Abstract
A transformation connecting two inertial framesS andS' must transform uniform motion of material bodies into uniform motion. However, sincec is an upper bound on velocities, physics merely states that straight lines in the light-cone (and not necessarilyall straight lines as for projective transformations) go over into straight lines. Nevertheless, we show in a quite elementary way that this weaker property also implies linearity. Constancy of light velocity then gives in a standard way the Lorentz transformations up to a «scale factor» λ which can, in principle, depend on the particular Lorentz transformationA and translation a. By a very simple group-theoretical argument it is shown that λ⦻ 1.
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