coordinate systems rotating as mirror images; one clockwise, the other anticlockwise, as relative velocity changes. In a transformation between the two symmetrical orthogonal coordinate systems of the SRRM, the spacetime interval is invariant using Pythagoras. It is concluded that, in a symmetrical model, spacetime in special relativity is Euclidian. The terms and equations of the SRRM are shown to be completely interchangeable with those of the generally used Lorenz Transformation. There is good evidence to conclude that the velocity term used in the SRRM is fundamental. Thus, the velocity term used in the Lorenz Transformation is an approximation to the fundamental definition of velocity. Almost all derivations of the Lorenz Transformation since special relativity was first described have been made after first assuming the definition of velocity. This unstated assumption has thus been a silent axiom of the theory, inherent in subsequent analysis, inevitably affecting the conclusions of the theory.