Abstract
LetT be a one-to-one mapping ofn-dimensional space-timeM onto itself. IfT maps light cones onto light cones and dimM≧3, it is shown thatT is, up to a scale factor, an inhomogeneous Lorentz transformation. Thus constancy of light velocity alone implies the Lorentz group (up to dilatations). The same holds ifT andT −1 preserve (x−y)2>0. This generalizes Zeeman's Theorem. It is then shown that ifT maps lightlike lines onto (arbitrary) straight lines and if dimM≧3, thenT is linear. The last result can be applied to transformations connecting different reference frames in a relativistic or non-relativistic theory.
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