  Dynamics with noncommutative coordinates invariant under three dimensional
rotations or, if time is included, under Lorentz transformations is developed.
These coordinates turn out to be the boost operators in SO(1,3) or in SO(2,3)
respectively. The noncommutativity is governed by a mass parameter $M$. The
principal results are: (i) a modification of the Heisenberg algebra for
distances smaller than 1/M, (ii) a lower limit, 1/M, on the localizability of
wave packets, (iii) discrete eigenvalues of coordinate operator in timelike
directions, and (iv) an upper limit, $M$, on the mass for which free field
equations have solutions. Possible restrictions on small black holes is
discussed.
