De Sitter relativity and Lorentz contraction I need help in understanding the elements of a paper that I think could turn out to be quite important, namely http://arxiv.org/abs/0711.2274 de Sitter Relativity: a New Road to Quantum Gravity R. Aldrovandi, J. G. Pereira) Inter aliathey say that: in de Sitter relativity “...... conformal transformations will naturally be incorporated in the kinematics of spacetime, and the corresponding conformal current will appear as part of the Noether conserved current .” This is because “ .... a cosmological term naturally introduces the conformal generators in the definition of spacetime transitivity.” I understand (probably wrongly) that the main feature of conformal transformations is that they are shape-preserving on a small enough scale. If this is so, I have a question: Lorentz transformations are not shape-preserving; the Lorentz contaction is uniaxial, as in the explanation of the null-result of the Michelson-Morley experiment. Are the conformal transformations of de Sitter SR bolt-on additions that leave Lorentz contraction intact, while providing dilation via a non-zero cosmological constant? And also, what exactly is the "proper conformal current" they talk of? Is it a sort of extra momentum-energy flux?