Abstract
It is shown how particular kinds of fractional-linear (or projective) transformations generalize the notion of inertial frame in that they ensure that free-particle motion goes over into free-particle motion. A ten-parameter group of such transformations is produced which generalize Lorentz transformations, and which involve besides c (velocity of light) a new fundamental length b; they encompass the ordinary Lorentz group in the limit that b becomes infinite. These extended Lorentz transformations are most simply understood as a type of rotation in the space of homogeneous coordinates, a rotation that unifies 3-space rotations, frame-shifts to moving frames, and space- as well as time-translations. The structure of the invariant differential line element and of the wave operator that generalize those of special relativity are discussed, and implications for the possible revision of usual physical statements are pointed out.
Keywords: projective relativity, 5-dimensional rotations
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