  The effect of non-commutativity on electromagnetic waves violates Lorentz
invariance: in the presence of a background magnetic induction field b, the
velocity for propagation transverse to b differs from c, while propagation
along b is unchanged. In principle, this allows a test by the Michelson-Morley
interference method. We also study non-commutativity in another context, by
constructing the theory describing a charged fluid in a strong magnetic field,
which forces the fluid particles into their lowest Landau level and renders the
fluid dynamics non-commutative, with a Moyal product determined by the
background magnetic field.
