Extending the Lorentz Transformation to Motion with Variable Velocity

Abstract

The problem considered is that of rectilinear motion with variable velocity. The paper gives, by an elementary construction, a system of coordinates which is conformal in the vicinity of the axis of motion. By a particular choice of the scale relation, such restricted conformal transformations can be made to reduce to the Lorentz transformation everywhere in the case of uniform velocity and locally in the case of variable velocity.